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

Abstract

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.

TGA-based solutions map method for four-position synthesis of planar 4R linkage

“…Gogate and Matekar (2012) used the evolutionary algorithm for the approximate motion synthesis of the 4R linkage and then applied this method to the synthesis of the Watt-I sixlink mechanism (Gogate and Matekar, 2014). Sundram and Larochelle (2015) solved the mixed exact-approximate synthesis problem based on the constrained nonlinear optimization toolbox of MATLAB. Similarly, Ravani and Roth (1983) used kinematic mapping to transform the problem of approximate motion synthesis into that of curve fitting in the image space, while Ge et al (2017) reduced this problem to that of finding a G-manifold that can best fit points in the image in the least-squares sense.…”