Figure 1. Schematic of the whisker in two dimensions.
(A) The whisker is modeled as a truncated cone of length LW, virtually extended to length L. (B) The base of the whisker (in the follicle, or attached to a galvo, Figures 4–6) is at point (x0, y0) and angle θ0, measured clockwise. The position of a point along the whisker is (x(s), y(s)) and its angle with the x-axis is θ(s). The contacted object is a cylindrical pole with radius rpole centered at (xcen, ycen); the pole and whisker are shown at a magnified scale in the inset on the left. The whisker contacts the object at the point (xobj, yobj) at an angle θobj. The object distance, d, is the distance between (xobj, yobj) and the whisker base. The pole applies a force on the whisker. (C) The concave forward (CF, left) and concave backward (CB, right) whisker configurations. Thick black lines, whiskers; solid circle, poles; gray arrows, movement directions. (D), Definition of the push angle, θp, which measures the strain on the whisker imposed by the object. The deflected and undeflected whiskers are shown as black and gray lines respectively. The pole is a dark gray circle. The undeflected whisker is translated and rotated in the plane such that it has the same x0, y0 and θ0 as the deflected whisker. This generates a virtual undeflected whisker (dashed gray line). A virtual pole (light gray circle) is generated by shifting the real pole such that it will be tangent to the virtual undeflected whisker. In addition, the distance from the contact point of the virtual unbent whisker and the virtual pole, (xvirtual, yvirtual) and the base (x0, y0) is equal to d, the distance between (xobj, yobj) and the base. The angle between the two line segments connecting the base with the real and virtual contact points is θp.