A Motion Propagation Force Analysis of Multi-DoF Systems Using the Partial Lagrangian Method

A partial Lagrangian method is proposed as an inverse dynamics analysis method for multi-link systems. This method, combined with automatic differentiation, allows for the derivation of equations of motion and analytical extraction of motion-induced torque components. We introduce the concept of motion propagation force to describe joint torque components generated by the motion of other joints. This concept aligns with existing notions such as interaction torque, while providing a novel analytical perspective. The effectiveness of the proposed method is confirmed through simulations using a three-DoF arm model, where motion propagation torques are visualized and validated. This method is useful for motion analysis and impedance control in complex robotic systems.