Randomized Optimal Design of Parallel Manipulators.

This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework. Observing that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality. The effectiveness of a workspace is characterized by the dexterity of the mechanism over every point in the workspace. Other performance indices, such as manipulability and stiffness, provide alternatives of dexterity characterization of workspace effectiveness. An optimal design problem, including constraints on actuated/passive joint limits and link interference, is then formulated to find the manipulator geometry that maximizes the effective regular workspace. This problem is a constrained nonlinear optimization problem without explicitly analytical expression. Traditional gradient based approaches may have difficulty in searching the global optimum. The controlled random search technique, as reported robust and reliable, is used to obtain an numerical solution. The design procedure is demonstrated through examples of a Delta robot and a Gough-Stewart platform. Note to Practitioners—The kinematic/dynamic performance of a parallel manipulator highly depends on its geometry, e.g., link lengths, positions of fixed actuator, shape, and size of end-effector. In designing a parallel manipulator, it is a crucial step to determine the best geometry that satisfies practical design requirements. For a general parallel manipulator, this paper provides a unified framework to formulate the optimal design problem by considering some key kinematic criteria, like regularity and volume of workspace and dexterity. The latter one is closely related to stiffness and control accuracy. Since the optimal design problem is a nonlinear optimization problem without analytic expression, traditional gradient-based search algorithms have difficulty to solve the problem. The controlled random search technique is used to search the global optimum. The design procedure is applicable for general parallel manipulators. Other design criteria, such as stiffness and accuracy, can be readily included in the design formulation. [ABSTRACT FROM AUTHOR]