A complete analytical solution for the dimensional synthesis of 3-DOF delta parallel robot for a prescribed workspace

This paper presents an analytical approach for the dimensional synthesis of the 3-DOF Delta parallel robot for a prescribed workspace. The dimensional synthesis of parallel robots is a challenging problem for which obtaining an analytical solution is a cumbersome task and no appropriate analytical closed-form solution has been developed for the DPR so far. First, the workspace is analytically calculated based on inverse kinematic and it showed that the workspace of DPR comes from some geometric conditions. Afterward, the largest possible box which can be inserted in the workspace is obtained. Optimal analytical dimensional design for a prescribed workspace is calculated by considering three types of construction constraints. Optimization objectives based on subjective and the smallest robot criterion have been defined which is optimized by resorting to the so-called Lagrange multiplier method. The results revealed that in the best case of the existing industrial robots, workspace expression is only close to %87.29 of the optimal workspace of this paper and in optimal design it could have up to %51.70 smaller robot with the same given workspace. (C) 2020 Elsevier Ltd. All rights reserved.