Towards optimal design of sport footwear based on muscle activity and minimum loading rate using simplified model

Recently, researchers have been looking for a model to relate the ground reaction force to the vibration parameters of sport shoes. A 4-degrees-of-freedom mass-spring-damper model and a dimensionless objective function have been used in the literature in order to simulate the functionality of the central nervous system based on muscle tuning paradigm. In this study, a two-phase optimization method was proposed in order to better simulate the functionality of the central nervous system. A comparison between the results of this method and those in the literature demonstrates more accuracy. Additionally, it has been reported that the loading rate in the time history of the ground reaction force has a role in overuse injuries in the tibia and tarsals; therefore, in order to introduce an optimum design for sport shoes, in this study, a new objective function was introduced and the proposed method was used in order to find the best possible range of shoe parameters for pre-fatigued and post-fatigued conditions. Results indicated that there is no possible solution which brings the loading rate to the desired value; however, the region in which the least values for the objective function achieved was introduced as the safe region. It was shown that the size of this safe region shrinks as muscles fatigue. The results also demonstrated high dependency of the safe region to the mass distribution and touchdown velocities of the lower extremities.