Asymmetric Friction Locomotion Driven by External Harmonic Vibrations

Asymmetric friction, that is, different friction forces resisting sliding in opposing directions, works as a rectifier, transferring the applied oscillations into unidirectional motion. Locomotion of devices based on asymmetric friction is investigated by considering a model system consisting of an asymmetric friction block connected to a symmetric friction block by a spring. The symmetric friction block models the resistance to the movement by the environment. It is found that under harmonic oscillation, the system displays two distinct types of motion: Recurrent Movement (stick-slip-type movement) and Sub-Frictional Movement. The Recurrent Movement occurs when the inertia force is sufficient to overcome the frictional force. In this case, the system with asymmetric friction exhibits unidirectional locomotion, while the system with only symmetric friction oscillates about a fixed point. The Sub-Frictional Movement occurs when the inertia is insufficient to overcome the frictional force. Then the symmetric friction block moves against the asymmetric friction block and sufficiently loads the spring to enable some movement of the system. Thus, motion is generated even when the external forces are below the static friction threshold. These types of motion have been found to exhibit different types of spectral fallout: while the Recurrent Movement produces a typically observed frictional fallout 1/ω, where ω is the frequency, the Sub-Frictional Movement produces a stronger 1/ω2 fallout, only observed in the development of an oblique fracture in rocks under compression. This discovery can shed light on mechanisms of rock failure in compression. Understanding of the unidirectional movement induced by asymmetric friction can be instrumental in designing novel locomotion devices that can move in narrow channels or fractures in the Earth’s crust or in extraterrestrial bodies utilising the (renewable) energy of external vibrations.