Manipulate the coiling and uncoiling movements of Lepidoptera proboscis by its conformation optimizing

Many kinds of adult Lepidoptera insects possess a long proboscis which is used to suck liquids and has the coiling and uncoiling movements. Although experiments revealed qualitatively that the coiling movement is governed by the hydraulic mechanism and the uncoiling movement is due to the musculature and the elasticity, it needs a quantitative investigation to reveal how insects achieve these behaviors accurately. Here a quasi-one-dimensional (Q1D) curvature elastica model is proposed to reveal the mechanism of these behaviors. We find that the functions of internal stipes muscle and basal galeal muscle which locate at the bottom of proboscis are to adjust the initial states in the coiling and uncoiling processes, respectively. The function of internal galeal muscle which exists along proboscis is to adjust the line tension. The knee bend shape is due to the local maximal spontaneous curvature and is an advantage for nectar-feeding butterfly. When there is no knee bend, the proboscis of fruit-piercing butterfly is easy to achieve the piercing movement which induced by the increase of internal hydraulic pressure. All of the results are in good agreement with experiential observation. Our study provides a revelatory method to investigate the mechanical behaviors of other 1D biologic structures, such as proboscis of marine snail and elephant. Our method and results are also significant in designing the bionic devices. keywords: Curvature, Proboscis, Equilibrium shape