Abstract
Birds, bats and many insects can tuck their wings against their bodies when at rest and deploy them to power flight. Whereas birds and bats use well-developed pectoral and wing muscles1,2, how insects control their wing deployment and retraction remains unclear because this varies among insect species. Beetles (Coleoptera) display one of the most complex mechanisms. In rhinoceros beetles, Allomyrina dichotoma, wing deployment is initiated by complete release of the elytra and partial release of the hindwings at their bases. Subsequently, the beetle starts flapping, elevates the hindwing bases and unfolds the hindwing tips in an origami-like fashion. Although the origami-like fold has been extensively explored3,4,5,6,7,8, limited attention has been given to the hindwing base movements, which are believed to be driven by the thoracic muscles5,9,10,11. Here we demonstrate that rhinoceros beetles can effortlessly deploy their hindwings without necessitating muscular activity. We show that opening the elytra triggers a spring-like partial release of the hindwings from the body, allowing the clearance needed for the subsequent flapping motion that brings the hindwings into the flight position. After flight, the beetle can use the elytra to push the hindwings back into the resting position, further strengthening the hypothesis of passive deployment. We validated the hypothesis using a flapping microrobot that passively deployed its wings for stable, controlled flight and retracted them neatly upon landing, demonstrating a simple, yet effective, approach to the design of insect-like flying micromachines.
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Data availability
All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information. Data are available at Figshare (https://doi.org/10.6084/m9.figshare.25703214)41. Source data are provided with this paper.
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Acknowledgements
This project was partially funded by the Swiss National Science Foundation through the NCCR Robotics programme, and by the Korean government (MSIT) (No. 2022R1A4A101888411) through the National Research Foundation of Korea (NRF).
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H.-V.P. conceived the idea, designed the research, built the flapping robots, performed all the experiments on the insects and robots, processed, analysed and interpreted the data, and originally drafted the manuscript. H.C.P. and D.F. contributed to the data analysis and the writing of the manuscript. All authors gave final approval for publication.
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Extended data figures and tables
Extended Data Fig. 1 Wing deployment kinematics of beetles.
a,b, At the end of the partial release (phase I of the deployment), the hindwing experiences decreasing oscillations around the equilibrium position, δh,base = 48.5 ± 0.7°: (a) elevation angle (b) and angular rate. c, Amplitude of the first oscillation (shown in a) is proportional to the releasing rate of the hindwing in b. Red line denotes the linear fit. d, Elevation angles of the elytron (orange) and the hindwing (dark blue). The time instant was set to 0 s when the elytron started elevating.
Extended Data Fig. 2 Beetle’s hindwing deployment experiments using a motor-driven flapping mechanism.
a, Experimental setup. b, Flapping mechanism design combining the Scotch-Yoke and pulley-string mechanisms to convert rotary motion of a d.c. motor to high-stroke flapping motion of the wing. c, Forces acting on the hindwing during flapping-and-elevation motion with a velocity V in the first cycle. With a vertical body orientation, gravitational force (W) and aerodynamic drag (D) hinder the hindwing elevation motion. Inertial force (FI) hinders the elevation during acceleration at the beginning of stroke but facilitates the elevation during deceleration at the end of stroke. In contrast, centrifugal force (Fc) and aerodynamic lift (L) drive the elevation motion. d, Hindwing kinematics in the first flapping cycle. The hindwing was fully elevated at the base (δh,base) during the first half of the upstroke motion while flapping at a high angle of attack (αh) with a folded wingtip (δh,tip). The angle of attack is defined as the angle between the wing surface and the direction of flapping motion. Shaded area corresponds to upstroke motion. The small magnitude of lift, due to high angles of attack and folded wingtip, does not contribute significantly to hindwing elevation. e, Hindwing deployment kinematics at various flapping frequencies.
Extended Data Fig. 3 Rhinoceros beetles use their elytra to depress the hindwings to the resting position after flight.
a,b, When at rest, the hindwings can be folded neatly inside the elytra. c, Stroke (dashed line) and elevation (solid line) angles of the elytron (orange) and hindwing (blue) during retraction. The time instant was set to 0 s when the elytron touched the hindwing while closing.
Extended Data Fig. 4 Deployment kinematics of the robotic wings.
a,b, Without wing membrane, the centrifugal force keeps the wing on the plane normal to the flapping axis (δ = 90°), even with the elevation threshold of δthreshold = 110° (b). c,d, Elevation angle (δ) (c) and rate (\(\dot{\delta }\)) (d) of the wings with (light blue) and without (orange) the membrane during the first flapping cycle. In the inertia-only case (orange), we added more mass to the leading-edge spar to compensate for the mass of the wing membrane. e, Stroke angle (ϕ) and angle of attack (α) at 50% wingspan. Shaded area denotes the upstroke motion. With the membrane, the wing operated at extremely high angles of attack during the upstroke but very small angles of attack during the downstroke in the first flapping cycle (Supplementary Video 7). Therefore, aerodynamic forces from the membrane hinder rather than facilitate elevation. As a result, they cause the wing to reach the elevation threshold slightly later than in the inertia-only case. Nevertheless, both cases enable the wing to elevate within a flapping cycle. f, Wing tip trajectory of the non-retractable wing when flapping at 20 Hz. The oscillation of the elevation angle is due to the bending of the leading-edge spar during flapping motion. g,h, Deviation of the elevation angles (g) from the threshold angles of 90° (cyan) and 100° (red) (Δδ = δ – δthreshold), and deviation rate (h). i,j, Stroke angular velocity (i) and acceleration (j). The downward movement of the wing is developed at the beginning of each stroke (the first half stroke denoted by the shaded area in g–j where the wing accelerates, similar to what was observed in the wing-inertia-only case.
Extended Data Fig. 5 The 18.2 gram flapping-wing robot with tracking markers used in flight experiments.
a, The markers added only 0.2 gram to the robot. The avionics system is covered with damping foam to reduce vibration noise during flapping flight and for protection. b,c, Close-up of the wing in folded (b) and extended (c) configurations. The wings remain folded at the lower threshold (about 5° from the wing root spar).
Extended Data Fig. 6 Additional untethered flight experiments.
a-d, Test #1: flight trajectory (a), and roll (b), pitch (c), and yaw (d) attitude angles. e-h, Test #2: flight trajectory (e), and roll (f), pitch (g), and yaw (h) attitude angles. i-l, Test #3: flight trajectory (i), and roll (j), pitch (k), and yaw (l) attitude angles. Red dashed line denotes the reference.
Supplementary information
Supplementary Video 1
Deployment procedure of the elytra and hindwings in the rhinoceros beetle. The video shows the two-phase wing deployment of a tethered beetle. In the first phase, the beetle fully elevates the elytra and partially releases the hindwings from the abdomen. Thereafter, the beetle initiates the second phase by activating synchronized flaps of both the elytra and hindwings, elevating the hindwings at the bases and unfolding the hindwing tips. The experiments were recorded by a high-speed camera at 2,000 fps and are played back at 60 fps and 30 fps.
Supplementary Video 2
Deployment procedure of the beetle's hindwing in a motor-driven flapping mechanism. This video shows that, by exciting the flapping motion at about 38 Hz, similar to that of the beetle, the hindwing can passively elevate at the base and unfold the wing tip. By deactivating the flapping, the hindwing is retracted by gravitational force. The video was recorded by a high-speed camera at 2,000 fps and is played back at 30 fps.
Supplementary Video 3
Retraction of the beetle's hindwing at the base in the presence of the elytron. This video shows that the rhinoceros beetle can use its elytra to depress the hindwings down to the abdomen. The video was recorded by a high-speed camera at 2,000 fps and is played back at 30 fps.
Supplementary Video 4
Retraction of the beetle's hindwing at the base without the elytron. This video shows that a rhinoceros beetle lacking the right elytron is unable to retract its right hindwing after flapping flight, whereas the intact left elytron can depress the left hindwing towards the abdomen. The video was recorded by a high-speed camera at 2,000 fps and is played back at 60 fps.
Supplementary Video 5
Rhinoceros beetle using its legs to retract the hindwing. This video shows that a rhinoceros beetle lacking the elytron can use its legs (middle leg) as an alternative way of depressing the hindwing to the resting position. The video was recorded by a high-speed camera at 2,000 fps and is played back at 60 fps.
Supplementary Video 6
Passive retraction of a robotic wing. The video shows that the elastic tendon at the armpit facilitates rapid wing retraction while still allowing wing elevation within one flapping cycle by the centrifugal effect. The experiments were recorded by a high-speed camera at 2,000 fps and are played back at 60 fps.
Supplementary Video 7
Passive deployment of a robotic wing. The video shows experiments demonstrating the passive elevation of the robotic wing through the activation of a flapping motion. The experiments were recorded by a high-speed camera at 2,000 fps and are played back at 30 fps.
Supplementary Video 8
Experiment of wing deployment and retraction in a tethered flapping microrobot. The video shows an experiment demonstrating the passive elevation and retraction of the robotic wings through the activation and deactivation of a flapping motion, respectively. The experiment was recorded by a high-speed camera at 500 fps and is played back at 50 fps.
Supplementary Video 9
Flapping microrobot flying with passive deploying–retracting wings. The robot can passively deploy its wings for take-off, perform stable hovering, and rapidly retract the wings against the body upon landing. The experiments were recorded by a high-speed camera at 500 fps and are played back at 100 fps and 50 fps.
Supplementary Video 10
Rapid retraction protecting the wings from a crash-landing due to in-flight wing collision. The video shows an experiment on in-flight wing collision, which causes the robot to destabilize and tumble. The robot then rapidly retracts its wings against the body before reaching the ground, thus helping to prevent wing damage. The experiment was recorded by a high-speed camera at 500 fps and is played back at 50 fps.
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Phan, HV., Park, H.C. & Floreano, D. Passive wing deployment and retraction in beetles and flapping microrobots. Nature 632, 1067–1072 (2024). https://doi.org/10.1038/s41586-024-07755-9
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DOI: https://doi.org/10.1038/s41586-024-07755-9
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