Closed-form dynamic modeling and performance analysis of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions

This paper presents an systematic dynamic modeling and performance analysis method of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions, where P, U, S, and R represent the prismatic joint, universal joint, spherical joint, and revolute joint, respectively. The process of the deduction of the over-constrained forces/moment is given. The Newton–Euler approach and natural orthogonal complement method are adopted to establish two types of dynamic models with and without constrained forces/moments with the consideration of the over-constrained forces/moments. The dynamic manipulability ellipsoid, which measures the uniformity of changing the position and orientation of the manipulator’s moving platform, is adopted to evaluate the dynamic performance of the parallel manipulator. To show the feasibility of the proposed method, numerical simulations are conducted to investigate the dynamic models and performance of the 2PUR-PSR manipulator. The actuation forces, constrained forces/moments, and the compatible deformation are calculated. Distribution of the DME index is also obtained. The proposed modeling approach provides a fundamental basis for the structural optimization and control scheme design of the over-constrained parallel manipulator.