Arthropod mechanoreceptive hairs: modeling the directionality of the joint.

Stimulus transformation in arthropod mechanoreceptive hairs is dominated by the mechanical properties of both the hair shaft and the hair's articulation. Here a mathematical model of the hair's articulation is developed based on simple relationships relevant for every anisotropic articulation. The mechanical behavior regarding deflection under load of a variety of hairs can be described quantitatively by using only two (in the case of double symmetric characteristics) or four parameters (in the case of only one symmetry): (1) joint stiffness S p in the preferred direction of deflection, (2) joint stiffness St in a plane transversal to the preferred direction, and (3, 4) the values of stiffness S for opposite directions of deflection. The applicability of the model was tested by measuring these stiffnesses S of spider tactile hair joints by deflecting the hairs statically in different directions. For comparison, data in the literature on insect and spider hairs sensitive to air flow were analyzed. The equation presented describes the directional characteristics of a wide range of structurally different cuticular hairs. It can also be used as a mathematical description of the joint mechanics when modeling the mechanics of hairs, for instance, by applying methods such as Finite Element Analysis.