A geometry-guided sizing and static force modeling protocol for compact antagonistic cable-driven joints

This paper presents a framework for the kinematic modelling, pseudo-static force analysis, and parametric evaluation of an antagonistic cable-driven robotic joint, demonstrated on a miniature elbow prototype. Analytical transformation and equilibrium models were formulated for a dual-cable architecture to resolve trade-offs between range of motion, actuation force, and cable displacement. Parametric sweeps across key structural dimensions identified a preferable base-to-platform distance ( $h=240\text{mm}$ ), enabling collision-free articulation across a ${135}^{\circ }$ range of motion. Evaluating the cable holder radius ( $r$ ) designated $r=40\text{mm}$ as the preferred configuration, satisfying geometric constraints while restricting cable displacement to limit motor spool size. Hardware-in-the-loop testing validated the analytical models across single- and dual-cable antagonistic configurations. Kinematic tracking yielded RMSEs of 3.82 mm (peak error: 8.92 mm) for flexion and 1.46 mm (peak error: 3.56 mm) for extension. Static force validation achieved RMSEs of 0.51 N (peak error: 1.55 N) in single-cable testing and 0.38 N (peak error: 0.48 N) during dual-cable antagonistic operation. The proposed methodology offers a guideline for developing compact, lightweight, single-degree-of-freedom cable-driven robotic systems.