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

Fracture-driven power amplification in a hydrogel launcher

Robotic tasks that require robust propulsion abilities such as jumping, ejecting or catapulting require power-amplification strategies where kinetic energy is generated from pre-stored energy. Here we report an engineered accumulated strain energy-fracture power-amplification method that is inspired by the pressurized fluidic squirting mechanism of Ecballium elaterium (squirting cucumber plants). We realize a light-driven hydrogel launcher that harnesses fast liquid vapourization triggered by the photothermal response of an embedded graphene suspension. This vapourization leads to appreciable elastic energy storage within the surrounding hydrogel network, followed by rapid elastic energy release within 0.3 ms. These soft hydrogel robots achieve controlled launching at high velocity with a predictable trajectory. The accumulated strain energy-fracture method was used to create an artificial squirting cucumber that disperses artificial seeds over metres, which can further achieve smart seeding through an integrated radio-frequency identification chip. This power-amplification strategy provides a basis for propulsive motion to advance the capabilities of miniaturized soft robotic systems.

Dynamic similarity and the peculiar allometry of maximum running speed

Animal performance fundamentally influences behaviour, ecology, and evolution. It typically varies monotonously with size. A notable exception is maximum running speed; the fastest animals are of intermediate size. Here we show that this peculiar allometry results from the competition between two musculoskeletal constraints: the kinetic energy capacity, which dominates in small animals, and the work capacity, which reigns supreme in large animals. The ratio of both capacities defines the physiological similarity index Γ, a dimensionless number akin to the Reynolds number in fluid mechanics. The scaling of Γ indicates a transition from a dominance of muscle forces to a dominance of inertial forces as animals grow in size; its magnitude defines conditions of "dynamic similarity" that enable comparison and estimates of locomotor performance across extant and extinct animals; and the physical parameters that define it highlight opportunities for adaptations in musculoskeletal "design" that depart from the eternal null hypothesis of geometric similarity. The physiological similarity index challenges the Froude number as prevailing dynamic similarity condition, reveals that the differential growth of muscle and weight forces central to classic scaling theory is of secondary importance for the majority of terrestrial animals, and suggests avenues for comparative analyses of locomotor systems.

Control of high-speed jumps in muscle and spring actuated systems: a comparative study of take-off energetics in bush-crickets (Mecopoda elongata) and locusts (Schistocerca gregaria)

The Orthoptera are a diverse insect order well known for their locomotive capabilities. To jump, the bush-cricket uses a muscle actuated (MA) system in which leg extension is actuated by contraction of the femoral muscles of the hind legs. In comparison, the locust uses a latch mediated spring actuated (LaMSA) system, in which leg extension is actuated by the recoil of spring-like structure in the femur. The aim of this study was to describe the jumping kinematics of Mecopoda elongata (Tettigoniidae) and compare this to existing data in Schistocerca gregaria (Acrididae), to determine differences in control of rotation during take-off between similarly sized MA and LaMSA jumpers. 269 jumps from 67 individuals of M. elongata with masses from 0.014 g to 3.01 g were recorded with a high-speed camera setup. In M. elongata, linear velocity increased with mass0.18 and the angular velocity (pitch) decreased with mass-0.13. In S. gregaria, linear velocity is constant and angular velocity decreases with mass-0.24. Despite these differences in velocity scaling, the ratio of translational kinetic energy to rotational kinetic energy was similar for both species. On average, the energy distribution of M. elongata was distributed 98.8% to translational kinetic energy and 1.2% to rotational kinetic energy, whilst in S. gregaria it is 98.7% and 1.3%, respectively. This energy distribution was independent of size for both species. Despite having two different jump actuation mechanisms, the ratio of translational and rotational kinetic energy formed during take-off is fixed across these distantly related orthopterans.

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.

Evolutionary diversification in the raptorial forelegs of Mantodea: Relations to body size and depth perception

Limb proportions have evolved among animals to meet functional demands among diverse environments. Studies from terrestrial, vertebrate locomotion have demonstrated that variation in limb proportions have adaptively evolved so animals can perform in a given environment. Most of the research on limb proportion evolution is among vertebrates and terrestrial locomotion, with little information on limb segment evolution in invertebrates or for other functional roles. For example, among invertebrates, multisegmented raptorial forelimbs have evolved multiple times independently to capture prey, but there is little information on the adaptive evolution and diversity of these limbs. Furthermore, as feeding performance is influenced by the sensory system, few studies have examined the coevolution of sensory-motor systems. Using mantises (Mantodea) I examined forelimb diversification among 97 species with a combination of methods, including ternary plots for morphospace visualization, phylogenetically informed allometric relationships, and comparison of evolutionary rates of diversification. Furthermore, using head width as a proxy for depth perception, I examined the correlated evolution of foreleg diversity with depth perception. The results show that among the three segments of the foreleg, the tibia is the smallest, most diverse, and has the highest rate of evolution after body size corrections. Furthermore, while all foreleg segments were related to head width, head width explained the most variation in tibial length compared with other foreleg segments. The results suggest a potential adaptive functional role of tibia length related to the displacement or force produced in this mechanical lever. Furthermore, results from this study support distinct ecomorphs of mantises, as several independent evolutions to grass mimicry evolve similar morphologies. RESEARCH HIGHLIGHT: This study demonstrates interspecific variation among segments of an invertebrate raptorial foreleg. Among Mantodea species the tibia is the most diverse and is related to a proxy for depth perception, while the other segments had strong relationships with body size. This suggests an adaptive, functional role of the tibia during prey capture.

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.

Planthopper bugs use a fast, cyclic elastic recoil mechanism for effective vibrational communication at small body size

Vibrations through substrates are an important source of information for diverse organisms, from nematodes to elephants. The fundamental challenge for small animals using vibrational communication is to move their limited mass fast enough to provide sufficient kinetic energy for effective information transfer through the substrate whilst optimising energy efficiency over repeated cycles. Here, we describe a vibratory organ found across a commercially important group of plant-feeding insects, the planthoppers (Hemiptera: Fulgoromorpha). This elastic recoil snapping organ generates substrate-borne broadband vibrations using fast, cyclical abdominal motion that transfers kinetic energy to the substrate through the legs. Elastic potential energy is stored and released twice using two different latched energy-storage mechanisms, each utilising a different form of elastic recoil to increase the speed of motion. Comparison to the acoustic tymbal organ of cicadas (Hemiptera: Cicadomorpha) reveals functional convergence in their use of elastic mechanisms to increase the efficacy of mechanical communication.

Planthopper insects produce fast abdominal twerks for vibrational communication through the substrate, employing a novel vibratory organ that uses two reciprocal elastic recoil mechanisms to generate fast cyclical motion.

Animals use substrate-borne vibrations for eavesdropping and communication over an immense range of body size—from elephants to nematodes. Vibrational communication is especially challenging for small animals because of the high mechanical power that is needed to transmit information effectively over extended distances through a substrate. Here, we show that planthoppers, a commercially important group of insects, produce vibrations for communication using a reciprocal elastic recoil mechanism that proves remarkably effective at small body size. By combining morphological and biomechanical analyses of a previously overlooked vibratory organ on the abdomen, we show that planthoppers use fast, cyclical abdominal motions to generate substrate-borne vibrations. This novel, to our knowledge, mechanism, which we term the snapping organ, makes use of slow energy storage and fast elastic recoil twice during each cycle of motion, involving two distinct elastic elements. This cyclical mechanism allows planthoppers to transmit signal pulses containing a broad range of frequencies to the substrate. The mechanism is efficient, achieving fast cyclical motion without relying on high muscle power and mass, both of which are limited for animals of small size. The snapping organ is ubiquitous across planthoppers and presents an interesting example of how elastic mechanisms can be used to enable nonacoustic vibrational communication between animals.

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.