Accuracy Based Design of DELTA Parallel Manipulator

Abstract

Design of parallel manipulators for desired accuracy and workspace is an important functional design requirement. Accuracy of parallel manipulators can be categorized into kinematic and dynamic accuracy. Kinematic accuracy is attributed to active joint input errors, and dynamic accuracy is attributed to finite stiffness of the manipulator structure. In this study, a bi-level cascaded design approach is proposed that yields manipulators possessing maximum dynamic accuracy, desired kinematic accuracy along each DOF, and desired reachable workspace. The proposed approach is validated through accuracy centric design of a 3-RSS Delta parallel manipulator. In Level 1 design, a multi-objective optimization problem, that minimizes the stiffness index and condition number of the stiffness matrix is resolved through Genetic Algorithms. In Level 2 design, the Brent-Drekker numerical solver is employed to compute maximum allowable error in active joint inputs that lead to desired positioning error along each DOF of the Level 1 optimized parallel manipulator. A geometric error model is derived to evaluate exact maximum positioning errors along each DOF due to errors in active joint inputs. The bi-level cascaded approach yields a finite set of pareto-optimal design solutions that meet design requirements of accuracy and workspace. It is found that the proposed approach is significantly less computationally expensive than interval analysis and set inversion-based approaches.