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Study of the Force Distribution in the Citrus Canopy During Harvest Using Continuous Canopy Shaker

Permanent Link: http://ufdc.ufl.edu/UFE0041324/00001

Material Information

Title: Study of the Force Distribution in the Citrus Canopy During Harvest Using Continuous Canopy Shaker
Physical Description: 1 online resource (198 p.)
Language: english
Creator: Udumala Savary, Sajith
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: accelerometer, ansys, canopy, citrus, harvesters, labview, shaker, solidworks, xbeepro, zigbee
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The study of mechanical harvesters used in citrus harvesting and their effect on the tree has been going on for the past 30 - 40 years. Over these years many researchers have analyzed and studied the dynamics of trees when different mechanical harvesters are used on it. The primary goal of most of the research works in the past has been to establish the parameters that are to be considered in the mechanical shaker to make it more efficient. The other important goal is to reduce the tree damage at the same time, as the use of mechanical harvesters might reduce the fruit yield in the subsequent years due to tree injury caused by them. While there have been many studies on tree shakers used for harvesting citrus fruits, there is not much work done using the canopy shaker. This is because canopy shakers are relatively new. Currently, continuous canopy shakers are the most widely used type of citrus mechanical harvesting machines in Florida. Better understanding of the interaction of harvesting machines and tree canopy during harvest, by measuring and analyzing the force distribution in the canopy under real harvesting conditions, could help to improve the existing canopy harvesting machines. The objective of this thesis was to study the dynamics of orange trees when subjected to harvesting using a canopy shaker. The force experienced by fruits is measured using the Multi-node, ZigBeeregistered trademark based wireless sensors equipped with 3-axis accelerometer sensors attached to them. The main objective of this research was to develop an analytical model for the force experienced by the fruits based on the various factors like location and weight of fruit, frequency of canopy shaker etc. Based on this analytical model, the next step is to design and develop more efficient citrus canopy shaker harvesting machines. This thesis studied the dependency of the shaking frequency, tine angle and forward speed of the canopy shaker on the force distribution in the tree canopy. The location and weight of the fruit in the tree canopy was considered as a factor in this study. An analytical model for the force distribution in the tree canopy was also developed. The study of the force in different parts of the canopy revealed that the forces were higher in the inner part of the canopy than the edges though the fruit removal was more at the edges. It was also observed that the variation of force was Gaussian while variation acceleration was exponential in nature along the branch. The simulation data from ANSYSregistered trademark model had a linear correlation with the actual experimental values with adjusted R2 values of 60% at 180 cpm and 54% at 230 cpm.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sajith Udumala Savary.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Ehsani, M Reza.
Local: Co-adviser: Salyani, Masoud.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041324:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041324/00001

Material Information

Title: Study of the Force Distribution in the Citrus Canopy During Harvest Using Continuous Canopy Shaker
Physical Description: 1 online resource (198 p.)
Language: english
Creator: Udumala Savary, Sajith
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: accelerometer, ansys, canopy, citrus, harvesters, labview, shaker, solidworks, xbeepro, zigbee
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The study of mechanical harvesters used in citrus harvesting and their effect on the tree has been going on for the past 30 - 40 years. Over these years many researchers have analyzed and studied the dynamics of trees when different mechanical harvesters are used on it. The primary goal of most of the research works in the past has been to establish the parameters that are to be considered in the mechanical shaker to make it more efficient. The other important goal is to reduce the tree damage at the same time, as the use of mechanical harvesters might reduce the fruit yield in the subsequent years due to tree injury caused by them. While there have been many studies on tree shakers used for harvesting citrus fruits, there is not much work done using the canopy shaker. This is because canopy shakers are relatively new. Currently, continuous canopy shakers are the most widely used type of citrus mechanical harvesting machines in Florida. Better understanding of the interaction of harvesting machines and tree canopy during harvest, by measuring and analyzing the force distribution in the canopy under real harvesting conditions, could help to improve the existing canopy harvesting machines. The objective of this thesis was to study the dynamics of orange trees when subjected to harvesting using a canopy shaker. The force experienced by fruits is measured using the Multi-node, ZigBeeregistered trademark based wireless sensors equipped with 3-axis accelerometer sensors attached to them. The main objective of this research was to develop an analytical model for the force experienced by the fruits based on the various factors like location and weight of fruit, frequency of canopy shaker etc. Based on this analytical model, the next step is to design and develop more efficient citrus canopy shaker harvesting machines. This thesis studied the dependency of the shaking frequency, tine angle and forward speed of the canopy shaker on the force distribution in the tree canopy. The location and weight of the fruit in the tree canopy was considered as a factor in this study. An analytical model for the force distribution in the tree canopy was also developed. The study of the force in different parts of the canopy revealed that the forces were higher in the inner part of the canopy than the edges though the fruit removal was more at the edges. It was also observed that the variation of force was Gaussian while variation acceleration was exponential in nature along the branch. The simulation data from ANSYSregistered trademark model had a linear correlation with the actual experimental values with adjusted R2 values of 60% at 180 cpm and 54% at 230 cpm.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sajith Udumala Savary.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Ehsani, M Reza.
Local: Co-adviser: Salyani, Masoud.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041324:00001


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1 STUDY OF THE FORCE DISTRIBUTION IN THE CITRUS CANOPY DURING HARVEST USING CONTINUOUS CANOPY SHAKER By SAJITH KUMAR JOSE UDUMALA SAVARY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009

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2 2009 Sajith Kumar Jose Udumala Savary

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3 To my teachers, in life and school

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4 ACKNOWLEDGMENTS There were many people who were instrumental in my completing this thesis successfully. First and foremost I am grateful for the timely input, encouragement and supervision of my advisor Dr. Reza Ehsani du ring the course of my thesis. I am also grateful for the useful suggestions provided by my thesis committee members, Dr. Masoud Salyani, Dr. John Schueller and Dr. My Tra Thai. I am thankful to Mr. Martin Hebel, Dr. Teixeira, Mr. Justin Townley, Dr. Megh S ingh and Mr. James Collee for their provided by Dr. Gene Albrigo, Dr. Bill Castle and Dr. Megan Dewdney about c itrus in general I am grateful for the funding provided b y the Citrus Initiative of Florida to complete my research work. I would also take this opportunity to thank all the staff at CREC who helped me especially the grove manager, Mr. Troy Gainey identified the sections of the grove where I could do my experime nts and the librarian, Mrs. Jennifer Dawson who helped me with the presentations and literature review I would like to thank Mr. Carson Futch for providing us the c anopy shaker for the experimental purposes. A special thanks to my friends in the mechanic al engineering department especially Karthik, Bhargav and Vijay ; discussion s with whom helped towards my understanding of the various basic principles required for my research. I am greatly indebted towards my colleagues in the lab, Dr. Maja, Dr. Karimi, R aghav, Andre, Ashish, Ramin, Rashidah, Sherrie and Ujwala who helped me during the experiments. It would be incomplete if I do not thank my parents and sister without whose unrelenting support and encouragement any of this would have been possible.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 9 LIST OF FIGURES ................................ ................................ ................................ ........ 14 ABSTRACT ................................ ................................ ................................ ................... 19 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 21 Citrus Industry in Florida ................................ ................................ ......................... 22 Reason for Mechanical Harvesting of Citrus in Florida ................................ ........... 23 Citrus Mechanical Harvesting in Florida ................................ ................................ .. 24 Objective of This Study ................................ ................................ ........................... 26 Report Organization ................................ ................................ ................................ 26 2 HISTORY AND LITERATURE REVIEW ................................ ................................ 28 Mechanical Harvesting ................................ ................................ ............................ 29 History of Mechanical Harvesting of Citrus in Florida ................................ ............. 31 Handling of Citrus ................................ ................................ ............................. 32 Harvesting Aids ................................ ................................ ................................ 33 Contact Harvesting ................................ ................................ ........................... 34 Mass Fruit Harvesters ................................ ................................ ...................... 35 Robotic Harvesting ................................ ................................ ........................... 37 Current Mechan ization in Citrus Harvesting ................................ ............................ 38 Trunk Shake and Catch (TSC) ................................ ................................ ......... 38 Continuous Canopy Shake and Catch (CCSC) ................................ ................ 39 Tractor Drawn Canopy Shake (TDCS) ................................ ............................. 39 Economic Impact of Mechanical Harvesting ................................ ........................... 41 Knowledge Gap ................................ ................................ ................................ ...... 41 Related Literature ................................ ................................ ................................ ... 42 3 MATERIALS ................................ ................................ ................................ ........... 54 Tree and Harvester ................................ ................................ ................................ 54 Continuous Canopy Shaker ................................ ................................ .............. 54 Citrus Trees ................................ ................................ ................................ ...... 55 Acceleration Acquisi tion ................................ ................................ .......................... 55 XBee PRO ................................ ................................ ................................ ..... 57 MMA7260Q accelerometers ................................ ................................ ............. 57 Sensor Computer Communication ................................ ................................ .......... 57

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6 Sensor and Transceiver Setup 1 ................................ ................................ ...... 58 Sensor and Transceiver Setup 2 ................................ ................................ ...... 60 4 FORCE DISTRIBUTION ................................ ................................ ......................... 6 3 First Field Experiment ................................ ................................ ............................. 63 Materials and Methods ................................ ................................ ..................... 63 Resultant force (F) ................................ ................................ ..................... 65 Duration of significant resultant force (T) ................................ ................... 66 Resultant yank (Y) ................................ ................................ ..................... 67 Resultant momentum (P) ................................ ................................ ........... 67 Results an d Discussion ................................ ................................ .................... 68 Type of force application ................................ ................................ ............ 70 Abscission chemical ................................ ................................ ................... 70 Region of tree shaken ................................ ................................ ................ 75 Variety of fruits ................................ ................................ ........................... 76 Location of fruits ................................ ................................ ......................... 79 Second Field Experiment ................................ ................................ ........................ 80 Materials and Methods ................................ ................................ ..................... 82 Tree and branch selection ................................ ................................ .......... 82 Experimental design ................................ ................................ .................. 82 Instrumenting the tree ................................ ................................ ................ 83 Data collection ................................ ................................ ........................... 84 Data analysis ................................ ................................ ............................. 86 Results and Discussion ................................ ................................ .................... 87 ANOVA on F p Y p P p and T p values ................................ ........................... 87 Distribution of resultant force proportional and acceleration valu es along the tree branch ................................ ................................ ........................ 88 Variation of adjusted R 2 with respect to changing machine parameters .... 97 Variation of equation coefficients with respect to changing machine parameters ................................ ................................ .............................. 98 5 MODEL AND VERIFICATION ................................ ................................ .............. 102 Model Development ................................ ................................ .............................. 102 Material and Methods ................................ ................................ ..................... 102 SolidWorks modeling ................................ ................................ ............. 103 ANSYS analysis and simulation ................................ ............................... 105 Re sults and Discussion ................................ ................................ .................. 107 Resultant acceleration at probe points ................................ ..................... 108 Resultant acceleration and equivalent stress ................................ ........... 110 Equivalent stress distribution ................................ ................................ ... 111 Resultant acceleration distribution ................................ ........................... 111 Material Properties Experiment ................................ ................................ ............. 115 Materials and Methods ................................ ................................ ................... 115 Preparation of samples ................................ ................................ ............ 118 Dimensio ns of samples ................................ ................................ ............ 118

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7 Density experiment ................................ ................................ .................. 119 Instron machine setting common for both modulus experiments ............. 120 ................................ ............................. 120 Shear modulus (G) experiment ................................ ................................ 121 Results ................................ ................................ ................................ ........... 124 Third Field Experiment ................................ ................................ .......................... 124 Materials and Methods ................................ ................................ ................... 125 Results an d Discussion ................................ ................................ .................. 128 Resultant acceleration values ................................ ................................ .. 128 Model for experimental values vs. simulation values ............................... 129 Goodness of fit for the model ................................ ................................ ... 133 Po ssible reasons for the low correlation ................................ .................. 134 6 CONCLUSION ................................ ................................ ................................ ...... 136 Summary of Conclusions ................................ ................................ ...................... 136 Recommendations for Similar Work ................................ ................................ ..... 139 APPENDIX A SENSORS AND COMMUNICATION ................................ ................................ .... 141 ZigBee ................................ ................................ ................................ .................. 141 Specification ................................ ................................ ................................ ... 142 XBee PRO ................................ ................................ ................................ ...... 144 Accelerometer ................................ ................................ ................................ ....... 144 Surface Micro machined Accelerometers ................................ ....................... 144 MMA7260Q and Features ................................ ................................ .............. 145 B CIRCUIT AND CODE ................................ ................................ ........................... 148 Setup 1 ................................ ................................ ................................ ................. 148 Circuit Schematic ................................ ................................ ........................... 148 Data Acquisition ................................ ................................ ............................. 149 Microprocessor and VB code ................................ ................................ ... 149 Data collection procedure ................................ ................................ ........ 151 Data e xtraction ................................ ................................ ......................... 152 Data a nalysis ................................ ................................ ........................... 153 Setup 2 ................................ ................................ ................................ ................. 153 Circuit Schematic ................................ ................................ ........................... 153 Data Acquisition ................................ ................................ ............................. 153 Data Extraction ................................ ................................ ............................... 156 Raw to acceleration ................................ ................................ ................. 156 Isolating sensors of each file ................................ ................................ .... 157 Consolidation of all files ................................ ................................ ........... 157 C DISTRIBUTION ALONG THE BRANCH RESULTS ................................ ........... 159

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8 D MODEL VALIDATION RESULTS ................................ ................................ ....... 169 LIST OF REFERENCES ................................ ................................ ............................. 189 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 198

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9 LIST OF TABLES Table page 2 1 Chronology of citrus mechanical harvesting. ................................ ...................... 31 4 1 Location, fruit variety and test parameters for the field tests. ............................. 65 4 2 Resultant force, yank and momentum exerted on the fruit during mechanical canopy shaking along with duration of significant force. ................................ ..... 69 4 3 Summary of ratios from the comparisons. ................................ .......................... 69 4 4 Comparison of traditional and canopy shaker force for removal of fruits. ........... 69 4 5 Comparison for small fruits with and without abscission treatment. .................... 71 4 6 Comparison for large fruits with and without abscission treatment. .................... 72 4 7 Comparison of canopy shaker runs on the same and other side of the sensors on the tree ................................ ................................ ............................ 72 4 8 Comparison of all instrumented fruits of Hamlin and Valencia. .......................... 77 4 9 Comparison of removed instrumented fruits of Hamlin and Valencia. ................ 77 4 10 Comparison based on the location of all instrumented fruits. ............................. 80 4 11 Comparison based on the location of removed instrumented fruits. ................... 80 4 12 Independent variables and their levels ................................ ............................... 83 4 13 Randomized order of the experiment. ................................ ................................ 83 4 14 ANOVA results for average force proport ional values. ................................ ....... 90 4 15 ANOVA results for maximum force proportional values. ................................ ..... 90 4 16 ANOVA results for variance of force proportional values. ................................ ... 90 4 17 ANOVA results for average yank proportional values. ................................ ........ 91 4 18 ANOVA results for maximum yank proportional values. ................................ ..... 91 4 19 ANOVA results for variance of yank proportional values. ................................ ... 91 4 20 ANOVA results for average momentum proportional values. ............................. 91 4 21 ANOVA results for maximum momentum proportional values. ........................... 92

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10 4 22 ANOVA results for variance of momentum proportional values. ......................... 92 4 23 ANOVA results for duration of significant force proportional values. .................. 92 4 24 Average and maximum resultant acceleration values of large trees. .................. 93 4 25 Average and maximum resultant acceleration values of small trees. ................. 93 4 26 Average and maximum resultant force proportional values of large trees. ......... 94 4 27 Average and maximum resultant force proportional values of small trees. ......... 94 4 28 Dis tance of locations from the origin for small and large trees. .......................... 95 4 29 Coefficients for the exponential equation of average resultant acceleration values ................................ ................................ ................................ ................ 95 4 30 Coefficients for the exponential equation of maximum resultant acceleration values ................................ ................................ ................................ ................ 96 4 31 Coefficients for the Gaussian equation of average resultant force proportional values. ................................ ................................ ................................ ................ 96 4 32 Coefficients for the Gaussian equation of maximum resultant force proportional values. ................................ ................................ ............................ 97 4 33 Average of adjusted R 2 values across all angle and frequency combinations for large and small trees. ................................ ................................ .................... 97 4 34 Adjusted R 2 values for resultant acceleration relation. ................................ ....... 98 4 35 Adjusted R 2 values for resultant force proportional values relation. .................... 99 4 36 Correlation between a djusted R 2 values for changing frequencies at different angles. ................................ ................................ ................................ ................ 99 4 37 Correlation between adjusted R 2 values for changing angles at different frequencies. ................................ ................................ ................................ ........ 99 4 38 for changing frequencies at different angles. ................................ ................................ ................................ 100 4 39 for changing angles at different frequencies. ................................ ................................ ................................ ...... 100 4 40 for changing frequencies at different angles. ................................ ................................ ................................ 100

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11 4 41 for changing angles at different frequencies. ................................ ................................ ................................ ...... 100 4 42 for changing frequencies at different angles. ................................ ................................ ................................ 101 4 43 for changing angles at different frequencies. ................................ ................................ ................................ ...... 101 5 1 Contact points in all three trees. ................................ ................................ ....... 107 5 2 Average acceleration of unengaged tines at 180 and 230 cpm frequencies. ... 107 5 3 Force input cycle for 180 cpm. ................................ ................................ .......... 107 5 4 Force input cycle for 230 cpm. ................................ ................................ .......... 107 5 5 Summary of average acceleration data from ANSYS based on location and tree at 180 and 230 cpm frequencies. ................................ .............................. 108 5 5 Continued. ................................ ................................ ................................ ........ 109 5 6 Summary of maximum acceleration data from ANSYS based on location and tree at 180 and 230 cpm frequencies. ................................ .............................. 109 5 7 Ratio of acceleration values. ................................ ................................ ............. 110 5 8 Average and maximum of maximum total acceleration and equivalent stress data at the end of each timestep for all trees and frequencies from ANSYS. ... 112 5 9 Ratio of total acceleration and equivalent stress values. ................................ .. 112 5 10 Dimensions of cube samples. ................................ ................................ ........... 118 5 11 Dimensions of cylindrical samples. ................................ ................................ ... 118 5 11 Continued. ................................ ................................ ................................ ........ 119 5 12 Pycnometer calibration. ................................ ................................ .................... 120 5 13 Solid density. ................................ ................................ ................................ .... 120 5 14 ................................ ................................ ........... 123 5 15 Shear modulus calculation. ................................ ................................ .............. 123 5 16 Property statistics. ................................ ................................ ............................ 124 5 17 Summary of properties measured and calculated. ................................ ........... 124

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12 5 18 Factors for the field experiment. ................................ ................................ ....... 128 5 19 Summary of average acceleration data from experiment based on l ocation and tree at 180 and 230 cpm frequencies. ................................ ....................... 129 5 19 Continued. ................................ ................................ ................................ ........ 130 5 20 Summary of maximum acceleration data from experiment based on location and tree at 180 and 230 cpm frequencies. ................................ ....................... 130 5 20 Continued. ................................ ................................ ................................ ........ 131 5 21 Ratio of acceleration values at 230 cpm and 180 cpm. ................................ .... 131 5 22 Average ratio of acceleration values at 230 and 180 cpm. ............................... 131 5 23 Correlation between the experimental and model data sets for average and maximum acceleration values. ................................ ................................ ......... 132 5 24 Coefficients for the different models for different trees. ................................ .... 133 5 25 Adjusted R 2 values for different models for all trees at 180 and 230 cpm frequencies. ................................ ................................ ................................ ...... 133 5 26 Ave rage adjusted R 2 values for the two different frequencies. ......................... 133 5 27 Average of the coefficients for the different models. ................................ ......... 134 A 1 ................................ ................................ .......... 141 A 1 Continued. ................................ ................................ ................................ ........ 142 A 2 g Select and sensitivity. ................................ ................................ .................... 147 C 1 Goodness of fit values for exponential distribution of average acceleration in small and large trees. ................................ ................................ ....................... 159 C 2 Goodness of fit values for exponential distribution of maximum acceleration in small and large trees. ................................ ................................ ................... 159 C 3 Goodness of fit values for Gaussian distribution of average force proportional values in small and large trees. ................................ ................................ ........ 160 C 4 Goodness of fit values for Gaussian distribution of maximum force proportional values in small and large trees. ................................ .................... 160 D 1 SSE values of different models for experimental vs. simulation values. ........... 169 D 2 R 2 values of different models for experimental vs. simulation values. .............. 169

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13 D 3 Adjusted R 2 values of different models for experimental vs. simulation values. 169 D 4 RMSE values of different models for experimental vs. simulation values. ........ 170

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14 LIST OF FIGURES Figure page 1 1 Mechanical harvested acreage of Citrus in Florida. ................................ ............ 24 1 2 Mechanical harvesting of Citrus in Florida using different shakers. .................... 25 2 1 Forces on fruit when the tree is shaken. ................................ ............................ 31 2 2 Trunk Shake and Catch (TSC).. ................................ ................................ ......... 39 2 3 Continuous Canopy Shake and Catch (CCSC). ................................ ................. 40 2 4 Tractor Drawn Canopy Shake (TDCS). ................................ .............................. 40 3 1 Whirls that will hold the tines. ................................ ................................ ............. 55 3 2 Defoliated tree. ................................ ................................ ................................ ... 56 3 3 XBee PRO used for data communication. ................................ .......................... 56 3 4 MMA7260Q Accelerometer for sensing acceleration. ................................ ......... 56 3 5 XBee PRO USB receiver. ................................ ................................ ................... 59 3 6 Accelerometer, XBee PRO and power on same board. ................................ ..... 59 3 7 Accelerometer separate from XBee PRO and power. ................................ ........ 60 3 8 Data collection schematic for setup 1. ................................ ................................ 60 3 9 Sensor and transceiver setup 2. ................................ ................................ ......... 61 3 10 Data collection schematic for setup 2. ................................ ................................ 62 4 1 Sensor attached to a fruit. ................................ ................................ .................. 64 4 2 Location of sensors in the tree. ................................ ................................ ........... 65 4 3 Effect of abscission on average resultant force on small fruits. .......................... 72 4 4 Effect of abscission on maximum resultant force on small fruits. ........................ 73 4 5 Effect of abscission on average resultant force on large fruits. .......................... 73 4 6 Effect of abscission on maximum resultant force on large fruits. ........................ 74

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15 4 7 Comparison of average resultant force when canopy shaker is the same and opposite sides. ................................ ................................ ................................ .... 74 4 8 Comparison of maximum resultant force when canopy shaker is the same and opposite sides. ................................ ................................ ............................. 75 4 9 Comparison of average resultant force of Hamlin and Valencia. ........................ 78 4 10 Comparison of maximum resultant force of Hamlin and Valencia. ..................... 78 4 11 Comparison of average resultant force based on fruit location in the tree canopy. ................................ ................................ ................................ ............... 81 4 12 Comparison of maximum resultant force based on fruit location in the tree canopy. ................................ ................................ ................................ ............... 81 4 13 Sensor board attached to the base of the trunk. ................................ ................. 84 4 14 Sensor attached to a location on the branch. ................................ ..................... 85 4 15 Schematic of the sensors on the tree. ................................ ................................ 85 5 1 Spline from the data points in SolidWorks. ................................ ....................... 104 5 2 Reference planes created at points along the spline in SolidWorks. ................ 104 5 3 Circles in the reference planes joined by loft feature in SolidWorks. ................ 104 5 4 Tree models created for the three trees used in field experiment. .................... 105 5 5 Sensors placed on the tines. ................................ ................................ ............ 106 5 6 Equivalent stress distribution at the end of simulation in tree 1. ....................... 1 12 5 7 Equivalent stress distribution at the end of simul ation in tree 2 ........................ 113 5 8 Equivalent stress distribution at the end of simulation in tree 3. ....................... 113 5 9 Total acceleration distribution at the end of simulation in tree 1. ...................... 114 5 10 Total acceleration distribution at the end of simulation in tree 2. ...................... 114 5 11 Total acceleration distribution at the end of simulation in tree 3. ...................... 115 5 12 Properties of wood experiment materials.. ................................ ....................... 116 5 12 Continued. ................................ ................................ ................................ ........ 117 5 13 Wood samples for properties of wood experiment.. ................................ .......... 117

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16 5 14 ................................ ....................... 121 5 14 Continued. ................................ ................................ ................................ ........ 122 5 15 Shear mod ulus experiment and results.. ................................ .......................... 122 5 15 Continued. ................................ ................................ ................................ ........ 123 5 16 Defoliated and instrumented tree with the sensors. ................................ .......... 126 A 1 ZigBee specification.. ................................ ................................ ....................... 143 A 2 Simplified transducer physical model.. ................................ ............................. 145 A 3 Schematic of the accelerometer.. ................................ ................................ ..... 146 B 1 Circuit details for setup 1.. ................................ ................................ ................ 148 B 1 Continued. ................................ ................................ ................................ ........ 149 B 2 GUI of Excel Macro. ................................ ................................ ......................... 150 B 3 Schematic of board used for experiment 3 and 4. ................................ ............ 154 B 4 Front panel for data acquisition on one channel. ................................ .............. 155 B 5 Front panel for data acquisition on one channel. ................................ .............. 155 B 6 Schematic of LabVIEW data acquisition program. ................................ ............ 156 C 1 Variation of maximum force proportional values with respect to distance from origin along the branch in small trees for all angle and frequency combination. ................................ ................................ ................................ ..... 161 C 2 Variation of average force proportional values with respect to distance from origin along the branch in small trees for al l angle and frequency combination. ................................ ................................ ................................ ..... 162 C 3 Variation of maximum acceleration values with respect to distance from origin along the branch in small trees for all angle and frequency combination. ................................ ................................ ................................ ..... 163 C 4 Variation of average acceleration values with respect to dis tance from origin along the branch in small trees for all angle and frequency combination. ........ 164 C 5 Variation of maximum force propo rtional values with respect to distance from origin along the branch in large trees for all angle and frequency combination. ................................ ................................ ................................ ..... 165

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17 C 6 Variation of average force proportional values with respect to distance from origin along the branch in large trees for all angle and frequency combination. ................................ ................................ ................................ ..... 166 C 7 Variation of maximum acceleration values with respect to distance from origin along the branch in large trees for all angle and frequency combination. ................................ ................................ ................................ ..... 167 C 8 Variation of average acceleration values with respect to distance from origin along the branch in large trees for all angle and frequency combination. ......... 168 D 1 Linear model for experimental vs. simulation values for tree 1 at 180 cpm.. .... 171 D 2 Linear model for experimental vs. simulation values for tree 2 at 180 cpm.. .... 172 D 3 Linear model for experimental vs. simulation values for tree 3 at 180 cpm.. .... 173 D 4 Linear model for experimental vs. simulation values for tree 1 at 230 cpm.. .... 174 D 5 Linear model for experimental vs. simulation values for tree 2 at 230 cpm.. .... 175 D 6 Linear model for experimental vs. simulation values for tree 3 at 230 cpm.. .... 176 D 7 Linear model with excluded data points for e xperimental vs. simulation values for tree 1 at 180 cpm.. ................................ ................................ ........... 177 D 8 Linear model with excluded data points for experimental vs. simula tion values for tree 2 at 180 cpm.. ................................ ................................ ........... 178 D 9 Linear model with excluded data points for experimental vs. simulation values for tree 3 at 180 cpm.. ................................ ................................ ........... 179 D 10 Linear model with excluded data points for experimental vs. simulation values for tree 1 at 230 cpm.. ................................ ................................ ........... 180 D 11 Linear model with excluded data points for experimental vs. simulation values for tree 2 at 230 cpm.. ................................ ................................ ........... 181 D 12 Linear model with excluded data points for experimental vs. simulation values for tree 3 at 230 cpm.. ................................ ................................ ........... 182 D 13 Quadratic model with excluded data points for experimental vs. simulation values for tree 1 at 180 cpm.. ................................ ................................ ........... 183 D 14 Quadratic model with excluded data points for experimental vs. simulation values for tree 2 at 180 cpm.. ................................ ................................ ........... 184 D 15 Quadratic model with excluded data points for experimental vs. simulation values for tree 3 at 180 cpm.. ................................ ................................ ........... 185

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18 D 16 Quadratic model with excluded data points for experimental vs. simulation values for tree 1 at 230 cpm.. ................................ ................................ ........... 186 D 17 Quadratic model with excluded data points for experimental vs. simulation values for tree 2 at 230 cpm.. ................................ ................................ ........... 187 D 18 Quadratic model with excluded data points for experimental vs. simulation values for tree 3 at 230 cpm.. ................................ ................................ ........... 188

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19 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science STUDY OF THE FORCE DISTRIBUTION IN THE CITRUS CANOPY DURING HARVEST USING CONTINUOUS CANOPY SHAKER By Sajith Kumar Jose Udumala Savary December 2009 Chair: Reza Ehsani Cochair: Masoud Salyani Major: Agricultural and Biological Engineering The study of mechanical harvesters used in citrus harvesting and their effect on the tree has been going on for the past 30 40 years. Over these years many researchers have analyzed and studied the dynamics of trees when different mechanical harvesters are used on it. The primary goal of most of the res earch works in the past has been to establish the parameters that are to be considered in the mechanical shaker to make it more efficient. The other important goal is to reduce the tree damage at the same time, as the use of mechanical harvesters might red uce the fruit yield in the subsequent years due to tree injury caused by them. While there have been many studies on tree shakers used for harvesting citrus fruits, there is not much work done using the canopy shaker. This is because canopy shakers are rel atively new. Currently, continuous canopy shakers are the most widely used type of citrus mechanical harvesting machines in Florida. Better understanding of the interaction of harvesting machines and tree canopy during harvest, by m easuring and analyzing t he force distribution in the canopy under real harvesting conditions, could help to improve the existing canopy harvesting machines.

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20 The objective of this thesis was to study the dynamics of orange trees when subjected to harvesting using a canopy shaker. The force experienced by fruits is measured using the Multi node, ZigBee based wireless sensors equipped with 3 axis accelerometer sensors attached to them. The main objective of this research wa s to develop an analytical model for the force experienced by the fruits based on the various factors like location and weight of fruit, frequency of canopy shaker etc. Based on this analytical model, the next step is to design and develop more eff i cient citrus canopy shaker harvesting machines. This thesis stud ied the dependency of the shaking frequency, tine angle and forward speed of the canopy shaker on the force distribution in the tree canopy. The location and weight of the fruit in the tree canopy w as considered as a fact or in this study. An analytical model for the force distribution in the tree canopy w as also developed. The study of the force in different parts of the canopy revealed that the forces were higher in the inner part of the canopy than the edges though the f ruit removal was more at the edges. It was also observed that the variation of force was Gaussian while variation acceleration was exponential in nature along the branch. The simulation data from ANSYS model had a linear correlation with the actual experi mental values with adjusted R 2 values of 60% at 180 cpm and 54% at 230 cpm.

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21 CHAPTER 1 INTRODUCTION Mechanization for crop production is an ongoing process in the agricultural industry. As described by Odigboh (1999) mechanization can be done at various levels of complexity ranging from a hand tool for simple tasks to a robot for very precise and complicated tasks. It all started with the use of hand tools and animals for doing tasks like tilling, harvesting, transpo rting etc. The advent of mechanically powered machines relaxed the limits imposed on mechanization because of the use of animal and human powered tools. The use of these machines was also more efficient and profitable compared to the use of animal and huma solely means the use of mechanically powered machines for accomplishing various tasks. Mechanization has always been aimed at making the tasks easier to accomplish within a limited time and with the use of less ef fort. This in economic terms translates to economic disparity among different nations has made mechanization very pertinent to remain competitive in the global market. This is very true especially for developed nations where manual labor is both expensive and scarce. Harvesting is a part of the crop production cycle which is very time consuming and a labor intense operation irrespective of the crop involved. Harvesting can be broken down into a sequence of smaller jobs which are based on the crop involved. The use of machines for a part of or the entire harvesting process is aimed at a reduction of labor and time involved. Mechanical harvesting concept has been pursued with vigorous interest for many crops. It has been successfully adopted for grain and vegetable crops like rice potatoes tomatoes etc and also for some fruit and nut crops like grapes,

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22 walnuts etc. For citrus, mechanically harvested acreage is on the ris e but it is still very negligible compared to the total acreage. One of the major reasons for the growers not yield because of mechanical harvest. In this chapter, ther e will be a brief discussion about the citrus industry in Florida, its history and the need for mechanical harvesting. This will be followed by the objective of this study and the organization of this report. Citrus I ndustry in Florida Citrus has many fami liar fruits, some of these being orange, tangerine and grapefruit. Except for grapefruit, a hybrid of orange and pomelo created during 1700s in the West Indies, all the other fruits are supposed to be native to Southeast Asia. Nowadays citrus is produced m ostly by tropical and subtropical America along with southern Europe, Japan, North Africa and the near East. Annual worldwide citrus production amounts to about 50 million metric tons (Janick, 2005) of which more than 50% are oranges and tangerines. The c itrus fruits are an excellent source of vitamin C and various fruit acids. They are borne on small wiry trees which do well in the sandy soils found in south central Florida, southern California and southern Texas. In 1500s, citrus was introduced in Florid a. The sandy soil and sub tropical climate of Florida proved to be ideal for growing citrus seeds brought by the early settlers. In mid 1800s, the wild groves of Florida were topworked with superior strains to start the commercial farming of citrus. (Janic k, 2005) Currently the citrus industry is one of the largest industries in Florida. According to Florida Department of Citrus (FDOC), c urrently there are about 576,000 acres of citrus groves and more than 75 million citrus trees in Florida. The citrus frui ts found in Florida are oranges, grapefruit and specialty fruit including Temple oranges, tangerines and

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23 tangelos. In global orange juice production Florida is second only to Brazil. Florida is also the leader in global grapefruit production. Nearly 87 pe rcent of Florida citrus is processed into canned, chilled or frozen concentrated juices. The Florida citrus industry generates $9.3 billion per year with about $1 billion in tax revenues. About 76,000 Floridians work in citrus related industry. Apart from the economic impact, citrus also of mature trees produced 16.7 tons of oxygen per year and there exist more than 159 native species within the grove ecosystems. (Florida Department of Citrus, 2008) Reason for M echanical H arvesting of C itrus in Florida Mechanical harvesting of citrus is an initiative that has its origins in the mid 1950s. It was initially started to address the inconsistent availability of labor for manua l harvesting. The increasing acreage of Florida citrus, along with the yields, during the 1950s and 1960s required more workers for manual harvesting. To overcome these problems and to improve the efficiency of available labor, the mechanical harvesting in itiative was started. The program was spearheaded by the Florida Department of Citrus, the United States Department of Agriculture and the University of Florida. I nterest in mechanical harvesting waned when the devastating freezes in 1983, 1985 and 1989 re duced the acreage and the yields noticeably (Futch et al, 2005). In the 1990s, mechanical harvesting research was revitalized. Florida is next only to Brazil in orange juice production but the labor availability and cost of harvesting is drastically differ ent for the competitors. In order to compete in the global market and maintain profitability, the production costs have to be reduced which can be achieved by harvesting citrus mechanically.

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24 Citrus M echanical H arvesting in Florida Mechanical harvesting of citrus in Florida was started in late 1990s. The Figure 1 1 shows the trend of mechanical harvesting of citrus in Florida. It can be observed from the graph that mechanical harvesting has been on the rise. The exception was in 2003 04 season, when the occu rrence of 3 hurricanes decreased the acreage harvested by the mechanical harvesters. In general, over 10 seasons the mechanically harvested acreage increased from around 5000 acres to about 32000 acres. This is about 650% increase in the mechanically harve sted acreage. During the 2007 08 season, the total acreage of citrus groves harvested by mechanical means was about 32000 acres. This is a little more than 5% of the total acreage of citrus in Florida. This illustrates the fact that though the use of mecha nical harvesters is on the rise, the growers are reluctant to use them. Figure 1 1. Mechanical harvest ed acreage of Citrus in Florida (Data provided courtesy of Florida Department of Citrus .)

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25 The mechanical picking systems that were used widely in Florida were the trunk shakers and continuous canopy shakers. Both these systems have the shake and catch mechanism. The graph in F igure 1 2 shows the citrus acreage in Florida harvested by trunk and canopy shaker. From the graph, it can be seen clearly that the trunk shaker was losing to canopy shaker in terms of acceptance by the citrus growers. Now, only continuous canopy shakers are being used in Florida to harvest citrus. Trunk shakers are no long er bei ng used for citrus harvesting. TSC Trunk Shake and Catch CS Canopy Shaker Figure 1 2. Mechanical harvesting of Citrus in Florida using different shakers (Data provided courtesy of Dr. Fritz Roka, SWFREC Univ. of Florida, Immokalee and Mr. Sandy Barros, Florida Department of Citrus .)

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26 O bjective of This S tudy As mentioned earlier, t he reluctance of the growers to accept mechanical harvesters coul d be due to their fear of reduc tion in yield in the long term as a result of unk nown tree health effects of continuous use of harvesting machine A better understanding of the tree harvester system will help allay their fears and can also help increase the efficiency of the harvesters. This report is about the study done using the continuous canopy sh akers to investigate the nature of distribution of force in the canopy of the trees during harvest. There are two types of parameters that affect t he fruit detachment force (FDF) in different parts of the tree canopy. One consists of natural parameters li ke the level of maturity, position in the tree and weight and size of fruits. The other parameter s are the machine parameters which affect the force distribution in the tree such as angle of tines, shaker forward speed and frequency In the initial part o f this study, field experiments were conducted to investigate the force distribution. The later part consisted of developing a model to predict the force at different points in the canopy. Report O rganization Chapter two is about the history of mechanical harvesting of citrus in Florida and the literature review related to this study. It also has section about the role of this research in the overall scenario. Chapter three is about the materials used for the experiments involved in this study. The different setups used are described here and are then referred to during the discussion of the experiments. Chapter four is about the two field tests conducted. First one was to get an idea about the distribution of force throug hout the canopy. Based on the first test, the second experiment was designed. Chapter five gives details about the finite element model developed in ANSYS for the

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27 force prediction along branches in the canopy. This model was then validated using the field experiment data. The analysis and validation are explained in this chapter. This chapter also has details about the experiment for determining the physical properties of the citrus wood. Chapter six has the summary of conclusions from this study. There is also a section about what can be done differently in this study. The appendices A and B give additional information about data acquisition, extraction, and analysis along with m ore details about the sensors and communication. Some tables and figures associ ated with the experiments are included in appendices C and D.

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28 CHAPTER 2 HISTORY AND LITERATU RE REVIEW The use of implements for the cultivation of crops was found necessary from the advent of crop cultivation to make the job easier and faster to accomplish. Oldest implements used were pointed ones for digging and sharp ones for harvesting. Current hand tools like rake, trowel, scythe and animal drawn plows and hoes are modifications of similar primitive tools. Nowadays large scale farming methods usually involve machines powered by diesel or gasoline fueled internal combustion engines which drive different agricultural implements designed for various stages of farming (History.com, 2009). Farmers rely heavily on spec ialized technology at all stages of crop production to sustain and increase production. For harvesting, the earliest machine was the mechanical reaper marketed by Cyrus McCormick in the early 1840s This was designed for harvesting grain crops only. Harves ters for root and vegetable crops were not invented until the 1930s (The Gale Group Inc., 2005). For fruit crops, harvesting in general can be divided into functions such as detachment and removal; control, cleaning and selection; conveying and loading (Ru iz Altisent and Oritz Canavate, 1999) To successfully mechanize the entire harvesting process, a system has to accomplish all these tasks. Most the harvesting systems have multiple stages and different machines for each of these tasks. A picker is general ly associated with the tasks of removal and cleaning, while a truck is associated with the movement of the harvested fruit from the picker to a trailer in the grove. There has not been a lot of change in the picking of citrus from the early years of its co mmercial production. Harvesting of citrus is mostly manual in Florida, even for the process oranges. Workers hand pick fruits from the tree, using ladders for those that are on the higher branches. These fruits are then

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29 transported, by specialized tractors used in orange groves been a significant amount of research done to mechanize the harvesting of citrus fruits. There were many projects purs ued relating to this area. In this chapter the discussion about mechanical harvesting in general will be followed by a brief history of mechanical harvesting of citrus and its impact on the current scenario. The final section will be about literature that is relevant to this study. Mechanical Harvesting Mechanical harvesting has been successfully adopted for many crops including some fruit crops. Harvesting method varies from crop to crop and so specialized harvesters are needed for different types of crop. Harvesters are available for many of the grain crops, vegetables, forage crops, and for some fruit crops For grain crops, harvesting is a process of cutting and threshing the harvested crop to separate the grain from the stalk (Kutzbach and Quick, 1999 ). The harvesters for forage crops also work in a similar way but for the threshing process, which is replaced by baling for grasses and a cutt ing for forage cereals (Cavalchini, 1999. ). For vegetables, harvesting is a more complex process and the operations are based on the vegetable being harvested. For root crops harvesting is accomplished by digging as in the case of potatoes or pulling as in the case of leeks (Manfredi and Peters, 1999 ). For surface crops cutting (cabbages), combing (green beans, peas), stripping (cucumbers), de stemming (onions), shaking (tomato) and threshing (peas from their pods) operations are used based on the crop being harvested. These operations are usually used in combination to first remove the required section of the plant (cu t the upper portion of the plant) and then isolate the harvest from the leaves or stem (de stem the onions or shake the tomatoes free) ( Ruitz

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30 Alti sent and Oritz Canavate, 1999 ). Mechanical harvesting of fruits is mostly done for process industry. Small fruits and wine grapes are harvested by a combination of contact and non contact methods. The small fruits like strawberries, raspberries etc. are harvested using a combination of s haking and soft combing. This is accomplished by using oscillatory motion of drums with fingers or spikes to apply a shaking effect on the plants. Grapes are harvested using straddle type (over the row) harvesters which shake the vines to remove the grape clusters from them. They use horizontal rods to shake the vines with frequencies ranging from 10 to 20 Hz. For tree fruits and nuts, the most common method used for harvesting is the shaking of the trees which causes vibration of the fruit. When the fruit vibrates, it experiences traction, twisting, bending and shear forces. It also experiences fatigue effects because of the repetitive action ( Ruiz Altisent and Oritz Canavate, 1999 ) These forces result in development of stresses at the point of contact, e ither at the stem calyx or at the branch stem junction which cause the removing of fruits from the tree Figure 2 1 illustrates some of the forces experienced by the fruits because of the shaking of trees. Citrus, prunes, apples, olives, almonds etc. are c urrently harvested using different type of shakers. Apart from the machines used for harvesting, there are mechanical aids available which make manual harvesting more efficient. These aids are used for vegetables (lettuce, cauliflower etc.) and also for fr uits (melons, pineapples, oranges etc.). For the fresh fruit market, mechanical picking of fruits is not desirable as this affects the quality of the fruit. One man self propelled platforms and multi level picking platforms are two of the mechanical aids u sed for the picking of fruits, while the rest of the harvesting process is mechanized ( Ruiz Altisent and Oritz Canavate, 1999 ).

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31 History of M echanical H arvesting of C itrus in Florida While harvesting, citrus fruits are first removed from the trees and then moved out of the groves to the processing plant or packinghouse for fresh fruit market. Based on this observation, the harvesting is broadly divided into two operations 1. Picking the fruit from the trees, and 2. Transporting the fruits to either the packinghous e or processing plant. Figure 2 1 Forces on fruit when the tree is shaken (Fridley, 1983). Table 2 1. C hronology of citrus mechanical harvesting. Year Developments 1950s Investigation into mechanization attempts Mechanical handling equipment Harve sting aids Early 1960s Focus on development of mass harvesters Late 1960s and 1970s Research to improve the harvesters Studies to simulate tree and/or fruit stem Early 1980s Some research in analysis of tree harvester system Late 1980s Robotic harvesting research 1980s 1990s Research in mechanical harvesting reduced 2000s Renewed interest in mechanical harvesting Renewed interest in robotic harvesting

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32 Attempts to mechanize citrus harvesting were done by mechanizing the two steps separately as they had different levels of complexity. The collection of the harvested fruit at a single location and then moving them out of the groves was simpler than picking the fruits from the trees by mechanical means. So the second of the two harvesting opera tions was mechanized early and with relative ease when compared to the picking operation. The T able 2 1 shows the brief chronology of mechanical harvesting of citrus. Handling of Citrus In the 1950s the second of the harvesting operations was mechanized reducing the labor required by at least two thirds (Whitney, 1995). Hedden and Churchill (1984) summarize the efforts done towards the m echanization of citrus handling M echanization of citrus handlin g was started with the use of two wheeled trailers. They were used for both fresh fruit and process fruit handling. For fresh fruit handling, the trailers were loaded with the fruits by using farm tractors and these trailers were hitched together, 5 or 6 a t a time, to be taken to the packinghouses. For process fruit handling, a trailer or truck mounted basket elevator system was used with the two wheeled trailer system. The standard field box was used to dump the fruits into the truck by two loaders. In th e late 1950s, the pallet bin and tractor fork lift system used in deciduous fruits was adopted for fresh citrus fruit handling in Florida, after several modifications done to the system. At the same time a grapple type pick up head was developed for the l oader boom used in the handling of processing fruits. The loader boom was mounted on a high lift truck next to the driver and could be made to lift and dump fruits. Another

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33 system was developed in the late 1950s which consisted of a tractor with a front en d loader and dump attachment. Field handling systems using farm tractors and trailers, front end loaders or fork lifts were never adopted to as large an extent as the truck mounted loader boom. This was because the truck mounted equipment does not need any supplemental transportation to travel from one grove to another at highway speeds. Some of the fruit collection schemes were based on vacuum system of fruit handling. One such system had the fruits to be transferred to the closed cylindrical hopper by the picker and then they were dumped directly into a roadside truck by the vacuum system. Other types of fruit handling systems developed were the windrow pickup machines. These machines were developed specifically for the Florida conditions and they were of two types. One was to pickup fruits from the windrow in the center of the row and the other to pickup fruits from the windrow under the tree drip line. A high list truck was used along with the pickup machines and the fruits were transferred to the truck t hat was usually towed behind the pickup machines (Churchill et al, 1976). Harvesting Aids While the handling of citrus was being mechanized, studies were being conducted to improve the efficiency of picking fruits from the tree. The initial work mostly con centrated on improving the efficiency of hand harvesters. Jutras and Coppock (1958) conducted t ime and motion studies on hand harvesters to understand where most of the time was being spent and how to improve their efficiency by reducing this time. These s tudies showed that the hand pickers spent 25% of their time in non productive activities or activities that were other than picking fruits. To cut down on this non productive time, different scenarios were investigated to design harvesting aids. Different types of harvesting aids were studied and evaluated to make hand harvesting

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34 more efficient and partially mechanize harvesting (Coppock and Jutras, 1960) The of fruits productivity of workers by 40% when compared to the conventional method. Another effort was the use of bag and ladder to simulate the ground conditions. This was based on the observation that the pickers at ground level were more efficient than the others. Though different kind of harvesting aids were investigated and developed which increased productivity, they were not economically very advantageous over conventional methods of picking. This shifted the focus to the removal of fruits from trees by machines. Contact Harvesting In the 1960s, some of the initial efforts to mechanize the picking of fruits were towards the development of machines that could duplicate manual harvesting. The reason was to develop one system that could be used for both process and fresh market oranges. Such a system could be very useful for the Florida citrus industry by reducing the picking costs. One of the earliest such effort was the development of an auger based mechanical picker (Lenker, 1970) This system used a set of augers that entered the tree cano py and removed the fruits by a rotating motion of the augers. The harvest trials done using a prototype resulted in only 65% fruit removal. Later Chen et al (1982) developed a contact harvester based on flexible fingers to harvest mature fruits selectively Though it had mature fruit removal of 85 to 90%, tree penetration was a problem. Such results did not economically justify the use of these machines. Because of these reasons, focus shifted away from contact harvesting and more towards mass harvesters li ke trunk shakers.

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35 Mass F ruit H arv esters Beginning in early 1960s, investigation into development of mass fruit harvesters started. These machines were intended for use of harvesting process oranges only, which also required bulk of the labor requirements. Research and development was done on trunk shakers, limb shakers, air shakers and foliage (canopy) shakers. These studies were coupled with development of catch frames for the harvested fruit so that it can be collected and later transported easily (Coppoc k, 1967 ; Coppock and Hedden, 1968 and Coppock, 1976) Amongst the aforementioned mass harvesters, continuous canopy shakers are the most recently developed mechanical harvesters. One of the earliest studies done regarding its development and design was in late 1990s by Peterson (1998). Coppock (1961) did i nitial studies to study the manual picking methods. From these studies it was concluded that the fruits can be removed by rotating them or by shaking them. The shaking concept had been used in harvesting nut crops and was already being used for harvesting prunes and peaches for processing. One of the initial inertia shaker to harvest citrus was designed based on the one developed for harvesting prunes by Adrian and Fridley (Coppock and Jutras, 1962). The s ystem was customized for citrus crop as there were physiological differences between the crops. Some of the earliest developed mass harvesters were primarily trunk and limb shakers.. There were studies conducted about the efficiency of these systems which was found to be pretty low. This was because of the low fruit removal and also the reduction of yields in the subsequent years. There was a 5 year study conducted by Hedden and Coppock (1968) about the reduction in yield because of persistent use of mechan ical pickers. The reduction in yield was very pronounced in the Valencia type during the mid season and

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36 late season harvesting. This called for a method to selectively harvest the mature fruits in order to reduce the impact of future yields. There were a c ouple of biophysical studies done about the Valencia type to come up with an approach to selectively harvest the mature fruits. The outcome of this research was that the shaking of the fruit bearing region of the tree, namely the canopy, would be more effe ctive and also the use of a chemical to loosen the mature fruits would help in selective harvesting. Abscission chemicals similar to the ones produced naturally by the mature fruits were developed for the selective removal of mature fruits. The use of the abscission chemicals along with the different shakers was investigated. Though the efficiency of the shakers was better, there were many problems because of wind, rain and other environmental factors affecting the influence of these chemicals on the fruits Furthermore, there was no reliable way to spray uniformly throughout the canopy so that the fruits would be removed by less force application (Whitney, 1978a) The research is still on going to make the chemical commercially available. In the 1970s the v ertical foliage shakers and air shakers were designed and developed These systems applied force to the canopy, which is the fruit bearing region. Hedden and Coppock (1971) conducted c omparative trials using foliage and limb shakers which showed that the f oliage shakers had better selectivity. Though this was encouraging, during the late season harvest considerable amount of young fruits were removed. It was also noticed that the fruits for the next year were bruised. The air shaker (Whitney, 1968 and Whitn ey and Patterson, 1972 ) did not come in contact with the fruits and was supposed to reduce the fruit bruising. But this system was only efficient when used along with the abscission chemical and even in that case it caused

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37 defoliation and peel damage. Copp ock et al (1981) conducted comparative studies with these shakers to understand the type of shaking action required to increase their efficiency. In late 1990s a prototype similar to the current canopy shaker was designed and developed by Peterson (1998). Harvest trials indicated a removal efficiency ranging from 80 to 90% which could be improved by changing the configuration of the system and finding optimal operating parameters. Now that the fruit can be picked off the tree by a machine, a system was required to catch these fruits and transport it. The handling equipment for fresh fruit market could be used but with some modifications. Based on the fruit handling, the mechanical pickers were classified into two categories. One category was of those whi ch dropped the fruits onto the ground. These fruits were then deposit ed by machines or manual workers into goat trucks or bins and later transferred to hauling trailers. Other category had catch frames which caught the harvested fruits and deposited them i n bins or directly into goat trucks following them. The design and development of these pick up machines and catch frames were done simultaneously with the mechanical pickers (Sumner and Churchill, 1977; Coppock and Hedden, 1968; Churchill et al, 1976; Cop pock, 1967; Coppock, 1976 and Hemmat et al, 1980). Robotic Harvesting Since the mechanical pickers were developed with good efficiency (about 80 90% of mature fruits) for processing fruits, study and development of systems for picking fruits for fresh fr uit market was started. With the advancement in technology, robotic fruit harvesting was investigated for picking fruits for fresh fruit market. One of the earliest studies was done by Parrish and Goskel ( 1977 ) to identify the location of fruits using a ca mera. They developed a rudimentary system that picked apples from a

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38 tree model in a laboratory. For citrus, robotic harvesting research was started in the early 1980s at University of Florida, Gainesville. Harrell et al (1985) conducted designed and develo ped a system to demonstrate the capability to see and recognize the citrus fruits. But the research was discontinued because of lack of funds. In the new millennium, renewed interest in the robotic harvesting has called up for further research into this ar ea. Using real time image processing, the fruits could be identified and then picked by a robotic arm. Research is on going in this field and though some researchers had developed prototypes as early as in late 1980s and early 1990s, these systems are not yet commercially viable. Some of the major obstacles were the recognition of fruits deep in the canopy and the movement of the robotic arm around the limbs. Current Mechanization in Citrus Harvesting Over the years many researchers have summarized the dev elopment of mechanization in citrus fruit harvesting (Whitney and Sumner, 1977; Whitney and Harrell, 1989; Brown, 2002; and Sanders, 2004). It is evident from this literature that for fresh fruit market, the mechanization is limited to handling and transpo rting of fruits from the grove to the packinghouse. This is done using the bins into which the workers place the fruits; goat trucks to transport the fruits from the bins to trailer; and finally the trailer to transport it to the packingh ouse. As for proce ssing fruits, commercial mechanical harvesting machines are already available and being used by some growers. Trunk Shake and Catch (TSC) The TSC system ( F igure 2 2) attaches to the trunk of a tree and shakes it for 5 to 10 seconds. The fruits are collecte d in an attached receiver which when full is transferred to a goat truck. The fruit removal is 95% at a harvesting speed of 235 tree/hr with labor productivity of 90 box/hr (for each crew member) ( Roka and Hyman 2004 ).

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39 Continuous Canopy Shake and Catch (C CSC) A CCSC system ( F igure 2 3) moves along the row at 1 to 2 mph and shakes the trees along the rows. The fruits are caught by the catch frame and conveyed to the following goat truck. The fruit removal is 95% at a harvesting speed of 450 500 tree/hr with labor productivity of 100 box/hr (for each crew member) ( Roka and Hyman 2004 ). Figure 2 2. Trunk Shake and Catch (TSC) (Source: http://citrusmh.ifas.ufl.edu/index.asp?s=2&p=3 Last accessed July, 2009). Tractor Drawn Canopy Shake (TDCS ) The TDCS system ( F igure 2 4) is similar to the CCSC but without the catch frame. The fruits are dropped to the ground and are either picked up by the ground crew or a pick up machine. The fruit removal is 95% at a harvesting speed of 300 400 tree/hr with l abor productivity of 20 30 box/hr (for each crew member) ( Roka and Hyman 2004 ). One of the biggest advantages of the continuous canopy shaker is that the machine does not need to stop at each tree like the trunk shakers. So the rate of harvest is more com pared to trunk shakers. From the 2007 08 season only the continuous canopy shakers are used for citrus mechanical harvesting. There are also

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40 pickup machines which are available commercially for the picking of citrus fruits that are left on the ground after harvesting. Current research in mechanical harvesting is on development of an abscission chemical for selective harvesting for late season Valencia and a variable rate shaker based on tree factors. Figure 2 3. Continuous Canopy Shake and Catch (CCSC). Figure 2 4. Tractor Drawn Canopy Shake (TDCS).

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41 Economic I mpact of Mechanical Harvesting Florida is the second largest producer of citrus next only to Brazil. But the production costs in Florida are almost three times that of Brazil (Roka and Rouse, 2004). For the Florida citrus industry to be competitive in the global market, the production costs have to be reduced. The cost for harvesting citrus is more than all the other production costs p ut together (Futch et al, 2005), an increased use of mechani cal harvesting will ensure a significant reduction in production costs. M echanical harvesting might not be the right solution for all growers. The economics of the mechanical harvesting should be determined based on the difference from the hand harvesting costs rather than the absolute costs. The initial changes to the design of groves are required for mechanical harvesting to be economically favorable. The web based spreadsheet designed by Dr. Roka ( http://citrustool.ifas.ufl.edu ) can be used by growers to determine whether the use of mechanical harvesting is profitable or not. For example, the net grower gain for a scenario where the difference between manual and mechanical harvesting is $0.25 with fruit recovery of 98% and a yield of 400bx/ac with deliver ed in price of $5/box will be $62/acre. The above example shows the net gain by shifting to mechanical harvesting but does not include the initial costs involved. Including the initial costs for adapting the groves to mechanical harvesting, increased retur ns can be seen in 1 to 3 years based on the grove conditions (Roka, 2004). Knowledge G ap Continuous canopy shaker is the latest addition to the family of mass mechanical harvesters developed for citrus. The optimal machine parameters for harvesting differe nt varieties of citrus and during different times of the season are not readily available. The machine operators use their experience to change the machine

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42 parameters to suit the conditions and harvest the fruits. This has given rise to a big gap in our un derstanding of these machines and how to make them more efficient. Since this machine has multiple contact points on the tree that constantly change, it is virtually impossible to develop exact equations for its interaction with the tree. But from the lite rature present, there are a lot of studies done using finite element method to understand the tree harvester interaction with single point of force application. A similar approach could be used to understand these machines and their interaction with the tr ees during harvest. As a first attempt towards the goal of understanding the canopy shaker tree interaction, this study tries to investigate whether the forces can be predicted for a simplified case. The important assumptions and constraints used in this s tudy are given below. Constraints: o Canopy shaker is stationary. o Tines are kept parallel to the ground. o Defoliation and trimming of the trees to reduce the complexity of the system. Assumptions : o Points of contact are same throughout the shaking duration o All the energy is transferred from the canopy shaker to the tree o The acceleration in un interested parts of the trees can be neglected. Though attempts have been made to make the system as ideal and simple as possible, complete correlation between the experi mental and predicted values is not expected. Further discussion on the development of the model and validation experiments can be found in Chapter 5 of this report. Related Literature Over the years many researchers have studied and analyzed the dynamics of tree when different mechanical harvesters are used on it b ut there was not much research

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43 done using the continuous canopy shaker. This was because canopy shakers are relatively new. Better understanding of the interaction of harvesting machines and tre e canopy during harvest could help improve the existing canopy shakers and their fruit removal efficiency This could be done by measuring and analyzing the force distribution in the canopy under real or simulated harvesting conditions There are many fact ors that might affect the distribution of force in the citrus canopy and it is virtually impossible to study the effect of all these factors together. So a set of factors have to be identified and their effect studied on the distribution of force in the ci trus canopy The literature presented here was used to identify the parameters used for experiments and model development. Though the literature involves different mechanical harvesters and sometimes even different types of fruits, there were many common f actors which could prove to be important for this analysis. The identified factors were then reduced to a relevant and manageable subset to complete this study within the given constraints. The basic principle behind the removal of fruits from the trees me chanically is to shake them for developing an inertial force on the fruits that is more than the bonding force between the stem and fruit ( Fridley and Adrian, 1960 ). Traditionally, fruit removal force has been determined by measuring the amount of axial fo rce required to remove a fruit from the stem. But in the case of a mechanical harvester based on the shaking principle, the force is different as it does not simulate the hand picking operation Based on the shaking principle, different types of mechanica l harvesting systems were developed during the 1960s and 1970s as was discussed earlier in this chapter. Starting from 1960s to the present time, researchers have looked at the characteristics of these different mechanical harvesters and also the crop char acteristics to increase the

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44 efficiency of harvesters. Some of the earliest studies were about harvest trials done on different varieties of citrus and other fruits to study the effect of mechanical harvesting uit removal. Markwardt et al (1964) did harvest trials using a limb shaker on cherry trees. Apart from harvest efficiency and yield; the removal of fruits with twigs, immature fruit removal, fruit quality and bark damage was also evaluated. Because of the removal of immature fruits, a feasibility study for selective harvesting of cherries by repetitive harvesting of fruits during different time s of harvesting season was done. This proved to be detrimental to the quality of next year crop as well as the late harvested cherries because of the damage caused by repeated mechanical harvesting. Whitney et al (1973) using a vertical foliage shaker for harvesting. The selected trees were mechanical harvested i n 1972 and hand harvested in 1973. The yield reduction and effect of different types of stroke and shake duration on the yield was analyzed. Sumner et al (1975) and Whitney et al (1975) designed a foliage shaker and studied the effect of different shaking modes on Hamlin and Valencia oranges. They concluded that the yield reduction was less for sinusoidal stroke and also when the duratio n was 10 sec onds when compared to 20 seconds In Valencia they found that late harvesting damaged /bruised the young fruit left on the trees Limb shakers were used by Sumner and Churchill (1978) on Hamlin tree limbs to study the effectiveness of different types shaking motions. They also did field tests to determine the selective removal of Valencia during the late harvest s eason. They conducted these tests with and without abscission chemicals. From these studies t hey concluded that a smoother action was better and a

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45 reduced FDF with the use of abscission chemical increases the effectiveness of the harvesters Study using di fferent air shaking patterns in air shakers on Pineapple, Queen and Hamlin trees was done by Whitney (1978 b ) Different air shaker patterns were generated using different configuration of the plates (center pivot, wobble and upstream pivot plates) in the s ystem. The center pivot plate having a more definitive air pulse and greater air shaking impulse was found to be far superior to the others. Trunk shakers were also used in a similar study by Hedden et al (1984) on Valencia and Hamlin trees. They used different modes of shaking (linear and multidirectional shakers) to determine their effectiveness. This study was done for four years from 1981 to 1984. They determined that the use of abscission chemical increased the percent fruit removal and there was a reduction in yield of Valencia because of the use of both abscission chemical and mechanical harvester as immature fruits were removed dur ing late season harvest. Apart from harvest trials, there has been considerable research done towards the modeling of fruit stem system and branches of trees so as to theoretically analyze the force on them when using mechanical harvesters. T his work has not been done on citrus tr ees and specifically not with the use of continuous canopy shakers as the mechanical harvesters. The second part of the thesis was to extend the ideas used in the development of analytical models from earlier research to our scenario. The validation such a model was done using field experiments. Researchers had always been interested in modeling of either entire or part of trees and fruit stem subsystem to simulate the mechanical harvesting conditions. There were basically two different types

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46 of approached followed. One was the empirical approach, where experiments were conducted and a model derived based on the experiment input and output values. The other approach was to theoretically derive equations based on some assumptions to simplify the problem and t hen solve these equations using computer program. Both these approaches required validation after the development of the model. Some of the papers were not involved in the actual development of a model but still studied the force transmission and related f actors. During their harvest trials, Markwadt et al (1964) concluded that since the force was applied at only one point of the tree the energy had to be transmitted from that point through the branches of the tree. This energy transmission varied according to the point of attachment and also the characteristics of tree such as branch diameter and length and the weight distribution of the tree. Some of the early experiments done to model the behavior of limbs were done in 1960s. Adrian et al (1965) used an o live branch from a tree and rigidly mounted it in the lab. They studied the effect of the clamping location on the amount of force required to remove the fruits. From the study they concluded that the force and power required increased as the location was moved towards the fixed end of the branch. Wang (1965) modeled the coffee cherry plant as a spring mass system and described a series of equations to determine the natural frequency of the coffee plants. A mechanical harvester designed based on the study was used to conduct some experiments to determine whether selective harvesting was possible or not. In these studies conducted by Wang, the damping properties of tree were not considered. Lenker and Hedden (1968 a ) tried to experimentally isolate the limb f actors that had an effect on fruit removal

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47 using 6 limbs from Valencia trees. They concluded that the limb displacement was directly proportional to the fruit removal. They were also able to arrive at a regression equation to predict the yield based on the factors selected. These regression equations were able to predict the removal pretty well. Later on in 1990, Whitney et al conducted experiments using a Cypress wood post to validate the mathematical developed for predicting the displacement and force at various points. The conclusion was that though this prediction. Another study by Diezma Iglesias ( 2005 ) tried to correlate the vibrational characteristics of the branches t o the fruit removal. Though they had high correlation in the laboratory tests, the complexity in trees caused problems in the field tests. Researchers who worked on developing theoretical models based on assumptions have used different theories to model th e limbs. The selection of the theory was based on the complexity of the system to be described and the difficulty of the equations to be solved. The complexity was reduced by making some reasonable assumptions. Apart from the modeling of trees, there has b een work done on determining the factors of mechanical harvesters using theoretical assumptions. Adrian and Fridley (1965) used the fundamental vibration theory to present the design criteria of inertia type shakers. They were able to predict the different parameters of the machine (mass ratio and eccentricity) to develop the required stroke and also the power requirements for that stroke and frequency. Studies were conducted using beam theory to describe the limbs by modeling them as cantilever beams of va rying properties along their length. The differential equations were then solved by finite element method using a computer program. Fridley

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48 and Lorenzen (1965) investigated the simulation approach to solve the tree shaking problem. The objective of their s tudy was to investigate the possibility of using an analog computer for simulating the shaking of tree limbs. A four cell simulated beam was used for stud ying the forced vibrations under the assumption that the Timoshenko beam theory was sufficient for pre dicting the behavior of the sha king tree limb. T he force was applied at di fferent locations to observe the effect of force location at different parts of the tree limb. Since only four elements were used the error in finite element approximation was high which could be reduced by increasing the number of elements used for the simulation. Schuler and Bruhn (1973) applied the damped Timoshenko beam theory to vibrating limbs. T he study was done using cherry tree limbs to compare the acceleration and displacem ent values from the experiments with the theoretical results. The experiments were done with and without leaves and it was concluded that it made little difference to the tree limb response. The comparison had good correlation at lower portions (fixed end) than the upper portions (free end) of the limb. This discrepancy was attributed to the torsion effects caused by the nonsymmetrical distribution of the branches. Yung and Fridley (1975) developed a finite element model for the entire tree using simple bea m theory and assuming that the tree limbs were truncated conical beams with their length and curvature very large compared to their diameters. A computer program was developed for these equations and the experimental values were compared against the calcul ated values. T he values were in good agreement and the model was used for analysis of a later experiment. They also studied the transmissibility of force along the branches of the trees and its effect on the harvesting efficiency and frequency to be used. It was concluded that stiff branches

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49 transmitted the force better than the flexible ones since they acted as dampers. The resonant frequency of fruits could be used to harvest the trees with stiff branches while it was not the case with limber branches. It was observed that branches having bigger diameters have better transmissibility because of their stiffness. Upadhyaya and Cooke (1980), Upadhyaya et al (198 0a) and Upadhyaya et al (1980b ) did a finite element analysis for limb impact harvesting. The model was developed to include small twigs and leaves which added damping to the system. Bernoulli Euler beam theory was used to model the limbs with twigs and leaves. An experimental study was done and the values were found to be in good agreement with theoretical values calculated from the model. In some cases the finite element analysis was not favored because of its complexity as was done by Philip et al (1970). They modeled the tree as a s ystem of cantilever beams attached to each other. The small branches were also modeled as cantilevers. These beams had mass and stiffness properties which varied with position along them. A set of differential equations were derived for this system of cant ilevers using Euler Bernoulli flexure theory. These equations were programmed to be solved by a computer. They used standard values for properties such as specific weight, modulus They also proposed that the size and configuration might follow a statistical pattern which can be then used to model a standard tree for a specific species. Rayleigh Ritz analysis of a simple limb was used instead of finite element analysis because of i ts ease of use. The model was validated using data from two experiments conducted by other researchers, one done on an actual Olive branch by Adrian and another done on a branched steel

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50 beam by Delattrez From their comparisons they were able to conclude t hat the computer calculated values were in good agreement with the experimental results available. From their simulations, they concluded that branches with too many bends and splits did not transmit the force effectively. Apart from beam theory, there wer equations and spring mass system used to model and study the behavior of tree limbs. Hussain et al (1975) studied the tree limb response to intermittent excitation of the branches instead of clamped excitation. They calculate the theoretical values for limbs. The limbs were again assumed to be cantilever beams with varying material properties along the branch. The natural frequency calculated from the model was comparable to the t heoretical value. They concluded that the intermittent excitation produced higher accelerations than the conventional methods used at that time. It was also observed that applying this kind of excitation closer to the fruit bearing regions would make remov al more effective and efficient. Ruff et al (1980) did an analysis of the air suspension stem vibration equations were solved numerically and the predicted mode shapes and na tural frequencies derived. The comparison of the predicted and experimental values gave a good correlation value. It was concluded that the fruit mass, stem length and air velocity had more influence than the stem mass or stiffness on the dynamic character istics of the model. Upadhyaya et al (1981) did a series of studies on impact harvesting of fruits. They developed a spring mass damper system to study the dynamics of the tree when harvesting is done using tree trunk impact. The single degree model was de veloped to

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51 approximate the above harvesting. This model was able to predict the dynamic behavior of the tree reasonably well at the time of impact and just after the impact. This model was also used to estimate the physical parameters of the tree. One of t he equations from this model gives an estimate of the energy transfer which could be used for correlating with the fruits removed. While developing all these theoretical models, the damping characteristics of trees were considered very important. These cha racteristics determine how well the force was distributed to different parts of the trees. Hoag et al (1970) studied the effect of external and internal damping on the dynamic response of tree limbs. In this study they used an instrumented Olive branch to record the acceleration and displacement values when it was shaken. Using the physical properties from previous experiments and the force information from this current one, the acceleration and displacement values were calculated. These values were compare d and analyzed. From the analysis, it was concluded that the damping increases with frequency when there are no leaves. It was also noticed that the external damping of the wood was only due to the leaves present and in their absence external damping could be ignored. Later in 1971 Hoag et al did an experiment to determine the damping properties of tree limbs which would be useful for analysis when studying the feasibility of selective harvesting. They used Almond wood in varying states of moisture content (from 70% moisture content wood to oven dried wood). They observed varied logarithmic decrement of damping with different moisture contents. They also observed that the external damping was due to drag by the leaves, and that it could vary with the changin g interaction of the leaves. The air damping of the wood itself was observed to be negligible.

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52 Though Hoag et al did trials to determine the damping properties, these experiments were not done on entire tree but on samples of the wood. If these results wer e used then the energy requirements of a shaker to harvest were considerably different from the actual values. Horvath and Sitkei did a couple of studies on the energy requirements of the shaker based on the entire tree soil mass system. In 2001 they studi ed the energy consumption based on different operational conditions. They considered the tree and the soil root body as the entire system instead of the tree alone and developed a mechanical model. They included the lateral and tilting motion of the tree a lso apart from the elastic deformation of the trunk in the model. Three different inertia type shakers were used for the experimental study and to study the relation between the acceleration, trunk diameter and the attachment point. They concluded that the power requirement and the total displacement were dependent on the attachment height of the trunk shaker. Later in 2005, Horvath and Sitkei conducted a study to determine the damping properties of the entire tree instead of just the wood samples from the tree as done by Hoag et al. They considered the root soil mass, trunk and the canopy as the components of the vibrating tree system. Since all the three components had different damping properties, they were determined separately by using the logarithmic d ecrement method. They used three different inertia type trunk shakers for this study. A direct energy method was used for determining the damping properties of the soil while common hammer test and later initial displacement test were done to find the damp ing properties of the canopy and the trunk. They observed that at low attachment heights, most the energy was absorbed by the soil. In the case of the canopy, they observed very high damping properties which were not completely

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53 explained by the air resista nce alone. They assumed that it may be because of the many small branches and leaves in the tree. It was concluded that the power consumption of the trunk shakers depended on the attachment heights. Though there were harvest trials done in citrus using ver tical foliage shakers in the 1970s, one of the earliest studies using a canopy shaker similar to the current machine (design and field trials) was done by Peterson (1998). A prototype canopy shaker was developed for process oranges and field trials were co nducted. The initial phase of this research concentrated on development of a shaker while the later part was about the development of the catching and conveyor system. Harvest trials were used to decide on a possible frequency for effective harvesting of o ranges. It was noted that 5Hz was the best effective fruit removal frequency. It was also concluded that additional research was needed to decide upon the optimum configuration of the system and also the operating parameters. The current study tries to use the commercially available continuous canopy shaker and study the force distribution in the canopy during harvest.

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54 CHAPTER 3 MATERIALS The basic components for all the experiments were the same, differing only in their setup and how they were used. Apart from the shaker and trees used, the other components were sensors and transceivers. The combination of the sensor and transceiver gave rise to two different setups used in this study. These two different setups will be discussed in detail in this ch apter along with the individual components used. Tree and Harvester Continuous Canopy Shaker Continuous canopy shakers are mass harvesting systems that move from one tree to another without stopping. H arvesting rates of 400 trees per hour can be achieved b y these machines (Roka and Hyman, 2004) As said in Chapter 2, t here are two types of canopy shakers. 1. Tractor Drawn Canopy Shaker (TDCS) 2. Continuous Canopy Shake and Catch (CCSC) The core unit of both the systems is a set of horizontally stacked whirls as can be seen in the F igure 3 1. Each whirl has about 16 tines with each of them being 6 to 7 ft long. The number of whirls present in the shaker depends on the model and make. Thes e tines enter the canopy and shake it causing the fruits to be detached from the tree limbs. The O xbo International Corporation manufactures both types of system s O xbo 3210 is a TDCS system manufactured by them. Figure 2 4 in Chapter 2 is the O xbo 3210 machine. This was the machine used for the different experiments conducted during the course of this study. This machine is a tractor powered continuous canopy shaker which removes the fruits from the trees and drops them on the ground

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55 for pickup. This mac hine has 12 whirls of tines stacked on top of each other. Each tine is about 6 to 7 feet in length. As seen in the Figure 3 1, there are six beams and each pair of whirls is attached to one beam. The adjacent whirls connected to the same beam move in oppos ite while shaking the tree. The entire set of tines is moved by using a single hydraulic system present in the canopy shaker. Figure 3 1 Whirls that will hold the tines Citrus Trees Different types of citrus trees were used for different experiments The selection of trees and their type for each of the experiment varied as per availability. The first experiment was done while the fruits were being harvested and were arbitrarily selected in Hamlin and Valencia groves The second experiment was done on Valencia trees of 2 different sizes. The third and final experiment was done using Late Navel trees which were defoliated ( F igure 3 2) so as to simulate ideal beam conditions. Acceleration Acquisition The acceleration of different locations of canopy was sensed using accelerometers. The data acquisition was done wirelessly for all the experiments. The

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56 transceiver module used for communication and the accelerometer used for sensing acceleration are described in this sectio n. Figure 3 2 Defoliated tree Figure 3 3 XBee PRO used for data communication ( Source: http://www.mycollegeproject.com/images/xbee pro module.jpg. Last accessed July, 2009.) Figure 3 4 MMA7260Q Accelerometer for sensing acceleration ( Source: http://www.robotshop.ca/Images/big/en/sfe mma7260q triple axis accelerometer.jpg. Last accessed July, 2009)

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57 XBee PRO XBee PRO ( F igure 3 3) is a Z ig B ee /802.15.4 compliant RF module used in these experiments. This is used for wireless communication between the accelerometers and the laptop for data acquisition. These modules are manufactured by Digi International (formerly known as Max S tream). Some of the k ey features of these modules which make them very favorable for agricultural sensing are low p ower and cost and reliable data transfer. They use ISM (Industrial, Scien tific and Medical) 2.4 GHz band and have source and destination addressing possible ( Digi International Inc., 2008 ). This module is a transceiver, used for transmitting data from the accelerometers and for data acquisition at the laptop end. The XBee PRO was attached to an USB port on the laptop to record the incoming data. MMA7260Q accelerometers An accelerometer senses the acceleration in a given direction and reports the same as an analog voltage. Since the tree can move in any direction, an accelerometer that could sense and report the acceleration in all the three directions was required. Tri axis accelerometers used in the experiments a re manufactured by Freescale TM Semiconductor Incorporated and the ir model is MMA7260Q ( F igure 3 4) It is a low cost, capacitive, micromachined accelerometer featuring signal conditioning with a 1 pole low pass filter, temperature compensation and g Select It allows for the selection among 4 sensitivities ( 1.5g/2g/4g/6g ) It has low current consumption ( ) with low operating voltage (2.2V to 3.6V) ( Freescale Semiconductor Inc., 2008 ). Sensor Computer Communication There were two different sensor communication setups used in this study. The reason for the second alternative setup being used was the problems faced with the first

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58 setup. In the first setup, the sensors were battery powered which disconnected when shaking the trees and so had to be checked and attached at end of each t rial. Both the setups were designed and developed with the help of Mr. Martin Hebel, Electronic Systems Technologies, Southern Illinois University Sensor and Transceiver S etup 1 In this setup, each accelerome ter was associated with one XBee P RO and a mic roprocessor chip, an Atmel AT m ega8L. The analog to digital conversion (ADC) was done by the microprocessor chip by the 10 bit, 5 channel analog to digital converter. This converted data was then ti me stamped and sent to the XBee P RO for transmission. The transmitted data was received at the laptop end by another XBee P RO module (F igure 3 5 ) The data coming in from the USB was monitored by Micro s oft (MS) Excel V isual B asic (VB) Macro which parse d the data and recorded it in the sp read sheet. Each accelerometer sen t 6 7 data points per second. Data were time tagged and id tagged with each unit unique ID name which was configured using the X CTU software provided by Digi International Inc E ach combina tion of the accelerometer, XBee P RO and microcontroller was powered by a 9V battery. The microprocessor also managed the status of each node that was acting under control of the computer based XBee PRO module by waking it up as required In this setup there were 2 types of boards used for sensor transceiver. One ha d the XBee PRO accelerometer and microprocessor on the same board along with the power source as shown in F igure 3 6 This was attached to the bigger fruits in the tree. But the weight of th is entire setup significantly increased the weight of the fruit itself for the smaller fruits. So to instrument the smaller and young fruits, another type of board was used This one had the accelerometer separated from the other components as

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59 seen in the F igure 3 7 The data communication between the tri axial accelerometer and the laptop was as shown in the schematic given in F igure 3 8 As explained earlier, this setup had problems because of the battery powered sensors. Another problem was the data co mmunication. When the number of sensors was increased the system became very slow and broke down. Due to the increase in the number of sensors, the MS Excel VB program was only able to collect data from a few sensors at the required rate. Since more senso rs were required for the third field experiment, a new setup was designed and developed. Figure 3 5 XBee PRO USB receiver Figure 3 6 Accelerometer, XBee PRO and power on same board

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60 Figure 3 7 Accelerometer separate from XBee PRO and power Figure 3 8 Data collection schematic for setup 1 Sensor and Transceiver Setup 2 The main differences between this setup and the previous one were a single power source for all sensors, the elimination of the microprocessor chip and the association o f two accelerometers with each XBee PRO module. The accelerometers outputs were connected directly to the analog to digital conversion ( ADC ) channels of the XBee PRO modules. The analog data from accelerometer wa s converted to digital data and then sent o ut by the XBee PRO module. At the laptop end, the raw data wa s received by an XBee PRO transceiver and written to a text file using a LabView TM V irtual I nstrument (VI) The laptop receive d 30 40 data points per second through the

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61 USB port from all the sensors on each channel used A ll the XBee PRO modules were powered up using a signal generator. This ensure d that all the points had the same voltage and helped to eliminate the problem of changing the batteries constantly This setup also reduced the tim e spent for data collection as the nodes were powered up properly throughout the experiment. Figure 3 9 shows an individual XBee PRO with two accelerometers connected to it. Since the data being written to the file was in hex format and had acceleration fr om 2 accelerometers, a more complicated code was needed to process the raw data. A Java TM program was a written which parsed the valid data from hex to decimal and then separated the data from the two accelerometers into separate files. This processed data was just the voltage values and had to be processed again by another Java program to extract the acceleration values for analysis. The schematic of the data collection for this setup is given in F igure 3 10 Figure 3 9 Sensor and transceiver setup 2

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62 Figure 3 10 Data collection schematic for setup 2

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63 CHAPTER 4 FORCE DISTRIBUTION Continuous canopy shakers harvest citrus fruit by shaking the canopy of the trees. The force is applied directly to the fruit bearing region and the points of force application are constantly changing as the machine moves along the row when it shakes the t rees. Compared to the trunk shaker which has a single point of force application, this is a more complex scenario. The first two experiments were conducted to study the force distribution in th e citrus canopy and the branches when the trees we re harvested using the continuous canopy shakers. The first experiment was for the purpose of analyzing how the force is distributed when a citrus tree is being harvested. The second experiment was designed to study the force distribution along just one single branch. This experiment was based on the premise that branches are the medium for the transfer of force from the contact points to the other locations of the tree. First Field Experiment This experiment was done during the actual harvest of citrus trees to get an idea of force distribution in those conditions The machine parameters used for this experiment were selected by the machine operators as per the harvesting conditions. The accelerometer data was collected from fruits in different locations of the tree. Th e force, yank and momentum experienced by the fruits and also the duration of significant force were calculated and analyzed. Materials and Methods The sensor transceiver setup 1 as explained in Chapter 3 was used for this experiment. The sensors were tied to the fruits directly as shown in the Figure 4 1 The locations of the fruits were chosen randomly such that they represented the entire

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64 canopy and not concentrated at any particular region of the canopy As the harvesting was done on a half tree basis, the fruits were instrumented on the half being harvested The F igure 4 2 shows the location of fruits in a tree canopy from which the data was collected. After the selected tree was harvested, the fruits were weighed and their dimensions measured. The numb er of fruits removed and their locations were also noted down for later analysis. T his experiment w as conducted in three di fferent groves, one Hamlin and two Valencia groves. The trials were done such that it was late harvest season for both Hamlin and Val encia. This was to ensure that the maturity levels were comparable. The details of the test locations and times are given in Table 4 1 During all the t rials the harvesting machine tine angle was kept constant at around 15 degrees. The frequency of the shaker was varied based on the harvesting necessity. For the abscission trial, the chemical 5 chloro 3 methyl 4 nitro lHpyrazole (CMNP) was used to study its effect on the forces experienced by the Valencia fruits. Figure 4 1 Sensor attached to a frui t

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65 Table 4 1 Location, fruit variety and test parameters for the field tests. Test 1 Test 2 Test 3 Date 02 1 07 05 09 07 05 21 07 Place Plant City Mud Lake, Bartow Arcadia Position 27.96022 N 82.20693 W 27.85742 N 81.77636 W 27.23070 N 81.68736 W Row spacing (ft) 26 26 26 Tree spacing (ft) 12 12 12 Variety Hamlin Valencia Valencia Shaking frequency (cpm) 275 246 185 Figure 4 2 Location of sensors in the tree Resultant force (F) The data was collected as per the method associated with the setup 1 explained in Chapter 3. After the data collection, the raw data (in terms voltage) had to be converted to acceleration values. The general formula for conversion of analog voltage data to acceleration is given in Equation 4 1.

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66 (4 1) reading at which there is no acceleration of the sensor. Theoretically the 0g value is 1.65 V, the mid point of the output voltage. But this value might change from sensor to sensor, so the sensor values when stationary were used as the 0g values. The average of the first 25 readings of the data was used as the 0g value if their standard deviati on was less than 2, or else the theoretical value was used as the 0g value. The sensitivity value used for this study was 0.2 V/g based on the 6g setting of the accelerometer The value (9.8 m/s 2 ) which is r equired to arrive at the acceleration values (in m/s 2 ) for all the axes. Based on these specifications of the sensor, the Equation 4 1 was arrived at for acceleration calculation. The force on a particular fruit was calculated by multiplying the accelerati on va lue with the weight of that fruit The resultant force on the fruit was then calculated using the Equation 4 2. (4 2) where, F r is resultant force in N, F x is force along X axis in N, F y is force along Y axis in N, and F z is force along Z axis in N. Duration of significant resultant force (T) Along with the force experienced, the duration for which there was significant force was also of interest. For calculating the duration of significant force, a threshold/range was required. Thi s was taken to be the range of ( statistical values of a particular sensor, the duration of significant force was calculated.

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67 The assumpti on was that the force was constant from the current reading to t he next reading from the sensor, s o the duration was measured as the time difference of the subsequent sensor readings. Resultant yank (Y) Jerk is defined as the time derivative of acceleration. Mass times jerk is defined as the yank, given in Equation 4 3. (4 3) Dimensionally, force divided by time is equivalent to yank. In our case, this yank was calculated by dividing the force by duration for which it was experie nced as shown in Equation 4 4. (4 4) Yank value, thus calculated, gave the measure of force and duration together. If the duration for which the force was experienced was very small then the yank value would be high even for a modest value of force. Resultant momentum (P) Momentum is defined as the mass times velocity. Force can be defined as first derivative of momentum and is given in Equation 4 5. (4 5) Dimensionally, force times time is equivalent to momentum as observed from Equation 4 5. In our case, this momentum was calculated by multiplying the force by duration for which it was experienced as shown in Equation 4 6. (4 6)

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68 Momentum value, thus calculated, gave the measure of force and duration together, but in a different sense from the yank value. If the momentum value was high, then both the force and duration for which the force was experienced cannot be very low. Resu lts and Discussion The statistics, such as mean, standard deviation, minimum, maximum and median values, for the resultant force (F), yank (Y) and momentum (P) were calculated for all the sensors. Based on the different factors used in the tests, the compa rison of the calculated values was done. The application of force (traditional and canopy shaker), abscission chemical (presence and absence), side of the tree shaken during harvest, variety (Hamlin and Valencia) and location of the fruits (edge and inside of the canopy) were the factors considered in this experiment. The maximum and average values were used for the comparison purposes, except for the application of force comparison where only maximum values were available. The average values gave an indica tion of high or small amount of force, yank or momentum for longer intervals of time. The maximum value of the force was an indicator of whether the threshold of bonding force was exceeded or not. For these reasons both the average and maximum values were compared. The ideal scenario would be to do the comparison using t test. But because of unavailability of enough replicates, the t test results obtained might not be completely true. Along with the t tests conducted, the ratios were also calculated to obse rve the effect of different factors on the force, yank and momentum. The summary of the values from all the tests is in the Table 4 2. The ratios of average and maximum resultant values for all the different factors are summarized in Table 4 3. In all the

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69 Table 4 2 Resultant force yank and momentum exerted on the fruit during mechanical canopy shaking along with duration of significant force. Test and fruit variety Fruit removed or not remo ved Sensor Count F, N T, s Y, N/s P, Ns Avg. Max. Avg. Max. Avg. Max. Test 1 Hamlin Removed 5 1.77 27.20 16.96 14.64 234.79 0.23 3.88 Not Removed 1 0.75 24.70 40.10 5.73 185.97 0.10 3.28 Test 2 Valencia Removed 3 2.60 20.54 15.72 18.23 155.76 0.43 4.14 Not Removed 2 0.44 11.87 53.52 3.28 87.34 0.06 1.87 Test 3 ** Valencia Removed (Large fruits) 3 3.28 12.12 36.18 13.04 85.16 1.39 6.00 Not Removed (Large fruits) 1 1.25 11.59 112.97 5.80 90.04 0.49 5.28 Removed (Small fruits) 1 0.05 0.16 115.30 0.20 1.47 0.02 0.17 Not Removed (Small fruits) 4 0.07 0.47 64.40 0.44 4.55 0.02 0.30 Test 3 Valencia Removed (Large fruits) 2 1.36 22.01 156.21 7.45 158.19 0.35 6.39 Not Removed (Large fruits) 2 0.08 2.57 135.20 0.55 25.72 0.03 0.95 Removed (Small fruits) 1 0.06 0.45 45.83 0.37 4.09 0.02 0.21 Not Removed (Small fruits) 5 0.05 1.21 162.19 0.39 8.13 0.01 0.47 Without abscission treatment. ** With abscission treatment. Table 4 3. Summary of ratios from the comparisons. Ratio type Avg. F, N Max. F, N T, s Avg. Y, N/s Max. Y, N/s Avg. P, Ns Max. P, Ns Side of tree shaken (same / other side) 8.11 8.38 0.48 12.42 8.81 12.08 7.67 Abscission treatment small fruits (un treated / treated) 0.81 2.53 1.91 21.46 26.59 0.63 1.50 Abscission treatment large fruits (un treated / treated) 0.46 1.45 2.02 0.61 1.43 0.29 0.89 Variety all fruits (Hamlin / Valencia) 0.90 1.49 0.33 1.41 2.01 0.95 1.45 Variety removed fruits (Hamlin / Valencia) 0.90 1.28 0.20 1.14 1.50 0.57 0.72 Location all fruits (edge of canopy / inside the canopy) 1.10 1.08 1.20 1.20 1.11 0.93 1.24 Location removed fruits (edge of canopy / inside the canopy) 0.85 1.06 0.95 0.87 0.82 0.70 1.14 Table 4 4. Comparison of traditional and canopy shaker force for removal of fruits. Type Force (N) Shaker (S) 17.07 Traditional (T) 96.10 Ratio (S/T) 0.18

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7 0 T ype of force application The traditional method to measure the fruit detachment force (FDF) is by pulling the fruits and measuring the force applied using a force gage. This measurement was done on ten different Valencia fruits from the block where the second trial was conducted. The average of these ten measurements was then used in the comparison with the maximum force experienced by the fruits removed when using canopy shaker in that test block. The force exerted by canopy shaker t o remove the fruits was considerably lesser than the traditional FDF measured. From Table 4 4, it can be seen that the canopy shaker exerts on an average a maximum force which was about 18% of the FDF measured the traditional way. Though the force was less the removal of the fruits can be explained because of the buildup of stress at the bonding point of the fruit with the stem or the stem with the branch. This stress was the result of the motion of the fruits in different directions and also the sudden na ture of the change in direction. This stress causes failure at one of the contact points resulting in removal of fruits. This was different from the traditional FDF, wherein the force was applied in only one direction, i.e. along the axis of the fruit. Abscission chemical Abscission chemical reduces the bonding force between the fruit and stem which can help removal of fruits with lesser force application. One of the trials was performed with and without the use of abscission chemical in a Valencia grove In this trial, both the small and large Valencia fruits were instrumented and the comparison was done separately for the different fruit sizes. Table 4 5 and 4 6 shows the average and maximum resultant force (F), yank (Y) and momentum (P) experienced by the small and large fruits respectively along with the duration of significant force (T). The Figures 4 3

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71 and 4 4 show the variation of average and maximum resultant force on small fruits because of the application of abscission chemical. Similarly, Figure s 4 5 and 4 6 show the variation of average and maximum resultant force on large fruits because of the application of abscission chemical. It can be observed that the values were not very different in both the cases of large and small fruits. The t test wa s conducted for all the resultant values at an alpha value of 0.05. The t test results for the large fruits showed no significant difference between the chemically treated and un treated fruits. But the average and maximum resultant yank for the smaller fr uits was significantly lesser for the chemically un treated fruits than the treated ones. But as these values themselves were small, as seen in Table 4 5, the significant difference does not mean much. T hough the t tests did not provide any significant di fference among the large fruits, the ratios for maximum resultant force and yank were more than 1.4 as seen in Table 4 6. It can also be seen that the duration of significant resultant force in large fruits that were chemically un treated was twice that of the treated ones. From the resultant force and duration ratios, it can be noted that the fruits that were chemically treated experienced higher forces for shorter duration. T he ratio of fruits removed among the chemically treated and un treated fruits rem ained the same at 0.5 s o it can be concluded that the chemically treated fruits were removed with a higher force applied for a shorter duration. Table 4 5. Comparison for small fruits with and without abscission treatment. Type Avg. F N Max F N T s Avg Y N/s Max Y N/s Avg P Ns Max P Ns Chemically un treated (U) 0.05 1.06 138.92 0.39 7.32 0.01 0.41 Chemically treated (T) 0.07 0.42 72.89 0.02 0.28 0.02 0.28 Ratio (U / T ) 0.81 2.53 1.91 21.46 26.59 0.63 1.50

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72 Table 4 6. Comparison for large fruits with and without abscission treatment. Type Avg. F N Max F N T s Avg Y N/s Max Y N/s Avg P Ns Max P Ns Chemically un treated (U) 1.04 17.15 150.9 6 5.72 125.07 0.27 5.03 Chemically treated (T) 2.27 11.86 74.57 9.42 87.60 0.94 5.64 Ratio (U / T ) 0.46 1.45 2.02 0.61 1.43 0.29 0.89 Table 4 7. Comparison of canopy shaker runs on the same and other side of the sensors on the tree Type Avg. F N Max F N T s Avg Y N/s Max Y N/s Avg P Ns Max P Ns Same half (S) 1.60 26.79 20.81 13.16 226.65 0.21 3.78 Other half (O ) 0.20 3.20 43.61 1.06 25.73 0.02 0.49 Ratio (S/ O ) 8.11 8.38 0.48 12.42 8.81 12.08 7.67 Figure 4 3. Effect of abscission on average resultant force on small fruits. 0 0.02 0.04 0.06 0.08 0.1 0.12 1 2 Resultant force, N Categories AVERAGE RESULTANT FORCE Effect of abscission on small fruits CATEGORY: 1 No abscission treatment. 2 Abscission treatment.

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73 Figure 4 4. Effect of abscission on maximum resultant force on small fruits. Figure 4 5. Effect of abscission on average resultant force on large fruits. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1 2 Resultant force, N Categories MAXIMUM RESULTANT FORCE Effect of abscission on small fruits CATEGORY: 1 No abscission treatment. 2 Abscission treatment. 0 0.5 1 1.5 2 2.5 3 3.5 1 2 Resultant force, N Categories AVERAGE RESULTANT FORCE Effect of abscission on large fruits CATEGORY: 1 No abscission treatment. 2 Abscission treatment.

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74 Figure 4 6. Effect of abscission on maximum resultant force on large fruits. Figure 4 7. Comparison of average resultant force when canopy shaker is the same and opposite sides. 0 5 10 15 20 25 1 2 Resultant force, N Categories MAXIMUM RESULTANT FORCE Effect of abscission on largefruits CATEGORY: 1 No abscission treatment. 2 Abscission treatment. 0 0.5 1 1.5 2 2.5 3 1 2 Resultant force, N Categories AVERAGE RESULTANT FORCE Two sides of the tree with respect to canopy shaker CATEGORY: 1 Sensors on the same side as the canopy shaker. 2 Sensors on the opposite side of the canopy shaker.

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75 Figure 4 8. Comparison of maximum resultant force when canopy shaker is the same and opposite sides. Region of tree shaken Harvesting of tree using canopy shaker is done on a half tree basis. In one of the trials, data was collected when both the halves were being shaken, with the sensors mounted on the same half during both the runs. The Table 4 7 summarizes the average and maximum values for the two runs. Figures 4 7 and 4 8 summarize the average an d maximum resultant force values, respectively. The t test conducted (at alpha value of 0.05) showed significant difference for all the values. Except for duration of significant resultant force, all the other values were significantly higher when the cano py shaker was on the same side as the sensors. This result indicates that the fruits on the other side of the shaker were highly unlikely to be removed. The average and maximum resultant force experienced were 8.11 and 8.38 times more, respectively, when t he 0 5 10 15 20 25 30 35 1 2 Resultant force, N Categories MAXIMUM RESULTANT FORCE Two sides of the tree with respect to canopy shaker CATEGORY: 1 Sensors on the same side as the canopy shaker. 2 Sensors on the opposite side of the canopy shaker.

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76 shaker was on the same side as the sensors. The average and maximum yank experienced were 12.42 and 8.81 times more, respectively, when the shaker was on the same side as the sensors. The average and maximum momentum experienced were 12.08 and 7.67 time s more, respectively, when the shaker was on the same side as the sensors. These high values indicate that the fruits on the other side of the shaker do not experience significant force, yank or momentum when compared to the fruits on the same side of the shaker. From the t test and the ratios obtained, it can be concluded that the force experienced by fruits when the canopy shaker was on the opposite side was not enough to remove the fruits. This can also observed from the fact that none of the instrumente d fruits were removed from the tree when the shaker was on the opposite side of the fruits with sensors. Variety of fruits The trials were done on Hamlin and Valencia fruits. The average and maximum resultant force (F), yank (Y) and momentum (P) along with duration of significant force (T) were compared across the two fruit varieties. Though most of the values were not found to be statistically different when compared using t test (at alpha of 0.05), the ratios were reported. The maximum resultant force and yank was significantly more for Hamlin than Valencia when all fruits were considered in the comparison. But when only the removed fruits were compared, the maximum resultant force and yank did not show any significant difference. The duration of significa nt force was significantly lower for Hamlin than Valencia for both the cases of comparison. Table 4 8 summarizes the comparison using all fruits, while the Table 4 9 compares only the removed fruits. As seen in the Table 4 8, Hamlin required more maximum resultant force yank and momentum; 1.49, 2.01 and 1.45 times that of

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77 Valencia, respectively. The duration of significant force for Hamlin was only 0.33 times that of Valencia When the comparison was done using only the fruits that were removed (Table 4 9 ), the maximum resultant force and yank were still more for Hamlin; 1.28 and 1.50 times that of Valencia, respectively. The duration of significant force for removed fruits of Hamlin was only 0.2 times that of Valencia. The ratio of average resultant force remained the same for both the cases. From the t test and ratios, it can be noted that the required duration of significant force to remove Hamlin fruits was lesser than that of the Valencia. So the shaking duration for harvesting Hamlin was significantly lesser. It can also be seen from Table 4 1 that the Hamlin fruits were harvested using a higher shaker frequency than Valencia which might explain the lower duration required for removing the Hamlin fruits. The ratio of momentum values being less than 1 ( 0.72 in Table 4 9) indicate that the removed Hamlin fruits experienced lesser significant resultant force than the Valencia fruits. Figures 4 9 and 4 10 give a graphical comparison of the average and maximum resultant forces, respectively, on Hamlin and Va lencia fruits. For this graphical comparison all the instrumented fruits were considered. Table 4 8. Comparison of all instrumented fruits of Hamlin and Valencia. Type Avg. F N Max F N T s Avg Y N/s Max Y N/s Avg P Ns Max P Ns Hamlin (H) 1.60 26.79 20.81 13.16 226.65 0.21 3.78 Valencia (V) 1.78 17.96 63.95 9.36 112.79 0.22 2.62 Ratio (H/V) 0.90 1.49 0.33 1.41 2.01 0.95 1.45 Table 4 9. Comparison of removed instrumented fruits of Hamlin and Valencia. Type Avg. F N Max F N T s Avg Y N/s Max Y N/s Avg P Ns Max P Ns Hamlin (H) 1.77 27.20 16.96 14.64 234.79 0.23 3.88 Valencia (V) 1.98 21.28 85.97 12.84 156.98 0.41 5.43 Ratio (H/V) 0.90 1.28 0.20 1.14 1.50 0.57 0.72

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78 Figure 4 9. Comparison of average resultant force of Hamlin and Valencia. Figure 4 10. Comparison of maximum resultant force of Hamlin and Valencia. 0 0.5 1 1.5 2 2.5 3 1 2 Resultant force, N Categories AVERAGE RESULTANT FORCE Effect of fruit type CATEGORY: 1 Hamlin. 2 Valencia. 0 5 10 15 20 25 30 35 1 2 Resultant force, N Categories MAXIMUM RESULTANT FORCE Effect of fruit type CATEGORY: 1 Hamlin. 2 Valencia.

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79 Location of fruits The fruits found on the edge and inside of the canopy were isolated and the comparison was done based on location of fruits. For this com parison, fruits marked as Far and High Far and Very High Very Far and Very High Far and Medium Near/Close and High Very High and Middle and Very High and the remaining close to trunk or ground. In this case also there was no statistical difference found using t test (at alpha of 0.05) for any of the compared values. Table 4 10 and 4 11 summarize the average and maximum resultant force (F), yank (Y) and momentum (P) along with the duration of significant resultant force for all instrumented fruits and removed fruits, respectively. From the Table 4 10, it can be observed that 1.5 times more fruits were removed from the edges than the inside of the canopy though the average resultant force at the edges was only 1.1 times that of the inside of the canopy From Table 4 10 it can also be observed that the average and maximum resultant force have similar ratios, 1.1 and 1.08. The fruits at the edges of the can opy experience slightly higher resultant forces, 1.1 and 1.08 times than the fruits inside the canopy. These fruits experience significant force for slightly longer duration, 1.2 times, than the fruits inside the canopy. Figures 4 11 and 4 12 show the grap hical comparison of the average and maximum resultant forces in Table 4 10, respectively, for the fruits inside and at the edges of the canopy. But when only the removed fruits were considered (Table 4 11), the average resultant force experienced by the f ruits at the edge was lower than the fruits inside the canopy by 0.85 times. The duration of significant resultant force was also shorter for the fruits at the edges, 0.95 times, though the values were comparable. From this ratio data, it can be noted tha t the fruits on the edge were removed with less

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80 average resultant force for a shorter shaking duration than the ones inside the canopy. This could be because of the different biophysical properties of the branches at different regions of the tree. Ones clo ser to the trunk are thicker than branches at the edge of the canopy. Another reason could be the radial arrangement of the tines which applies different forces at different regions of the trees. This data reinforces the notion that the fruits at the edges of the canopy of the tree are removed easily when compared to the fruits inside the tree canopy. Table 4 10. Comparison based on the location of all instrumented fruits. Type Avg. F N Max F N T s Avg Y N/s Max Y N/s Avg P Ns Max P Ns Fraction of removed fruits Edge (E) 1.56 21.75 63.76 11.80 175.18 0.24 4.32 0.88 Inside (I) 1.42 20.10 53.26 9.81 157.25 0.26 3.49 0.57 Ratio (E/I) 1.10 1.08 1.20 1.20 1.11 0.93 1.24 1.53 Table 4 11. Comparison based on the location of removed instrumented fruits. Type Avg. F N Max F N T s Avg Y N/s Max Y N/s Avg P Ns Max P Ns Edge (E) 1.77 24.49 53.56 12.32 152.10 0.28 4.94 Inside (I) 2.08 23.07 56.42 14.09 185.03 0.41 4.35 Ratio (E/I) 0.85 1.06 0.95 0.87 0.82 0.70 1.14 Second Field Experiment The objective of this experiment was to study the force distribution along an individual tree branch in Valencia trees. This distribution of force was studied against the backdrop of different machine parameters and sizes of the trees. There are several factors that affect the force distribution along a tree branch to varying degrees. Some of these factors are travel speed, tine configuration, angle of tines number of tines, tine material, tine length, shak er frequency and amplitude. In this ex periment, the effect of tree size, angle of tines and shaker frequency were investigated with respect to the force distribution along the branch.

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81 Figure 4 11. Comparison of average resultant force based on fruit location in the tree canopy. Figure 4 12. Comparison of maximum resultant force based on fruit location in the tree canopy. 0 0.5 1 1.5 2 2.5 3 1 2 Resultant force, N Categories AVERAGE RESULTANT FORCE Effect of location CATEGORY: 1 Edge of the canopy 2 Inside the canopy. 0 5 10 15 20 25 30 1 2 Resultant force, N Categories MAXIMUM RESULTANT FORCE Effect of location CATEGORY: 1 Edge of canopy. 2 Inside the canopy.

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82 Materials and Methods The same sensor setup that was used for first experiment was used for this experiment also. But in this case the sensors were attached along a t ree branch rather than individual fruits in the canopy. The rationale beh ind this being that the force was transmitted to different parts of the canopy via the branches, from the points of contact of the shaker. Tree and branch selection The trees selecte d for this experiment were from a block of Valencia grove. Since size of trees was one of the factors of interest, two different sizes of trees were selected. The size selection was done based on visual inspection of canopy density and height. The smaller trees had average height of 2 8 m while the larger ones had an average height of 3 6 m. The average widths of the smaller and larger trees were 1 m and 1 .5 m respectively. Four trees for each size were selected with eight trees in total for the experiment T he force m easurements were to be done along one branch, so a single branch was selected in all trees such that it was perpendicular to the ground and located towards the center of the tree canopy. The reasoning being that such a branch would have locati ons that are close to the ground, trunk and also in the canopy and at the edges of the canopy. Experimental design A n ested experimental design was used for this experiment. In this nested model, the shaker frequency and angle of tines were nested in tree size. This was done because of the limited number of available sensors and time constraints such as the availability of the harvester and time required for attaching the sensors to the branches. The independent variables of the experiment and their levels are given in the T able 4

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83 12 Based on the nested experimental design, the order of the trees was fir st randomized and then the combinations of angle of tines and shaker frequency were randomized for each tree. The random order of experimen t can be found in the Table 4 13 Table 4 12. Independent variables and their levels N umbe r Name Levels 1 Tree size Small Large 2 Angle of tines 5 20 35 3 Frequency of the canopy shaker 200 cpm 250 cpm 300 cpm Table 4 13. Randomized order of the experiment Tree order Trial order (angle of tines, frequency of shaker) 1 2 3 4 5 6 7 8 9 L1 35, 200 5, 250 20, 250 20, 200 5, 300 20, 300 5, 200 35, 300 35, 250 M3 20, 300 5, 300 20, 250 5, 250 35, 250 5, 200 35, 200 35, 300 20, 200 L2 20, 200 20, 300 5, 300 5, 250 35, 300 5, 200 35, 250 20, 250 35, 200 M2 35, 250 5, 300 20, 250 20, 300 35, 300 20, 200 5, 250 35, 200 5, 200 L4 20, 300 20, 200 5, 200 35, 250 20, 250 35, 300 5, 250 35, 200 5, 300 M4 20, 250 5, 250 5, 300 35, 250 20, 200 35, 300 35, 200 5, 200 20, 300 L3 20, 200 20, 300 20, 250 5, 250 35, 200 5, 200 35, 300 5, 300 35, 250 M1 20, 300 35, 200 5, 250 20, 250 35, 300 35, 250 5, 300 20, 200 5, 200 Instrumenting the tree The sensors were attached to the selected branch before that particular tree was shaken. They were attached from the base of the branch near the trunk, until the location where the radius of the branch was less than 2.5 cm (1 inch) The base of the branch was defined as the location wher e the selected branch branched out from the trunk. A schematic and image of the instrumented tree are shown in the Figures 4 1 3 to 4 1 5 The sensors were attached at distances of 50 cm from each other. The y were

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84 attached to the branches using zip ties and duct tape such that the accelerometer was in contact with the branch Since e ach tree branch was instrumented before doing the trial on it, the same sensors were used for all the trials unless they broke and had to be replaced with newer ones. Data collect ion After instrumenting the desired tree, the angle of tines and shaker frequency were set according to the table and the tree was shaken by the canopy shaker. T his was repeated for all nine combinations on each tree. The data was collected for each trial in a separate Excel file. After each trial, all the sensors were tested to check whether any of them were broken and replaced when required. T he diameter of the branches was measured at intervals of 25 cm from the base of the branch using Vernier calipers. These diameter values were later used to estimate the volume of the branch segments. The location of the sensors was also noted down by using a local coordinate system for each tree Figure 4 1 3 Sensor board attached to the base of the trunk

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85 Figu re 4 1 4 Sensor attached to a location on the branch Figure 4 1 5 Schematic of the sensors on the tree

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86 Data analysis The Equation 4 1 was used for calculation of the acceleration values from the raw data collected. The procedure for the extraction of the data was similar to the one used in first experiment. In the earlier experiment, the weight of the fruits was measured to calculate the force values at different locations. But in this case, weighing the branches was not possible and so the relatio n between volume and weight was used to arrive at a value proportional to the force experienced. Any regular geometrical object will satisfy the following equation (4 7) where, M is mass of the object in kg, V is volume of the object in m 3 and d is density of the material of the object in kg/m 3 For an object made of same material, it can be assumed that the density is constant. Under this assumption, the Equation 4 7 becomes (4 8) For any object of regular geometry, if the dimensions are kno wn then the volume can be calculated. And since force is the product of mass and acceleration, the product of volume and acceleration gives a value that is proportional to the force experienced by that object. (4 9) where, F is force experienced by the object in N, M is mass of the object in kg, and a is acceleration of the object in m/s 2 If we define F p from Equations 4 8 and 4 9 Equation 4 10 can be derived. (4 10)

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87 I n our case we do not hav e a regular shaped object. In order for the Equation 4 10 to hold for our experiment, t he branch segments were assumed to be regular cylinders The average of diameter values measured at every 25 cm intervals was used as their diameters. This was done beca use the difference in diameter along each segment was very less in most of the cases which did not warrant the need to use the truncated cone assumption Based on the above assumptions, the resultant force proportional (F p ) value was calculated. The durati on of significant force proportional values (T p ) was calculated in this case using the mean and standard deviation of F p values instead of actual force. Similar to resultant force proportional values, the resultant yank proportional (Y p ) and resultant mome ntum proportional (P p ) values were also calculated using the Equations 4 11 and 4 12, respectively. (4 11) (4 12) The subsequent data analysis was done on the values of F p Y p and P p ANOVA was done using the average, maximum and variance of F p Y p and P p values for the entire branch so as to observe the effect of changing machine parameters and tree size ANOVA was also conducted on the T p values calculated. Results and Discussion ANOVA on F p Y p P p and T p va lues ANOVA was conducted on all the calculated values. The ANOVA results were interpreted at the significance level, alpha = 0.05. The average resultant force proportional value was significantly affected because of the varying tree size (Tables 4 14 to 4 16). At this significance level, the resultant yank proportional values were not

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88 significantly affected by the machine parameters and tree size (Tables 4 17 to 4 19). In the case of resultant momentum proportional values, the tree size was significant for both the average and maximum values (Tables 4 20 to 4 22). It can be observed from Table 4 23 that the duration of significant force proportional values was also affected by tree size only. The tree size became significant for average resultant yank propor tional values if the significance level was increased to alpha = 0.07 (Table 4 17). Similarly at higher significance level of alpha = 0.2, the maximum resultant force proportional (Table 4 15) and resultant yank proportional (Table 4 18) values were also a ffected by the tree size factor. The variance of resultant force was not affected by any of the factors used in the study, even the tree size. From the ANOVA tables it can be seen that the tree size was the most influencing factor on the force distributio n than the machine factors. This does not mean that the other factors can be considered insignificant. The reason for the insignificance of the machine parameters could be the high variance observed among the values rather than their actual insignificance. A better selection of trees with a different experimental design could help in understanding the effect of machine parameters on force. Distribution of resultant force proportional and acceleration values along the tree branch The resultant acceleration a nd force proportional values for each location along the branch were calculated. The averages of the maximum and average resultant values from the 4 large and small trees were collected for each combination of angle and frequency. The Tables 4 24 to 4 27 s ummarizes the average and maximum resultant acceleration and force proportional values for large and small trees. The Table 4 28 has the distance of the locations from the origin for both large and small trees. The

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89 relation between the resultant accelerati on and force proportional values with respect to the distance from the origin was investigated. This relation would indicate the type of distribution along the branch. Matlab Curve Fitting Toolbox TM was used to determine the relationship. The relation bet ween resultant acceleration and distance from origin was exponential in nature, given by the Equation 4 13 The relation between resultant force proportional values and distance from origin was Gaussian in nature, given by the Equation 4 14 The coefficien ts for the different equations under different conditions are summarized in the Tables 4 29 to 4 32 (4 13) (4 14) The plots of the resultant acceleration and force proportional values vs. distance from the origin were created and reported in the Appendix C ( Figures C 1 to C 8 ). The different goodness of fit values, from Matlab, are also reported in Appendix C ( Tables C 1 to C 4 ). The variation of average and maximum resultant acceleration values with the distance from origin along the branch was described pretty well by the exponential model for both small and large trees. The variation of the average resultant acceleration values was described well than the maximum values by the exponenti al equation. The adjusted R 2 value for average resultant acceleration was about 1.7 times that of the one for maximum resultant acceleration. The variation of average and maximum resultant force proportional values with the distance from origin along the b ranch was described well by the Gaussian model. For the resultant force proportional values, the relation better fit the maximum values than the average values in the case of both large and small trees. The adjusted

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90 R 2 value for maximum values was about 1.2 times that of the one for average values. From the Table 4 33, it can be observed that this was the trend in both small and large trees. The average adjusted R 2 values are reported in Table 4 33 for all relations. F rom the Table 4 33 it can also be seen that the average adjusted R 2 values were more for average acceleration by at least 0.27 than the maximum acceleration. In the case of force proportional values, the average adjusted R 2 was more for maximum values by at least 0.1 than the average values. Table 4 14. ANOVA results for average force proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 4495.45 4495.45 149.26 <.0001 Angle(Tree_Size) 4 24.55 6.13 0.20 0.935 Frequency(Tree_Size) 4 57.59 14.39 0.48 0.751 Angle*Freque ncy (Tree_S ize ) 8 27.13 3.39 0.11 0.998 Table 4 15. ANOVA results for maximum force proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 5173.73 5173.73 1.69 0.198 Angle(Tree_Size) 4 11836.84 2959.21 0.97 0.431 Frequency(Tree_Size) 4 11644.68 2911.17 0.95 0.440 Angle*Freque ncy (Tree_S ize ) 8 23683.50 2960.43 0.97 0.469 Table 4 16. ANOVA results for variance of force proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 221462.44 221462.44 0.90 0.347 Angle(Tree_Size) 4 970973.52 242743.38 0.98 0.423 Frequency(Tree_Size) 4 976941.75 244235.43 0.99 0.420 Angle*Freque ncy (Tree_S ize ) 8 1970082.50 246260.31 1.00 0.447

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91 Table 4 17. ANOVA results for average yank proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 216.93 216.93 3.66 0.061 Angle(Tree_Size) 4 23.73 5.93 0.10 0.982 Frequency(Tree_Size) 4 237.84 59.46 1.00 0.414 Angle*Freque ncy (Tree_S ize ) 8 116.23 14.52 0.24 0.980 Table 4 18. ANOVA results for maximum yank proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 471047.35 471047.35 1.80 0.185 Angle(Tree_Size) 4 1053586.08 263396.52 1.01 0.412 Frequency(Tree_Size) 4 1013270.01 253317.50 0.97 0.432 Angle*Freque ncy (Tree_S ize ) 8 1784748.28 223093.53 0.85 0.561 Table 4 19. ANOVA results for variance of yank proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 1694987219 1694987219 0.98 0.326 Angle(Tree_Size) 4 6698463021 1674615755 0.97 0.431 Frequency(Tree_Size) 4 7172448659 1793112165 1.04 0.396 Angle*Freque ncy (Tree_S ize ) 8 13265491196 1658186399 0.96 0.476 Table 4 20. ANOVA results for average momentum proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 0.148 0.148 10.05 0.002 Angle(Tree_Size) 4 0.023 0.005 0.39 0.811 Frequency(Tree_Size) 4 0.077 0.019 1.31 0.278 Angle*Freque ncy (Tree_S ize ) 8 0.023 0.002 0.20 0.990

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92 Table 4 21. ANOVA results for maximum momentum proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 290.74 290.74 6.48 0.013 Angle(Tree_Size) 4 128.11 32.02 0.71 0.585 Frequency(Tree_Size) 4 19.41 4.85 0.11 0.979 Angle*Freque ncy (Tree_S ize ) 8 344.59 43.07 0.96 0.476 Table 4 22. ANOVA results for variance of momentum proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 35.89 35.89 0.93 0.337 Angle(Tree_Size) 4 115.32 28.83 0.75 0.561 Frequency(Tree_Size) 4 92.25 23.06 0.60 0.663 Angle*Freque ncy (Tree_S ize ) 8 337.53 42.19 1.10 0.378 Table 4 23. ANOVA results for duration of significant force proportional values. Source DF Type I SS Mean Square F Value Pr > F Tree_Size 1 280.58 280.58 4.42 0.040 Angle(Tree_Size) 4 98.71 24.67 0.39 0.816 Frequency(Tree_Size) 4 371.31 92.82 1.46 0.226 Angle*Freque ncy (Tree_S ize ) 8 390.96 48.87 0.77 0.631

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93 Table 4 24. Average and maximum resultant acceleration values of large trees. Angle, frequen cy (, cpm) Location 1 resultant acceleration, m/s 2 Location 2 resultant acceleration, m/s 2 Location 3 resultant acceleration, m/s 2 Location 4 resultant acceleration, m/s 2 Location 5 resultant acceleration, m/s 2 Avg. Max. Avg. Max. Avg. Max. Avg. Max. Avg. Max. 5, 200 12.20 98.60 13.74 108.80 10.44 105.95 11.76 103.61 23.88 130.85 5, 250 5.05 64.50 18.55 110.99 8.79 85.51 16.51 104.22 19.87 136.01 5, 300 13.04 83.38 16.14 104.80 16.79 116.89 13.36 95.53 22.33 99.47 20, 200 4.43 52.50 8.75 93.60 8.72 87.68 64.17 11839 19.68 104.27 20, 250 4.27 60.12 8.35 87.96 8.94 92.51 10.14 106.88 16.46 105.97 20, 300 6.42 70.99 13.12 109.40 17.04 111.53 17.82 110.23 29.35 126.52 35, 200 15.65 35.35 6.94 72.61 6.39 88.85 10.72 111.24 31.01 99.74 35, 250 3.17 46.89 11.03 105.72 8.48 96.36 12.41 104.20 17.63 129.83 35, 300 12.23 74.33 12.67 94.80 17.30 129.69 19.16 115.28 39.22 132.19 Table 4 25. Average and maximum resultant acceleration values of small trees. Angle, frequency (, cpm) Location 1 resultant acceleration, m/s 2 Location 2 resultant acceleration, m/s 2 Location 3 resultant acceleration, m/s 2 Location 4 resultant acceleration, m/s 2 Location 5 resultant acceleration, m/s 2 Avg. Max. Avg. Max. Avg. Max. Avg. Max. Avg. Max. 5, 200 4.1 7 53.27 16.63 112.72 5.24 69.03 29.84 134.39 20.87 101.43 5, 250 6.09 36.34 12.15 100.33 18.48 113.46 24.03 126.83 27.37 126.45 5, 300 5.32 39.35 14.57 105.16 19.35 112.92 24.68 130.59 30.94 136.96 20, 200 6.04 44.29 15.81 114.70 18.85 112.53 28.70 128.93 16.45 134.25 20, 250 3.58 38.50 14.62 106.10 12.28 101.78 26.93 112.54 26.73 124.91 20, 300 15.69 47.66 17.63 110.65 19.91 109.25 30.20 123.59 37.20 131.54 35, 200 10.99 39.23 14.71 122.61 15.60 93.65 27.67 128.46 26.01 116.98 35, 250 6.82 35.54 13.52 101.84 14.77 109.01 25.04 125.63 20.57 105.66 35, 300 4.48 34.40 15.07 103.44 15.04 85.12 35.26 137.95 37.21 133.65

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94 Table 4 26. Average and maximum resultant force proportional values of large trees. Angle, frequency (, cpm) Location 1 resultant F p values, m 4 /s 2 Location 2 resultant F p values, m 4 /s 2 Location 3 resultant F p values, m 4 /s 2 Location 4 resultant F p values, m 4 /s 2 Location 5 resultant F p values, m 4 /s 2 Avg. Max. Avg. Max. Avg. Max. Avg. Max. Avg. Max. 5, 200 2.3 5 17.37 3.50 27.48 1.41 14.36 0.80 6.84 0.58 3.29 5, 250 0.89 11.11 4.50 27.06 1.21 11.78 1.15 6.92 0.51 3.42 5, 300 2.46 14.31 4.04 26.42 2.27 15.84 0.92 6.38 0.52 2.65 20, 200 0.77 9.15 2.23 23.67 1.20 12.12 3.37 587.33 0.47 2.59 20, 250 0.77 10.62 2.19 22.28 1.23 12.72 0.68 7.21 0.42 2.67 20, 300 1.17 12.49 3.24 27.54 2.30 15.09 1.24 7.48 0.82 3.22 35, 200 2.65 6.34 1.79 18.36 0.86 11.99 0.67 7.44 0.69 2.63 35, 250 0.56 8.28 2.87 26.87 1.14 13.05 0.95 7.86 0.39 3.29 35, 300 2.40 13.00 3.32 24.40 2.33 17.62 1.28 7.59 1.03 3.34 Table 4 27. Average and maximum resultant force proportional values of small trees. Angle, frequenc y (, cpm) Loc ation 1 resultant F p values m 4 /s 2 Loc ation 2 resultant F p values m 4 /s 2 Loc ation 3 resultant F p values m 4 /s 2 Loc ation 4 resultant F p values m 4 /s 2 Loc ation 5 resultant F p values m 4 /s 2 Avg. Max. Avg Max. Avg. Max. Avg. Max. Avg. Max. 5, 200 0.7 5 12.12 2.09 14.01 0.27 3.34 0.74 3.34 0.10 0.50 5, 250 0.97 7.08 1.63 12.34 1.20 7.09 0.62 3.29 0.14 0.63 5, 300 0.94 7.53 2.03 13.98 1.14 6.58 0.67 3.37 0.24 1.02 20, 200 1.64 11.72 1.86 14.04 1.04 6.40 0.65 3.24 0.12 1.03 20, 250 0.63 9.04 1.86 13.23 0.78 5.93 0.66 2.80 0.21 0.96 20, 300 1.88 8.52 2.59 14.32 1.31 6.44 0.98 3.57 0.32 0.99 35, 200 1.46 8.10 1.88 15.10 1.10 5.76 0.73 3.25 0.13 0.58 35, 250 0.94 7.48 1.67 12.49 0.88 6.38 0.49 3.04 0.17 0.84 35, 300 0.87 7.63 1.93 12.79 1.01 5.50 0.88 3.47 0.28 1.01

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95 Table 4 28. Distance of locations from the origin for small and large trees. Locatio n number Distance from origin, cm Large trees Small t rees 1 55 49 2 105 101 3 155 144 4 197 189 5 245 225 Table 4 29. Coefficients for the exponential equation of average resultant acceleration values Angle, frequency (, cpm) Large trees Small trees a b a b 5, 200 5.985 0.0050 5.360 0.0068 5, 250 3.275 0.0075 6.102 0.0069 5, 300 11.510 0.0027 6.460 0.0071 20, 200 0.016 0.0420 9.553 0.0040 20, 250 3.476 0.0062 4.975 0.0079 20, 300 5.529 0.0067 10.020 0.0058 35, 200 1.910 0.0109 8.502 0.0053 35, 250 3.507 0.0065 7.261 0.0053 35, 300 5.271 0.0079 4.920 0.0093

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96 Table 4 30. Coefficients for the exponential equation of maximum resultant acceleration values Angle, frequency (, cpm) Large trees Small trees a b a b 5, 200 91.45 0.0012 61.96 0.0028 5, 250 60.08 0.0031 54.49 0.0042 5, 300 88.68 0.0005 54.97 0.0044 20, 200 59.05 0.0025 61.03 0.0038 20, 250 61.92 0.0025 54.48 0.0039 20, 300 75.71 0.0021 60.90 0.0037 35, 200 44.09 0.0039 60.43 0.0034 35, 250 55.36 0.0035 57.82 0.0035 35, 300 72.35 0.0026 45.35 0.0052 Table 4 31. Coefficients for the Gaussian equation of average resultant force proportional values. Angle, frequenc y (, cpm) Large trees Small trees a b c a b c 5, 200 3.386 96.33 71.48 2.304 89.08 37.96 5, 250 4.494 108.10 42.44 1.590 104.90 81.03 5, 300 3.919 104.20 74.22 1.849 104.70 73.40 20, 200 2.250 111.70 55.00 1.867 80.80 93.93 20, 250 2.065 116.00 67.04 1.667 104.00 61.82 20, 300 3.061 123.10 77.89 2.374 89.35 92.41 35, 200 4.374 0.0091 1.814 89.54 91.33 35, 250 2.838 113.30 49.19 1.546 98.38 74.60 35, 300 3.058 103.40 111.90 1.645 108.30 84.62

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97 Table 4 32. Coefficients for the Gaussian equation of maximum resultant force proportional values. Angle, frequenc y (, cpm) Large trees Small trees a b c a b c 5, 200 26.33 102.0 76.02 16.24 78.71 55.38 5, 250 25.89 108.0 60.41 11.82 98.62 71.77 5, 300 25.72 108.5 71.82 13.33 96.38 65.31 20, 200 23.77 109.4 55.81 14.25 81.88 77.94 20, 250 20.87 111.9 74.16 13.08 89.34 68.56 20, 300 26.27 110.9 68.27 13.71 93.54 67.41 35, 200 17.31 121.6 74.14 14.98 92.86 57.15 35, 250 25.79 113.6 59.13 11.97 95.22 70.05 35, 300 24.07 114.2 77.55 12.11 93.16 68.48 Table 4 33. Average of adjusted R 2 values across all angle and frequency combinations for large and small trees. Type of trees Average adjusted R 2 values for the different relations Avg. acceleration relation Max. acceleration relation Avg. force proportional values relation Max. force proportional values relation Large 0.705 0.403 0.685 0.837 Small 0.648 0.375 0.736 0.875 Variation of adjusted R 2 with respect to changing machine parameters The Table 4 34 summarizes the adjusted R 2 values for the different angle and frequency combination for average and maximum resultant acceleration vs. distance from origin relation. The correlation between the adjusted R 2 for varying frequencies at different angles was i nvestigated (Table 4 36). The correlation values were not very consistent to indicate any particular trend in the adjusted R 2 values as the frequency increases. The same exercise was repeated for changing angles at different frequencies (Table 4 37) with a similar result. The same analysis was done for the

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98 average and maximum force proportional values found in Table 4 35. The results of this correlation were also reported in the Table s 4 3 6 and 4 37. Even in this case, there was no apparent relationship bet ween the factors and the strength of the relation. Variation of equation coefficients with respect to changing machine parameters The individual coefficients of the relation describe the behavior of the curve. In this case they describe the behavior of the distribution of resultant force proportional and Equati on 4 13 describe how steep the exponential curve will be. Similarly in the Equation 4 14 the respectively, of the Gaussian curve with the being the height of the peak. The variance of these coefficients with respect to angle and frequency was investigated for any trend. But no apparent trend was observed. The correlation values have been tabulated for all the different coefficients in Tables 4 38 to 4 43. Table 4 34. Adjusted R 2 values for resultant acceleration relation. Angle, frequency (, cpm) Adjusted R 2 for average resultant acceleration relation Adjusted R 2 for maximum resultant acceleration relation Large trees Small trees Large trees Small trees 5, 200 0.117 0.106 0.327 0.167 5, 250 0.896 0.921 0.350 0.499 5, 300 0.946 0.914 0.328 0.605 20, 200 0.939 0.045 0.386 0.495 20, 250 0.873 0.706 0.686 0.470 20, 300 0.890 0.927 0.530 0.544 35, 200 0.180 0.774 0.554 0.167 35, 250 0.694 0.614 0.519 0.192 35, 300 0.810 0.827 0.600 0.568

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99 Table 4 35. Adjusted R 2 values for resultant force proportional values relation. Angle, frequency (, cpm) Adjusted R 2 for average resultant F p values relation Adjusted R 2 for maximum resultant F p values relation Large trees Small trees Large trees Small trees 5, 200 0.758 0.502 0.904 0.822 5, 250 0.625 0.974 0.721 0.941 5, 300 0.924 0.783 0.951 0.859 20, 200 0.474 0.930 0.880 0.932 20, 250 0.625 0.411 0.833 0.912 20, 300 0.643 0.785 0.850 0.849 35, 200 0.945 0.899 0.759 0.853 35, 250 0.420 0.846 0.676 0.913 35, 300 0.755 0.496 0.957 0.789 Table 4 36. Correlation between adjusted R 2 values for changing frequencies at different angles. Angle pair L arge trees S mall trees Resultant acceleration Resultant F p values Resultant acceleration Resultant F p values Avg. Max. Avg. Max. Avg. Max. Avg. Max. 5, 20 0.953 0.886 0.160 0.646 0.969 0.402 0.936 0.028 5, 35 0.993 0.811 0.578 0.848 0.287 0.727 0.227 0.657 20, 35 0.910 0.448 0.713 0.144 0.040 0.921 0.130 0.736 Table 4 37. Correlation between adjusted R 2 values for changing angles at different frequencies. Frequency pair L arge trees S mall trees Resultant acceleration Resultant F p values Resultant acceleration Resultant F p values Avg. Max. Avg. Max. Avg. Max. Avg. Max. 200, 250 0.344 0.254 0.800 0.609 0.676 0.421 0.722 0.734 200, 300 0.036 0.856 0.502 0.406 0.999 0.805 0.435 0.118 250, 300 0.951 0.716 0.116 0.972 0.646 0.200 0.309 0.587

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100 Table 4 38. for changing frequencies at different angles. Angle pair L arge trees S mall trees Resultant acceleration Resultant F p values Resultant acceleration Resultant F p values Avg. Max. Avg. Max. Avg. Max. Avg. Max. 5, 20 0.181 0.404 0.353 0.776 0.115 0.563 0.120 0.975 5, 35 0.103 0.140 0.893 0.942 0.931 0.588 1.000 0.955 20, 35 0.959 0.962 0.736 0.942 0.256 0.337 0.128 0.864 Table 4 for changing angles at different frequencies. Frequency pair L arge trees S mall trees Resultant acceleration Resultant F p values Resultant acceleration Resultant F p values Avg. Max. Avg. Max. Avg. Max. Avg. Max. 200, 250 0.905 0.533 0.349 0.225 0.233 0.796 0.057 0.844 200, 300 0.939 0.993 0.037 0.867 0.451 0.511 0.150 0.077 250, 300 0.996 0.430 0.949 0.681 0.973 0.927 0.996 0.600 Table 4 for changing frequencies at different angles. Angle pair L arge trees S mall trees Resultant acceleration Resultant F p values Resultant acceleration Resultant F p values Avg. Max. Avg. Max. Avg. Max. Avg. Max. 5, 20 0.033 0.675 0.544 0.888 0.262 0.258 0.788 0.893 5, 35 0.313 0.450 0.968 0.991 0.951 0.610 0.843 0.677 20, 35 0.959 0.962 0.736 0.942 0.050 0.923 0.333 0.274 Table 4 for changing angles at different frequencies. Frequency pair L arge trees S mall trees Resultant acceleration Resultant F p values Resultant acceleration Resultant F p values Avg. Max. Avg. Max. Avg. Max. Avg. Max. 200, 250 0.815 0.355 0.053 0.935 0.312 0.514 0.428 0.062 200, 300 0.440 0.937 0.634 0.999 0.311 0.356 0.991 0.749 250, 300 0.879 0.006 0.738 0.951 1.000 0.619 0.544 0.707

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101 Table 4 for changing frequencies at different angles. Angle pair L arge trees S mall trees Resultant F p values Resultant F p values Avg. Max. Avg. Max. 5, 20 0.048 0.894 0.669 0.877 5, 35 0.147 0.906 0.891 0.958 20, 35 0.995 0.620 0.933 0.978 Table 4 for changing angles at different frequencies. Frequency pair L arge trees S mall trees Resultant F p values Resultant F p values Avg. Max. Avg. Max. 200, 250 0.033 0.987 0.783 0.880 200, 300 0.991 0.737 0.929 0.253 250, 300 0.166 0.836 0.958 0.682

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102 CHAPTER 5 MODEL AND VERIFICATI ON The second part of this study was to develop a theoretical model that could predict the force experienced at different locations in the tree. The idea was to create a CAD model of the tree and simulate the shaking action using ANSYS which would be then verified using field experiment data. This chapter is divided into three sections. The first section describes the model that was developed followed by the section of experiments conducted to determine the material propert ies of citrus wood which was necessary for the simulation in ANSYS software. The final and thir d section includes experiments conducted for the simulation verification and the comparison of the simulation and experimental data. Model Development There is available literature where simulation studies have been done by modeling the tree or branches as cantilever beams with varying circular cross section. Experiments have shown that this kind of modeling could predict the behavior of trees when they were being harvested. Trunk shakers and limbs shakers have definite points of contact and so the input fo rce could be modeled easily in their case. For canopy shakers, the points of contact of tines against the trees are not constant. The initial model developed was based on the assumption that the contact points are same throughout the shaking period. Materi al and Methods For this model, the tree branches we re considered as tapering structured with circular cross section and distributed mass. The material properties of wood were measured by experiments conducted in the lab and assigned to the tree model. The

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103 distributed mass of the tree wa s assigned through the density property of the material For modeling the tree, the locations were marked at intervals of 10 cm from the base of the trunk along the branches which had the sensors attached to them. The locatio ns were assigned coordinates using a local Cartesian coordinate system for each tree. Additional diameter and location values were noted down whenever there was a sudden change in direction or a split of the branch. These measurements were taken from the t rees that were used for the experimental verification of the model. The diameter values were measured using Vernier calipers wherever possible. At times when the calipers were not big enough, the circumference of the tree was measured using a thread and th e diameter was calculated assuming that it was a circle. The coordinate position was measured by dropping a weighted string to the ground for projection of the point onto the X Y plane and measure the X and Y coordinates. The length of the string was taken to be the Z value. SolidWorks modeling Using the above collected data, the tree was modeled in SolidWorks. The points noted down were first plotted in 3 D space in SolidWorks. These plotted points were then connected using 3 D spline feature of the software. Figure 5 1 shows the points and the 3D spline. After this, reference planes were drawn at each point. T hese reference planes were perpendicular to the spline joining two adjacent points. The end surfaces or planes were made perpendicular to the curve. The circular cross sections, at each point, were then drawn on the reference planes using the measured diam eters. The Figure 5 2 shows the image with the reference planes. All the circles were joined together using the loft feature of the software as shown the Figure 5 3 All the three

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104 trees used for the experiment were modeled using the steps explained above. The Figures 5 4 A to C show all the three trees after they were modeled in SolidWorks. Figure 5 1. Spline from the data points in SolidWorks. Figure 5 2. Reference planes created at points along the spline in SolidWorks. Figure 5 3. Circles in the reference planes joined by loft feature in SolidWorks.

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105 A B C Figure 5 4. Tree models created for the three trees used in field experiment A) Tree 1. B) Tree 2. C) Tree 3. ANSYS analysis and simulation The SolidWorks models created were imported into ANSYS. The imported geometries were used to create the mesh using default meshing options. The system used tetrahedral solid element to mesh the trees. The physics preference selected for the mesh was mechanical. All the tree meshes were crea ted using the same procedure. The meshes created were then used to simulate the shaking action of the trees. Flexible dynamic analysis was chosen for the simulation of the trees as it was the most appropriate for our purposes. The simulation time was selec ted to be 30s as the actual shaking during the experiment was about the same. The time steps were selected such that the calculations were done ten times for every second. This was so because each sensor transmitted about 10 to 12 points per second. The da taset thus generated was used for the comparison against the experimental values. Input forces were given based on the observations done during the experiment. The force locations were noted and the coordinates recorded ( Table 5 1 ). Application of force was done on the basis that there was complete energy transfer from the shaker to the tree. Based on this assumption the force on the individual tine was chosen to be the input at the contact points on the tree. The

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106 acceleration values were measured on the tines when the shaker was unengaged. The average of the resultant acceleration ( Table 5 2) for the two different frequencies was taken for the calculation of the force. From Table 5 2 it can be observed that the resultant acceleration did not change very much with change in frequency. So the average of the two resultant accelerations, 26.25 m/s 2 was used. The weight of the tine was measured to be 3.06 kg (6.75 lb). The force was then calculated as the average resultant acceleration ti mes the weight of an individual tine (26.25 3.06 = 80.33 N). From the data provided by Oxbo engineers, on an average the pressure of the hydraulic system increases from 400 psi to 1300 psi when the shaker is engaged (G. Michaels, personal communication, 18 March 2009) This increase in pressure depended on the tree and how much resistance it provided, s o the force calculated was scaled up by 4 times to 320 N. The Tables 5 3 and 5 4 give the force input cycle for 1s duration at 180 cpm and 230 cpm, respec tively. Since the tines were parallel to the ground during the experiment, the force was applied in only one direction i.e. parallel to the fixed base of the tree. The other force components were assumed to be zero. Figure 5 5. Sensors placed on the ti nes.

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107 Table 5 1. Contact points in all three trees. Tree numb er Location 1 in m Location 2 in m Location 3 in m Location 4 in m X Y Z X Y Z X Y Z X Y Z 1 0.14 0.35 2.10 0.05 0.66 2.06 0.06 0.43 1.33 2 0.15 0.58 1.80 0.34 0.59 2.01 0.14 0.26 1.12 0.87 0.11 1.29 3 0.63 0.12 1.65 0.16 0.61 2.00 0.37 0.90 1.73 0.24 0.60 1.35 Table 5 2 Average acceleration of unengaged tines at 180 and 230 cpm frequencies. Frequency, cpm Average acceleration, m/s 2 180 24.42 230 28.08 Table 5 3. Force input cycle for 180 cpm. Time, s Force, N 0. 0 0.16 320 0.32 320 0.48 320 0.64 320 0.8 320 0.96 320 Table 5 4. Force input cycle for 230 cpm. Time, s Force, N 0. 0 0.13 320 0.26 320 0.39 320 0.52 320 0.65 320 0.78 320 0.91 320 1.04 320 Results and Discussion Reports were generated for each tree simulation. The resultant acceleration values were extracted from the ANSYS environment manually for each probe point which represented the sensor locations. The maximum resultant accelera tion and equivalent stress in each tree at each time step were also extracted from the simulation.

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108 These maximum values were not limited to the probe values but all the nodes in that tree. Resultant a cceleration at probe points The average and maximum resu ltant acceleration values for each location were calculated. The summary of average and maximum resultant acceleration values are reported in Tables 5 5 and 5 6, respectively. The ratio of the resultant acceleration values at 230 cpm to the values at 180 c pm was calculated for each location (Table 5 7). On an average the ratios for both average and maximum resultant values were greater than 1 indicating that the resultant acceleration values at 230 cpm were more than the ones at the 180 cpm. This observatio n was as expected. A visual observation of the actual tree shaking operation indicated overall higher acceleration at the higher frequency of 230 cpm. The varying ratios in the Table 5 7 can be explained by the difference in structures of the three trees. The ratio of maximum values was observed to be a maximum of 0.22 more than the ratio of average values. This small difference also emphasizes the increase in the overall resultant acceleration of the tree with increase in frequency instead of localized inc rease in resultant acceleration. Table 5 5. Summary of average acceleration data from ANSYS based on location and tree at 180 and 230 cpm frequencies. Locatio n Average acceleration, m/s 2 Tree 1 Tree 2 Tree 3 180 cpm 230 cpm 180 cpm 230 cpm 180 cpm 230 cpm 1 0.31 0.40 0.47 0.68 0.02 0.08 2 3.63 4.33 5.20 7.03 3.34 8.20 3 2.40 2.59 10.04 15.09 9.49 18.68 4 5.18 3.64 20.00 24.16 9.58 19.87 5 9.44 6.14 20.93 24.50 20.89 26.95 6 20.36 9.02 66.88 43.68 40.69 52.39 7 10.13 16.87 38.52 36.16 104.95 159.32 8 5.05 5.98 39.03 33.15 209.56 305.70

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109 Table 5 5. Continued. Locatio n Average acceleration, m/s 2 Tree 1 Tree 2 Tree 3 180 cpm 230 cpm 180 cpm 230 cpm 180 cpm 230 cpm 9 11.96 10.10 10.87 15.13 9.91 23.06 10 20.83 24.27 13.40 29.25 37.35 38.32 11 2.98 3.99 17.19 64.09 24.95 102.10 12 4.89 5.97 17.92 62.79 14.60 44.61 13 13.20 24.14 14.79 22.92 16.67 26.25 14 26.09 32.73 14.50 21.46 29.13 44.97 15 21.39 57.72 17.13 23.62 30.38 45.52 16 14.12 9.35 21.48 29.44 33.82 55.03 17 38.49 31.35 Table 5 6. Summary of maximum acceleration data from ANSYS based on location and tree at 180 and 230 cpm frequencies. Locatio n Maximum acceleration, m/s 2 Tree 1 Tree 2 Tree 3 180 cpm 230 cpm 180 cpm 230 cpm 180 cpm 230 cpm 1 0.81 1.12 1.10 1.87 0.06 0.17 2 9.50 12.49 13.13 22.37 8.58 18.82 3 6.08 8.37 27.28 49.62 25.82 54.71 4 10.30 13.30 41.93 79.29 25.83 52.02 5 15.07 17.48 43.97 79.91 58.39 102.38 6 37.06 29.06 139.18 127.49 107.42 170.68 7 34.99 53.08 77.63 93.94 196.50 305.73 8 13.25 17.39 76.56 88.87 371.69 537.89 9 31.74 40.20 29.24 49.97 30.01 84.71 10 63.11 93.39 39.68 75.96 97.50 167.44 11 7.88 11.99 63.67 163.76 62.06 220.82 12 11.62 17.38 62.39 160.53 41.56 123.49 13 27.63 58.48 40.51 79.80 47.75 109.10 14 86.18 143.34 35.31 72.98 82.47 194.39 15 84.12 158.31 45.46 76.75 84.02 193.81 16 32.98 34.71 56.58 93.41 92.79 221.15 17 99.40 136.74

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110 Table 5 7. Ratio of acceleration values. Locatio n Acceleration ratio (230 cpm value / 180 cpm value) Tree 1 Tree 2 Tree 3 Avg Max Avg Max Avg Max 1 1.282 1.380 1.458 1.700 3.712 2.959 2 1.195 1.315 1.350 1.703 2.457 2.193 3 1.079 1.375 1.502 1.819 1.968 2.119 4 0.703 1.292 1.208 1.891 2.074 2.014 5 0.650 1.160 1.171 1.817 1.290 1.753 6 0.443 0.784 0.653 0.916 1.287 1.589 7 1.666 1.517 0.939 1.210 1.518 1.556 8 1.183 1.312 0.849 1.161 1.459 1.447 9 0.844 1.266 1.392 1.709 2.327 2.823 10 1.165 1.480 2.182 1.915 1.026 1.717 11 1.341 1.521 3.728 2.572 4.092 3.558 12 1.221 1.496 3.504 2.573 3.056 2.971 13 1.829 2.117 1.549 1.970 1.574 2.285 14 1.254 1.663 1.480 2.067 1.544 2.357 15 2.698 1.882 1.379 1.688 1.498 2.307 16 0.662 1.053 1.371 1.651 1.627 2.383 17 0.815 1.376 Averag e ratio 1. 224 1.411 1.607 1.773 2.032 2.252 Resultant a cceleration and equivalent stress The Table 5 8 is a summary of the maximum resultant acceleration and equivalent stress, respectively. The average in the table is the average of the maximum values at all time steps of that tree and maximum is t he overall maximum. The Table 5 9 gives the ratio of values at 230 cpm to the values of 180 cpm. From the Table 5 9, it can be observed that not only the resultant acceleration increases with increasing frequency but so does the equivalent stress in the tr ee structure. From Table 5 9 it can be noted that the average equivalent stress increases by 1.3 times while the maximum equivalent stress increases by 2 times when the frequency increases from 180 cpm to 230 cpm. The increase in equivalent stress was obse rved to be more than the resultant acceleration with increasing frequency, by 1.16 and 1.66 times for average and

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111 maximum values, respectively. The increasing equivalent stress with frequency also indicates a higher probability of branch breakage and thus of tree injury due to excessive shaking. Equivalent stress distribution The Figures 5 6 to 5 8 show the equivalent stress distribution at the end time of simulation. From the Figures 5 6 to 5 8, it can be noted that the equivalent stress was more at locati ons where the contour changed abruptly. For example, in Figure 5 6, the highest point of equivalent stress was at the base where the branches were formed and also along the curvature of two other branches. The increase in equivalent stress with the increas ing frequency was also apparent and reinforces the earlier conclusion. Though the color maps were different for the frequencies, comparing the actual ranges, it can be noted that there was an obvious increase in equivalent stress experienced by the entire tree at 230 cpm when compared to 180 cpm. This was the trend observed in all the trees and throughout the entire structure and not in isolated cases. Resultant a cceleration distribution The Figures 5 9 to 5 11 show the resultant acceleration distribution a t the end of simulation for all trees at frequencies 180 cpm and 230 cpm. From the Figures 5 9 to 5 11, it was apparent that the highest resultant acceleration was always encountered at the ends of the branches. This was because of the flexible nature of t he thinner ends. Another observation was that the lower half of the tree had very low resultant acceleration especially for the trees 2 and 3 (Figure 5 10 and 5 11). This indicated that the resultant acceleration at the trunk was very low and was observed with significant difference only when the branches had split into thinner ones. An increase in frequency did not cause any significant increase in the resultant acceleration of points on the

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112 trunk. This was emphasized by the values at locations 1 and 2 of Tables 5 5 and 5 6. Comparing the resultant acceleration distribution at frequencies 180 cpm and 230 cpm for each tree, it was apparent that the acceleration increases with increasing frequency. This observation reiterates the conclusion made from the rati os tabulated in Tables 5 7 and 5 9. Table 5 8. Average and maximum of maximum total acceleration and equivalent stress data at the end of each timestep for all trees and frequencies from ANSYS. Tree Frequency cpm Equivalent stress, N/m Total acceleration, m/s 2 Avg. Max. Avg. Max. 1 180 3.54E+06 6.88E+06 77.47 143.61 230 4.15E+06 1.59E+07 69.19 162.21 2 180 3.64E+06 7.04E+06 74.12 142.26 230 5.73E+06 1.81E+07 76.45 168.57 3 180 1.15E+07 1.98E+07 212.78 374.02 230 1.39E+07 2.71E+07 311.45 542.48 Table 5 9. Ratio of total acceleration and equivalent stress values. Tree R atio (230 cpm value / 180 cpm value) Equivalent stress, N/m Total acceleration, m/s 2 Avg. Max. Avg. Max. 1 1.172 2.311 0.893 1.130 2 1.574 2.571 1.031 1.185 3 1.209 1.369 1.464 1.450 Average ratio 1.318 2.084 1.129 1.255 A B Figure 5 6. Equivalent stress distribution at the end of simulation in tree 1 at A) 180 cpm B) 230 cpm.

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113 A B Figure 5 7. Equivalent stress distribution at the end of simulation in tree 2 at a) 180 cpm b) 230 cpm. A B Figure 5 8. Equivalent stress distribution at the end of simulation in tree 3 at a) 180 cpm b) 230 cpm.

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114 A B Figure 5 9. Total acceleration distribution at the end of simulation in tree 1 at a) 180 cpm b) 230 cpm. A B Figure 5 10. Total acceleration distribution at the end of simulation in tree 2 at a) 180 cpm b) 230 cpm.

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115 A B Figure 5 11. Total acceleration distribution at the end of simulation in tree 3 at a) 180 cpm b) 230 cpm. Material Properties Experiment The objective of modeling the tree and applying the forces was to simulate the behavior of the tree. For any simulation, the properties of the object of interest are very essential. In our case, these are the mechanical prop erties of the citrus wood. As the experiment was conducted on Late Navel trees, the properties were also determined from the wood sampled from these trees. The experiments were conducted in material properties lab with the help of Dr. Arthur A. Teixeira an d Mr. Justin Townley. Properties of interest odulus Shear m odulus and d ensity which could be measured and used for calculating Bulk m odulus and r atio Materials and Methods The experiment was conducted using the instruments present in the material properties lab. The samples were weighed and the dimensions were accurately measured before conducting the experiments. The electronic weighing scale XP 300 (Figure 5 12A) was used for accurately weighing the samples. The dimensions of the samples were measured using the electronic digital calipers with a resolution of 0.01

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116 mm. For the measurement of volume for the density calculation, multi pycnometer from Quanta Chrome ( Figure 5 12B ) was used. The stress strain curves for the different samples were obtained using the Instron 5566 (Figure 5 12C) instrument. Bluehill software was used for recording the data used for calculating the modulus values. A B Figure 5 1 2. Properties of wood experiment materials. A) Weighing scale XP 300 B) Multi p ycnometer C) Instron 5566

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117 C Figure 5 1 2. Continued A B Figure 5 13. Wood samples for properties of wood experiment. A) Cylindrical samples of Late Navel wood B) Cube samples of Late Navel wood

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118 Preparation of samples The samples from late navel wood were prepared as per requirement so that they c ould be used with the instruments mentioned above. There were 6 cubes of 2 cm a side and 6 cylinders of 2 cm diameter T he samples ( Figures 5 13 A and B ) were machined using lathe machine. Dimensions of samples The height, width and thickness directions were marked on the cubes such that the thickness of the cube was along the grain Similar markings were made on cylindr ical samples also showing the direction of the grain These directions were used as reference to position the cubes and cylinders on the Instron machine. T he dimensions of each sample were measured using the electronic digital calipers in mm. For each dime nsio n, 3 readings were taken at the two e n d s and at the center of the sample. The average of these three values was used in all the calculations. For the cylinder, t hree diameter readings were taken in the region that would be between the cutting edges of the double shear tool. All the dimension s are reported in the Tables 5 10 and 5 11 Table 5 1 0. Dimensions of cube samples. Sample number Thickness, cm Height, cm Width, cm Mass, g 1 22.35 20.93 22.54 9.47 2 21.26 20.87 22.43 8.89 3 22.69 22.88 24.58 11.24 4 23.73 22.88 24.41 11.52 5 21.74 20.81 22.69 9.22 6 23.53 22.94 24.23 11.22 Table 5 11. Dimensions of cylindrical samples. Sample number Diameter, mm 1 20.19

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119 Table 5 11. Continued. Sample number Diameter, mm 2 21.63 3 20.97 4 21.42 5 20.45 6 18.65 Density experiment For cal culating the solid volume, the m ulti p ycnometer instrument manufactured by Quanta Chrome was used. It was calibrated using a metal sphere. The calibration procedure entailed placing t he metal sphere in the pycnometer instead of the samples The pressure values in the cell containing the sphere, and the reference chamber were used for calculation of the volume. At first the pressure in the cell and reference chamber were made 0 psi. This was done by setting t he pressure of the cell to 0 psi. Then the dial wa s set to point to reference, the pressure of reference was checked to be 0 psi. After this, c ompressed air wa s let in to increase the pressure to approximately 17 psi in the reference chamber. Th e pressure value in reference chamber wa s noted down as P 1 psi T he pressure in the cell containing the metal sphere wa s noted down as P 2 psi This was repeated 3 times. The volume was calculat ed using the Equation 5 1 (5 1) where V c is volume of the cell, 148.145 cm 3 and V r is volume of the reference chamber, 88.839 cm 3 .From the Table 5 12 the mean volume from pycnometer was 56.85 5 cm 3 The volume of sphere from calculation using the radius information was 56.541 cm 3 The difference of these two values gives a correction factor of 0.31 4 cm 3 This correction factor can be applied to the volume of samples measured from pycnometer

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120 The pycnometer experiment was repeated with all the 6 cubes. The P 1 and P 2 values were no ted for the cubes and the total volume was calculated. The Table 5 13 giv es the details about this part. All the samples were weighed together and this weight was used with the volume found to calculate the solid density of wood. Table 5 12. Pycnometer c alibration. Trial number P 1 psi P 2 psi V p cm 3 1 17.156 8.462 56.870 2 17.337 8.551 56.865 3 17.387 8.574 56.830 Average 56.855 Table 5 13. Solid d ensity. Trial number Mass, g P 1 psi P 2 psi V p cm 3 Corrected V p cm 3 Density, g/cm 3 1 61.38 17.625 8.108 43.868 43.554 1.409 2 61.38 17.003 7.943 46.813 46.499 1.320 3 61.38 17.018 7.971 47.314 47.000 1.306 Average g/cm 3 1.345 Instron machine setting common for both modulus experiments The load cell was calibrated before the experiments were started on the wood samples. This calibration was done automatically by the BlueHill software. Before each trial, preload of 0.6Kgf was applied so that the crosshead was properly in contact with the sample. The rate of the crosshead movement was 10Kgf/min while preloading. After the system balance d i.e. it was in contact with the samples, the rate of crosshead was 10mm/min. In both the experiments, the force was applied till the sample deformed or th e maximum upper limit of the load cell was reached. is defined as the slope of the stress strain curve obtained from the samples when a compressive or tensile force is applied. In our case wood was

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121 considered was calculated only along the direction perpendicular to the grain. The cubes were placed such that the grain was normal to compressive force on the platform of Instron machine. The dimensions of the cube were entered in the BlueHill software and the compressive force applied. The raw data was then exported as .csv file. Three trials were conducted using the three different cubes available. The Figure 5 14A shows the application of the force while Figure 5 14B shows the graphs of stress strain values obtained through BlueHill software. Shear modulus (G) experiment Shear modulus is the slope of the stress strain curve when a shearing force is applied to the samples. In our case the direction that wa s perpendicular to the grain of wood was used to measure the shear modulus value. The cylinders were loaded on the double shear tool such that the grain was perpendicular to the direction of shear. The dimensions were entered in the Bluehill software and the raw values extracted into a .csv file. The Figure 5 15A shows the application of the force while Figure 5 15B shows the graphs of stress strain values obtained through BlueHill software. A Figure 5 14. Application of compressive force to obtain the You odulus B) Stress strain curves from compressive loading.

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122 B Figure 5 14. Continued A Figure 5 15. Shear modulus experiment and results. A) Application of shea ring force to obtain the Shear m odulus. B) Str ess strain curves from applying shearing force

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123 B Figure 5 15. Continued. Table 5 odulus calculation Sampl e numbe r X 1 mm/mm Y 1 kgf/cm 2 X 2 mm/mm Y 2 kgf/cm 2 kgf/cm 2 1 0.0057 2.4834 0.0202 24.8277 1538.858 3 0.0202 5.9283 0.0402 40.6891 1736.302 5 0.0208 4.0216 0.0401 38.6806 1799.535 Average, kgf/cm 2 1691.565 Table 5 15. Shear m odulus calculation Sampl e numbe r X 1 mm/mm Y 1 kgf/cm 2 X 2 mm/mm Y 2 kgf/cm 2 Shear Modulus, kgf/cm^2 1 0.0505 29.5025 0.0602 36.3449 711.271 2 0.0502 15.8107 0.0604 22.1327 622.859 3 0.0503 33.1735 0.0602 40.2887 717.985 4 0.0502 32.9167 0.0601 40.0721 727.917 5 0.0503 37.6176 0.0602 45.8957 831.976 Average, kgf/cm 2 722.402

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124 Results The density values were calculated using the volume measurements of Pycnometer and the weight of all the samples by using the formula: m ass/ v olume ( Table 5 13 ) The strain curve that was created from the raw data from BlueHill software ( Tables 5 14 and 5 15, and Figures 5 14B and 5 15B ) calcula ted using the following Equations 5 2 and 5 3, respectively. The mean and standard deviati on of the experimental values are given in Table 5 16 It can be noted that the sample values did not vary very much because the standard deviation was within 10% of the mean value for all the three properties. The summary of all the properties measured an d calculated are reported in the Table 5 17 (5 2) (5 3) Table 5 16. Property statistics. Property Average Standard deviation Solid density, Kg/m 3 1345.08 56.04 Young's modulus, MPa 165.89 13.33 Shear modulus, MPa 70.84 7.29 Table 5 17. Summary of properties measured and calculated Property Measured / calculated value Solid density, Kg/m 3 1345.08 Shear modulus, MPa 70.84 165.89 Bulk modulus, MPa 83.98 Poisson ratio, no unit 0.1708 Third Field Experiment Field experiment was conducted on Late Navel trees The objective of this experiment was verification of the model developed that was discussed i n the first

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125 section of this chapter As we we re n ot trying to check the significance of any parameter on the force distribution the number of trees and th e number of varying parameters we re significantly reduced in this field experiment from the earlier field experiments Materials and M ethods For this experiment, the sensor and transceiver setup 2 discussed in Chapter 3 was used. This experiment was conducted on Late Navel trees belonging to the same block. Three trees were selected such that they were of similar sizes. The model developed was under th e assumption that there are no leaves on the branches. This was done to remove the complexity of including leaves and small branches in the model. So as to closely resemble the model, t he selected trees were defoliated. To defoliate the trees, they were sp rayed with a chemical called Reglone This was done with help The mixture to defoliate the trees was prepared with half pint of Reglone in 4 gallon of water. A backpack sprayer was used for spraying the trees. All the three trees were treated 2 weeks prior to the experiment date. All the leaves and fruits were covered with the chemical as uniformly as possible. After 2 weeks, most of the leaves and fruits were removed. Additionally smaller branches were removed from the branches on the side of the tree which would be shaken. The locations along the selected branches were marked for attaching the accelerometers. The sensors were attached to the branches at intervals of 50 cm using zip ties. One XBee PRO node was placed between two accele rometers and was used to communicate with the computer for data acquisition The power lines for the XBee PRO nodes were tied to the branches using zip ties so that they d id not come apart while the tree was shaken. The Figure 5 16 below shows the instrum ented tree branches. The red spots are the accelerometers while the yellow ones are the XBee

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126 PRO nodes to which the accelerometers are attached. The Figure 5 16 is just a portion of the instrumented tree. Totally each tree had 16 accelerometers attached to 8 XBee PRO nodes. Figure 5 16. Defoliated and instrumented tree with the sensors. For t he experiment the tines were made parallel to the ground using an a ngle meter Two different shaker frequencies w ere used for this experiment. This was done so that the model could be verified and compared for different shaker frequencies. The shaker frequencies were selected such that they were the minimum and maximum of the shaker frequency range generally used for harvesting. So as to eliminate the complic ation of the moving contact points, the canopy shaker was kept stationary throughout the experiment The details about these values are given in Table 5 18 below The trees were randomly ordered for the experiment and then the branches were

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127 instrumented. T he shaker frequency was randomly selected and the tree was shaken to collect the data. The shaking period was about 30 second s for each of the trial. At end of each trial, the sensors were tested whether they were working or not and were replaced as requir ed. The data acquired from the sensors during the field experiment was raw hexadecimal data. This data was acquired using LabVIEW VI, which recorded the data coming in at the USB port in a text file. The raw hexadecimal data was first converted to decimal values using a Java program. The Java program reads the raw data and divides them into data packets based on the format of the data packet from the XBee PRO. After this, the conversion was done on the hexadecimal values extracted from the data region of th e entire packet. There were 6 values in one data packet as each XBee PRO was configured to send data from two accelerometers. The decimal values extracted were digital values and not the actual acceleration values. T he next step was to convert these digital values into acceleration values and also to separate the two accelerometers. Another Java program was written to convert the digital values to acceleration and also to separate the two accelerometers data. The analog to digital converter (ADC) in X Bee PRO is a 10 bit converter which is similar to the ADC in the microprocess or used in the first experiment, s o the same procedure used in first experiment and explained in Chapter 4 (Equation 4 1) was used to calculate the acceleration values along each axis of each sensor. Since the comparison was to be done against the resultant acceleration values from the ANSYS model, the resultant acceleration was calculated using Equation 5 4 (5 4)

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128 where, a r is resultant acceleration, m/s 2 a x is acceleration along X axis, m/s 2 a y is acceleration along Y axis, m/s 2 a z is acceleration along Z axis, m/s 2 More details about the Java programs and LabVIEW VI are given in the Appendix B Table 5 18. Factors for the field experiment. S.No Factor Valu e 1. Forward speed of canopy shaker 0 mph (stationary) 2. Angle of tines 0 (perpendicular to ground) 3. Frequency of canopy shaker 180 cpm 23 0 cpm Results and Discussion Resultant a cceleration values Similar to the ANSYS data, the average and maximum resultant acceleration for each location was calculated. Because of the malfunctioning of the sensors, the data at locations 1 and 2 for tree 3 at 230 cpm were not available. The summary of average and max imum resultant acceleration is given in the Table s 5 19 and 5 20. The ratio of values at 230 cpm and 180 cpm were calculated for each location of all trees. Table 5 21 summarizes the ratio data for both average and maximum resultant acceleration. The average ratio in the Table 5 21 indicates that the accelerat ion values were more at 230 cpm than 180 cpm. The average resultant acceleration values at 230 cpm were 1.692 times the values at 180 cpm whereas the maximum values were 1.379 times the values at 180 cpm. This reiterates the conclusion made from the ANSYS simulation data that the acceleration increased when shaker frequency increased. It can also be observed from Table 5 21 that the ratio of maximum resultant acceleration was lesser than or equal to the ratio of the average resultant acceleration in all th e three trees. The average across all three trees showed that the average resultant acceleration values were 1.227 times the maximum values. This could be

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129 because of high acceleration values for prolonged periods of time instead of just momentary spurts in the acceleration values. The ratios calculated from the ANSYS simulation data and the experimental data were compared and are tabulated in Table 5 22. From the simulation data, the ratios were always more for maximum resultant acceleration values than the average values. T his was the opposite of the trend observed in experimental data. This comparison indicated that a perfect correlation between the experimental and simulation values would not be possible with the current model and some reasons for this ar e discussed towards the end of this chapter. Model for e xperimental values vs. simulation values The average and maximum resultant acceleration values could be used for measuring the correlation between the experimental and simulation values. To use the dataset that would give a good correlation, a preliminary comparison of the experimental and simulation resultant acceleration values was done. This initial correlation between the experimental and simulation values was done using the Excel. This function calculates the Pearson product moment correlation coefficient. This value gives the strength of linear dependence between the two data sets. The correlations calculated are summarized in Table 5 23. This step revealed that there was a better linear dependence between the maximum resultant acceleration values than the average acceleration values. Table 5 19. Summary of average acceleration data from experiment based on location and tree at 180 and 230 cpm frequencies. Locatio n Average acceleration, m/s 2 Tree 1 Tree 2 Tree 3 180 cpm 230 cpm 180 cpm 230 cpm 180 cpm 230 cpm 1 0.97 1.31 62.41 51.56 13.78 2 4.73 7.92 3.70 3.53 1.81

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130 Table 5 19. Continued. Locatio n Average acceleration, m/s 2 Tree 1 Tree 2 Tree 3 180 cpm 230 cpm 180 cpm 230 cpm 180 cpm 230 cpm 3 18.70 23.57 12.60 30.65 4.81 6.23 4 8.45 11.00 7.84 24.90 4.95 6.59 5 3.67 5.89 13.28 27.09 10.89 14.88 6 4.02 3.89 19.68 35.12 3.21 3.40 7 4.68 4.94 12.15 16.77 7.06 13.07 8 2.51 3.74 17.73 20.16 18.42 23.59 9 7.13 8.52 17.24 29.25 29.08 29.30 10 8.48 20.46 6.38 8.77 10.52 9.05 11 13.96 18.25 24.61 32.11 7.74 7.33 12 19.61 19.78 12.95 29.58 19.62 20.16 13 6.68 5.00 18.90 41.38 14.94 5.24 14 13.24 18.13 21.56 38.50 19.93 12.08 15 7.14 21.64 9.03 13.84 6.45 10.19 16 5.76 17.17 4.21 44.59 10.97 14.60 17 5.64 9.07 Table 5 20. Summary of maximum acceleration data from experiment based on location and tree at 180 and 230 cpm frequencies. Locatio n Maximum acceleration, m/s 2 Tree 1 Tree 2 Tree 3 180 cpm 230 cpm 180 cpm 230 cpm 180 cpm 230 cpm 1 13.47 19.40 71.32 60.72 24.83 2 16.19 21.85 21.29 39.62 19.22 3 27.36 34.07 23.44 80.07 26.85 40.70 4 26.97 28.10 47.11 116.01 21.36 25.72 5 14.00 17.62 34.46 92.21 28.55 37.04 6 18.14 18.82 95.69 122.25 28.77 31.67 7 21.21 21.16 64.08 101.81 42.20 102.97 8 18.46 23.60 61.30 105.51 113.80 134.05 9 55.53 49.92 29.98 44.09 61.11 67.74 10 87.17 88.46 80.04 93.44 77.17 103.93 11 61.70 69.48 103.33 114.75 88.47 70.63 12 28.19 30.48 93.28 125.37 70.15 73.08 13 24.13 22.37 94.10 123.15 58.92 54.69 14 93.82 106.67 131.70 136.57 71.90 81.39

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131 Table 5 20. Continued. Locatio n Maximum acceleration, m/s 2 Tree 1 Tree 2 Tree 3 180 cpm 230 cpm 180 cpm 230 cpm 180 cpm 230 cpm 15 90.43 75.80 24.93 35.11 73.83 82.94 16 28.31 83.85 81.12 87.02 89.80 110.89 17 20.51 43.81 Table 5 21. Ratio of acceleration values at 230 cpm and 180 cpm. Location Acceleration ratio (230 cpm value / 180 cpm value) Tree 1 Tree 2 Tree 3 Avg Max Avg Max Avg Max 1 1.361 1.440 0.826 0.851 2 1.673 1.349 0.956 1.861 3 1.261 1.245 2.433 3.417 1.295 1.516 4 1.302 1.042 3.175 2.462 1.331 1.204 5 1.605 1.259 2.040 2.676 1.367 1.297 6 0.970 1.037 1.785 1.278 1.060 1.101 7 1.055 0.998 1.379 1.589 1.850 2.440 8 1.489 1.279 1.137 1.721 1.280 1.178 9 1.196 0.899 1.696 1.471 1.007 1.108 10 2.412 1.015 1.374 1.167 0.860 1.347 11 1.308 1.126 1.305 1.111 0.946 0.798 12 1.009 1.081 2.285 1.344 1.027 1.042 13 0.748 0.927 2.189 1.309 0.350 0.928 14 1.369 1.137 1.786 1.037 0.606 1.132 15 3.031 0.838 1.532 1.408 1.581 1.123 16 2.982 2.962 10.58 5 1.073 1.332 1.235 17 1.610 2.135 Average ratio 1.552 1.281 2.280 1.611 1.245 1.246 Table 5 22. Average ratio of acceleration values at 230 and 180 cpm. Data source Acceleration ratio (230 cpm value / 180 cpm value) Tree 1 Tree 2 Tree 3 Avg Max Avg Max Avg Max Experiment 1.552 1.281 2.280 1.611 1.245 1.246 ANSYS 1. 224 1.411 1.607 1.773 2.032 2.252

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132 Table 5 23. Correlation between the experimental and model data sets for average and maximum acceleration values. Tree numbe r Frequenc y, cpm Correlation between the experimental and model values Average acceleration Maximum acceleration 1 180 0.124 0.582 230 0.315 0.621 2 180 0.175 0.357 230 0.017 0.640 3 180 0.132 0.581 230 0.350 0.792 Based on the initial correlation information, the maximum resultant acceleration values were used to find the relation between experimental and simulation data. The relation was determined by fitting linear and quadratic curves for experimental vs. simulat ion value plots. The Matlab C urve F it ting T oolbox was used for the purpose of determining the curve. Linear and quadratic curves were fit to the data of each tree separately. Because of the differences in the tree structures and the different distances of the locations from their local origins, the average of all the trees was not used to create one global model for all trees. The equations used by the solver in Matlab were Equation 5 5 and 5 6 for linear and quadratic curves, respectively. (5 5) (5 6) The Table 5 24 gives the summary of the results for the different curves. The initial curve fit was done using all the data points. The linear model thus created was not able to explain the variability in the data very well (linear model in Table 5 25). So some of the data points were excluded and the adjusted R 2 values were compared to see the improvement in the model. The points were excluded based on the ratio between the experimental and simulation val ues. A maximum of four set of points were excluded

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133 from the data sets. The linear model and the quadratic model constructed for this data set had a better adjusted R 2 value than the linear model developed using the entire data set. Table 5 24. Coefficient s for the different models for different trees. Frequenc y, cpm Tree numbe r Coefficients for linear model Coefficients for linear model with exclusions Coefficients for quadratic model with exclusions p1 p2 p1 p2 p1 p2 p3 180 1 0.530 20.15 1.026 4.09 0.00792 0.278 15.39 2 0.377 47.36 0.684 18.08 0.00677 1.709 11.59 3 0.188 40.40 0.677 20.24 0.00600 1.343 6.53 230 1 0.352 26.92 0.488 19.42 0.00156 0.743 13.74 2 0.485 52.45 0.485 55.82 0.00681 1.839 0.78 3 0.207 35.19 0.314 25.06 0.00127 0.742 3.35 Goodness of fit for the model Table 5 25. Adjusted R 2 values for different models for all trees at 180 and 230 cpm frequencies. Frequenc y, cpm Tree numbe r Adjusted R 2 values for different models Linear model Linear model with exclusions Quadratic model with exclusions 180 1 0.295 0.792 0.799 2 0.065 0.482 0.550 3 0.291 0.538 0.518 230 1 0.344 0.528 0.491 2 0.367 0.393 0.565 3 0.597 0.689 0.746 Table 5 26. Average adjusted R 2 values for the two different frequencies. Frequenc y cpm Linear model Linear model with e xclusions Quadratic model with exclusions 180 0.217 0.604 0.622 230 0.436 0.537 0.601 The summary of the goodness of fit values and the plots of residuals along with the data points and the models are available in Appendix D ( Tables D 1 to D 4 and Figures D 1 to D 18 ). The goodness of fit parameters show a better fit for the data when the fit was changed from linear model to linear model with exclusions to quadratic model

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134 with exclusions. The adjusted R 2 values ( Ta ble 5 2 5) show that the quadratic model with exclusion was only marginally better, when it was not worse, than the linear model with exclusions, with one exception. The Table 5 26 summarizes the average adjusted R 2 values of each model across the trees at the different frequencies. From the Table 5 2 6, it can be concluded that the linear model with exclusions described on an average 60% and 54% variation between the experiment and simulation values at 180 cpm and 230 cpm, respectively. For all three trees, the linear model was able to describe the variability better at the lower frequency of 180 cpm than at 230 cpm. The Table 5 27 summarizes the average of the model coefficients at 180 cpm and 230 cpm. By observing the coefficients of the linear model with exclusions in Table 5 27 it can be noted that the slope of the line for 180 cpm was 1.8 times that of the slope of the model at 230 cpm. This observation reiterates the fact that the linear dependence was more pronounced between the datasets at 180 cpm tha n 230 cpm. The y intercept of linear model at 230 cpm was 2.2 times that of the model at 180 cpm. This observation of y intercept reiterates the fact that the acceleration values were higher at 230 cpm than the 180 cpm. Table 5 27. Average of the coeffici ents for the different models. Frequency, cpm Coefficients for linear model Coefficients for linear model with exclusions Coefficients for quadratic model with exclusions p1 p2 p1 p2 p1 p2 p3 180 0.365 35.97 0.796 14.14 0.00162 1.110 3.44 230 0.348 38.19 0.429 33.43 0.00321 1.108 3.20 Ratio (180/230) 1.050 0.942 1.854 0.423 0.504 1.002 1.074 Possible reasons for the low correlation A perfect correlation between the simulation and experimental resultant acceleration values was not expected. This was because of the obvious differences

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135 between the actual physical system and the model developed to describe that system. In spite of that, there were many other reasons for the correlation between the simulation and experimental values to be low. Some of these reasons are listed below. The f ree branch ends in the ANSYS model were not actual free ends in the tree Only a part of the tree was m odeled, so the extra mass of the tree was not accounted for in the simulation. Small branches were not modeled which affects the damping of the entire tree structure. The material properties were measured only in one direction (normal to grain) There was no reliable method to calculate the force on contact. So t he force input, calculated as the product of average resultant acceleration and mass of an individual tine was another deviation from actual value Force was applied in only plane though during the experiment there might have been forces in other planes also. There were some momentary contact points that were arbitrary and were not accounted for in the simulation. The c ircular cross section assumption of the branches was not true always, especially at junctions where the branches split off. The method used for measurement of the coordinates was not very accurate. Though range of acceleration values was large enough, the values were not uniformly scattered throughout this range. All the above assumpti ons and approximations made while developing the model and conducting the experiment made the simulation values deviate more and more from the actual experimental values. By eliminating some of the above assumptions and approximations, better correlation c ould be attained. But from this study it can be concluded that a tapering cylinder approximation for tree branches along with finite element analysis could be used for the simulation of tree shaking by stationary canopy shaker with good correlation to ac tual conditions.

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136 CHAPTER 6 CONCLUSION The overall objective of this study was to add to our understanding of the interaction between the canopy shakers and trees during harvest. Three different experiments were conducted towards achieving this objec tive. The first one was aimed at comparing the forces experienced by fruits at different locations in the tree under varying conditions. This was followed by the two experiments first of which studied the force distribution along the branches and the other was about development of a model to simulate the shaking action of trees under certain constraints to make the model simple. This chapter summarizes the conclusions from all the experiments and also contains a section about some recommendations to conside r while proceeding with a similar study in the future. Summary of Conclusions From the first experiment, the average maximum force exerted by the canopy shaker to remove the fruits was found to be 18% of the FDF measured the traditional way. This was not expected but logical, as the fruits when shaken undergo twisting and bending ac tion which aid in their removal. It was observed that when the large fruits were treated with abscission chemical, on an average, they were removed by the application of a higher force (almost 2 times), but for a shorter duration (almost half), when compar ed to the ones which were not treated with abscission chemical. The fruits that were not present on the half shaken by the canopy shaker were not removed emphasizing the use of canopy shaker for both halves. Comparison of Hamlin and Valencia varieties indi cate that the Hamlin fruits required lesser average force (0.9 times) but higher maximum force (1.28 times) for shorter duration (0.2 times) to be

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137 removed than the Valencia fruits. Another observation that was expected was that the fruits at the edge of th e canopy were removed with lesser force (0.85 times) and a shorter shaking duration (0.95 times) than the fruits on the inside of the canopy. From this experiment, it can be concluded that the force required to remove fruits depended on their variety and l ocation in the tree. It can also be observed that if the estimates of force applied by using different shaking frequency, angle and amplitude were known then the optimum values could be estimated based on the FDF for different varieties of fruits measured the traditional way. The ANOVA results of second experiment indicated that the resultant force was significantly different for the two tree sizes used in the experiment. Though the angle of tines and shaker frequency were not significant with respect to t he force along the branch, this could not mean that they were insignificant. Using a more uniform set of trees and changing the experimental design, to reduce the variance in the data, would give a better understanding about their effect on force distribut ion in the tree. An investigation into the distribution of resultant acceleration and force showed that they were exponential and Gaussian in nature, respectively, with respect to the distance along the tree branch from the base of the tree trunk. Using th e current set of machine parameter values, no visible trend was detected for the strength of the relationship or for the coefficients of equations with respect to the machine parameter values for both resultant acceleration and force. From this experiment, it can be concluded that high resultant force values can be observed in the middle region of the canopy than the edges or near the trunk. To achieve a more uniform distribution of force in the tree canopy, the mean should be lowered and the variance of th e Gaussian distribution

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138 increased. This can result in a more uniform distribution along the branch and hence the canopy in general. From the experimental and ANSYS simulation maximum resultant acceleration values, a linear model was developed after excludi ng some points. On an average, this linear model was able to describe the variation in the two set of values by 60% and 54% at 180 cpm and 230 cpm, respectively. Comparing the correlation (adjusted R 2 ) between the frequencies of individual trees, it was no ted that the correlation was higher for 180 cpm than 230 cpm by 1.12 times. A comparison of the slope of the linear models also indicated that the linear dependence was more pronounced at 180 cpm than 230 cpm. The larger y intercept observed for 230 cpm th an 180 cpm reiterated the fact that the resultant acceleration values were more at 230 cpm than 180 cpm. Based on the ANSYS simulation, it was observed that the equivalent stress and resultant acceleration increase with the increasing frequency. Th is incre ase was observed to be more in equivalent stress than the resultant acceleration by 1.16 and 1.66 times for average and maximum values. The average equivalent stress increased by 1.3 times while the maximum equivalent stress increased by 2 times when the f requency increased from 180 cpm to 230 cpm. The increasing resultant acceleration value with increasing shaker frequency was also observed in the experimental data. From the experimental data it was observed that the average and maximum resultant accelera tion values at 230 cpm were 1.692 times and 1.379 times that of the values at 180 cpm, respectively. Though the actual ratios were different when looking at the simulation values, still the average and maximum resultant acceleration values at 230 cpm were 1.129 times and 1.255 times that of the values at 180 cpm, respectively. Most of the tree trunk region had very

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139 low acceleration values though the stress was high at locations of discontinuities along it. The acceleration started to be noticeably higher on ly from the first branching from the trunk region of the tree. The low correlation between the experimental and simulated resultant acceleration values can be improved by developing a model that does not incorporate as many assumptions as the current one. Some steps to improve the model are measurement of wood properties along all three directions, selection of locations to get a more uniformly distributed range of resultant acceleration values, and a more detailed CAD model of the trees. Another important change would be a better estimate of the force applied to the tree by the shaker and the locations where it is applied. From this comparison, it can be concluded that the model used in this study can be used, with modifications to tree model and force appl ication, to predict the tree behavior when engaged with the canopy shaker. Recommendations for Similar Work This section is about the things that could have been done differently and some of the observations during the experiments which would be useful for similar studies in the future by making life easier while conducting similar experiments. Listed below are the observations made during the experiments. Most of these observations are about the sensor and the communication part. Following the observations are the recommendations for future work to look into the different aspects of fruit removal and force distribution. Observations: o When using the setup 1 explained in Chapter 3, one laptop was able to support only one XBee PRO receiver. But this was not the problem with the setup 2.

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140 o When using the setup 2 explained in Chapter 3, one XBee PRO receiver was able to support only 4 XBee PRO transmitters with a data rate of 10 to 12 data points per second per sensor. Increasing the number of transmitters caused some of the data to be dropped and some nodes data was never received. o To use batteries for powering the XBee PRO nodes, the connector and batteries should be placed within an enclosure so that the battery does not disconnect during data collection. o The n odes have to be placed so that they are not facing the canopy shaker in order to reduce the damage to them. o An automatic test routine that could test all the connected XBee PRO nodes and report the defective ones at end of each trial would reduce the exper iment time. o Post processing the hexadecimal data from the sensors can increase the data points collected per second. o Using the ADC in the XBee PRO also reduces the hardware required and the overall cost of the board. Each XBee PRO can support up to 6 ADC c hannels. Recommendations: o Using two accelerometers on opposite sides of the same fruit can give data about its rotation and its effect on fruit removal. o Using a more reliable method to find the coordinates in the tree canopy or along the tree branches can improve the accuracy of the study. o Using more branches in a tree and a factorial experimental design to study the effect of machine parameters on the force distribution along the tree branches. o axis of the samples to make the material orthotropic in nature as it should be. o Measuring the hydraulic pressure in order to calculate the input force on the tree for simulation purposes. o Measuring the acceleration along the tines while shaking the tree an d using that curve instead of just a triangular curve for the force input on the tree structure. o Modeling the entire tree instead of just half of the tree along with the leaves and smaller branches to simulate the shaking action.

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141 APPENDIX A SENSORS AND COMMUNICATION This appendix gives some details about the communication protocol and sensors used. The communication protocol, ZigBee, is described in general followed by the specifics of the XBee PRO used for the experiments. The accelerometer operatio n is in general described followed by the special functions of the MMA7260Q accelerometer used in the experiments. Z ig B ee Though there are other short range protocols like 802.11 and 802.15 (Bluetooth), there was a need for a simpler protocol which will re sult in less expensive devices. ZigBee/802.15.4 protocol was created to fill this gap. It is a specification of high level communication protocols to be used with small, low powered radios built on the IEEE 802.15.4 TM standard. It is intended for networks that require low data rate, long battery life and secure networking. The networks using ZigBee devices run in unlicensed frequencies like the ISM (Industrial, Medical and Scientific) band (2.4 GHz band) in the U.S (Wexler, 2003). The ZigBee standard is ma intained and published by a group of ZigBee is used for wireless automated monitoring and control, home appliance networks and such wherein the sensors can operate for years and not hours as is the case of more c omplex protocols like Bluetooth. Table A 1 gives a brief chronology of development of ZigBee ( Wikipedia contributors, 2009b and Smith, 2008). Table A Year Development stage 1998 Many engineers saw the need for a self organizing ad hoc digital radio networks. 2003 IEEE 802.15.4 standard was completed 2004 ZigBee specifications were ratified on 14 December 2004.

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142 Table A 1. Continued. Year Development stage 2005 ZigBee 2004 Specification was publicly made available in June 2005. ZigBee Alliance membership exceeded 200 companies by December 2005. 2006 ZigBee 2006 Specification, an enhanced version was made available in December 2006. 2007 ZigBee PRO the enhanced version was finalized and made available in October 2007. Specification F igure A 1 shows a schematic of the ZigBee specification. ZigBee adds specifications for the network layer, application layer, ZigBee device objects (ZDO) and applicat ion objects on top of the physical and medium access control layer defined by IEEE 802.15.4 standard. Network layer supports star, tree and generic mesh topologies and handles network addressing and routing through the MAC layer. The routing protocol used is the a d hoc o n d emand d istance v ector (AODV) based routing algorithm for discovering paths to nodes in the network. The application layer is the highest layer and is supposed to include the application support sub layer, ZDOs and the application objects defined by the manufacturer. The application objects are the software at the endpoints which control the ZigBee devices. The ZDOs define what kind of device is the current device, whether it is a coordinator, router or end device within the network. The ZD Os are also responsible for communication between application support sub layer and network layer. It also has a security service provider which provides security mechanism for the network and application support sub layer. The application support sub laye r provides data services for application and ZigBee device profiles. It maintains the binding tables as a database which provides information about the various devices present as per the service needed. The basic channel access mode is carrier sense, multi ple access/collision avoidance (CSMA/CA) for the ZigBee devices. The security of

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143 ZigBee specification builds on the security framework defined in 802.15.4 standard. It uses 128 bit keys and they can be specified both for layers or links. ZigBee protocols s upport beacon and non beacon enabled networks. Non beacon enabled networks use an un slotted CSMA/CA channel access mechanism for communication. The receivers are continuously active requiring a reliable power supply. These networks typically have a coordi nator and end devices. In beacon enabled networks, there are routers which transmit beacons periodically between which they can sleep. This lowers the power usage but the timing constraints might increase the cost of the device (Wikipedia contributors, 200 9a). Figure A 1. ZigBee specification ( Author: Rob Blanco. Source: http://en.wikipedia.org/wiki/File:ZigBee_protocol_stack.png. Last accessed August, 2009).

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144 XBee PRO XBee P RO is an RF OEM module that meets the 805.15.4 standards. It operates on the ISM 2.4 GHz band. It is engineered to support low power, low cost wireless networks. Some of the key features are listed below (Digi International Inc., 2008) It has long range wit h 100m for indoor and 1500 m outdoor (line of sight) applications. It requires low power with 215 mA for transmission and 55 mA for reception at 3.3 V. It has digital I/O, I/O line passing and ADC. It supports unicast and broadcast communications. It supports source/ d estination addressing. It supports coordinator and end device operations. It has a small form factor. Accelerometer An accelerometer is a device (sensor) to measure (sense) the acceleration or deceleration of a moving object by mechanical or electromechanical means. There are different types of sensors used for measuring the acceleration based on piezo film, electromechanical servo, piezoelectric, liquid tilt, bulk micro machined piezo resistive, capacitive, and surface micro machined capac itive. All of them have different characteristics which makes them preferable for different applications. Braking systems, detecting vibrations in machinery, sports training product and computer peripherals are some of the places where accelerometers are u sed (PC Control Ltd., 2008). Surface M icro machined A ccelerometers Silicon micro machined sensors with on chip integration are used for measuring acceleration /vibration. They require very few external components and provide on chip

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145 sensor and signal condi tioning. They are made up of springs, masses, and motion sensing components. IC photolithography and selective etching are used to create a 3D structure that is suspended and allowed to move in all directions. The core is a mass suspended above the substra resistance to movement due to acceleration. The mass and wafer have fixed plates forming a differential capacitor and any movement of the mass unbalances the capacitor resulting in a square wave output w ith amplitude proportional to acceleration (PC Control Ltd., 2008). Figure A 2 shows a schematic of such a transducer model of the MMA7260Q accelerometer used. The signal processing components are present for each axis and the final analog signal is conver ted to a duty cycle output based on an external resistor. The analog output can be used to measure the acceleration using the timing of the duty cycle and the period of each axis. Figure A 2 Simplified transducer p hysical m odel Copyright of Freescale Semiconductor, Inc. 2009, Used by Permission (Source: http://www.freescale.com/files/sensors/doc/ data_sheet/MMA7260QT .pdf. Last accessed August, 2009). MMA7260Q and F eatures The Freescale accelerometer, MMA7260Q, used for the experiments in this study is a surface micro machined accelerometer. It has two surface micro machined capacitive sensing cells (also called g cells) and a signal conditioning ASIC (Application Specific Integrated Circuit) found in a single IC package (Figure A 3) The

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146 g cell can be modeled as a set of beams attached to a movable central mass that moves between fixed beams. The mass moves towards a fixed beam and this distance moved gives the measure of acceleration (Figure A 2) The g cell can be seen as a back to back capacitors and the ASIC uses switched capacitor techniques to measure the g cell capacit ance and extract acceleration data from the difference between the m Some of the features of the MMA7260Q sensor are listed below (Freescale International Inc., 2008) Figure A 3. Schematic of the accelerometer Copyright of Freescale Semiconductor, Inc. 2009, Used by Permission (Source: http://www.freescale.com/files/sensors/doc/ data_sheet/MMA7260QT .pdf. Last accessed August, 2009). g Select: This feature allows the user to sele ct any of the 4 sensitivities as listed in table by changing the input on pins 1 and 2 of the sensor. Table A 2 gives the input for selecting the different g ranges. Sleep mode: The sensor can be put to sleep mode, by giving a low signal on pin 12, which r battery power. It also has a fast turn on time of 1 millisecond. Filtering: The presence of switched capacitors, requirement of external passive components to set cut off frequency is elimina ted.

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147 Ratiometricity: The output offset voltage and sensitivity will scale linearly with the applied voltage. Table A 2. g Select and sensitivity Copyright of Freescale Semiconductor, Inc. 2009, Used by Permission (Source: http://www.freescale.com/files/ sensors/doc/ data_sheet/MMA7260QT .pdf. Last accessed August, 2009). g Select2 g Select1 g Range, g Sensitivity, mV/g 0 0 1.5 800 0 1 2 600 1 0 4 300 1 1 6 200

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148 APPENDIX B CIRCUIT AND CODE In this experiment two different setups were used for data collection. The circuit and data acquisition details about the two setups described in Chapter 3 are discussed in this appendix. The code used for data extraction from the raw data of the sensors i s also discussed briefly in this appendix. Setup 1 Circuit Schematic The Figures B 1 A and B show the details of the board used for experiments 1 and 2 explained in Chapter 4. Figure B 1A is the overall schematic of the board showing the radio, microproce ssor and sensor. Figure B 1B shows the connections between the pins of the different components on the board. The connections between components for the setup with the sensor separated are also same as the ones in Figure B 1B. A Figure B 1. Circuit det ails for setup 1. A) Schematic of board used for experiment 1 and 2. B) Connections between microprocessor, radio and sensor.

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149 B Figure B 1. Continued Data A cquisition Microprocessor and VB code The data acquisition involves programs running on the mi croprocessor and the laptop. The microprocessor and VB code was written by Mr. Martin Hebel, Southern

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150 Illinois University for Dr. Reza Ehsani, University of Florida. The microprocessor chip used in the circuit is an ATmega8L with a clock frequency of 8 MHz and small memory model with data stack size of 256. The microprocessor receives input from the user via the graphical user interface (GUI) in Excel .The microprocessor can be instructed to do the following via Excel GUI. Set the address and chann el of the USB connected XBee PRO Set the G value and data mode of the remote units. Put the remote units to sleep and wake them up on user input. Test the remote units. Start and stop data transmission by the remote units. Figure B 2. GUI of Excel Macro. The VB macro in Excel uses StampDAQ from Parallax, Incorporated and a macro created by Mr. Martin Hebel, Selma Ware Solutions. A screenshot of the GUI is given in Figure B 2 and all the input fields and buttons are explained below. 1. User input fields: a. Port : user input for the CO M port at which the USB XBee PRO is available.

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151 b. Wake Units: user input for waking up the units. c. Status: status display about the connectivity of the USB XBee P RO. 2. Buttons: a. Connect: connects to and initializes the port for communicati on. b. Clear Events: clears the events displayed on the console window. c. Set: sets the address and channel of the XBee P RO connected to the computer d. g value for all the units on the channel indicated. e. Set Mode: sets the data acquisition mode for all the units on the channel indicated. f. Unit Sleep: puts all the units on the selected channel to sleep. g. Unit Test: pings all the units on the selected channel to test their availability. h. XMIT Data: starts data transmission from all the units on the s elected channel. i. Quit XMIT: end the data transmission from all the units. j. Reset Timer: resets the timer to time the data coming in on the COM port. k. Clear Columns: clears the columns in the Excel sheet to enter new data. Data collection procedure For every user action a step or a sequence of steps are performed by the microprocessor. To collect data from the remote units, the following series of steps are to be followed. The main bullets are user input while the others are operations done by the microprocess or Select the correct port and press o Initialize the variables for the microprocessor. o Initialize the variables for the USART communication. o Initialize the variables for the ADC.

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152 o Display the events on the GUI. o Put the unit to sleep. Set the local address to FFFF and channel to the desired one and hit the button. Select the correct g value (in this case 6) and hit the Select the correct mode of transmission ( aw mode ) and hit the button. Select th To put the units to sleep in between button. o Wake the unit up. o Ready to transmit data. Press the remote units ar e all up and working. The units on the selected channel are displayed on the console. In order to clear the console, press the data in the current excel shee t. If this is not done then the data is appended to the existing rows. starts correctly for the new data. P o Conve rt the analog data to digital values. o Transmit the data as per the mode requested. T o Stop transmission of data. Data e xtraction The raw data for each of the trial was stored in a separate Excel file. To analyze the data, first it had to be converted to acceleration values and then to force values based. The raw data was first separated into different sheets depending on the sensor

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153 name. After this a macro was written to process all files in a given folder and calculate the acceleration values based on the Equations 4 1 to 4 4. The steps involved are as follows. 1. User selects the folder containing the files. 2. The folder is traversed re cursively. 3. The recursion stops at the folder with no sub folders. 4. The first file is opened. 5. The formulas are added in the required columns as per the equation. 6. The formulas for summary values are also added. 7. The file is closed after saving. 8. The steps 4 to 7 are repeated for all the files in a folder. 9. Before exiting the folder, a summary file is created. 10. The summary values from all the files are collected and added to a new file. 11. The new Excel file is then saved and closed. 12. The steps 4 to 11 are repeated for all the folders with files in them. Data a nalysis ANOVA was done in SAS The data was arranged as per the SAS requirements. T he SAS program was run on each data set model in the SAS program. The interaction was studi ed between the angle, frequency and tree size. Setup 2 Circuit Schematic Figure B 3 shows the schematic of the board used in the experiment for validation of the analytical model developed using ANSYS. In this board, there is no microprocessor and the X, Y and Z are connected directly to the analog to digital pins of the XBee PRO module which are displayed on the Figure B 3 as AD0 to AD5. D ata A cquisition In this setup, because of the change in circuit, LabVIEW was used for data acquisition. The LabVIEW VI used for data acquisition is a simple serial read where the

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154 incoming data is recorded in a text file. The user is first asked to select the file name for the trial. To this file name, the channel name is appended and the file is created in the user or else an error is encountered. If the file already exists, then the data is appended to the file. Figure B 4 and B 5 show the front panel and block diagram for data acquisi tion on one channel acquisition (in this case for channel F) respectively. The Nam actual data coming in at the port as Hex string. Figure B 3. Schematic of board used for experiment 3 and 4.

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155 Figure B 4. Front panel for data acquisition on one channel. Figure B 5. Front panel for data acquisition on one channel.

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156 Figure B 6. Schematic of LabVIEW data acquisition program. Data E xtraction Raw to acceleration The data that was collected using LabVIEW was stored in 58 files for all the trials. These files were in hexadecimal (HEX) format and had to be parsed properly so as to extract the acceleration values properly for each of the sensor location. A Java progra m was written which parsed the data and extracted the acceleration values. The program asks for user input of the root folder which contains all the HEX files. It finds all the subfolders containing the text files with the HEX data. It opens the first text file in the list. It parses the HEX data based on the packet format of XBee PRO data. It calculates the acceleration values for each axis and also the resultant value using the Equations 4 1 and 5 4 given in Chapter 4 and 5, respectively.

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157 It creates two f iles, one for the parsed HEX data and the other for the the data is separated by commas. It writes the data into their respective files and closes all the open files. It repeat s the steps for all the files present in the list. Isolating sensors of each file The HEX data and the acceleration data are created in two different folders at the same level as the root folder selected by the user. These two folders have the same sub fol der structure as the root folder selected. One file has data from more than one sensor as it was created based on the channel on which they were transmitting the data. So these files had to be split into multiple files for further processing. This was done by another Java program written for this purpose. The program asks for user input of the root folder which contains all the files present in this folder including the subfolders It opens the first text file in the list. It separates the data based on the address of the XBee PRO unit and then points are created as each XBee PRO was connected to two accelerometers. It creates one PRO unit on that channel. For It writes the data into their respective files and closes all the open files. It repeats the steps for all the files present in the list. Consolidation of all files When the program is finished, there is a folder present which contains one file for each of accelerometer used. This folder is on the same level as the root input folder and has the same subfolder structure. At the end of these two Java programs, 400 plus files

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158 are created for each of the accelerometer used for data collection. To consolidate all the folders found under a The user selects the folder in which the files are present through a dialog box. into one file so that one sheet is created for one level higher. f it was created from the into the current summary file. key so that the summary values can be identified. This file is then manually formatted so that the values are separated as per tree number and frequency used for that trial.

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159 APPENDIX C DISTRIBUTION ALONG T HE BRANCH RESULTS Table C 1. Goodness of fit values for exponential distribution of average acceleration in small and large trees. Angle Frequency Large trees Small trees SSE R 2 Adj. R 2 RMSE SSE R 2 Adj. R 2 RMSE 5 200 69.09 0.411 0.117 5.88 314.45 0.330 0.106 10.24 5 250 9.69 0.931 0.896 2.20 17.67 0.941 0.921 2.43 5 300 1.62 0.964 0.946 0.90 24.63 0.935 0.914 2.87 20 200 99.87 0.959 0.939 7.07 187.70 0.283 0.045 7.91 20 250 7.40 0.905 0.873 1.57 88.37 0.780 0.706 5.43 20 300 23.04 0.918 0.890 2.77 18.65 0.945 0.927 2.49 35 200 252.61 0.385 0.180 9.18 37.08 0.830 0.774 3.52 35 250 25.89 0.770 0.694 2.94 56.24 0.711 0.614 4.33 35 300 70.15 0.857 0.810 4.84 105.23 0.870 0.827 5.92 Table C 2 Goodness of fit values for exponential distribution of maximum acceleration in small and large trees. Angle Frequency Large trees Small trees SSE R 2 Adj. R 2 RMSE SSE R 2 Adj. R 2 RMSE 5 200 313.91 0.496 0.327 10.23 3779.21 0.125 0.167 35.49 5 250 1416.92 0.512 0.350 21.73 2121.51 0.625 0.499 26.59 5 300 220.39 0.115 0.328 10.50 1790.31 0.704 0.605 24.43 20 200 616.75 0.591 0.386 17.56 1987.23 0.621 0.495 25.74 20 250 339.08 0.765 0.686 10.63 1809.46 0.602 0.470 24.56 20 300 601.46 0.648 0.530 14.16 1501.65 0.658 0.544 22.37 35 200 1164.96 0.665 0.554 19.71 3337.47 0.375 0.167 33.35 35 250 1341.28 0.639 0.519 21.14 2924.93 0.394 0.192 31.22 35 300 722.01 0.700 0.600 15.51 2299.21 0.676 0.568 27.68

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160 Table C 3 Goodness of fit values for Gaussian distribution of average force proportional values in small and l arge trees. Angle Frequency Large trees Small trees SSE R 2 Adj. R 2 RMSE SSE R 2 Adj. R 2 RMSE 5 200 0.70 0.879 0.758 0.59 0.61 0.751 0.502 0.55 5 250 1.96 0.813 0.625 0.99 0.02 0.987 0.974 0.09 5 300 0.30 0.962 0.924 0.38 0.19 0.891 0.783 0.31 20 200 0.31 0.825 0.474 0.56 0.07 0.965 0.930 0.19 20 250 0.37 0.813 0.625 0.43 0.45 0.706 0.411 0.47 20 300 0.71 0.821 0.643 0.60 0.32 0.893 0.785 0.40 35 200 0.12 0.958 0.945 0.20 0.09 0.949 0.899 0.21 35 250 1.14 0.710 0.420 0.75 0.10 0.923 0.846 0.22 35 300 0.42 0.878 0.755 0.46 0.35 0.748 0.496 0.42 Table C 4 Goodness of fit values for Gaussian distribution of maximum force proportional values in small and l arge trees. Angle Frequency Large trees Small trees SSE R 2 Adj. R 2 RMSE SSE R 2 Adj. R 2 RMSE 5 200 17.22 0.952 0.904 2.93 12.80 0.911 0.822 2.53 5 250 45.56 0.861 0.721 4.77 2.30 0.971 0.941 1.07 5 300 8.29 0.976 0.951 2.04 6.80 0.930 0.859 1.84 20 200 9.28 0.960 0.880 3.05 4.11 0.966 0.932 1.43 20 250 17.92 0.916 0.833 2.99 4.25 0.956 0.912 1.46 20 300 25.59 0.925 0.850 3.58 7.81 0.925 0.849 1.98 35 200 17.56 0.880 0.759 2.96 9.03 0.926 0.853 2.12 35 250 53.28 0.838 0.676 5.16 3.48 0.956 0.913 1.32 35 300 5.87 0.979 0.957 1.71 8.48 0.894 0.789 2.06

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161 Figure C 1. Variation of maximum force proportional values with respect to distance from origin along the branch in small trees for all angle and frequency combination.

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162 Figure C 2. Variation of average force proportional values with respect to distance from origin along the branch in small trees for all angle and frequency combination.

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163 Figure C 3. Variation of maximum acceleration values with respect to distance from origin along the branch in small trees for all angle and frequency combination.

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164 Figure C 4. Variation of average acceleration values with respect to distance from origin along the branch in small trees for all angle and frequency combination.

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16 5 Figure C 5. Variation of m aximum force proportional values with respect to distance from origin along the branch in large trees for all angle and frequency combination.

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166 Figure C 6. Variation of average force proportional values with respect to distance from origin along the br anch in large trees for all angle and frequency combination.

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167 Figure C 7. Variation of maximum acceleration values with respect to distance from origin along the branch in large trees for all angle and frequency combination.

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168 Figure C 8. Variation of average acceleration values with respect to distance from origin along the branch in large trees for all angle and frequency combination.

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169 APPENDIX D MODEL VALIDATION RESULTS Table D 1. SSE values of different models for experimental vs. simu lation values. Tree number Frequen cy, cpm Linear model Linear model w ith excluded data points Quadratic model with excluded data points 1 180 8453.36 2120.10 1870.43 230 8332.03 5266.71 5170.03 2 180 14611.85 4884.70 3821.32 230 9323.65 6133.28 4029.29 3 180 8506.21 3188.30 2994.00 230 5145.88 2338.39 1694.43 Average 180 10523.81 3397.70 2895.25 230 7600.52 4579.46 3631.25 Table D 2. R 2 values of different models for experimental vs. simulation values. Tree number Frequen cy, cpm Linear model Linear model with excluded data points Quadratic model with excluded data points 1 180 0.339 0.810 0.832 230 0.385 0.568 0.576 2 180 0.128 0.529 0.632 230 0.409 0.439 0.632 3 180 0.338 0.580 0.605 230 0.628 0.720 0.797 Average 180 0.268 0.640 0.690 230 0.474 0.576 0.668 Table D 3. Adjusted R 2 values of different models for experimental vs. simulation values. Tree number Frequen cy, cpm Linear model Linear model with excluded data points Quadratic model with excluded data points 1 180 0.295 0.792 0.799 230 0.344 0.528 0.491 2 180 0.065 0.482 0.550 230 0.367 0.393 0.565 3 180 0.291 0.538 0.518 230 0.597 0.689 0.746 Average 180 0.217 0.604 0.622 230 0.436 0.537 0.601

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170 Table D 4. RMSE values of different models for experimental vs. simulation values. Tree number Frequen cy, cpm Linear model Linear model with excluded data points Quadratic model with excluded data points 1 180 23.74 13.88 13.68 230 23.57 21.88 22.74 2 180 32.31 22.10 20.61 230 25.81 22.61 19.14 3 180 24.65 17.86 18.24 230 20.71 16.12 14.55 Average 180 26.90 17.95 17.51 230 23.36 20.20 18.81

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171 A B Figure D 1. Linear model for experimental vs. simulation values for tree 1 at 180 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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172 A B Figure D 2. Linear model for experimental vs. simulation values for tree 2 at 180 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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173 A B Figure D 3. Linear model for experimental vs. simulation values for tree 3 at 180 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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174 A B Figure D 4. Linear model for experimental vs. simul ation values for tree 1 at 230 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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175 A B Figure D 5. Linear model for experimental vs. simulation values for tree 2 at 230 cpm. A) Experimental vs. sim ulation values with linear model. B) Residual values for the linear model.

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176 A B Figure D 6. Linear model for experimental vs. simulation values for tree 3 at 230 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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177 A B Figure D 7. Linear model with excluded data points for experimental vs. simulation values for tree 1 at 180 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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178 A B Figure D 8. Linear model with excluded data points for experimental vs. simulation values for tree 2 at 180 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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179 A B Figure D 9. Linear model with ex cluded data points for experimental vs. simulation values for tree 3 at 180 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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180 A B Figure D 10. Linear model with excluded data points for experimen tal vs. simulation values for tree 1 at 230 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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181 A B Figure D 11. Linear model with excluded data points for experimental vs. simulation values for tree 2 at 230 cpm. A) Experimental vs. simulation values with linear model. B) Residual values for the linear model.

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182 A B Figure D 12. Linear model with excluded data points for experimental vs. simulation values for tree 3 at 230 cpm. A) Experiment al vs. simulation values with linear model. B) Residual values for the linear model.

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183 A B Figure D 13. Quadratic model with excluded data points for experimental vs. simulation values for tree 1 at 180 cpm. A) Experimental vs. simulation values with quadratic model. B) Residual values for the quadratic model.

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184 A B Figure D 14. Quadratic model with excluded data points for experimental vs. simulation values for tree 2 at 180 cpm. A) Experimental vs. simulation values with quadratic model. B) Re sidual values for the quadratic model.

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185 A B Figure D 15. Quadratic model with excluded data points for experimental vs. simulation values for tree 3 at 180 cpm. A) Experimental vs. simulation values with quadratic model. B) Residual values for the quadratic model.

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186 A B Figure D 16. Quadratic model with excluded data points for experimental vs. simulation values for tree 1 at 230 cpm. A) Experimental vs. simulation values with quadratic model. B) Residual values for the quadratic model.

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187 A B Figure D 17. Quadratic model with excluded data points for experimental vs. simulation values for tree 2 at 230 cpm. A) Experimental vs. simulation values with quadratic model. B) Residual values for the quadratic model.

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188 A B Figure D 18. Quad ratic model with excluded data points for experimental vs. simulation values for tree 3 at 230 cpm. A) Experimental vs. simulation values with quadratic model. B) Residual values for the quadratic model.

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189 LIST OF REFERENCES Abdel Fattah, H.M., K.A. Shackel, and D.C. Slaughter. 2003. Methodology for determining almond shaker displacement and frequency. Applied Eng. in Agric. 19(2):141 144. Adrian, P.A., and R.B. Fridley. 1965. Dynamics and design criteria of inertia type tree shakers. Trans. ASAE 8(1):12 14. Adrian, P.A., R.B. Fridley, and C. Lorenzen. 1965. Forced vibration of a tree limb. Trans. ASAE 8(4):473 475. Bora, G., R. Ehsani, M. Hebel, and K.Lee. 2007. In situ measurement of the detachment force of individual oranges harvested by a canopy shaker harvesting machine. Proc. Fla. State Hort. Soc 120:38 40. Brown, G.K. 2002. Mechanical harvesting systems for the Florida citrus juice industry. ASAE Paper No. 021108. St. Joseph, Mich.: ASAE. Burks, T.F., F. Villegas, M.W. Hannan, S.J. Flood, B.Sivaraman, V.Subramanian, and J.Sikes. 2005. Engineering and horticultural aspects of robotic fruit harvesting: Opportu nities and constraints. Hort. Technology 15:79 87. Cavalchini, A.G. 1999. Harvesters and threshers: Forage crops. In CIGR handbook of agricultural engineering Vol.III Plant production engineering, 348 380. International commission of agricultural engineeri ng ed. St. Joseph, Mich.: ASAE. Ceres, R. J.L. Pons, A.R. Jimenez, J.M. Martin, and L. Calderon. 1998. Design and implementation of an aided fruit harvesting robot (Agribot). Industrial Robot: An International Journal 25(5): 337 346. Chen, P., J.J. Mehlsch au, and J. Oritz Canavate. 1982. Harvesting Valencia oranges with flexible curved fingers. Trans. ASAE 25(3):534 537. Churchill, D.B., H.R. Sumner, and S.L. Hedden. 1976. Developments in citrus pickup equipment. ARS S 84. New Orleans, Louisiana: USDA Agric ultural Research Service. Coppock, G.E. 1961. Picking citrus fruit by mechanical means. Proc. Fla. State Hort. Soc 74:247 251. Coppock, G.E. 1967. Harvesting early and midseason citrus fruit with tree shaker harvest systems. Proc. Fla. State Hort. Soc 80 :98 104. Proc. Fla. State Hort. Soc 84:84 88.

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191 Fridley, R.B. 1983. Vibration and vibratory mechanism for the harvest of tree fruits. In Principles & practices for harvesting & handling fruits & nuts 157 188. M. O'Brien, B. F. Cargill, and R. B. Fridley eds. Westport, Conn.: AVI Publishing Company, Inc. Fridley, R.B., and P.A. Adrian. 1960. Some aspects of vibratory fruit harve sting. Agricultural Engineering 41(1):28 31. Fridley, R.B., and C. Lorenzen. 1965. Computer analysis of tree shaking. Trans. ASAE 8(1):8 11, 14. Fridley, R. B., and C. Yung. 1975. Computer analysis of fruit detachment during tree shaking. Trans. ASAE 18(3) :409 415. Futch, S.H., J.D. Whitney, J.K. Burns, and F.M. Roka. 2005. Harvesting: From Manual to Mechanical. Gainesville, Fla.: University of Florida Institute of Food and Agricultural Sciences Available at: http://edis.ifas.ufl.edu/pdffiles/HS/HS21800.pdf. Accessed 29 June 2009. Green, D.W., J.E. Winandy, and D.E. Kretschmann. 1999 .Mechanical properties of wood. Available at: http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr113/ch04.pdf. Accessed 29 June 2009. Harrell, R.C. 1987. Economic analysis of robotic citrus harvesting in Florida. ASAE Paper No. 021108. St. Joseph, Mich.: ASAE. Harrell, R.C., P.D. Adsit, and D.C. Slaughter. 1985. Real time vision servoing of a robotic tree fruit harvester. ASAE Paper No. 021108. St. Joseph, Mich.: ASAE. Hedden, S.L. 1964. Engineering problems in harvesting citrus fruits. Trans. ASAE 7(2):188 189. Hedden, S.L., and D.B. Churchill. 1984. Fruit handling systems for Florida citrus. In Intl Symposium on Fruit, Nut and Vegetabl e Harvesting Mechanization 164 170. St.Joseph, Mich.: ASAE. Hedden, S.L., and G.E. Coppock. 1968. Effects of the tree shaker harvest system on subsequent citrus yields. Proc. Fla. State. Hort. Soc 81:48 52. Hedden, S.L., and G.E. Coppock. 1971. Comparati ve harvest trials of foliage and limb Proc. Fla. State Hort. Soc 84:88 92. Hedden, S.L., D.B. Churchill, and J.D. Whitney. 1984. Orange removal with trunk shakers. Proc. Fla. State Hort. Soc 97:47 50. Hedden, S.L., H.R. Sum ner, and D.B. Churchill. 1979. Collecting and handling mechanically harvested oranges in South Florida (LaBelle). Proc. Fla. State Hort. Soc 92:59 61.

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192 Hedden, S.L., H.R. Sumner, G.E. Coppock, J.G. Blair, W.C. Wilson, D.L. Deason, and C.L. Anderson. 1972. Shaker pickup harvest system for early and midseason oranges. Proc. Fla. State Hort. Soc 85:245 249. Hemmat, A., P. Chen, and W.J. Chancellor. 1980. Determining proper thickness of cushioning materials for fruit catching frames. Trans. ASAE 23(3):558 561, 567. History.com. 2009. Agricultural machinery Available at: http://www.history.com/encyclopedia.do?articleId=200413. Accessed June 2 9, 2009. Hoag, D.L., R.B. Fridley, and J.R. Hutchinson. 1971. Experimental measurement of internal and external damping p roperties of tree limbs. ASAE Paper No. 69 818. St. Joseph, Mich.: ASAE. Hoag, D.L., J.R. Hutchinson, and R.B. Fridley. 1969. Effect of proportional, nonproportional and nonlinear damping on dynamic response of tree limbs. ASAE Paper No. 69 125. St. Joseph Mich.: ASAE. Industry Profile: Fruit and tree nut farming. Available at: http://premium.hoovers.com/subscribe/ind/fr/profile/basic.xhtml?ID=372 Accessed 29 June 2009. Horvath, E., and G. Sitkei. 2001. Energy consumption of selected tree shakers under different operational conditions. J. Agric. Engng. Res. 80(2):191 199. Horvath, E., and G. Sitkei. 2005. Damping properties of plum trees shaken at their trunks. Trans. ASA E 48(1):19 25. Hussain, A.A.M., G.E. Rehkugler, and W.W. Gunkel. 1975. Tree limb response to a periodic discontinuous sinusoidal displacement. Trans. ASAE 18(4):614 617. Igoe, T. 2005. MMA 7260 Q. ITP, New York University. Available at: http://itp.nyu.edu/ physcomp/sensors/Reports/MMA7260Q. Accessed 2 9 June 2009. Janick, J. 2005. Fruit & nut crops. Available at: http://www.hort.purdue.edu/newcrop/tropical/lecture_34/fruits_nuts_R.html Accessed 29 June 2009. Jutras, P.J., and G.E. Coppock. 1958. Mechanizati on of citrus fruit picking. Proc. Fla. State Hort. Soc 71:201 204. Kraft, M. 1997. Development of a digital micromachined accelerometer employing oversampling conversion. PhD diss. Coventry, UK: Coventry University, School of Engineering. Available at: ht tp://users.ecs.soton.ac.uk/mk1/. Accessed 29 June 2009.

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198 BIOGRAPHICAL SKETCH Sajith Kumar Jose Udumala Savary was born in 1981, to U. Savary and K. Alphonsamma in Pondicherry, India. He attended the Birla Institute of Technology and Science (B.I.T.S.), Pilani, India from 1999 to 2004. He earned his Master of Science degree in m ath ematics and Bachelor of Engineering degree in e lectrical and e lectronics as a part of c oncurrent degree program in May 2004. He joined the University of Florida to pursue his higher education. He received his Master of Science in c omputer e ngineering and a gricultural and b iological e ngineering from the Univer sity of Florida in August 2008 and December 2009, respectively