Dimensional synthesis of a spherical linkage crank slider mechanism for motion generation using an optimization algorithm

Abstract. In the present study, Fourier theory is applied to establish the expression of rigid-body poses of a spherical four-bar crank slider rigid-body guidance mechanism. According to an analysis of the harmonic components of the trajectory curve and rigid-body rotation angle, it has a certain relationship with the geometric parameters of the mechanism. On this basis, the rigid-body poses are normalized by preprocessing. Then, the rotation angle of the curve around the y axis and z axis is determined, respectively. The theoretical formulas used for calculating the real sizes and the installation position parameters of the desired spherical four-bar crank slider rigid-body guidance mechanism are established. Besides this, a genetic optimization algorithm and theoretical formulas are applied to solve the dimensional synthesis of motion generation for the spherical four-bar crank slider mechanism. The effectiveness of the proposed method is illustrated by an example. The maximum Euclidean distance error of the rigid-body position of the results with the highest similarity is 0.0086, and the average Euclidean distance error is 0.0044. The maximum error of the rigid-body orientation is 0.0179, and the average error is 0.0065.