Parallel mechanisms have the advantages of strong reconfigurability, excellent dynamic performance, and high accuracy, and have been widely used in aerospace and other fields. As an important branch of parallel mechanism research, design has significant value and development prospects, so many researchers have made great efforts and achieved many results in this area. However, with the continuous advancement of parallel mechanisms, from single-dimension and topology designs to their integration, synchronous design methods based on topology superposition and full-variable orthogonal design have undergone extensive research and application. Nonetheless, these methods exhibit notable drawbacks, such as low design efficiency. To address these concerns, a method for designing parallel mechanisms that synchronizes topology and dimension was presented based on structural similarity. The method used slight variations in dimensional parameters while maintaining the same mass retention ratio during topology optimization as the starting point. It then employed topology parameterization scaling and stiffness-mass metamodels construction to efficiently synchronize dimension and topology for parallel mechanisms. Using a typical 3-P-RS parallel mechanism as an instance, numerical verification and a comparative analysis were conducted. The findings demonstrated that under the same mass conditions, the proposed design method obtained greater isotropic stiffness compared with traditional dimension design methods. In summary, topology optimization made the material distribution of RS links more reasonable. This research not only offerred beneficial guidance for producing physical 3-P-RS parallel mechanism prototypes, but also established a theoretical basis for designing other parallel mechanisms.