Optimal Synthesis for Path Generation for a Spherical Four-Bar Mechanism

Abstract

Abstract. An optimal synthesis method is proposed to solve the path generation problem of a spherical four-bar mechanism. A kinematic model of the coupler point of the spherical four-bar mechanism is established, and the coupler point of the mechanism is processed to generate a feature coupler circle (FCC). An analysis of the formation principle of the feature coupler circle reveals an inherent relationship between the trace circle and the feature coupler circle of the spherical four-bar mechanism. A method is proposed to determine the input angles corresponding to coupler points. The main advantages of this method are that there are few optimization variables, the variable dimensions do not change as the number of prescribed points increases, and the solution accuracy is high. In particular, the dimension of the optimization variables for the path generation problem is only 6 and 5 for unprescribed and prescribed timing, respectively. A differential evolution (DE) algorithm is used in the method to optimize the objective function. Three examples are presented to demonstrate the feasibility and efficacy of the proposed method. Compared to classic optimization methods, the number of function evaluation decreased by 99%, and the error has been reduced by 92%.