Inverse Analysis of a Planar Two-Spring System

摘要

In this article, a novel closed-form solution to the inverse analysis of a planar two-spring system is presented which may be extendible to the spatial three-spring system. It involves finding the six equilibrium configurations of a system of two springs connected at one end to a common pivot and at the other to a base. This formulation involves a transformation into polar coordinates where a sixth degree polynomial is obtained in terms of tan-half-angle for the rise angle of one of the springs. The derivation and the coefficients of this polynomial are much simpler than those obtained by Pigoski and Duffy, "An inverse force analysis of a planar two-spring system," presented at the First Austrian IFTOMM Symposium, Seggauberg, Austria, July 4-9, 1993, also in press Trans. ASME where a sixth degree polynomial in one of the spring lengths was obtained.