Coupled fatigue–wear degradation and nitinol SMA integration in a tendon-driven hand prosthesis: A predictive analytical framework for hybrid actuation

Tendon-driven prosthetic hands fail in service because the steel cable fatigues at the guide bends while, simultaneously, the polymer channel wears at the same contact. The two mechanisms are coupled: the wear groove changes the geometry that sets the stress concentration, so fatigue accelerates on a surface that is itself degrading. Static finite-element analysis misses this interaction entirely. We develop here a purely analytical framework—Goodman fatigue criterion, Archard wear law, Monte Carlo uncertainty propagation—for a cable-driven prosthesis with Nylon 6/10 phalanges and DC gear-motor actuation; no experimental results are reported, and every prediction is formulated as a falsifiable hypothesis for subsequent testing. The model predicts a median cable life of 2.1×10 ⁶ cycles (95% CI: 1.3–3.4×10 ⁶ ), roughly 210 days of intensive use, with 0.53 mm of cumulative channel wear. Parametric sweeps show that the guide radius and the wear coefficient K dominate the service-life estimate. Finite-element results locate the critical fatigue zone at the medial phalanx of the middle finger, where the peak von Mises stress reaches 72.5 MPa—well within the 139 MPa limit of the glass-fibre reinforced grade, but above the yield point of unreinforced Nylon 6/10. To break the degradation loop at its source, we size a 0.5 mm ×100 mm Nitinol wire from the martensite–austenite transformation ( σ act = 200 MPa) and model the heating–cooling transient with both a lumped-capacitance and a one-dimensional finite-difference approach. The wire delivers 30 N of grip force with a thermomechanical fatigue life exceeding 10 ⁷ cycles and eliminates cable–channel contact during the load-bearing phase, but its passive cooling time constant ( τ ≈ 26 s in still air) is too slow for rapid finger positioning. A hybrid concept is therefore proposed: a conventional DC motor performs fast open/close transients, and the Nitinol wire takes over for sustained grip. The test-rig programme that should follow this analytical study is described in detail.