Biomechanical study on the nonlinear stiffness behavior of the calf muscle and ground reaction force estimation during running

Understanding the biomechanical behavior of the human body in different conditions of locomotion can be very advantageous for many purposes, such as developing the humanoid robots. With this approach, the aim of this study is investigating the nonlinear stiffness behavior of the calf muscle and the exerted ground reaction force (GRF) during running. For this purpose, a new active model of human body is proposed, which the distinctive features of this model are as follows: 1) The simulation model is considered to be five degrees of freedom (5-DOF) by using the standard solid model to simulate the calf muscle; 2) The optimum values of the considered mechanical parameters are obtained using the particle swarm optimization (PSO) algorithm; 3) The stiffness of the calf muscle is considered to be nonlinear and active, which is appropriately formulated with regard to the viscoelasticity nature of the calf muscle. This model is tested for two types of hard and soft shoes, and validated by the results of previous studies. Then the effects of different conditions of body mass distribution, touchdown velocities, and different types of shoes on the GRF are investigated and discussed. The results of this study can be used in producing and development of humanoid robots, artificial limbs, etc.