This paper presents a new idea to determine a set of optimal design parameters of a linear Delta robot (LDR) whose workspace is as close as possible of being equal to a prescribed cuboid dexterous workspace (PCDW). The optimal design procedure on the basis of three algorithms is introduced in this paper. The kinematic problem is analyzed in brief to determine the design parameters and their relation. Two algorithms are designed to determine the reachable, rectangular dexterous workspace, and the maximal inscribed rectangle of dexterous workspace in the O-xy plane. Another algorithm is used to solve the optimal problem. As applying example, the results of four cases PCDW to LDR are presented. And the design result is compared with a new concept of the distance between the best state of the LDR and the requirement of the operation task. The method and result of this paper are very useful for the design and comparison of the parallel robot.
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.
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