Dimensional synthesis of motion generation in a spherical four-bar mechanism

A new objective function for optimizing spherical, four-bar mechanisms for motion generation is presented. Rigid-body poses of a spherical four-bar mechanism in a standard installation position are investigated, and a normalization processing method is proposed. After processing the coupler points of the mechanism, the feature points generated are located on the circles. The formation principle of the feature coupler circles is analysed, and the internal relationship between the centre angle of the adjacent feature points on the feature coupler circles and the coupler angle of the spherical four-bar mechanism is determined. An input angle determination method is proposed for the spherical four-bar mechanism in a general installation position. An objective function is then established to optimize the basic dimensional types, relative input angles, and installation position parameters of the desired spherical four-bar mechanism. The proposed method is applicable to both prescribed and unprescribed timing problems. Notably, the dimension of the optimization variables is only eight, which is exceptionally low for multiple position motion generation without prescribed timing; therefore, the global optimal solution is more easily obtained. The optimization process is carried out by the genetic algorithm. The feasibility and effectiveness of our proposed method are demonstrated by examples.