Title Page
 Table of Contents
 List of Tables
 List of Figures
 Linear noncommensurate systems
 Physical consistency of jacobian...
 Inverse velocity kinematics
 Manipulator manipulability
 Decomposition of spaces
 Summmary and conclusions
 Biographical sketch

Title: Algebraic properties of noncommensurate systems and their applications in robotics
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00082363/00001
 Material Information
Title: Algebraic properties of noncommensurate systems and their applications in robotics
Physical Description: xii, 124 leaves : ill. ; 29 cm.
Language: English
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 )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 1995
Copyright Date: 1995
Subjects / Keywords: Electrical Engineering thesis, Ph. D
Robots -- Control systems   ( lcsh )
Dissertations, Academic -- Electrical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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.
Thesis: Thesis (Ph. D.)--University of Florida, 1995.
Bibliography: Includes bibliographical references (leaves 119-123).
Statement of Responsibility: by Eric M. Schwartz.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00082363
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 002046269
oclc - 33417401
notis - AKN4201

Table of Contents
    Title Page
        Page i
        Page ii
        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
        Page xi
        Page xii
        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
        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
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
    Biographical sketch
        Page 124
        Page 125
        Page 126
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