Mechanisms Modeling the Double Rotation of the Elytra in Beetles (Coleoptera)

We recorded transient movements, i.e. opening and closing, of beetle elytra. The beetles were tethered from below and filmed under a skew mirror; two markers were glued on each elytron at the apex and at the base. Body-fixed 3D traces of the apical and basal markers were reconstructed. The trace of the basal marker was, as a rule, non-parallel to the apical trace. The costal edge of the elytron uniformly supinated in the course of adduction of the apical marker. We found two essential attributes of double rotation: (1) the elytron to body articulation is approximately a spherical mechanism; (2) transient opening and closing possess single degree of freedom. The double rotation was modeled with two mechanisms: (1) a flexagon model of the Haas and Wootton's type simulated the elytral movement relative to the movement of one facet of the flexagon; (2) a screw and nut model provided traces as two sectors of a helical thread, one sector was phase shifted with respect to other one. Screw guideways in a spherical mechanism give rise to discrepancies. Exact solution for a spherical mechanism with two guideways was proposed. The modeling revealed the attribute (3): the elytron is actuated by two linked but differently directed drives. Experimental investigations on the elytron to body articulation may be oriented at search of those mechanisms.