Modeling and Simulation of a Cable-Driven Three-Degree-of-Freedom Joint

This paper addresses the mathematical modeling, simulation, and analytical study of a cable-driven three-degree-of-freedom joint. Firstly, we introduce the detailed structure and working principle of the cable-driven 3 DOF joint. The range of motion for the joint angles were determined using the geometric method. Secondly, we derive the dynamic equation of the mechanism from an energy perspective using the Lagrange equation. Subsequently, we conduct an analysis of cable tensions and propose a novel tension distribution algorithm. Finally, by analyzing the simulation results, we demonstrate that the elongated and shortened cables exhibit different changes in length upon reaching the target joint angle, thereby validating the effectiveness of the tension distribution algorithm. This study offers theoretical support and design guidance for implementing cable-driven joints in robotic arms and bionic robots, demonstrating engineering practicality.