A General Approach for Optimal Design of Parallel Manipulators

This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators. A unified framework is proposed for optimal design of parallel manipulators. By observation that regular (e.g., hyperrectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects both requirements on the workspace shape and quality. Dexterity index is utilized to characterize the effectiveness of the workspace. Other performance indices, such as manipulability, stiffness, and minimal natural frequency, can be readily included. The optimal design problem is then formulated to find a manipulator geometry that maximizes the effective regular workspace. Since the optimal design problem is a constrained nonlinear optimization problem without explicit analytical expression, the controlled random search (CRS) technique, which was reported robust and reliable, is applied to numerically solve the problem. Some typical parallel manipulators, the five-bar parallel linkage, the 3RRR planar parallel manipulator, the rotational DELTA robot, and the Stewart-Gough platform are employed as examples to demonstrated the design procedure.