This study introduces a novel single-degree-of-freedom polycentric knee mechanism specifically designed for transfemoral prostheses to address dual challenges of stability during the stance phase and biomimetic motion during the swing phase. Leveraging analytical kinematic synthesis, the proposed mechanism integrates separate kinematic designs for each of the gait phases into a combined structure that prevents singularity issues during full knee flexion, which is a significant limitation in conventional active designs. The stance phase mechanism emphasizes stability through precise control of the instantaneous center of rotation (ICR) and weight-bearing support, while the swing phase mechanism adopts a biomimetic motion trajectory. In order to validate the proposed methodology, kinematic synthesis, numerical simulations, and visual analyses were conducted. Incorporating insights from polycentric prostheses and orthotic applications, the proposed mechanism achieves a seamless transition between two different configurations by keeping its overall mobility. Additionally, its possible compatibility with motorized actuation offers a foundation for active prosthesis systems, paving the way for adapting the advantages of polycentric prosthesis to active devices. This innovative approach offers a scientifically grounded pathway for improving transfemoral prosthetic systems, advancing both their biomechanical utility and user comfort.