The Mechanics of Whiskers
Why study whisker mechanics?
Rats rhythmically brush and tap their whiskers (also called vibrissae) against objects to explore their world through the sense of touch. This behavior is called whisking, and a whisk is defined as one full cycle of whisker protraction and retraction. Using tactile information from its whiskers, a rat is able to determine an object's size, shape, orientation, and texture.
We study the mechanics of whiskers in order to gain insight into how the rat's brain is able to interpret mechanical signals to determine object properties.
An overview of whisking and whisker mechanics is shown in this video from Science Bytes. The video explains some basic mechanical principles, such as how stiffness and distance affect how much the whisker bends. The video also describes how the bending of the whisker underlies the rat's extraordinary sensing capabilities and explains some connections to future developments in robotics.
Unlike the antenna of an insect, a rat whisker has no sensors along its length. Instead, when a whisker collides with an object it bends and vibrates, and these mechanical signals are transmitted to sensors (mechanoreceptors) in the follicle at the whisker base. Therefore, we only need to look at the mechanical signals at the whisker base in order to quantify all the mechanical information available to the rat through its whiskers.
As described below, the material properties of the whisker as well as the whisker's morphology (shape) will have a large effect on the whisker's bending characteristics. In turn, the way that the whisker bends will directly contribute to the mechanical signals at the whisker base. We can then examine how these mechanical signals might allow the rat to determine object properties. Using the Digital Rat we ultimately aim to quantify the mechanical signals across the entire whisker array during each whisk, taking into account whisker dynamics.
We are interested in quantifying the material properties of individual whiskers, with particular emphasis on how these properties can help us understand exploratory rat behavior. For instance, experiments in the lab have shown that Young's modulus is around 1.25 - 4 GPa (Quist et al., 2011). This value helps us determine how much a whisker will bend as the rat gradually rotates it against an object during exploratory whisking.
Morphology (shape) of the whisker
The shape and orientation of the vibrissa can greatly magnify the signals that the rat feels. Whiskers have an intrinsic curvature, and they are oriented on the rat's face so that most collisions with objects will occur with the whisker oriented concave forward (Quist and Hartmann, 2012). The video shows the difference between the mechanical signals generated when a whisker collides with an object concave forward versus concave backwards.
Models of vibrissal bending
You can download Elastica2D, our two-dimensional (2D) model for whisker bending.
We have developed both 2D (Solomon and Hartmann, 2006; Birdwell et al., 2007; Solomon and Hartmann, 2011) and three-dimensional (Huet and Hartmann, in preparation) numerical models of quasi-static whisker bending. The models are based on cantilever beam theory for large angle deflections of a tapered beam. With these models, we quantify the forces and moments at the base of the whisker and thus the inputs to the vibrissal sensory system. The video shows a whisker being moved along a path and the resulting bending moments and axial force at the base.
Determination of object properties using mechanical signals
We have performed several studies to examine how a rat might determine object properties using mechanical signals at the whisker base. Several of these studies have used hardware models (robots) to examine the plausibility of particular computations. You can read more about this research on our Whisker-Based Robots page. In simulation work, we have used our 2D model to demonstrate a one-to-one mapping between mechanical signals at the vibrissal base and the (r,θ) position of an object. Specifically, we have shown that only axial force and bending moment are needed to determine an object's 2D location (Solomon and Hartmann, 2011).
Models of whisker dynamics
The work described above is all based on quasistatic models of whisker mechanics. In collaboration with Professor Todd Murphey and his students, we have also been constructing a physics-based model of whisker dynamics to explain the behavior of whiskers during non-contact whisking and during collisions with an object. In earlier work, we performed studies of vibrissal resonance tuning (Hartmann et al., 2003).