The three degree of freedom (3DOF) was able to implement by the parallel manipulators 3UPSPU and 4UPSPU with intermediate constraints PU chain are taken as study object. The mechanism model and mathematical model were established through the kinematics analysis of the mechanism, meanwhile the whole Jacobian matrix were deduced. The Global Dexterity Index and the Global Stiffness Index of performance were set up, and the two kinds of parallel manipulators were performed of multiobjective optimization based on the Particle Swarm Optimization (PSO) algorithm, and were compared and analyzed. The results show that 4UPSPU redundant parallel manipulator has better Global Dexterity and Global Stiffness Index than that of 3UPSPU parallel manipulator.