Multi-objective optimization of mechanism design using a bi-level game theoretic formulation

This article 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 multi-objective 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 four-bar mechanism is presented. It is shown that significant improvement in both kinematic and dynamic performance measures is simultaneously achieved using the proposed approach.