Equivalent 1D wave propagation model for shocktransmission in lower-limb prostheses

Abstract This study presents a continuous dynamic model to analyse shock and vibration transmission through Running Specific Prostheses (RSPs), used by lower-limb amputee athletes. Traditional models primarily focus on global kinematics and neglect the dynamic effects of ground impacts, which are critical to both performance and injury prevention. To address this, an equivalent one-dimensional (1D) wave propagation model is proposed, that treats the prosthetic components and residual member as continuous elastic bar segments. The transfer function of the equivalent 1D system is evaluated to determine the influence of key parameters – including the impedance ratio between the blade and the sole, the sole equivalent thickness, and the body mass – on dynamic force transmission and resonance characteristics. The study also explores the transient response of the prosthesis in the time domain. This continuous analytical model enables detailed evaluation of how impact forces propagate through the prosthesis and affects the athlete’s body. Parametric studies reveal that the sole’s material properties and thickness significantly influence the system’s response, identifying optimal configurations that minimise harmful resonance and vibration transmission. The model also demonstrates the importance of matching prosthetic design parameters to the frequency content of ground reaction forces. This work provides a foundation for optimising prosthetic soles to enhance athlete comfort, reduce injury risk, and improve performance.