Deriving a closed form of equations of motion of musculoskeletal system of human body: Using Lagrangian dynamics

Musculoskeletal simulation of human body is one of the most fascinating research areas in biomechanics. The cornerstone of this type of simulation, regardless of the approach, is obtaining the differential equations of the system. The purpose of this paper is deriving equations of motion of an arbitrary musculoskeletal model of the human body by using Denavit-Hartenberg parameters in accompanied by Lagrangian dynamics. A closed form algorithm has been developed to obtain the governing equations of motion. Skeletal muscle system has been included in this model and the generalized force of this kind of actuator has been derived in the model. To verify the obtained equations, a simple two-link model has been considered. To overcome the difficulty of redundancy, a static optimization approach was used. The obtained results, which were muscle forces, showed quite a well correspondence with the input trajectories for each joint.