Multi-Objective Mechanism Design Using a Bi-Level Game Theoretic Formulation

Abstract

This paper considers the design of a high speed mechanism as a multi objective optimization problem wherein the kinematic and dynamic criteria are optimized simultaneously. The kinematic criteria include minimization of the structural error and a minimization of deviation of the transmission angle from its ideal value. The dynamic criterion used is minimization of the peak torque required to drive the input link over a cycle. A Stackelberg (leader-follower) game theoretic approach is proposed to solve the multiobjective problem. Three variants, wherein both the kinematic and the dynamic criteria are treated as the leader, are considered. The design variables are the mechanism dimensions. A computational procedure using sensitivity information is proposed for approximating rational reaction sets needed for capturing exchange of information between the leader and the follower problems. A numerical example dealing with the design of a path generating 4-bar mechanism is presented. It is shown that significant improvement in both kinematic and dynamic performance measures is simultaneously achieved using the proposed approach.