Using Optimization for the Mixed Exact-Approximate Synthesis of Planar Mechanisms

Exact synthesis algorithms for planar mechanisms for rigid-body guidance are limited by the number of poses the mechanism can position the rigid-body in Euclidean space. The mixed exact-approximate synthesis algorithm described guides a rigid exactly through two positions and approximately through n guiding positions. It breaks down a rigid-body guidance task into n sub-problems of three positions to be solved by an exact synthesis algorithm. A novel algorithm utilizing MATLAB’s constrained non-linear optimization tools is proposed. The algorithm can be utilized to find within a bounded design parameter space the RR dyad that exactly reaches two positions and minimizes the distance to n positions. Two such dyads can be synthesized independently and then combined to yield a planar four-bar mechanism. An example using the proposed algorithm to design a planar four-bar mechanism to solve McCarthy’s 11-position synthesis problem stated at the 2002 ASME Conference is included.