A novel method for optimal path synthesis of mechanisms based on tracking control of shadow robot

Abstract

In this paper, we present a more effective and robust approach for synthesizing mechanisms such that their path is optimized with respect to the desired trajectory, especially in the case where a particular set of crank angles or timings is also required. Our approach is based on the introduction of a shadow robot that is equivalent to the mechanism and finding an optimal control for it to track the desired trajectory. We propose a contour-error based proportional-derivative (PD) objective function that is inspired by well-known concepts of tracking control theory. This objective function addresses the nature of path synthesis problem more accurately and efficiently. Furthermore, we devised appropriate formulation and adopted an existing global optimization technique to solve the problem. We found that our approach leads to a better optimal solution with higher degree of robustness. We demonstrate the effectiveness of the approach by describing several numerical examples.