The Performance Indices Optimization of a Symmetrical Fully Spherical Parallel Mechanism for Dimensional Synthesis

The 3(UPS)-S fully spherical parallel manipulator is the most famous fully spherical parallel robot. Therefore, dimensional synthesis of the manipulator to optimize kinematics and dynamic performance indices is very important. In this paper, we proposed a new kinematics index that is called global workspace conditioning index (GWCI). This index is a suitable criteria to compare workspace of the spherical parallel manipulators. Using this index, and other performance indices such as; Global Conditioning Index (GCI), Global Gradient Index (GGI) and Dynamic Dexterity Index (DDI), we optimize dimensions of the manipulator based on single and multi-objective optimizations. Two dimensionless design parameters are advised to obtain an optimal solution. The manipulator is optimized with regard to the joints constraint and range of motion actuators as functions of the design parameters. For this purpose, we elaborate kinematics analyses and also obtain the mass matrix of the manipulator using its kinetic energy. Next, single-objective optimizations based on Genetic Algorithm (GA) and Pattern Search (PS) are presented. The comparison between GA and PS in the single-objective optimization shows that the accuracy of both methods is rather equal, but in elapsed time PS is better than GA. Finally, multi-objective evolutionary algorithm based on the non-dominated sorting genetic algorithm II (NSGA-II) is adopted to find the true optimal solutions and Pareto fronts. The obtained solution will be a set of optimal geometric parameters to adjust the dynamic and the kinematic performance.