A Methodology for Determining the Maximal Regular-shaped Dexterous Workspace of the PMs

A methodology for determining the maximal regular-shaped dexterous workspace (MRsDW) of parallel manipulators (PMs) is proposed. The MRsDW is the maximal subset of the dexterous workspace with prescribed dexterity, and has a regular shape such as a circle or rectangle for the planar and a cuboid or cylinder for the spatial situation. It is one of the objects of optimal design of the PMs while the workspace size and shape are considered. The concept of the utilizable ratio of dexterous workspace (URDW) is introduced, which is a new measure for the rationality of design parameters of a PM. The methodology based on the stratified workspace boundary search technique can determine both the dexterous workspace and their MRsDW. After the problem of determination of the MRsDW is defined formally, a numerical method is proposed to solve this problem by three algorithms. Finally, the validity and efficiency of the proposed method are verified through application of the 2-DOF planar PM and the linear delta robot.