Spatial elastic behavior is characterized by a 6×6 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.
The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division January 21, 2000. Associate Editor: E. Fahrenthold.
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Huang , S., and Schimmels, J. M. (January 21, 2000). "The Duality in Spatial Stiffness and Compliance as Realized in Parallel and Serial Elastic Mechanisms ." ASME. J. Dyn. Sys., Meas., Control. March 2002; 124(1): 76–84. https://doi.org/10.1115/1.1434273
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