Earwig fan designing: Biomimetic and evolutionary biology applications

Abstract

Technologies to fold structures into compact shapes are required in multiple engineering applications. Earwigs (Dermaptera) fold their fanlike hind wings in a unique, highly sophisticated manner, granting them the most compact wing storage among all insects. The structural and material composition, in-flight reinforcement mechanisms, and bistable property of earwig wings have been previously studied. However, the geometrical rules required to reproduce their complex crease patterns have remained uncertain. Here we show the method to design an earwig-inspired fan by considering the flat foldability in the origami model, as informed by X-ray microcomputed tomography imaging. As our dedicated designing software shows, the earwig fan can be customized into artificial deployable structures of different sizes and configurations for use in architecture, aerospace, mechanical engineering, and daily use items. Moreover, the proposed method is able to reconstruct the wing-folding mechanism of an ancient earwig relative, the 280-million-year-old Protelytron permianum This allows us to propose evolutionary patterns that explain how extant earwigs acquired their wing-folding mechanism and to project hypothetical, extinct transitional forms. Our findings can be used as the basic design guidelines in biomimetic research for harnessing the excellent engineering properties of earwig wings, and demonstrate how a geometrical designing method can reveal morphofunctional evolutionary constraints and predict plausible biological disparity in deep time.

Keywords: aerospace engineering; biomimetics; deployable structure; dermaptera; origami.

Fig. 1.

Earwig hind wing in unfolded and folded shapes. Long and short ribs are in red and blue, respectively; bridge veins are in green. (A) Unfolded left hind wing of F.auricularia. (B) Detail of rib base. (C) Oval-shaped bending points (hinges). (D) Zigzagging of long and short ribs. (E) Folded left hind wing of F. auricularia as seen from above, corresponding to the shaded area in A. (F) Micro-CT image showing the conformation of veins inside a folded right hind wing of A. harmandi in underside view. (G) Diagram of F. (H) Same as F, in lateral view. Ap, apical stretch of long ribs; ba, basal stretch of long ribs.

Fig. 2.

Geometrical drawing method of the earwig fan. (A) Construction of the starting geometric elements (circle O, point A, and line MN) and projection of lines H_iF_i. (B) Construction of the radial folding lines and the ring-fold lines. (C) Modification system of the ring fold used to adjust the clearances between ring-fold lines in the folded shape, without interference to the flat foldability. (D) Idealized earwig venation drawn on a constructed crease pattern, showing the same characteristics as in the actual earwig wings (Fig.1 A–D). (E and F) Schematic folding movements of the normal fan and the designed earwig fan, respectively.

Fig. 3.

Two basic design strategies of earwig-fan inspired deployable structures. (A) Parallel-edge approach. (B) Equal-clearance approach.

Fig. 4.

Examples of models using the design software. (A) Extended circular model, resulting from extending the pattern around the rib base. This design can be used for deployable structures such as antenna reflectors and umbrellas. (B) Symmetrical circular model. (C) Deployable wing for microair vehicle, obtained by simplifying the earwig folding patterns. See Movie S5. (D) Interference control of the hinge parts by the provided designing software. (E) Three-dimensional printed earwig fan frame based on the model shown in D. All hinge parts can be stored compactly without interference.

Fig. 5.

Wing-folding pattern in P. permianum using the proposed geometrical designing method, and two hypothetical evolutionary pathways explaining the folding pattern of extant earwigs. (A) Right hind wing of P. permianum, MCZ-ENT-PALE-3366b. Image credit: Museum of Comparative Zoology, Harvard University. Copyright President and Fellows of Harvard College. (B) Reconstructed crease pattern of the wing of P. permianum. Black thick lines indicate mountain folds. Red and blue lines indicate mountain and valley folding, respectively, in mode A; the opposite assignment corresponds to mode B. (C) Shrinking and moving rib base hypothesis, in folding mode A, and the predicted crease pattern in a hypothetical transitional form (Right). Continuous and dashed lines indicate mountain and valley fold, respectively. (D) Second ring fold hypothesis, in folding mode B, and the predicted crease pattern in a hypothetical transitional form (Right). RF = ring fold. See SI Appendix, Text 2 and Figs. S5 and S6.