Asymptotic self-restabilization of a continuous elastic structure

TL;DR

This paper demonstrates that certain elastic structures can spontaneously recover their original shape after deformation due to a configurational force, enabling cyclic soft mechanisms in soft robotics.

Contribution

It introduces the concept of asymptotic self-restabilization driven by configurational forces, supported by theoretical analysis and experimental validation.

Findings

Theoretically proves self-restabilization via elastica solution and stability analysis.

Designs and tests a prototype demonstrating the self-restabilization behavior.

Shows potential for innovative soft robotic mechanisms.

Abstract

A challenge in soft robotics and soft actuation is the determination of an elastic system which spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behaviour is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the Elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behaviour can be obtained in a real mechanical apparatus.