Path synthesis of four-bar mechanism using harmony search optimization

Abstract

The study of four-bar linkage to trace a desired path is an important part of obtaining the optimal geometry of a four-bar linkage which is used in design. When the number of the precision points exceeds a certain number, it is not possible to apply or it is difficult to apply analytical methods. Alternatively some intelligence optimization methods can be used based on the complexity of the problem. Path synthesis of four-bar linkages with multiple number of precision points has been illustrated as an optimization problem. The objective to be minimized is sum square error of all the points reached by the coupler point. The important constraints included are 1) Grashof’s condition to have a crank rocker linkage,2) the transmission angle criterion and 3) input link angle sequence. The variables included are the link lengths and angles. A new optimization scheme known as harmony search method is implemented to get the optimum solutions. Harmony search method is based on musical performance process that occurs when a musician searches for a better state of harmony. The pitch of each musical instrument determines aesthetic quality just as objective function value assigned to variables. A computer programme based on this algorithm is implemented in MATLAB to obtain the optimum dimension of four-bar linkage. The function files are employed to generate initial feasible solutions and effective object function based on penalty function method. Four examples are illustrated to show the effectiveness of the method. It is found that the method is quite convenient and works in-par with other non conventional optimization methods like genetic algorithms and particle swam optimization.