Optimum design of multi-degree-of-freedom closed-loop mechanisms and parallel manipulators for a prescribed workspace using Monte Carlo method

Abstract

In this work, we use the Monte Carlo method in conjunction with gradient based optimization algorithms to optimally design multi-degree-of-freedom parallel manipulators and closed-loop mechanisms. The design procedure takes into account practical constraints such as joint limits and guarantees well-conditioning of the desired workspace. As a first step, an appropriate bounding box representing the wanted workspace is obtained by using the Monte Carlo method and then the geometrical dimensions of the manipulator are obtained through a gradient based optimization method by accounting for the joint and other constraints. The computational advantages of the Monte Carlo technique over other search based methods in evaluating the objective function for the optimization problem is illustrated. The constraint Lagrange multipliers are obtained and sensitivity of the workspace dimensions to the constraints on joint limits and conditioning have been demonstrated. The approach is illustrated with the design of a two-degree-of-freedom planar 5-bar closed-loop mechanism and a spatial, six-degree-of-freedom Stewart platform manipulator.