Optimal synthesis for a continuous prescribed dexterity interval of a 3-dof parallel planar manipulator for different prescribed output workspaces

In this paper, a numerical optimization methodology for synthesizing parallel manipulators for a desired workspace, previously developed by the authors, is extended to determining the design of a three degree of freedom planar parallel manipulator with regard to a specified continuous dexterity capability. In particular the extended method seeks, for a prescribed (2-D) physically reachable output workspace, a design that yields an output workspace that will not only fully enclose the prescribed physical output workspace with the specified continuous dexterity capability at each point, but will also be optimally conditioned. The performance index chosen corresponds to the condition number of the Jacobian of the manipulator, and the optimum design with respect to the manipulator design variables, is obtained by minimizing the condition number over the enclosed prescribed physical workspace for a continuous range of platform orientations. The proposed optimization methodology produces convincing results, indicating it to be a stable and efficient numerical method for designing planar parallel manipulators for continuous dexterity capability. Copyright (c) 2006 John Wiley & Sons, Ltd.