More Effective Optimum Synthesis of Path Generating Four-Bar Mechanisms

The one-phase synthesis method using evolutionary or heuristic optimization algorithms can successfully solve the dimensional synthesis problems of path generating four-bar mechanisms discussed in the literature, where the input angles are usually used as design variables and the constraint of the rotational sequence of the input angles is necessary. However, there is still room for improvement in solution reliability and accuracy. To understand the influence of the input angles used as design variables, a new one-phase synthesis method without using the input angles as design variables is presented where the square deviation of the nearest distance between the target point and the coupler curve is used as the error metric and the differential evolution is used to solve the optimum synthesis problems. A scale-rotation-translation transformation technique, which can transform the coupler curve of the initial guess nearer to the desired curve in a similar scaling, orientation and location, is proposed. Findings show that the new one-phase synthesis method can improve solution accuracy markedly. Moreover, the scale-rotation-translation transformation technique for the initial guess is effective to improve solution reliability, accuracy or efficiency. Keywords—evolutionary algorithm; dimensional synthesis; mechanism optimization; path generation; scale-rotation-translation transformation