Optimal synthesis of four-bar path generator linkages using Circular Proximity Function

This paper presents a new objective function for the optimization of path-generator four bar linkages. A four-bar linkage includes four revolute joints, two of which are connected to the coupler link. These two joints, which are known as the moving joints of the linkage, have a remarkable characteristic: both trace circular curves. Using this fact, a new methodology is presented. In this methodology, a dyad is considered which exactly traces the desired path. On the plane attached to the moving link of the dyad, an unlimited number of points can be defined. Among these points, the point which traces a circular curve is very important since this point together with the moving joint of the dyad can be considered as the two moving joints of a four-bar linkage. In order to evaluate the path generated by each point and find the point that traces a near-circular curve, the Circular Proximity Function (CPF) is implemented. Using CPF, a new objective function is introduced that has the lowest number of optimization variables. The optimization process is carried out by the method of differential evolution (DE). Three example problems were solved which resulted in the synthesis of crank-rocker four-bar linkages. Three example problems are solved in this paper demonstrating the efficacy of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.