Optimal synthesis of a spatial RRSS mechanism for path generation

A mathematical model of the coupler points generated by the revolute-revolute-spherical-spherical (RRSS) mechanism is established. A characteristic of the projection of feature points is identified by extending preprocessing to the coupler points. Based on this finding, the 16-geometric-parameter design process is divided into three steps. In the first step, a new objective function for optimizing the linkage angle parameters is presented. In the second step, an additional objective function based on the relationship of wavelet coefficients between the mechanism elliptical phase angles and coupler angles is proposed to optimize the linkage length parameters. In the third step, the remaining geometric parameters are calculated based on the relationship between the precision points and coupler points generated by the obtained geometric parameters. Because there are fewer independent variables in each step, the dimensionality reduction synthesis method can yield design solutions with high precision in a short time. Five examples are presented to demonstrate the efficacy of the proposed method.