Optimum Design of High-Speed 4-Bar Mechanisms Using a Bi-Level Game Theoretic Approach

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 criteria include minimization of input driving torque and shaking forces transmitted to the ground link. A Stackelberg (leader-follower) game theoretic approach is proposed to solve the multiobjective problem. Two variants, wherein both the kinematic and the dynamic criteria are treated as the leader, are considered. The design variables include mechanism dimensions and counterweight parameters. A partitioning of the design variables amongst the leader and follower objective functions is discussed. A computational procedure using sensitivity information is used 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.