Jumping of flea beetles onto inclined platforms

The flea beetle, Altica cirsicola, escapes predators by jumping and landing in a dense maze of leaves. How do they land on such varied surfaces? In this experimental study, we filmed the take-off, flight, and landing of flea beetles on a configurable angled platform. We report three in-flight behaviors: winged, wingless, and an intermediate winged mode. These modes significantly affected take-off speed, acceleration, and the duration that wings were deployed. When wings were closed, flea beetles rolled or pitched up to five times in the air. This work may help to understand how insects can jump and right themselves onto variable surfaces.

Engineered jumpers overcome biological limits via work multiplication

For centuries, scientists have explored the limits of biological jump height^1,2, and for decades, engineers have designed jumping machines^3-18 that often mimicked or took inspiration from biological jumpers. Despite these efforts, general analyses are missing that compare the energetics of biological and engineered jumpers across scale. Here we show how biological and engineered jumpers have key differences in their jump energetics. The jump height of a biological jumper is limited by the work its linear motor (muscle) can produce in a single stroke. By contrast, the jump height of an engineered device can be far greater because its ratcheted or rotary motor can 'multiply work' during repeated strokes or rotations. As a consequence of these differences in energy production, biological and engineered jumpers should have divergent designs for maximizing jump height. Following these insights, we created a device that can jump over 30 metres high, to our knowledge far higher than previous engineered jumpers and over an order of magnitude higher than the best biological jumpers. Our work advances the understanding of jumping, shows a new level of performance, and underscores the importance of considering the differences between engineered and biological systems.

Jump takeoff in a small jumping spider

Jumping in animals presents an interesting locomotory strategy as it requires the generation of large forces and accurate timing. Jumping in arachnids is further complicated by their semi-hydraulic locomotion system. Among arachnids, jumping spiders (Family Salticidae) are agile and dexterous jumpers. However, less is known about jumping in small salticid species. Here we used Habronattus conjunctus, a small jumping spider (body length ~ 4.5 mm) to examine its jumping performance and compare it to that of other jumping spiders and insects. We also explored how legs are used during the takeoff phase of jumps. Jumps were staged between two raised platforms. We analyzed jumping videos with DeepLabCut to track 21 points on the cephalothorax, abdomen, and legs. By analyzing leg liftoff and extension patterns, we found evidence that H. conjunctus primarily uses the third legs to power jumps. We also found that H. conjunctus jumps achieve lower takeoff speeds and accelerations than most other jumping arthropods, including other jumping spiders. Habronattus conjunctus takeoff time was similar to other jumping arthropods of the same body mass. We discuss the mechanical benefits and drawbacks of a semi-hydraulic system of locomotion and consider how small spiders may extract dexterous jumps from this locomotor system.

Jumping Locomotion Strategies: From Animals to Bioinspired Robots

Jumping is a locomotion strategy widely evolved in both invertebrates and vertebrates. In addition to terrestrial animals, several aquatic animals are also able to jump in their specific environments. In this paper, the state of the art of jumping robots has been systematically analyzed, based on their biological model, including invertebrates (e.g., jumping spiders, locusts, fleas, crickets, cockroaches, froghoppers and leafhoppers), vertebrates (e.g., frogs, galagoes, kangaroos, humans, dogs), as well as aquatic animals (e.g., both invertebrates and vertebrates, such as crabs, water-striders, and dolphins). The strategies adopted by animals and robots to control the jump (e.g., take-off angle, take-off direction, take-off velocity and take-off stability), aerial righting, land buffering, and resetting are concluded and compared. Based on this, the developmental trends of bioinspired jumping robots are predicted.

Why do Large Animals Never Actuate Their Jumps with Latch-Mediated Springs? Because They can Jump Higher Without Them

As animals get smaller, their ability to generate usable work from muscle contraction is decreased by the muscle's force-velocity properties, thereby reducing their effective jump height. Very small animals use a spring-actuated system, which prevents velocity effects from reducing available energy. Since force-velocity properties reduce the usable work in even larger animals, why don't larger animals use spring-actuated jumping systems as well? We will show that muscle length-tension properties limit spring-actuated systems to generating a maximum one-third of the possible work that a muscle could produce-greatly restricting the jumping height of spring-actuated jumpers. Thus a spring-actuated jumping animal has a jumping height that is one-third of the maximum possible jump height achievable were 100% of the possible muscle work available. Larger animals, which could theoretically use all of the available muscle energy, have a maximum jumping height that asymptotically approaches a value that is about three times higher than that of spring-actuated jumpers. Furthermore, a size related "crossover point" is evident for these two jumping mechanisms: animals smaller than this point can jump higher with a spring-actuated mechanism, while animals larger than this point can jump higher with a muscle-actuated mechanism. We demonstrate how this limit on energy storage is a consequence of the interaction between length-tension properties of muscles and spring stiffness. We indicate where this crossover point occurs based on modeling and then use jumping data from the literature to validate that larger jumping animals generate greater jump heights with muscle-actuated systems than spring-actuated systems.

Jumping and take-off in a winged scorpion fly (Mecoptera, Panorpa communis)

High-speed videos were used to analyse whether and how adults of a winged species of scorpion fly (Mecoptera, Panorpa communis) jump and determine whether they use the same mechanism as that of the only other mecopteran known to jump, the wingless snow flea, Boreus hyemalis Adult females are longer and heavier than males and have longer legs, but of the same relative proportions. The middle legs are 20% longer and the hind legs 60% longer than the front legs. A jump starts with the middle and hind legs in variable positions, but together, by depressing their coxo-trochanteral and extending their femoro-tibial joints, they accelerate the body in 16-19 ms to mean take-off velocities of 0.7-0.8 m s^-1; performances in males and females were not significantly different. Depression of the wings accompanies these leg movements, but clipping them does not affect jump performance. Smooth transition to flapping flight occurs once airborne with little loss of energy to body rotation. Ninety percent of the jumps analysed occurred without an observable stimulus; the remaining 10% were in response to a mechanical touch. The performance of these jumps was not significantly different. In its fastest jumps, a scorpion fly experiences an acceleration of 10 g , expends 23 µJ of energy and requires a power output less than 250 W kg^-1 of muscle that can be met by direct muscle contractions without invoking an indirect power amplification mechanism. The jumping mechanism is like that of snow fleas.

Beyond power amplification: latch-mediated spring actuation is an emerging framework for the study of diverse elastic systems

Rapid biological movements, such as the extraordinary strikes of mantis shrimp and accelerations of jumping insects, have captivated generations of scientists and engineers. These organisms store energy in elastic structures (e.g. springs) and then rapidly release it using latches, such that movement is driven by the rapid conversion of stored elastic to kinetic energy using springs, with the dynamics of this conversion mediated by latches. Initially drawn to these systems by an interest in the muscle power limits of small jumping insects, biologists established the idea of power amplification, which refers both to a measurement technique and to a conceptual framework defined by the mechanical power output of a system exceeding muscle limits. However, the field of fast elastically driven movements has expanded to encompass diverse biological and synthetic systems that do not have muscles - such as the surface tension catapults of fungal spores and launches of plant seeds. Furthermore, while latches have been recognized as an essential part of many elastic systems, their role in mediating the storage and release of elastic energy from the spring is only now being elucidated. Here, we critically examine the metrics and concepts of power amplification and encourage a framework centered on latch-mediated spring actuation (LaMSA). We emphasize approaches and metrics of LaMSA systems that will forge a pathway toward a principled, interdisciplinary field.

Effectiveness and efficiency of two distinct mechanisms for take-off in a derbid planthopper insect

Analysis of the kinematics of take-off in the planthopper Proutista moesta (Hemiptera, Fulgoroidea, family Derbidae) from high-speed videos showed that these insects used two distinct mechanisms involving different appendages. The first was a fast take-off (55.7% of 106 take-offs by 11 insects) propelled by a synchronised movement of the two hind legs and without participation of the wings. The body was accelerated in 1 ms or less to a mean take-off velocity of 1.7 m s^-1 while experiencing average forces of more than 150 times gravity. The power required from the leg muscles implicated a power-amplification mechanism. Such take-offs propelled the insect along its trajectory a mean distance of 7.9 mm in the first 5 ms after take-off. The second and slower take-off mechanism (44.3% of take-offs) was powered by beating movements of the wings alone, with no discernible contribution from the hind legs. The resulting mean acceleration time was 16 times slower at 17.3 ms, the mean final velocity was six times lower at 0.27 m s^-1, the g forces experienced were 80 times lower and the distance moved in 5 ms after take-off was 7 times shorter. The power requirements could be readily met by direct muscle contraction. The results suggest a testable hypothesis that the two mechanisms serve distinct behavioural actions: the fast take-offs could enable escape from predators and the slow take-offs that exert much lower ground reaction forces could enable take-off from more flexible substrates while also displacing the insect in a slower and more controllable trajectory.

Do enlarged hind legs of male thick-legged flower beetles contribute to take-off or mating?

The volume of the hind femora in adult male flower beetles, Oedemera nobilis, is 38 times greater than in adult females. To determine what advantage limbs with swollen femora might provide, the behaviour of these insects was analysed with high speed videography. First, because large hind legs are often associated with jumping and take-off, the performance of this behaviour by the two sexes was determined. Take-off was generated by a series of small amplitude wing beats followed by larger ones with the hind legs contributing little or no propulsion. The mean acceleration time to take-off was not significantly different in males (46.2 ms) and females (45.5 ms), but the mean take-off velocity of males was 10% higher than in females. Second, to determine if enlarged hind legs were critical in specifically male behaviour, interactions between males and females, and between males were videoed. A male mounted a female and then encircled her abdomen between the enlarged femora and tibiae of both his hind legs. The joint between these leg parts acted like a mole wrench (vise grip) so that when the tibia was fully flexed a triangular space of 0.3 square mm remained in which a female abdomen (cross-sectional area 0.9 square mm) could be compressed and restrained firmly without inflicting damage. The flexor tibiae muscle in a male hind femur was 5.9 times larger than the extensor. In interactions between males, attempts to achieve a similar entrapment were frequently thwarted by the pursued male extending his hind legs vertically.

The principles of cascading power limits in small, fast biological and engineered systems

Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

Energy and time optimal trajectories in exploratory jumps of the spider Phidippus regius

Jumping spiders are proficient jumpers that use jumps in a variety of behavioural contexts. We use high speed, high resolution video to measure the kinematics of a single regal jumping spider for a total of 15 different tasks based on a horizontal gap of 2–5 body lengths and vertical gap of +/−2 body lengths. For short range jumps, we show that low angled trajectories are used that minimise flight time. For longer jumps, take-off angles are steeper and closer to the optimum for minimum energy cost of transport. Comparison of jump performance against other arthropods shows that Phidippus regius is firmly in the group of animals that use dynamic muscle contraction for actuation as opposed to a stored energy catapult system. We find that the jump power requirements can be met from the estimated mass of leg muscle; hydraulic augmentation may be present but appears not to be energetically essential.

Jumping performance of flea hoppers and other mirid bugs (Hemiptera, Miridae)

The order Hemiptera includes jumping insects with the fastest take-off velocities, all generated by catapult mechanisms. It also contains the large family Miridae or plant bugs. Here, we analysed the jumping strategies and mechanisms of six mirid species from high-speed videos and from the anatomy of their propulsive legs, and conclude that they use a different mechanism in which jumps are powered by the direct contractions of muscles. Three strategies were identified. First, jumping was propelled only by movements of the middle and hind legs, which were, respectively, 140% and 190% longer than the front legs. In three species with masses ranging from 3.4 to 12.2 mg, depression of the coxo-trochanteral and extension of femoro-tibial joints accelerated the body in 8-17 ms to take-off velocities of 0.5-0.8 m s^-1 The middle legs lost ground contact 5-6 ms before take-off so that the hind legs generated the final propulsion. The power requirements could be met by the direct muscle contractions so that catapult mechanisms were not implicated. Second, other species combined the same leg movements with wing beating to generate take-off during a wing downstroke. Third, up to four wingbeat cycles preceded take-off and were not assisted by leg movements. Take-off velocities were reduced and acceleration times lengthened. Other species from the same habitat did not jump. The lower take-off velocities achieved by powering jumping by direct muscle contractions may be offset by eliminating the time taken to load catapult mechanisms.

Take-off mechanisms in parasitoid wasps

High speed video analyses of the natural behaviour of parasitoid wasps revealed three strategies used to launch themselves into the air. Which strategy is the most energy efficient? In Pteromalus puparum, 92% of take-offs by were propelled entirely by movements of the middle and hind legs which were depressed at their coxo-trochanteral and extended at their femoro-tibial joints. The front legs left the ground first, followed by the hind legs, so that the middle legs provided the final propulsion. Second, in other species of a similar mass, Cotesia glomerata and Leptopilina boulardi, all take-offs were propelled by a mean of 2.8 and 3.8 wingbeats respectively with little or no contribution from the legs. The first strategy resulted in take-off times that were four times shorter (5 versus 22.8 ms) and take-off velocities that were four times faster (0.8 versus 0.2 m s–1). Calculations from the kinematics indicate that propulsion by the legs was the most energy efficient strategy, because more energy is put into propulsion of the body, whereas in take-off propelled by repetitive wing movements energy is lost to generating these movements and moving the air. In heavier species such as Netelia testacea and Amblyteles armatorius, take-off was propelled by the combined movements of the middle and hind legs and wingbeats. In A. armatorius, this resulted in the longest mean take-off time of 33.8 ms but an intermediate take-off velocity of 0.4 m s–1. In all three strategies the performance could be explained without invoking energy storage and power amplification mechanisms.

Take-off speed in jumping mantises depends on body size and a power-limited mechanism

Many insects such as fleas, froghoppers and grasshoppers use a catapult mechanism to jump, and a direct consequence of this is that their take-off velocities are independent of their mass. In contrast, insects such as mantises, caddis flies and bush crickets propel their jumps by direct muscle contractions. What constrains the jumping performance of insects that use this second mechanism? To answer this question, the jumping performance of the mantis Stagmomantis theophila was measured through all its developmental stages, from 5 mg first instar nymphs to 1200 mg adults. Older and heavier mantises have longer hind and middle legs and higher take-off velocities than younger and lighter mantises. The length of the propulsive hind and middle legs scaled approximately isometrically with body mass (exponent=0.29 and 0.32, respectively). The front legs, which do not contribute to propulsion, scaled with an exponent of 0.37. Take-off velocity increased with increasing body mass (exponent=0.12). Time to accelerate increased and maximum acceleration decreased, but the measured power that a given mass of jumping muscle produced remained constant throughout all stages. Mathematical models were used to distinguish between three possible limitations to the scaling relationships: first, an energy-limited model (which explains catapult jumpers); second, a power-limited model; and third, an acceleration -: limited model. Only the model limited by muscle power explained the experimental data. Therefore, the two biomechanical mechanisms impose different limitations on jumping: those involving direct muscle contractions (mantises) are constrained by muscle power, whereas those involving catapult mechanisms are constrained by muscle energy.

Jumping mechanisms in adult caddis flies (Insecta, Trichoptera)

To understand the jumping mechanisms and strategies of adult caddis flies, leg morphology and movements were analysed in three species with mean masses of 3.9 to 38 mg. Two distinct jumping strategies were found. First (67% of 90 jumps), take-off was propelled solely by the middle and hind legs while the wings remained closed. Second (33% of jumps), the same leg movements were combined with wing movements before take-off. The hind legs were 70% and the middle legs were 50% longer than the front legs and represented 105% and 88%, respectively, of body length. Both hind and middle trochantera were depressed together, approximately 15 ms before take-off. The front legs apparently did not contribute to thrust in either strategy and were the first to be lifted from the ground. The hind legs were the next to lose contact, so that the middle legs alone provided the final thrust before take-off. Jumping performance did not differ significantly in the two jumping strategies or between species, in acceleration times (range of means for the three species 14.5–15.4 ms), take-off velocities (range 0.7–1 m s−1) and trajectory angles. A significant difference in jumps propelled only by the legs was the lower angle (9.3±1.9 deg) of the body relative to the horizontal at take-off compared with jumps involving wing movements (35.3±2.5 deg). Calculations from the kinematics indicated that jumps were produced by direct muscle contractions and did not require power amplification or energy storage.