Cable-driven parallel robots (CDPRs) are increasingly favored in rehabilitation, medical devices, and material transportation due to their flexible structure and large transmission distance. The CDPRs with a highly modular and flexible structure are usually easy to be quickly reorganized. It is important to study the dimension and shape optimization of the basis and moving platforms for rapidly reconstructing a high-performance CDPR. The influence of each parameter of CDPRs’ dimension and shape on performance is mutually coupled. Therefore, obtaining the global optimal result by simply superimposing each optimum parameter is usually difficult. To this end, the concepts of a constant stiffness space (CSS) and a cable-tension-constrained workspace (CTCW) and their calculation methods are introduced, and the CDPRs’ dimension and shape are optimized with the maximum CSS and CTCW volume as the optimization indicators. First, the response surface optimization model between CDPRs’ performance and multi-objective optimization parameters is established, taking into account the coupling relationship of each CDPR optimization parameter and the effect on performance, and it is solved by using the Latin hypercube design method. Then, the effect of CDPRs’ dimension and shape on performance is analyzed by using the response surface optimization model, and the CDPRs’ optimization dimensions are provided.