Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel
Document Type
Article
Publication Date
12-1998
Source Publication
Journal of Mechanical Design
Source ISSN
1050-0472
Abstract
In this paper, the synthesis of an arbitrary spatial stiffness matrix is addressed. We have previously shown that an arbitrary stiffness matrix cannot be achieved with conventional translational springs and rotational springs (simple springs) connected in parallel regardless of the number of springs used or the geometry of their connection. To achieve an arbitrary spatial stiffness matrix with springs connected in parallel, elastic devices that couple translational and rotational components are required. Devices having these characteristics are defined here as screw springs. The designs of two such devices are illustrated. We show that there exist some stiffness matrices that require 3 screw springs for their realization and that no more than 3 screw springs are required for the realization of full-rank spatial stiffness matrices. In addition, we present two procedures for the synthesis of an arbitrary spatial stiffness matrix. With one procedure, any rank-m positive semidefinite matrix is realized with m springs of which all may be screw springs. With the other procedure, any positive definite matrix is realized with 6 springs of which no more than 3 are screw springs.
Recommended Citation
Huang, S. and Schimmels, Joseph M., "Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel" (1998). Mechanical Engineering Faculty Research and Publications. 56.
https://epublications.marquette.edu/mechengin_fac/56
Comments
Journal of Mechanical Design, Vol. 120, No. 4 (December 1998): 520-526. DOI.