In this study, we propose a systematic design methodology to address the conflicting multi-objective optimization problem of balancing structural strength and weight reduction for a novel continuous passive motion (CPM) rehabilitation aid. The research was conducted in two phases. First, a finite element analysis (FEA) model was established and experimentally validated using displacement measurements obtained from a displacement transducer and sensor interface, thereby ensuring that the numerical model accurately reflected the structural behavior of the physical CPM device. Second, the Taguchi method and grey relational analysis were systematically applied to consolidate maximum equivalent stress and weight into a single performance index, thereby achieving a balanced evaluation. The Taguchi results confirmed the factor influence ranking (D > B > C > A) and identified the optimal design parameter combination as A2B1C2D3. The optimized design achieved a 55.5% reduction in maximum stress compared with the baseline design and a 15% reduction in weight. The subsequent FEA results demonstrated that the maximum equivalent stress of the optimized design was significantly lower than the yield strength of the material, thereby confirming structural safety. Furthermore, the results confirmed that the selected design factors significantly affected overall performance and that strong interaction effects existed among them. Overall, the proposed optimization framework effectively balanced structural strength and weight reduction, providing a practical reference for the structural design of rehabilitation devices.