Synthesis of Compliant Mechanisms With Specified Equilibrium Positions

Abstract

This paper presents a synthesis procedure for a compliant four-bar linkage with three specified equilibrium configurations. The finite position synthesis equations are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Solutions to these design equations were computed using a polynomial homotopy solver. In order to provide a design specification, we first compute the six equilibrium configurations of a known compliant four-bar mechanism. We use these results as design requirements to synthesize a compliant four-bar. The solver obtained eight real solutions which we refined using a Newton-Raphson technique. A numerical example is provided to verify the design methodology.