Kinematic modeling and optimal design of a partially compliant four-bar linkage using elliptic integral solution

Abstract

This paper deals with the kinematic modeling and optimal design of compliant mechanisms with one flexible joint designed from a rigid four-bar linkage. An equivalent mechanism is proposed to describe the large-deflection motion of a compliant four-bar linkage. In light of the elliptic integral solution, the kinematics and strain energy of the compliant four-bar linkage are derived and verified by a numerical comparison study. Then, by taking the path deviation and strain energy as two objectives, the multi-objective optimization problem is solved at a given initial configuration of the rigid mechanism, followed by a discussion of the best initial configuration where the rigid joint is replaced by elastic flexures. Both the finite element analysis and experimental verification are carried out. The results show that the output motion of the optimized compliant mechanism matches the desired path very well, which demonstrates the feasibility of designing compliant mechanisms by this approach.