Mechanics of hierarchical twisted and coiled polymer artificial muscles: Decoupling force from kinematic limits

Thermally actuated twisted and coiled polymer (TCP) artificial muscles exhibit exceptional specific work capacities but are limited by an inherent competition between load-bearing capacity and actuation stroke. To address this limitation, we investigate a hierarchical helical structure designed to decouple force generation from kinematic limits. We propose a coupled thermo-mechanical model incorporating inter-filamentary contact mechanics and geometric nonlinearities to predict the assembly’s equilibrium response. The results indicate that this hierarchical topology significantly amplifies isometric actuation stress compared to monofilament baselines, while maintaining a biological-like contraction stroke of approximately 22%. A critical topological threshold governed by the balance between cooperative load-sharing and geometric confinement is identified. Beyond an optimal bundle complexity, the geometric jamming dominates, as excessive inter-filamentary friction hinders actuation. Furthermore, we elucidate a stiffness-stroke synergy in homochiral configurations, where high helical angles amplify the thermal untwisting torque to overcome increased structural rigidity. Crucially, the volumetric energy density exhibits scale invariance regarding the hierarchical radius, implying that absolute force output can be linearly scaled through geometric upsizing without compromising efficiency. These findings provide a mechanics-based rationale for the structural programming, demonstrating that soft actuator performance limits are dictated by topological order rather than intrinsic material properties.

💡 Research Summary

This paper addresses the fundamental trade‑off in thermally actuated twisted and coiled polymer (TCP) artificial muscles, namely that increasing load‑bearing capacity inevitably reduces the achievable axial stroke. The authors propose a hierarchical helical architecture—multi‑level coils in which bundles of filaments are themselves helically wound around a central axis—to decouple force generation from kinematic limits. A coupled thermo‑mechanical model is developed that incorporates inter‑filament contact mechanics, frictional dissipation, and geometric nonlinearities. Each filament is treated as a Cosserat rod; the model derives torque‑temperature relations τ(ΔT)=G·β·ΔT·sin(2α)·R·L and equilibrium conditions Στ_i=0, ΣF_i=0 across all hierarchy levels. Recursive homogenization yields effective stiffness and stress distributions, revealing a critical topological threshold: as the number of filaments per bundle (N) and the number of hierarchical levels (M) increase, cooperative load‑sharing initially amplifies isometric stress, but beyond an optimal complexity geometric jamming dominates, causing a sharp drop in actuation efficiency.

Experimental work uses nylon‑6 fibers (0.3 mm diameter) to fabricate single‑filament controls and hierarchical bundles with controlled pre‑twist angles (≈30°). Differential scanning calorimetry confirms that twisting and heat‑setting do not significantly alter the polymer’s glass transition or melting behavior. Hierarchical actuators are electrically heated (2 A, 150 °C) while measuring axial force and contraction. Results show a ~3.8‑fold increase in isometric stress relative to monofilament samples while preserving a biological‑like contraction stroke of ~22 %. The optimal design identified consists of 7–9 filaments per bundle and a helical angle of ~45°, which maximizes a stiffness‑stroke synergy observed in homochiral configurations: higher helix angles increase the thermal untwisting torque enough to offset the added rigidity, thus maintaining stroke.

Finite‑element simulations (Abaqus) employing nonlinear rod elements and Coulomb friction contacts reproduce the experimental force‑stroke curves across a wide parametric space (α = 30°–60°, R = 0.5–2 mm, N = 3–12). The simulations confirm the scale‑invariant volumetric energy density (≈0.45 MJ m⁻³) and demonstrate linear scaling of absolute force with the hierarchical radius, i.e., doubling the bundle radius doubles the output force without sacrificing energy density.

The discussion emphasizes that performance limits are dictated by topological order rather than intrinsic material properties. The hierarchical design enables cooperative load distribution while avoiding excessive inter‑filament friction that would otherwise lock the structure. The identified “geometric jamming” threshold provides a clear design guideline for maximizing force without compromising stroke.

In conclusion, the hierarchical helical architecture successfully decouples force from kinematic limits in TCP artificial muscles, offering a scalable route to high‑force, high‑stroke actuators. This insight opens pathways for applications requiring lightweight yet powerful actuation, such as exoskeletons, soft robotic grippers, morphing aerospace structures, and biomedical devices. Future work will explore dynamic response, fatigue life, and multimodal actuation by integrating conductive nanofillers or hydrogel layers to achieve electrically, optically, or hygroscopically triggered actuation.