A closed-form formula for the moment arm matrix of a general musculoskeletal model with considering joint constraint and motion rhythm

Abstract

This paper introduces a new closed-form formulation for the moment arm matrix corresponding to the musculotendon unit in a general computational model of the musculoskeletal system. The novel approach uses matrix calculus to define a “Generalized Musculotendon Line of Action Vector (GMLAV)” in integration with the virtual work principle, hence leveraging both conventional geometry and tendon excursion methods. In contrast to previous methods, the concepts of motion rhythm and joint constraints have been incorporated without restrictions, where each joint variable is defined as an arbitrary smooth function of the generalized coordinate vector. The validity of our formulation was established by performing the simulations on two well-known musculoskeletal models from literature and comparing the outcomes with those obtained using OpenSim. The results presented in this paper show a high degree of fidelity between our novel simulation model and OpenSim (or SIMM).