Optimal design of a parallel machine based on multiple criteria

This paper proposes to optimally design a parallel machine based on multiple criteria. Many criteria, workspace, condition number, accuracy, stiffness, maximum velocity, and maximum force, are considered. The optimal design problem is proposed as to find a set of design parameters such that (a) the Cartesian workspace generated by the resulting manipulator contains a prescribed workspace; (b) the resulting manipulator possesses a good condition number at each points in the prescribed workspace; (c) the resulting manipulator possesses good performance on accuracy, stiffness, velocity/force transmission factor. By some manipulations, the requirements on the latter four criteria are reduced to constraints on singular values of the kinematic Jacobian. A trade-off must be made since there're opposite requirements among those four criteria. The singular values of kinematic Jacobian are limited in a given interval to guarantee good properties. All the requirement are finally reduced to polynomial inequalities with respect to design parameters. The optimal design problem is transformed into a Max-Det optimization problem that can be efficiently solved. The Orthoglide is used as an example to demonstrate the procedure.