Theoretical considerations of the mechanics of whisker sensors

Employing elastic rod theory we study the question which forces and moments measured at the base of a mammal’s whisker (tactile sensor) allow for the prediction of the location in 3D space of the point at which the whisker makes contact with an object. We show that, in the case of non-tip contact, the minimum number of independent forces or moments is three but that conserved quantities of the rod equilibrium equations prevent certain triples from giving a unique solution. The existence of these conserved quantities depends on the shape and material properties of the whisker. For tapered or intrinsically curved whiskers there is no obstruction to the prediction of the contact point. Our results explain recent numerical observations in the literature and offer guidance for the design of robotic tactile sensory devices.