| | Title Page |
| | Dedication |
| | Acknowledgement |
| | Table of Contents |
| | List of Tables |
| | List of Figures |
| | Abstract |
| | Introduction |
| | Linear noncommensurate systems |
| | Physical consistency of jacobian... |
| | Inverse velocity kinematics |
| | Manipulator manipulability |
| | Decomposition of spaces |
| | Summmary and conclusions |
| | Appendix |
| | Reference |
| | Biographical sketch |
| | Copyright |
|
| Full Citation |
| Material Information |
| |
Title: |
Algebraic properties of noncommensurate systems and their applications in robotics |
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Physical Description: |
xii, 124 leaves : ill. ; 29 cm. |
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Language: |
English |
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Creator: |
Schwartz, Eric Michael, 1959- ( Dissertant )
Doty, Keith L. ( Thesis advisor )
Bullock, Thomas E. ( Thesis advisor )
Staudhammer, John ( Reviewer )
Crane, Carl D. ( Reviewer )
Yeralan, Sencer ( Reviewer )
Phillips, Winfred M. ( Degree grantor )
Holbrook, Karen A. ( Degree grantor ) |
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Publisher: |
University of Florida |
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Place of Publication: |
Gainesville, Fla. |
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Publication Date: |
1995 |
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Copyright Date: |
1995 |
| Subjects |
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Subjects / Keywords: |
Electrical Engineering thesis, Ph. D
Robots -- Control systems ( lcsh )
Dissertations, Academic -- Electrical Engineering -- UF |
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Genre: |
bibliography ( marcgt )
non-fiction ( marcgt ) |
| Notes |
| |
Abstract: |
Several algebraic properties for systems in which either or both the input and output vectors have elements with different physical units. The condition son linear transformation A for a physically consistent noncommensurate system, u=Ax, are given. Linear noncommensurate systems do no generally have eigenvalues and eigenvectors. The requirements for noncommensurate linear systems do not have a physically consistent singular value decomposition. The manipulator Jacobian maps possibly noncommnesurate robot joint-rate vectores into noncommensurate twist vectores. The inverse velocity problem is often solved through the use of the pseudo-inverse of the Jacobian. This solution is generally scale and frame dependent. The pseudo-inverse solution is physically inconsistent, in general, requiring the addition of elements of unlike physical units. For some manipulators there may exist points—called decouple points—at which the pseudo-inverse of the Jacobian is physically consistent for all frames at these points. In decouple frames, the pseudo-inverse is shown to be equivalent to the weighted generalized-inverse with identity metrics. An entire class of nonidentity metrics used with the weighted generalized-inverse are shown to give identical solutions to the pseudo-inverse solution at decouple points. At decouple points, the twist and wrench spaces can be decomposed into two metric-independent subspaces. This decomposition is accomplished with kinestatic filtering projection matrices. The Mason/Raibert hybrid control theory of robotics is shown to be useful only for frames located at decouple points and is not optimal in any objective sense. The current manipulability theory, which depends on the eigensystem of various functions of the Jacobian, is shown to be invalid. Two new classes of manipulators are introduced, self-reciprocal manipulators and decoupled manipulators. The twists of freedom of a self-reciprocal manipulator are reciprocal. The class of self-reciprocal manipulators consists of planar manipulators, spherical manipulators, and prismatic-jointed manipulators. Decoupled manipulators are show to decouple at every point. The manipulators of this class are planar manipulators, prismatic-jointed manipulators, and SCARA-type manipulators. Results that are generalized from decoupled manipulators often prove to b invalid for manipulators that do not decouple at every point. |
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Thesis: |
Thesis (Ph. D.)--University of Florida, 1995. |
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Bibliography: |
Includes bibliographical references (leaves 119-123). |
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Statement of Responsibility: |
by Eric M. Schwartz. |
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General Note: |
Typescript. |
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General Note: |
Vita. |
| Record Information |
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Bibliographic ID: |
UF00082363 |
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Volume ID: |
VID00001 |
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Source Institution: |
University of Florida |
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Holding Location: |
University of Florida |
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Rights Management: |
All rights reserved by the source institution and holding location. |
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Resource Identifier: |
aleph - 002046269
oclc - 33417401
notis - AKN4201 |
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| Table of Contents |
|
Title Page
Page i
Dedication
Page ii
Acknowledgement
Page iii
Table of Contents
Page iv
Page v
List of Tables
Page vi
Page vii
List of Figures
Page viii
Page ix
Page x
Abstract
Page xi
Page xii
Introduction
Page 1
Page 2
Page 3
Page 4
Page 5
Page 6
Page 7
Page 8
Page 9
Page 10
Page 11
Page 12
Page 13
Page 14
Page 15
Page 16
Page 17
Page 18
Linear noncommensurate systems
Page 19
Page 20
Page 21
Page 22
Page 23
Physical consistency of jacobian functions
Page 24
Page 25
Page 26
Page 27
Page 28
Page 29
Page 30
Page 31
Page 32
Page 33
Page 34
Page 35
Page 36
Page 37
Page 38
Page 39
Inverse velocity kinematics
Page 40
Page 41
Page 42
Page 43
Page 44
Page 45
Page 46
Page 47
Page 48
Page 49
Page 50
Page 51
Page 52
Page 53
Page 54
Page 55
Page 56
Manipulator manipulability
Page 57
Page 58
Page 59
Page 60
Page 61
Page 62
Page 63
Decomposition of spaces
Page 64
Page 65
Page 66
Page 67
Page 68
Page 69
Page 70
Page 71
Page 72
Page 73
Page 74
Page 75
Page 76
Page 77
Page 78
Page 79
Page 80
Page 81
Page 82
Page 83
Page 84
Page 85
Page 86
Page 87
Page 88
Page 89
Page 90
Page 91
Page 92
Page 93
Page 94
Page 95
Page 96
Page 97
Page 98
Page 99
Page 100
Page 101
Summmary and conclusions
Page 102
Page 103
Page 104
Page 105
Appendix
Page 106
Page 107
Page 108
Page 109
Page 110
Page 111
Page 112
Page 113
Page 114
Page 115
Page 116
Page 117
Page 118
Reference
Page 119
Page 120
Page 121
Page 122
Page 123
Biographical sketch
Page 124
Page 125
Page 126
Copyright
Copyright
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