Application of convex optimization in integrated design of five-bar mechanism

In this paper, we presented an integrated design methodology for a five-bar mechanism. Five-bar mechanisms are often used in applications that require high speed and high precision motion control. One example of such applications is the semiconductor wire bonding process. In this process, the tip acceleration needs to reach 10g to 15g with sub-micron precision and little vibration. In order to meet such strict design requirements, we first developed a dynamic equation for the rigid five-bar mechanism and obtained a simplified model for designing the structure distribution of the mechanism. Secondly, taking both mechanical and controller parameters as design variables, we formulated the settling time and overshoot functions of the closed-loop system and investigated the convexity features of them. By properly choosing optimal variables, we obtained a convex function which is treated as an objective function with a set of real constraints in an optimization problem. Finally, by optimization algorithm of differential evolution, we obtained a set of global optimal values including mechanical and controller parameters. The effectiveness of the proposed design approach is demonstrated by simulation results.