An Inverse Force Analysis of a Planar Two-Spring System

[+] Author and Article Information
T. M. Pigoski

Merritt Systems Incorporated, Merritt Island, FL

J. Duffy

Center for Intelligent Machines and Robotics, University of Florida, Gainesville, FL

J. Mech. Des 117(4), 548-553 (Dec 01, 1995) (6 pages) doi:10.1115/1.2826717 History: Received August 01, 1993; Revised April 01, 1995; Online December 11, 2007


A closed-form inverse force analysis was performed on a planar two-spring system. The two springs were grounded to pivots at one end and attached to a common pivot at the other. A known force was applied to the common pivot of the system, and it was required to determine all of the assembly configurations. By variable elimination, a sixth degree polynomial in the resultant length of one spring was derived, and from this, six real solutions of the point of application of force were obtained. Following this, the applied force was incremented along a line and the six paths of the moving pivot were tracked starting from the zero-load configurations. An analysis of these results showed stability phenomena indicating the workspace of this system contained regions of negative spring stiffness and points of catastrophe.

Copyright © 1995 by The American Society of Mechanical Engineers
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