This paper presents a systematic theory for metric relations between the invariant properties of displacement groups, and shows this theory application to mechanism kinematics. Displacement groups, their invariant properties and operations are briefly described. Kinematic constraints are then introduced as tools for relating abstract group properties to actual mechanism constraints. Criteria and operating rules to employ metric relations for the generation of a meaningful set of closure equations for kinematic chains are detailed.

1.
Albala
H.
,
1982
, “
Displacement Analysis of the General N-Bar, Single-Loop, Spatial Linkage
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
104
, pp.
504
525
.
2.
Angeles, J., Hommel, G., and Kovacs, P., eds., 1993, Computational Kinematics, Kluwer Academic Publisher.
3.
Duffy, J., 1980, Analysis of Mechanisms and Robot Manipulators, Edward Arnold.
4.
Fanghella
P.
,
1988
, “
Kinematics of Spatial Linkages by Group Algebra: A Structure-Based Approach
,”
Mechanism and Machine Theory
, Vol.
23
, pp.
171
183
.
5.
Fanghella, P., 1993, “A Systematic Approach to the Kinematics of Single-Loop Mechanisms and Serial Robot Arms,” accepted by Meccanica.
6.
Fanghella
P.
, and
Galletti
C.
,
1989
, “
Particular or General Methods in Robot Kinematics?
Mechanism and Machine Theory
, Vol.
24
, pp.
383
394
.
7.
Fanghella, P., and Galletti, C., 1993, “A Modular Method for Computational Kinematics,” Computational Kinematics, J. Angeles et al., ed., Kluwer Academic Publisher, pp. 275–284.
8.
Fanghella
P.
, and
Galletti
C.
,
1994
, “
Mobility Analysis of Single-Loop Kinematic Chains: an Algorithm Approach Based on Displacement Groups
,”
Mechanism and Machine Theory
, Vol.
29
, pp.
1187
1204
.
9.
Herve´
J.
,
1978
, “
Analyse Structurelle des Me´canismes par Groupe des De´placements
,”
Mechanism and Machine Theory
, Vol.
13
, pp.
437
450
.
10.
Hiller, M., and Kecskeme´thy, A., 1993, “Dynamics of Multibody System with Minimal Coordinates,” NATO Advanced Institute on Computer Aided Analysis of Rigid and Flexible Mechanical Systems, Troia, Portugal.
11.
Kramer, G. A., 1992, “Solving Geometric Constraint Systems,” MIT Press.
12.
Liu
Y.
, and
Popplestone
R.
,
1994
, “
A Group Theoretic Formalization of Surface Contact
,”
The International Journal of Robotics Research
, Vol.
13
, pp.
148
161
.
13.
Raghavan, M., and Roth, B., 1990, “A General Solution of the Inverse Kinematics of All Series Chains,” Proc. Eight CISM-IFToMM Symp. on Theory and Practice of Robot and Manipulators, Cracow, Poland, pp. 24–32.
14.
Samuel
A. E.
,
McAree
P. R.
, and
Hunt
K. H.
,
1991
, “
Unifying Screw Geometry and Matrix Transformations
,”
International Journal of Robotics Research
, Vol.
10
, pp.
454
472
.
15.
Stifter, S., and Lenarcic, J., eds., 1991, Advances in Robot Kinematics With Emphasis on Symbolic Computation, Springer-Verlag.
16.
Thomas
F.
, and
Torras
C.
,
1988
, “
A Group Theoretic Approach to the Computation of Symbolic Part Relations
,”
IEEE Journal of Robotics and Automation
, Vol.
4
, pp.
622
634
.
17.
Wampler
C. W.
,
Morgan
A. P.
, and
Sommese
A. J.
,
1990
, “
Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
112
, pp.
59
68
.
This content is only available via PDF.
You do not currently have access to this content.