  This study introduces a novel approach for deriving the governing equations
of the musculoskeletal system in the human body. The proposed formalism offers
a framework to effectively incorporate the kinematic characteristics of
biological joints and the complexities of kinematic chains into the
differential equations of motion. This approach, known as "Empirically-based
multibody dynamics," relies on experimental data pertaining to the skeletal
system. To establish the formulations, a novel calculus of matrix-valued
functions is employed. In contrast to alternative methods that utilize
Differential-Algebraic Equations (DAEs), the current approach provides the
governing equations of the musculoskeletal system in the form of ordinary
differential equations, simplifying the computational process. This formalism
shall be employed to simulate a generic constrained multibody system with
holonomic constraints. The proposed formalism is applied to simulate various
conventional multibody systems, including the four-bar linkage, five-bar
linkage, and Andrew's squeezer mechanism. Additionally, the human shoulder
mechanism is simulated, incorporating empirically-derived constraints to
capture the shoulder rhythm. Furthermore, a novel method for deriving a
closed-form formula for the moment arm matrix of a general musculotendon model
is presented in this work.

Applied Physics;Dynamical Systems