Kinematic performance evaluation method of a 3-DOF redundantly actuated parallel manipulator

Error transformation can be used to evaluate the kinematic performance of a parallel manipulator. However, the terminal error of redundantly actuated parallel manipulators is difficult to calculate from joint errors. This paper proposes a method to approximate the terminal error of a redundantly actuated parallel manipulator by taking the minimum terminal error among all corresponding nonredundant counterparts. The local Frobenius norm index (LFNI) is proposed to estimate the expectation of terminal error. Additionally, the global Frobenius norm index (GFNI) is introduced to describe the worst case of terminal error in the workspace, which is then used for the optimum design of a RPU-UPR-2UPU redundantly actuated parallel manipulator. After the optimum design, the average root mean square error of the manipulator is reduced. Furthermore, a control mode determination strategy for allocating force/position control to a certain chain is also proposed to minimize the terminal error, whose effectiveness is validated through simulation.