A Novel method for mathematical modeling of the skeletal system of the human body: Incorporating the kinematic characteristics of biological joints and the effects of complex kinematic chains of the skeletal system

In the current study, a novel method for deriving the governing equations of the skeletal system of the human body has been presented. In this method, a novel approach for incorporating the kinematic characteristics of biological joints and also the effects of complex kinematic chains of the skeletal system has been proposed. The suggested method while utilizing the calculus of matrix-valued functions, derives the governing equations of the skeletal system in the form of ordinary differential equations. Moreover, since the formulations were presented in a recursive fashion, this paper suggests a computationally efficient algorithm to derive the differential equations of motion for the skeletal system. In order to examine the validity of the proposed formulations, a benchmark mechanism with three closed-loop kinematic constraints were considered. We compared the results obtained from our formulations with the outcomes presented in other studies and validated the proposed formulations. Besides, in order to investigate the application of the suggested method in simulation of the skeletal system of the human body, dynamical modeling of the shoulder rhythm was taken into consideration. Two models were employed for describing the shoulder rhythm: Original model and simplified model. The discrepancies observed between the outcomes of these two models delineate the necessity of using the original data for the shoulder rhythm. While the limitations of the available formulations have compelled the researchers to employ the simplified model for the shoulder rhythm, with the method we propose in this study this problem is obviated.