Optimal Design of Parallel Robots for the Prescribed Regular Dexterous Workspace

Abstract

This paper presents a method for determining design parameters of parallel robots (PRs) in its optimal kinematic design. To produce a more compact and economical PR, the determination of an optimal workspace is important. This includes defining a workspace that encases the prescribed regular dexterous workspace (PRDW). Two requirements should be simultaneously satisfied: ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) the local or global performance index; ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) a regular shape. In this paper, the optimal problem is firstly discussed and translated into two linear problems. Then, an optimal design procedure which adopts the generalized pattern search algorithm in the genetic algorithm and direct search toolbox of Matlab is proposed to solve these problems. Taken as an example, a linear Delta robot is designed for the four different PRDWs, and its optimal result provides some useful information in measuring the distance between a PRDW and the maximal sized normalized robot. On the basis of the value of distance, some wrong solutions of PR are clarified. It is concluded that the optimal design method is useful for the design and comparison of a general PR.