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A Reverse Force Analysis of a Spatial Three-Spring System

Y. Zhang
C. Liang
Journal / Anthology

Mechanical Machine Theory
Year: 1997
Volume: 32
Issue: 6
Page range: 667-678

A reverse force analysis of a spatial three-spring system is presented which determines equilibrium positions when an external force is applied. The system consists of three linear springs, each of which is attached 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 multiple equilibrium positions are computed by deriving and solving a 22nd degree polynomial in a single spring length. The degree of this polynomial is verified in the Appendix independently of the analysis, using geometry. Following this, corresponding pairs of the remaining two spring lengths are computed, which determine the multiple equilibrium positions. These results have been verified by numerical examples. The symbolic computation was performed by the computer algebra system Mathematica.

*Engineering > Mechanical and Structural Engineering