Distributed modeling and torque transmission analysis of a cable-driven robotic joint

Cable-driven actuation provides spatial flexibility for remote power transmission and offers inherent mechanical compliance. However, torque transmission is compromised by coupled nonlinear phenomena, including distributed friction, curvature-induced normal forces, pretension redistribution, and elasticity-induced hysteresis. Existing models typically address only a subset of these effects or depend on empirical mappings, thereby limiting their predictive accuracy for torque-level integration. In this work, we model a dual-cable tendon–sheath transmission as a bidirectionally coupled dynamic subsystem and develop a distributed spring–friction-unit formulation that explicitly links routing geometry, pretension, and distal dynamics to transmitted torque, hysteresis, and apparent stiffness variation. To facilitate practical deployment, we derive a reduced analytical representation through model-order reduction combined with a curvature-informed averaged-pretension approximation, and assess its validity via discretization-sensitivity analysis. Experiments on two dedicated dual-cable joint testbeds validate torque prediction across diverse routing and loading conditions and demonstrate partial feedforward friction compensation that enhances interaction transparency. Practical limitations and deployment considerations are also discussed.