Transmission State Transition and Error Accumulation in a Multi-Cable-Driven Serial Chain: A Dynamic Investigation

This study investigates the motion synchronization of serially connected, flexible multi-cable-driven systems, a configuration critical for compact robotic joints. A high-fidelity nonlinear dynamic model is established using a discrete element method, explicitly incorporating cable elasticity, damping, and nonlinear cable-sheave contact. The model effectively captures the coupled multi-body dynamics essential for analyzing error propagation. Simulations reveal that under sufficient pre-tension and low load, the system maintains a stable bidirectional transmission state, with synchronization error accumulating along the drive chain. However, when the resistance torque exceeds a critical threshold, a qualitative transition to a unidirectional state occurs, characterized by cable slackness, a dramatic rise in error, and loss of kinematic constraint. This state transition defines a key performance boundary, directly impacting the joint's backdrivability and bidirectional impact resistance. The analysis provides quantitative insights into how pre-tension (enhancing effective stiffness) and resistance torque (perturbing tension distribution) govern synchronization. The proposed model serves as a design tool for determining crucial parameters, such as the minimum pre-tension and maximum allowable load, to ensure precise and robust synchronization in cable-driven robotic transmissions.