Kinematic, dynamic, and performance analysis of a new 3-DOF over-constrained parallel mechanism without parasitic motion

Abstract This research proposes a novel over-constrained parallel mechanism without parasitic motion. The parasitic motion analysis and the kinematic problem of the mechanism are presented, especially the reason for non-parasitic motion property is clarified and analytical solutions for the forward kinematics are obtained. Since the proposed mechanism both possesses active and passive redundant constraints, the solution for dynamic analysis cannot be uniquely determined. To solve the problem, the classical optimization criterion and the deformation compatibility condition are introduced to form an optimization model, in which the least square norm of driving forces is the optimization objective, and the compatible equations and the dynamic equation based on Newton-Euler method are served as constraint equations. Then the driving forces and constraint forces/moments can be uniquely determined by solving the optimization model. The result also shows the friction effect and the internal mechanical behaviors of the mechanism. Meanwhile, an efficient dynamic model is also developed based on the principle of virtual work. A case study is performed and the dynamic formulations are verified with the results obtained in Adams. Finally, the motion/force transmission and dynamic manipulability ellipsoid are adopted to evaluate the local and global performances of the mechanism.