Numerical workspace optimization for a 3-DOF delta parallel robot on constrained geometric solid models

Abstract

For the workspace optimization of Delta Parallel Robot (DPR), this paper employs Geometric Modeling Kernel (GMK) to construct DPR’s solid workspace model constrained by two categories of angles with non-toroidal boundaries. Leveraging slicing and interpolating techniques, the maximal inscribed regular space within the DPR’s workspace is obtained in conjunction with numerical optimization methods. With the objective of maximizing effective volume utilization (the volume ratio between the prescribed regular space to the DPR’s workspace) and a prescribed regular space dimension, the Hook-Jeeves direct search method is coupled with the Interior-Point method to attain the optimal geometric DPR parameters on the constrained solid model of workspace. The effectiveness of the algorithm is validated through a design case. This numerical optimization methodology possesses generality, intuitiveness, precision, and high efficiency, theoretically applicable to the workspace optimization for other parallel mechanisms.