Modeling strain sensing by the gyroscopic halteres, in the dipteran soldier fly, hermetia illucens

Abstract

Dipteran insects are known to receive mechanosensory feedback on their aerial rotations from a pair of vibratory gyroscopic organs called halteres. Halteres are simple cantilever-like structures with an end mass that evolved from the hind wings of the ancestral four-winged insects form. In most Diptera, including the soldier fly Hermetia illucens, the halteres vibrate at the same frequency as the wings. These vibrations occur in a vertical plane such that any rotation about this plane imposes orthogonal Coriolis forces on the halteres causing their plane of vibration to shift laterally by a small degree. This motion results in strain variation at the base of the haltere shaft, which is sensed by the campaniform sensilla. This strain variation is, therefore, a key parameter for sensing body rotations. In this paper, we present a study of the basic mechanism of soldier fly halteres to demonstrate its use as a vibratory gyroscope. First, we use a static force sensor to determine the stiffness of the haltere, to evaluate the natural frequency along the flapping direction, followed by nanoindentation-based measurement of its elastic modulus. We then model the haltere as a simple structure with the measured material properties and carry out an analysis to estimate the gyroscopic strain. We also use Finite Element simulations to verify our estimates. This study is intended to provide a better understanding of the mechanism of the natural vibratory gyroscope.