The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms

Document Type

Article

Publication Date

3-2002

Source Publication

Journal of Dynamic Systems, Measurement, and Control

Source ISSN

0022-0434

Abstract

Spatial elastic behavior is characterized by a 636 positive definite matrix, the spatial stiffness matrix, or its inverse, the spatial compliance matrix. Previously, the structure of a spatial stiffness matrix and its realization using a parallel elastic system have been addressed. This paper extends those results to the analysis and realization of a spatial compliance matrix using a serial mechanism and identifies the duality in spatial stiffness and compliance associated with parallel and serial elastic mechanisms. We show that, a spatial compliance matrix can be decomposed into a set of rank-1 compliance matrices, each of which can be realized with an elastic joint in a serial mechanism. To realize a general spatial compliance, the serial mechanism must contain joints that couple the translational and rotational motion along/about an axis. The structure of a spatial compliance matrix can be uniquely interpreted by a 6-joint serial elastic mechanism whose geometry is obtained from the eigenscrew decomposition of the compliance matrix. The results obtained from the analysis of spatial compliant behavior and its realization in a serial mechanism are compared with those obtained for spatial stiffness behavior and its realization in a parallel mechanism.

Comments

Journal of Dynamic Systems, Measurement, and Control, Vol. 124, No. 1 (March 2002): 76-84. DOI.

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