Kinematic modeling of musculoskeletal systems considering muscle inertia for monoarticular muscles

Understanding human musculoskeletal dynamics is the key to further advancement in both biomedical engineering and humanoid robotics. Numerical models today have certain setbacks that hinder the accuracy of analyses, especially in orthopedic surgery and robotic design. A kinematic behavior-based analytical model of musculoskeletal systems is presented that explores muscle inertia and center of mass (COM) variations across six configurations and modes. This model incorporates long and asymmetric tendons, along with a dynamically reducing joint radius relative to the joint angle. A novel 2D wrapping radius method extends the radius by up to 50% compared to the Garner and Pandy method for monoarticular muscles. Additionally, a new analytical method for calculating muscle contraction speed, the velocity of the COM of muscle-tendon systems, and joint positions is proposed. An algorithm for calculating system velocity and acceleration is introduced based on this method. MATLAB simulations compared the model's accuracy against OpenSim results, showing consistency at shorter angles and demonstrating that the algorithm remains reliable at wider angles, unlike the Garner and Pandy algorithm. Results highlight that COM and dynamic tendon length variations can be incorporated into the suggested algorithm, which is essential for biomechanical analysis and the development of therapeutic and robotic applications.