Motorizing fibres with geometric zero-energy modes

Responsive materials^1-3 have been used to generate structures with built-in complex geometries^4-6, linear actuators^7-9 and microswimmers^10-12. These results suggest that complex, fully functional machines composed solely from shape-changing materials might be possible ¹³ . Nonetheless, to accomplish rotary motion in these materials still relies on the classical wheel and axle motifs. Here we explore geometric zero-energy modes to elicit rotary motion in elastic materials in the absence of a rigid wheel travelling around an axle. We show that prestrained polymer fibres closed into rings exhibit self-actuation and continuous motion when placed between two heat baths due to elastic deformations that arise from rotational-symmetry breaking around the rod's axis. Our findings illustrate a simple but robust model to create active motion in mechanically prestrained objects.