This paper addresses the issue of determining the optimal geometric parameters of a 3-DOF parallel manipulator. One of the advantages of the manipulator is that the moving platform exhibits high tilting capabilities, e.g., as much as ±50deg. The first step of the new optimal methodology proposed in this paper to achieve the optimum design involves developing a design space that includes all possible basic similarity manipulators. The next step deals with the graphical representation of atlases that can illustrate relationships between performance criteria and design parameters. With such atlases, the designer can identify an optimum region with respect to the specification on performances. The region contains the optimum candidates, from which we can select one directly. Finally, the geometric parameters of the manipulator can be reached by comparing the desired workspace and the good-conditioning workspace. The design methodology discussed in this paper has no process to establish the objective function and does not involve any optimization algorithm, which is normally used in traditional optimization. We expect that since each manipulator in the developed design space represents all of its similarity manipulators in terms of performances, this method will guarantee an optimum design result.