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The kinematics performance analysis and optimal design of 4—UPS—RPU (4-universal joints-prismatic pairs-spherical joints/revolute joints-prismatic pairs-universal joints) redundant actuation parallel mechanism was studied. The Jacobian matrix of the mechanism was established, and the three dexterity measures, which were conditional number, the smallest singular value and operation, were obtained. On this basis, the global dexterity coefficient, which was used to evaluate the dexterity of various configurations, was defined. And the distribution of different dexterity measures when parallel mechanism was kept in different attitudes, such as in single attitude of different Euler angles α and different Euler angles β, at the same Euler angle α and different Euler angles β, in the workspace were analyzed, respectively. Finally, based on the global dexterity coefficient, the structure parameters which include the distribution angle on stationary platfrom and motion platform and the distribution radius on stationary platfrom and motion flatfrom, were optimized by genetic algorithm. Compared with the global dexterity coefficient before and after optimization, it was found that the global dexterity coefficient after optimization was bigger than that before optimization. Thus the kinematic performance of 4—UPS—RPU redundant actuation parallel mechanism after optimization was much better than that before optimization, and the optimized effect was obvious. This research can provide important theoretical base of the structure design for the redundant actuation parallel mechanism.