Investigation of Knee Torque Dynamics in Single-Leg Transfemoral Prosthetic during Walking Using Mathematical Modeling

Transfemoral amputees rely on prosthetic devices to restore their mobility and maintain their independence. However, the design and performance of these devices can significantly affect the amputee’s gait and overall functionality. In this study, we investigate the knee torque dynamics of a single-leg transfemoral prosthetic during walking using a mathematical model that takes into consideration knee friction force (β₂), the horizontal component of the ground reaction force (F₁), and the vertical component of the ground reaction force (F₂). By carrying out model simulation in the MATLAB tool, along with Simulink, we derived the tracking error between the generated knee torque of the transfemoral prosthesis and the knee torque trajectory for a normal human leg. This error was evaluated using the normalized root mean square error (NRMSE) method. Our results show that when β₂ = 0.3 N.s.m⁻¹, F₁ = 320 N, and F₂ = 800 N, a tracking error of NRMSE = 0.342868% occurs. A comparison between the simulated knee torque and a desired knee torque trajectory for a normal leg study in the literature suggests that the tracking error generated will force the amputee to use higher metabolic energy to minimize discomfort while walking. These findings highlight the importance of optimizing the design and performance of transfemoral prosthetic devices to improve the knee torque dynamics and overall functionality of amputees. Our mathematical model provides a useful tool for future research in this field, which could help develop more effective prosthetic devices for transfemoral amputees.