Absolute ethanol-preserved specimens of flea beetles were selected. The meta-femurs were carefully removed and dried at the critical point (hcp-2, Hitachi Inc., Tokyo, Japan), and then glued to the tip of a micropipette using nail polish. Hind legs of seven species [Altica cirsicola Ohno, Clavicornaltica sp., Hespera lomasa Maulik, Nonarthra sp., Asiophrida xanthospilota Baly, Podontia lutea (Olivier, 1790), Psylliodes sp.] were scanned with a MicroXCT-400 scanner (Xradia Inc., California, USA. Beam strength: 60 kV, absorption contrast). Pixel size of images: 0.5~5μm; optical magnification: 4–40× (depending on different specimen size). In most scans, 900–1100 sections of images were obtained, then imported to Amira 5.4.1 (Visage Imaging, San Diego, California, USA) for 3D reconstructions. Autodesk maya 2014 (Autodesk Inc., San Rafael, California, USA) was used to smooth and render the 3D structures.

Hind legs of flea beetles across 13 genera were further dissected and examined (list of species dissected: Agasicles hygrophila Selmen et Vogt, Altica cirsicola, Chaetocnema constricta Ruan, Konstantinov et Yang, Clavicornaltica sp., Hemipyxis sp., Hespera lomasa, Luperomorpha xanthodera (Fairmaire), Nonarthra sp., Asiophrida xanthospilota, Podontia lutea, Psylliodes sp., Stenoluperus sp., Trachytetra obscura (Jacoby)). These genera and species were chosen to represent flea beetles with different body sizes. A conventional optical imaging system consisting of a Zeiss Axiostar plus microscope (Zeiss Inc., Göttingen, Germany), Nikon D300 digital camera (Nikon Inc., Tokyo, Japan) and Helicon Focus 6 software was used to capture and compose 2D images. The figure plates were prepared with Photoshop CS5 (Adobe, San Jose, USA) and Illustrator CS5 (Adobe, San Jose, USA).

The general morphological terminology used throughout this report follows Furth (1988).

Four species of flea beetles (Chaetocnema picipes Stephens, Altica cirsicola, Asiophrida xanthospilota, Psylliodes punctifrons Baly) were collected in the field in Beijing, China from July to October 2015 for high-speed filming. During the study, the flea beetles were reared in the laboratory in plastic containers and fed on their host plants. Videos of their jumps were recorded at 4580–6800 fps using a Phantom M110 high-speed camera (Vision Research Inc., USA). Take-off velocity and acceleration were determined by the recorded videos, which were played frame-by-frame and analyzed using PCC 2.5 software (PHANTOM CAMERA CONTROL 2.5.744.0, Vision Research Inc., USA).

Our findings on the hind leg musculature are mostly in accord with those described by Barth (1954) and Nadein and Betz (2016). However, our 3D reconstructions and dissection show that flea beetles have another small structure related to jumping in their hind leg, described here as the ‘elastic plate’ (Figs 1H, 5F: epl), it resembles a small tendon: semi-transparent, milky white, nearly ellipsoid and elastic structure with weak sclerotization; it is attached to the inner wall of the femur, ventro-distally, situated near the femorotibial joint (Fig. 5H). The base of the elastic plate is sclerotized and fused with the inner wall of femur, while the apical and middle part is rubber-like and has great elasticity.

Figure 1. 

Jumping apparatus in the flea beetle hind leg. A a model of a generic flea beetle (lateral view), indicating the enlarged hind leg B hind leg of Trachytetra obscura under a light microscope (dark-field microscopy) C–H X-ray computer tomography-based 3D reconstructions of the hind leg of the flea beetle Asiophrida xanthospilota C lateral view of the hind leg and internal structures D dorsal view of the hind leg E lateral view of the hind leg (view from an opposite direction of inset C) F lateral view of the metafemoral spring G ventral view of the metafemoral spring H femorotibial joint. Abbreviations: epl: elastic plate; piv: tibial pivot of femorotibial joint; tli-1: primary tibial ligament; tli-2: secondary tibial ligament; tpl: Lever’s triangular plate.

Figure 2. 

Internal structures of the hind leg of Altica cirsicola. A the flea beetle Altica sp. on foliage B–F X-ray computer tomography 3D reconstructions of the hind leg of A. cirsicola B lateral view of the left hind leg C lateral view of the metafemoral spring D distal view of the metafemoral spring E distal view of the metafemoral spring and tibial extensors F features of the femorotibial joint. Abbreviations: cox: coxa; exa: extended arm of the metafemoral spring; epl: elastic plate; fem: femur; msp: metafemoral spring; ner: nerve; piv: tibial pivot of the femorotibial joint; rfl: recurve flange of the metafemoral spring; tar: tarsi; tex-1: primary tibial extensor; tex-2: secondary tibial extensor; tfl: tibial flexor; tib: tibia; tli-1: primary tibial ligament; tli-2: secondary tibial ligament; tpl: Lever’s triangular plate; tra: trachea; tro: trochanter.

Figure 3. 

Variation in the metafemoral spring of different flea beetle species (3D reconstructions). A hind femur of Altica cirsicola B hind femur of Podontia lutea C hind femur of Psylliodes sp. D hind femur of Nonarthra sp. E hind femur of Clavicornaltica sp. F hind femur of Hespera lomasa. Scale bar: 0.2 mm.

The elastic plate was found inside the hind femora of all 13 genera of flea beetles that were dissected. In some other jumping insects that we have examined [Galerucines (Chrysomelidae, Galerucini); Scirtes sp. (Coleoptera, Scirtidae); Rhynchaenus sp. (Coleoptera, Curculionidae); Lycorma delicatula (White) (Hemiptera, Fulgoridae); Locusta migratoria (L.) (Orthoptera, Acrididae); Tridactylidae sp. (Orthoptera, Tridactylidae); Brachymeria sp. (Hymenoptera, Chalcididae)], the elastic plate is absent. However, a thin membrane is present in the same area, which may serve to protect the femorotibial joint in locomotion. It is very possible that the elastic plate is developed from this membrane.

Based on our morphological observations and the high-speed filming, we hypothesize that a typical flea beetle jump can be divided into four major phases (Fig. 4, Supplementary files movie S1–S3).

Figure 4. 

Take-off strategy of flea beetles (Asiophrida xanthospilota is shown in the photos at the top of the figure). Acceleration data were calculated based on three typical jumps recorded by a high-speed camera. The three different species were chosen to represent flea beetles with different sizes A Phase I (Crunching): tibial flexor muscles contract, causing flexion of the tibia B Phase II (Co-contraction): tibial extensor muscles and tibial flexor muscles contract simultaneously, catching the triangular plate and hindering the extension of the tibia C Phase III (Triggering and Acceleration), the triangular plate is dislodged, causing the explosive release of energy D Phase IV (Relaxation), the flea beetle is catapulted into the air and the muscles begin to relax.

Phase I entails the preparation for a jump, wherein the flea beetle flexes its hind legs until the femorotibial angle reaches a minimum of approximately 20°. This flexion usually takes no more than 20 ms (Fig. 4A).

Phase II is an initiation phase in which elastic strain energy cumulatively builds up inside the femur as the femorotibial angle increases from approximately 20° to 60°, which takes approximately 4–5 ms (Fig. 4B). Inside the femur, the tibial extensor and tibial flexor muscles contract simultaneously [Co-contraction (Nadein and Betz 2016)]. Given that the tibial extensor muscle generates greater force than the tibial flexor, the tibia starts to revolve (or extend) around the tibial pivot (Fig. 1H: piv). As a result, the triangular plate (also as: Lever's triangular plate) (Fig. 5F: tpl) could be drawn out of the femur, but momentarily gets caught by and stuck on the elastic plate (Fig. 5F: epl). Thus, the metafemoral spring (Figs 1F, G; 3) is stretched by the tibial extensor muscle, establishing a catapult-like structure inside the femur. The metafemoral spring stores the huge elastic strain energy required to trigger the catapult, while the triangular and elastic plates comprise a ‘trigger system’ that catches the ‘sling’ and prepares to trigger the catapult.

Phase III is the most dramatic phase, yet it only takes 1–2 ms (Fig. 4C). Due to an increase in the femorotibial angle and accumulating tension, the elastic plate is no longer able to hold the catapult sling in position; subsequently, the triangular plate is dislodged abruptly from the elastic plate and slips out of the femur, triggering the explosive jump. The acceleration of the flea beetle increases explosively, peaking in less than 1 ms, and then abruptly dropping to near zero. The femorotibial angle extends from approximately 60° to 130° in 1–2 ms.

Finally, in phase IV (Fig. 4D), when the femorotibial angle reaches approximately 130°, the acceleration drops to almost zero, and no more strain energy is released. After the femorotibial angle extends beyond approximately 160°, the flea beetle leaves the ground.

Furthermore, an experiment was designed to test the four phases of the catapult mechanism identified by the position of the elastic plate during a simulated jump (Supplementary files movie S4).

To understand the explosive manner of the flea beetle jump, we analyzed the mechanical dynamics involved in the jumping process.

For the mechanical analysis, we generated 3D reconstructions of the hind legs during the four different phases of the catapult jump (Fig. 5). Here we use F₁ and F₂ to denote two forces acting on the tibia via the tibial ligaments, where F₁ is generated by the tibial extensor muscle and F₂ is indirectly generated by the tibial flexor muscle; d₁ and d₂ denote the moment arms (i.e., lever arms) of F₁ and F₂, respectively, corresponding to the femorotibial joint. The total torque generated by muscle around the joint (i.e., the tibial pivot), denoted by M, can be expressed as M=F₁d₁–F₂d₂. The 3D reconstructions of the hind leg at phases I, II, III and IV of the jump are detailed in panels A, B, C and D of Fig. 5, respectively, which shows how the force F_j and its moment arm d_j (j=1, 2) change during the different phases. During the extension of the hind leg, d₁ is at its minimum at the start of the extension and at its maximum during the middle of the extension; by contrast, d₂ is at its maximum at the start of the extension and at its minimum at the end. Furthermore, the force F₂ comprises two forces, F₂₁ and F₂₂, where F₂₁ is the constrained force generated by the elastic plate and F₂₂ is generated by the tibial flexor muscle (Fig. 5E). F₂₁ and F₂₂ can be simply expressed as F₂₁=F₂sinθ and F₂₂=F₂cosθ, where θ is the angle between F₂ and F₂₂ (Fig. 5E). The lateral and dorsal views of the triangular plate – elastic plate complex are shown in Fig. 5F, G, and the dorsal views of the elastic plate and triangular plate under a light microscope are shown in Fig. 5H, I.

Figure 5. 

The dynamics of the catapult mechanism of the flea beetle hind leg powered by the elastic plate (Asiophrida xanthospilota, micro-CT 3D reconstructions from four different phases of the jumping leg). (F₁ indicates the force generated by tibial extensor muscles responsible for extension of the tibia; F₂ indicates the force responsible for flexion of the tibia which is indirectly generated by tibial flexor muscles). A–D 3D reconstructions of four hind legs through each of the four phases of the jump, indicating variable d₁ (moment arm of F₁) and d₂ (moment arm of F₂). d₁ is at its minimal length at the start of the hind leg extension and at its maximal length during the middle; by contrast, d₂ is at its maximal length at the start of the hind leg extension and at its minimal at the end A phase I B phase II C phase III D phase IV E the positive feedback mechanism in the take-off process. F₂ comprises F₂₁, which is the constrained force generated by the elastic plate, and F₂₂, which is generated by the tibial flexor muscle F the triangular plate – elastic plate complex (lateral view) G the triangular plate – elastic plate complex (dorsal view) H the elastic plate (dorsal view, under light microscope, dark-field microscopy) I the triangular plate (dorsal view, under light microscope, dark-field microscopy). Abbreviations: epl: elastic plate; tli-2: secondary tibial ligament; tpl: triangular plate; ten: tendon of tibial flexor.

At the beginning of phase II, the total torque M is close to zero, since F₁d₁≈F₂d₂. Therefore, in this phase, the tibia extends very slowly, and the metafemoral spring is stretched by F₁ and F₂₂, such that the huge energy generated by the antagonistic muscles (tibial extensor and flexor) is stored. In phase III, the continuous extension of the hind leg causes a rapid increase in d₁ while d₂ decreases; simultaneously, θ decreases and F₂₂ does not change, thereby dramatically decreasing F₂=F₂₂/cosθ. This ‘positive feedback mechanism’ leads to the explosive increase in the total torque M=F₁d₁–F₂d₂ (at this point, F₁d₁>>F₂d₂). When θ decreases to near zero, the triangular plate is dislodged and slips out of the femur. Meanwhile, the enormous elastic strain energy, previously stored in the metafemoral spring, is rapidly converted into kinetic energy, allowing the flea beetle to attain an extraordinarily high acceleration.

Taken together, these results suggest that two structures play a significant role in the catapult mechanism – the elastic plate and the triangular plate, which control the timing of the jumping process, the triggering of the catapult, and the explosive release of energy.

In order to explore the efficiency of flea beetle jumping, we compared their jumping dynamics with that of humans. Morphologically, the flea beetle hind leg resembles the human leg since both are ‘two-segment systems’ (Alexander 1995). In a typical human jump, assuming the tibial extensor muscle generates a constant force, the uplift force and work efficiency of the leg are almost proportional to the knee angle (femorotibial angle) (Martin and Stull 1969; Zhao and Li 2008). The dynamics of this mechanism can be generally expressed as: F α tan β (where F is the uplift force and β is the knee angle) (Zhao and Li 2008), which means that the energy generated by the tibial extensor muscle (or the elastic strain energy stored in elastic elements) can be turned into kinetic energy more efficiently at a later stage of a jump. Similarly, instead of accelerating constantly throughout its jump, the flea beetle also uses this high-efficiency mechanism to store colossal strain energy at an early stage and release it at a later, higher-efficiency stage. In this way, the flea beetles avoid muscle fatigue (or energy waste) and improve their jumping performance simultaneously.

High-speed film data demonstrate that the peak acceleration is approximately 10 times as great as that at the start of the jump (in Phase II). As shown by our kinematic data based on high-speed filming, Psylliodes punctifrons jumped with an average acceleration of 3450±10 m/s² and took 6 ms to complete a jump, yet the main acceleration occurred in approximately 1 ms, peaking at 8650±10 m/s² at the end of the whole jumping process. This scenario differs from that seen in other jumping insects, which have either a near-constant (Bonsignori et al. 2013) or gently increasing (Sutton and Burrows 2011) acceleration during take-off.

An individual P. punctifrons has an average mass of 1.6 mg, with the hind legs comprising only 17% of the total body mass. The jump pushes individuals to a final velocity of 5.58±0.5 m/s. The peak instantaneous power output (per unit mass) calculated for the hind legs in this species was 2.2±0.1 × 10⁵ W/kg, which is approximately 449 times that of the fastest-known muscle (Weis-Fogh and Alexander 1977) and some 100–200 times that of a powerful rally car engine.

In the field, flea beetles conduct contiguous jumps when encountering interference (based on our field observations in this study). When stimulated continuously in the laboratory (tested in this study), they can jump more than 30 times in a row without significant fatigue. Given that the power output of a catapult can be greater than the power input (Bennet-Clark and Lucey 1967; Alexander and Bennet-Clark 1977), because of the amplification of the power output, flea beetles thrust themselves across a distance hundreds of times their own body length in only a few milliseconds. In this way, flea beetles achieve extremely efficient and effective locomotion.

Jumping can be a very effective mode of locomotion for small robots (Kovač et al. 2008). If designed using a catapult mechanism, a jumping leg could propel a robot into the air in an explosive manner (Fig. 6), while the robot could also return to a regular walking mode at any time by the catapult mechanism being switched off, such as a flea beetle does. A preliminary design of a robotic jumping leg is given in Figure 6. Its working principles are as follows. The required energy for a jump is provided by two ‘motors’ operating simultaneously and generating the forces F₁ and F₂, respectively, F₁ is designed to be much greater than F₂. At the beginning of a jump (Fig. 6B), when the motors are turned on, F₁ > F₂, the ‘tibia’ starts to extend. However, a ‘trigger’ (mimicking the ‘elastic plate’ of the flea beetle leg) is designed to block the process and it leads to the stretching of a ‘volute spring’ (mimicking the metafemoral spring of the flea beetle leg). Thus, the work generated by the ‘motors’ is stored in the ‘volute spring’. At a certain stage (Fig. 6C), when the ‘trigger’ can no longer constrain the huge tension built up inside the femur, the ‘latch element’ (mimicking the triangular plate of the flea beetle leg) dislodges suddenly from the ‘trigger’ and the huge amount of energy stored in the ‘volute spring’ is released. This leads to the explosive extending movement of the tibia. The leg thereby propels the robot into the air.

Figure 6. 

Bionic design of a jumping limb inspired by the flea beetle leg. A preparation position for jumping B building up elastic strain energy C triggering the jump D acceleration. The required energy for a jump is provided by two ‘motors’ operating simultaneously and generating the forces F₁ and F₂, respectively. At the beginning (inset B), F₁ > F₂, the ‘tibia’ rotates clockwise, but the ‘trigger’ blocks the process and leads to the stretching of ‘volute spring’. Thus, the work generated by the ‘motors’ is stored in the ‘volute spring’. At a certain stage (inset C), when the ‘trigger’ can no longer constrain the huge tension built up inside the femur, the ‘latch element’ dislodges suddenly from the ‘trigger’ and the huge amount of energy stored in the ‘volute spring’ is released. This leads to the explosive clockwise movement of the tibia. The leg thereby propels the robot into the air in an explosive manner. The leg can be switched to regular walking mode as required by operating only one ‘motor’ (one to flex the leg and the another to extend it) at a time.

The leg can also be switched to a regular walking mode as required by operating only one ‘motor’ at a time (as the ‘trigger’ will stop working when only one motor is turned on). In the regular walking mode, one motor could be turned on to flex the leg and the other to extend it, respectively.