This paper presents an optimum design of a 4-PSS-PU redundant parallel manipulator by taking the workspace, conditioning performance, and acceleration into account. On the basis of rank of the Jacobian matrix, a method to directly find out the workspace is presented, rather than the search method. Based on the dynamic model, a maximum acceleration index is defined. The corresponding atlases of these performance indices are represented graphically in the established design space. Based on these atlases, the optimum design is performed and the optimum region is determined. It is expected to realize the high acceleration of parallel manipulators by using the optimum method.