Significance of the Asymmetry of the Haltere: A Microscale Vibratory Gyroscope

Nature has evolved a beautiful design for small-scale vibratory gyroscopes in the form of halteres located in the metathorax region of the dipteran flies that detect body rotations based on the Coriolis principle. The specific design of the haltere is in contrast to the existing MEMS vibratory gyroscope, where the elastic beams supporting the proof mass are typically designed with symmetric cross-sections so that there is a mode matching between the actuation and sensing vibrations. The mode matching provides high sensitivity and low bandwidth. Hence, the objective of the manuscript is to understand the mechanical significance of the haltere's asymmetry. In this study, the distributed Coriolis force and the corresponding bending stress by incorporating the actual mass variations along the haltere length are estimated. In addition, it is hypothesied that sensilla sense the rate of rotation based on the differential strain (difference between the final strain (strain due to the inertial and Coriolis forces) and the reference strain (strain due to inertial force)). This differential strain always occurs either on the dorsal or ventral surface of the haltere and at a distance away from the base, where the campaniform sensilla are located. This study brings out one specific feature—the asymmetric geometry of the haltere structure—that is not found in current vibratory gyroscope designs. This finding will inspire new designs of MEMS gyroscopes that have elegance and simplicity of the haltere along with the desired performance.