A REVERSE FORCE ANALYSIS OF A SPATIAL 3-SPRING SYSTEM

A reverse force analysis of a spatial three-spring system is presented which determines equilibrium positions when an external force is appl ied. The system consists of three linear springs, each of which is att ached to the ground via pivots which form a triangular base. The three springs are joined at a common pivot at the other end, thus forming a tetrahedron. A known force is applied at the common pivot. The multip le equilibrium positions are computed by deriving and solving a 22nd d egree polynomial in a single spring length. The degree of this polynom ial is verified in the Appendix independently of the analysis, using g eometry. Following this, corresponding pairs of the remaining two spri ng lengths are computed, which determine the multiple equilibrium posi tions. These results have been verified by numerical examples. The sym bolic computation was performed by the computer algebra system MATHEMA TICA. (C) 1997 Elsevier Science Ltd.