Selective Precision Synthesis—A General Method of Optimization for Planar Mechanisms

Abstract

A general method of optimal design of planar mechanisms is presented here called Selective Precision Synthesis (SPS for short), suitable for path, motion or function generation, with different arbitrary limits of accuracy at various discrete positions. It was found that the method yields fundamentally stable solutions: while in closed-form synthesis, small changes in prescribed values often result in very different solutions or no solutions at all, in SPS small perturbations in problem specifications often produce only small variations in the synthesized linkage dimensions. Such stability is rarely found in Burmester theory and other synthesis techniques. Applying nonlinear programming and introducing the dyadic construction of mechanisms, the SPS technique is applicable to the synthesis of most planar mechanisms including four-bar, five-bar, multi-loop, multi-degree of freedom and adjustable mechanisms. Also, dyadic construction simplifies the optimization process and renders the method readily manageable in interactive computer-aided design. The SPS digital computer programs for batch and tele-processing are made available to interested readers.

Optimum exact/approximate point synthesis of planar mechanisms

“…In many applications only two or three exact positions suffice. Thus a hybrid of exact/approximate point synthesis approach would free the designer from having to specify points exactly if the problem does not require it [26][27][28][29][30][31][32]. The main focus in this chapter is on the exact/approximate synthesis.…”

Optimal synthesis of mechanisms with genetic algorithms

“…One of the first authors who studied these methods was Han [10], whose work was later improved by Kramer and Sandor [11] and Sohoni and Haug [12]. They optimized one of the most common goal functions: the error between the points tracked by the coupler and its desired trajectory.…”

Topology and Dimensional Synthesis of Linkage Mechanism Based on the Constrained Superposition Method

“…The positions of joint A, joint B and joint C are (0, 0), (10, -10) and (10,10), respectively. The input distance is set to be 4 units and our objective is to maximize the distance between the initial position and the final position of joint B.…”

“…Khade et al, Kwong et al and Hall is one of the first to come up with the idea of optimal design for kinematics synthesis [6][7][8]. Han, Kramer, Sandor, Sohoni and Haug optimized the error between the points tracked by the coupler and its desired trajectory for mechanism design [9][10][11] . The problem setup of the optimal design problem using numerical method mainly consists of three parts:…”