Optimal Synthesis of Planar Mechanisms via an Extensible-Link Approach

This paper presents a novel approach to optimize the design of planar mechanisms with revolute joints for function-generation or path synthesis. The proposed method is based on the use of an extensible-link mechanism model whose strain energy is minimized to find the optimal rigid design. This enables us to get rid of assembling constraints and the use of natural coordinates makes the objective function simpler. The optimization strategy is divided into two stages: the first one relies on multiple partial optimizations and provides hot starting point for the second stage which involves all the variables and all the energy contributions. The question of finding the global optimum is reviewed. Instead, a simple algorithm is proposed to explore the design space and to find several local optima among which the designer may choose the best one taking other criteria into account (e.g. stiffness, collision, size,. . . ). Two applications are presented to illustrate the whole process