Methodologies for the optimal design of parallel manipulators

In this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two di erent strategies, resulting in two di erent types of optimization problem are considered. The rst strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two speci c formulations of the constrained problem are proposed. The rst constrained problem simply aims to t the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well-conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2-dof planar parallel manipulator, and the nal formulation is also applied to a 3-dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators