Achieving an Arbitrary Spatial Stiffness with Springs Connected in Parallel

[+] Author and Article Information
S. Huang, J. M. Schimmels

Department of Mechanical and Industrial Engineering, Marquette University, Milwaukee, WI 53201-1881

J. Mech. Des 120(4), 520-526 (Dec 01, 1998) (7 pages) doi:10.1115/1.2829309 History: Received April 01, 1997; Revised August 01, 1998; Online December 11, 2007


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.

Copyright © 1998 by The American Society of Mechanical Engineers
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