The Synthesis of Parallel Manipulators for Optimal Desired Workspaces With Respect to the Condition Number

The main objective of this paper is to find a fundamentally sound and robust numerical methodology for synthesizing parallel manipulators for desired workspaces. The constrained optimization formulation presented here is aimed at determining a manipulator design so that a prescribed workspace is fully enclosed, but that the workspace is also well-conditioned with respect to some performance index. The particular manipulators used to illustrate and evaluate the formulation are planar 2- and 3-dof parallel manipulators. Solutions to the manipulator design problems are found in an efficient and convincing manner.