This paper looks at spatio-geometric modeling of elastically coupled rigid bodies. Desirable properties of compliance families are defined (sufficient diversity, parsimony, frame-indifference, and port-indifference). A novel compliance family with the desired properties is defined using geometric potential energy functions. The configuration-dependent wrenches corresponding to these potential functions are derived in a form suitable for automatic computation.

Issue Section:
Technical Papers
Topics:
Modeling, Computation, Potential energy
1.
Dimentberg, F., 1965, The Screw Calculus and Its Applicalions in Mechanics, U.S. Dept. of Commerce. Translation No. AD680993.
2.
Griffis
M.
, and
Duffy
J.
,
1991
, “
Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement
,”
ASME Journal of Mechanical Design
, Vol.
113
, pp.
508
–
515
.
3.
Howard, W., Zˇefran, M., and Kumar, V., 1995, “On the 6 × 6 Stiffness Matrix for Three Dimensional Motions,” Proc. 9th IFToMM, pp. 1575–1579.
4.
Howell, L., and Midha, A., 1994, “Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms,” ASME Design Technical Conferences, 23rd Biennial Mechanisms Conference, pp. 405–412.
5.
Huang, S., and Schimmels, J., 1997, “The Realizable Space of Spatial Stiffnesses Achieved With a Parallel Connection of Simple Springs,” Proc. of the ASME Dynamic Systems and Control Division, pp. 519–525.
6.
Loncˇaric´
J.
,
1987
, “
Normal Forms of Stiffness and Compliance Matrices
,”
IEEE Trans. on Robotics and Automation
, Vol.
3
, pp.
567
–
572
.
7.
Loncˇaric´, J., 1988, “On Statics of Elastic Systems and Networks of Rigid Bodies,” Technical Report SCR TR 88-13, Systems Research Center, University of Maryland.
8.
Marsden, J., and Hughes, T., 1983, Mathematical Foundations of Elasticity, Prentice-Hall.
9.
Patterson
T.
, and
Lipkin
H.
,
1993
a, “
A Classification of Robot Compliance
,”
ASME Journal of Mechanical Design
, Vol.
115
, pp.
581
–
584
.
10.
Patterson
T.
, and
Lipkin
H.
,
1993
b, “
Structure of Robot Compliance
,”
ASME Journal of Mechanical Design
, Vol.
115
, pp.
576
–
580
.
11.
Zˇefran, M., and Kumar, V., 1997, “Affine Connections for the Cartesian Stiffness Matrix,” Proc. IEEE Int. Conf. on Robotics and Automation, pp. 1376–1381.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.