The mechanics of elevation control in locust jumping

The effects of temperature on elastic energy storage and release in a system with a dynamic mechanical advantage latch

Changes in temperature alter muscle kinetics and in turn affect whole-organism performance. Some organisms use the elastic recoil of biological springs, structures which are far less temperature sensitive, to power thermally robust movements. For jumping frogs, the use of elastic energy in tendons is facilitated through a geometric latching mechanism that operates through dynamic changes in the mechanical advantage (MA) of the hindlimb. Despite the well-documented use of elastic energy storage, frog jumping is a locomotor behavior that is significantly affected by changes in temperature. Here, we used an in vitro muscle preparation interacting in real time with an in silico model of a legged jumper to understand how changes in temperature affect the flow of energy in a system using a MA latch. We used the plantaris longus muscle-tendon unit (MTU) to power a virtual limb with changing MA and a mass being accelerated through a real-time feedback controller. We quantified the amount of energy stored in and recovered from elastic structures and the additional contribution of direct muscle work after unlatching. We found that temperature altered the duration of the energy loading and recovery phase of the in vitro/in silico experiments. We found that the early phase of loading was insensitive to changes in temperature. However, an increase in temperature did increase the rate of force development, which in turn allowed for increased energy storage in the second phase of loading. We also found that the contribution of direct muscle work after unlatching was substantial and increased significantly with temperature. Our results show that the thermal robustness achieved by an elastic mechanism depends strongly on the nature of the latch that mediates energy flow, and that the relative contribution of elastic and direct muscle energy likely shapes the thermal sensitivity of locomotor systems.

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.

Control of high-speed jumps: the rotation and energetics of the locust (Schistocerca gregaria)

Locusts (Schistocerca gregaria) jump using a latch mediated spring actuated system in the femur-tibia joint of their metathoracic legs. These jumps are exceptionally fast and display angular rotation immediately after take-off. In this study, we focus on the angular velocity, at take-off, of locusts ranging between 0.049 and 1.50 g to determine if and how rotation-rate scales with size. From 263 jumps recorded from 44 individuals, we found that angular velocity scales with mass^-0.33, consistent with a hypothesis of locusts having a constant rotational kinetic energy density. Within the data from each locust, angular velocity increased proportionally with linear velocity, suggesting the two cannot be independently controlled and thus a fixed energy budget is formed at take-off. On average, the energy budget of a jump is distributed 98.7% to translational kinetic energy and gravitational potential energy, and 1.3% to rotational kinetic energy. The percentage of energy devoted to rotation was constant across all sizes of locusts and represents a very small proportion of the energy budget. This analysis suggests that smaller locusts find it harder to jump without body rotation.

Omnidirectional Jump Control of a Locust-Computer Hybrid Robot

Jumping locomotion is critical for microrobots to overcome obstacles. Among the microjumping robots, the development of an omnidirectional jumping mechanism is challenging. To avoid the complicated microfabrication process, we present an insect-computer hybrid robot by controlling the locomotions of an Oriental Migratory Locust (Locusta migratoria manilensis, Meyen 1835). The insect-computer hybrid robot achieves repetitive omnidirectional jumps of ∼100 mm high. A series of experiments on jumping control, turning control, and collaborative directional jumping control are carried out. We also demonstrate the implementation of a wireless stimulator backpack that provides remote locomotion control, which transforms the insect into a hybrid robot. Moreover, a feedback jump control system is subsequently presented. The results indicate that the hybrid robot could easily achieve an omnidirectional jump and maintain body righting after landing. This robot is well-suited for applications that require locomotion on uneven terrains, such as environmental surveillance and search and rescue.

Blood python (Python brongersmai) strike kinematics and forces are robust to variations in substrate geometry

Snake strikes are some of the most rapid accelerations in terrestrial vertebrates. Generating rapid body accelerations requires high ground reaction forces, but on flat surfaces snakes must rely on static friction to prevent slip. We hypothesize that snakes may be able to take advantage of structures in the environment to prevent their body from slipping, potentially allowing them to generate faster and more forceful strikes. To test this hypothesis, we captured high-speed video and forces from defensive strikes of juvenile blood pythons (Python brongersmai) on a platform that was either open on all sides or with two adjacent walls opposite the direction of the strike. Contrary to our predictions, snakes maintained high performance on open platforms by imparting rearward momentum to the posterior body and tail. This compensatory behavior increases robustness to changes in their strike conditions and could allow them to exploit variable environments.

Insect-inspired jumping robots: challenges and solutions to jump stability

Some insects can jump to heights that are several times their body length. At smaller scales, jumping mechanisms are constrained by issues relating to scaling of power generation, which insects have resolved over the course of their evolution. These solutions have inspired the design of small jumping robots. However, the insect' solution for the power constraint came at a price of instability and limited control over jump performance and these drawbacks were inherited by the jumping robots inspired by them. This review focuses on the jumping mechanisms of insects and robots, the challenges it imposes on control and stability and possible solutions. Although jump stability might not be a critical problem for insects, it poses substantial challenges for engineers of small jumping robots, who hope to develop autonomous devices with improved mobility over rough terrain.

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.

JumpDetector: An automated monitoring equipment for the locomotion of jumping insects

Continuous jumping behavior, a kind of endurance locomotion, plays important roles in insect ecological adaption and survival. However, the methods used for the efficient evaluation of insect jumping behavior remain largely lacking. Here, we developed a locomotion detection system named JumpDetector with automatic trajectory tracking and data analysis to evaluate the jumping of insects. This automated system exhibits more accurate, efficient, and adjustable performance than manual methods. By using this automatic system, we characterized a gradually declining pattern of continuous jumping behavior in 4th-instar nymphs of the migratory locust. We found that locusts in their gregarious phase outperformed locusts in their solitary phase in the endurance jumping locomotion. Therefore, the JumpDetector could be widely used in jumping behavior and endurance locomotion measurement.

The Effect of Ground Type on the Jump Performance of Adults of the Locust Locusta migratoria manilensis: A Preliminary Study

The jump performance of locusts depends on several physiological and environmental factors. Few studies have examined the effects of different ground types on the jump performance of locusts. Here, mature adult locusts (Locusta migratoria manilensis) were examined using a custom-developed measuring system to test their jump performance (including postural features, kinematics, and reaction forces) on three types of ground (sand, soil, and wood). Significant differences were primarily observed in the elevation angle at take-off, the tibial angle at take-off, and the component of the mass-specific reaction force along the aft direction of the insect body between wood and the other two ground types (sand and soil). Slippage of the tarsus and insertion of the tibia were often observed when the locusts jumped on sand and soil, respectively. Nevertheless, comparisons of the different parameters of jump initiation (i.e., take-off speed and mass-specific kinetic energy) did not reveal any differences among the three types of ground, indicating that locusts were able to achieve robust jump performance on various substrates. This study provides insights into the biomechanical basis of the locust jump on different types of ground and enhances our understanding of the mechanism underlying the locust jump.

Impact of Different Developmental Instars on Locusta migratoria Jumping Performance

Ontogenetic locomotion research focuses on the evolution of locomotion behavior in different developmental stages of a species. Unlike vertebrates, ontogenetic locomotion in invertebrates is poorly investigated. Locusts represent an outstanding biological model to study this issue. They are hemimetabolous insects and have similar aspects and behaviors in different instars. This research is aimed at studying the jumping performance of Locusta migratoria over different developmental instars. Jumps of third instar, fourth instar, and adult L. migratoria were recorded through a high-speed camera. Data were analyzed to develop a simplified biomechanical model of the insect: the elastic joint of locust hind legs was simplified as a torsional spring located at the femur-tibiae joint as a semilunar process and based on an energetic approach involving both locomotion and geometrical data. A simplified mathematical model evaluated the performances of each tested jump. Results showed that longer hind leg length, higher elastic parameter, and longer takeoff time synergistically contribute to a greater velocity and energy storing/releasing in adult locusts, if compared to young instars; at the same time, they compensate possible decreases of the acceleration due to the mass increase. This finding also gives insights for advanced bioinspired jumping robot design.

What goes up must come down: biomechanical impact analysis of falling locusts

Many insects are able to precisely control their jumping movements. Once in the air, the properties of the actual landing site, however, are almost impossible to predict. Falling insects thus have to cope with the situation at impact. In particular, for insects jumping to escape predators, a controlled landing movement appears to be a major evolutionary advantage. A quick recovery into an upright and stable body posture minimizes the time to prepare for the next escape jump. In this study, we used high-speed recordings to investigate the falling and in particular the impact behavior of Schistocerca gregaria locusts, a common model organism for studies on the biomechanics of jumping. Detailed impact analyses of free-falling locusts show that most insects typically crashed onto the substrate. Although free-falling locusts tended to spread their legs, they mostly fell onto the head and thorax first. The presence of wings did not significantly reduce impact speed; however, it did affect the orientation of the body at impact and significantly reduced the time to recover. Our results also show that alive warm locusts fell significantly faster than inactive or dead locusts. This indicates a possible tradeoff between active control versus reduced speed. Interestingly, alive insects also tended to perform a characteristic bending movement of the body at impact. This biomechanical adaptation might reduce the rebound and shorten the time to recover. The adhesive pads also play an important role in reducing the time to recover by allowing the insect to anchor itself to the substrate.

Mosquitoes modulate leg dynamics at takeoff to accommodate surface roughness

Insects perform takeoffs from a nearly unquantifiable number of surface permutations and many use their legs to initiate upward movement prior to the onset of wingbeats, including the mosquito. In this study we examine the unprovoked pre-takeoff mechanics of Aedes aegypti mosquitoes from two surfaces of contrasting roughness, one with roughness similar to polished glass and the other comparable to the human forearm. Using high-speed videography, we find mosquitos exhibit two distinct leg actions prior to takeoff, the widely observed push and a previously undocumented leg-strike, where one of the rearmost legs is raised and strikes the ground. Across 106 takeoff sequences we observe a greater incidence of leg-strikes from the smoother surface, and rationalize this observation by comparing the characteristic size of surface features on the mosquito tarsi and each test surface. Measurements of pre-takeoff kinematics reveal both strategies remain under the mechanosensory detection threshold of mammalian hair and produce nearly identical vertical body velocities. Lastly, we develop a model that explicates the measured leg velocity of striking legs utilized by mosquitoes, 0.59 m s^-1.

The effect of aging on the mechanical behaviour of cuticle in the locust Schistocerca gregaria

Despite some previous work on the morphology and mechanical properties of parts of the insect exoskeleton, there is very little known about how these properties change over time during the life of the insect. We examined the hind tibia of the adult desert locust (Schistocerca gregaria) as a function of time up to 63 days following the final moult, a much longer period that previously studied. We identified an initial growth phase, lasting on average 21 days, in which leg thickness increased rapidly (averaging 1.8μm/day) by endocuticle deposition, and a subsequent mature phase in which the deposition rate slowed to 0.3μm/day. Cantilever bending tests revealed that Young's modulus and failure stress also increased rapidly during the growth phase, but remained almost constant during the mature phase, with average values of 8.3GPa (± 2.3GPa) and 175MPa (±31.5MPa) respectively, which are considerably higher than previously measured for fresh insect cuticle. Biomechanical analysis showed that the failure mode also changed, from local buckling of the tubular leg during the growth phase to failure at the material's ultimate strength in the mature phase. Over time, the ratio of radius/thickness of the leg decreased, passing through the estimated optimal value which would confer the best strength/weight ratio. This is the first ever biomechanical study to track changes in arthropod cuticle over a large part of adult life of the animal, and has revealed some unexpected and complex changes which may shed light on how arthropods regulate their load-bearing skeletal parts during aging.

Structures, properties, and energy-storage mechanisms of the semi-lunar process cuticles in locusts

Locusts have excellent jumping and kicking abilities to survive in nature, which are achieved through the energy storage and release processes occurring in cuticles, especially in the semi-lunar processes (SLP) at the femorotibial joints. As yet, however, the strain energy-storage mechanisms of the SLP cuticles remain unclear. To decode this mystery, we investigated the microstructure, material composition, and mechanical properties of the SLP cuticle and its remarkable strain energy-storage mechanisms for jumping and kicking. It is found that the SLP cuticle of adult Locusta migratoria manilensis consists of five main parts that exhibit different microstructural features, material compositions, mechanical properties, and biological functions in storing strain energy. The mechanical properties of these five components are all transversely isotropic and strongly depend on their water contents. Finite element simulations indicate that the two parts of the core region of the SLP cuticle likely make significant contributions to its outstanding strain energy-storage ability. This work deepens our understanding of the locomotion behaviors and superior energy-storage mechanisms of insects such as locusts and is helpful for the design and fabrication of strain energy-storage devices.

Joint torques in a freely walking insect reveal distinct functions of leg joints in propulsion and posture control

Determining the mechanical output of limb joints is critical for understanding the control of complex motor behaviours such as walking. In the case of insect walking, the neural infrastructure for single-joint control is well described. However, a detailed description of the motor output in form of time-varying joint torques is lacking. Here, we determine joint torques in the stick insect to identify leg joint function in the control of body height and propulsion. Torques were determined by measuring whole-body kinematics and ground reaction forces in freely walking animals. We demonstrate that despite strong differences in morphology and posture, stick insects show a functional division of joints similar to other insect model systems. Propulsion was generated by strong depression torques about the coxa-trochanter joint, not by retraction or flexion/extension torques. Torques about the respective thorax-coxa and femur-tibia joints were often directed opposite to fore-aft forces and joint movements. This suggests a posture-dependent mechanism that counteracts collapse of the leg under body load and directs the resultant force vector such that strong depression torques can control both body height and propulsion. Our findings parallel propulsive mechanisms described in other walking, jumping and flying insects, and challenge current control models of insect walking.

Dynamics and stability of directional jumps in the desert locust

Locusts are known for their ability to jump large distances to avoid predation. The jump also serves to launch the adult locust into the air in order to initiate flight. Various aspects of this important behavior have been studied extensively, from muscle physiology and biomechanics, to the energy storage systems involved in powering the jump, and more. Less well understood are the mechanisms participating in control of the jump trajectory. Here we utilise video monitoring and careful analysis of experimental directional jumps by adult desert locusts, together with dynamic computer simulation, in order to understand how the locusts control the direction and elevation of the jump, the residual angular velocities resulting from the jump and the timing of flapping-flight initiation. Our study confirms and expands early findings regarding the instrumental role of the initial body position and orientation. Both real-jump video analysis and simulations based on our expanded dynamical model demonstrate that the initial body coordinates of position (relative to the hind-legs ground-contact points) are dominant in predicting the jumps’ azimuth and elevation angles. We also report a strong linear correlation between the jumps’ pitch-angular-velocity and flight initiation timing, such that head downwards rotations lead to earlier wing opening. In addition to offering important insights into the bio-mechanical principles of locust jumping and flight initiation, the findings from this study will be used in designing future prototypes of a bio-inspired miniature jumping robot that will be employed in animal behaviour studies and environmental monitoring applications.

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.

Bridging the gap: wound healing in insects restores mechanical strength by targeted cuticle deposition

If an insect is injured, can it repair its skeleton in a manner which is mechanically strong and viable? Previous work has described the biological processes that occur during repair of insect cuticle, but until now, there has been no biomechanical assessment of the repaired area. We analysed the biomechanics of the injury repair process in the desert locust (Schistocerca gregaria). We show that after an incision, a healing process occurred which almost doubled the mechanical strength of locust tibial cuticle, restoring it to 66% of the original, intact strength. This repair process occurred by targeted cuticle deposition, stimulated by the presence of the injury. The cut surfaces remained unrepaired, but a patch of endocuticle was deposited, reinforcing the area and thus increasing the effective fracture toughness. The deposition rate of endocuticle inside the tibia increased fourfold compared with uninjured controls, but only on the dorsal side, where the incision was placed. The limb is highly loaded during jumping, so this partial restoration of strength will have a profound effect on the fitness of the insect. A finite-element model provided insights into the mechanics of the repair, predicting that the patch material reaches its ultimate strength before the fracture toughness of the existing cuticle is exceeded.

Jumping Robot with Initial Body Posture Adjustment and a Self-Righting Mechanism

To improve jumping performance, this paper presents a jumping robot with initial body posture adjustment and a self-righting mechanism. A segmental gear, stretching and triggering a spring for the storage and rapid release of energy, is used for the jumping mechanism. Pairs of front and hind supporting legs are used for the initial body posture adjustment. One end of each jumping leg is connected to a spring, while the other end is connected to the necessary wiring. In this way, the robot can correct its orientation from an upside down posture upon landing, simultaneously recovering its jumping legs and storing energy. Experimental results indicate that a jumping robot with a size of 78 mm × 43 mm × 40 mm and a weight of 30 g can jump across an obstacle with a controlled trajectory. It can also control its air pitching posture using the initial body posture adjustment. In addition, the robot can recover its body posture on the ground and store energy for a second jump. This work may provide useful data for further research into take-off posture control mechanisms.

Buckling failures in insect exoskeletons

Thin walled tubes are often used for load-bearing structures, in nature and in engineering, because they offer good resistance to bending and torsion at relatively low weight. However, when loaded in bending they are prone to failure by buckling. It is difficult to predict the loading conditions which cause buckling, especially for tubes whose cross sections are not simple shapes. Insights into buckling prevention might be gained by studying this phenomenon in the exoskeletons of insects and other arthropods. We investigated the leg segments (tibiae) of five different insects: the locust (Schistocerca gergaria), American cockroach (Periplaneta americana), death's head cockroach (Blaberus discoidalis), stick insect (Parapachymorpha zomproi) and bumblebee (Bombus terrestris audax). These were tested to failure in cantilever bending and modelled using finite element analysis (FEA). The tibiae of the locust and the cockroaches were found to be approximately circular in shape. Their buckling loads were well predicted by linear elastic FEA, and also by one of the analytical solutions available in the literature for elastic buckling. The legs of the stick insect are also circular in cross section but have several prominent longitudinal ridges. We hypothesised that these ridges might protect the legs against buckling but we found that this was not the case: the loads necessary for elastic buckling were not reached in practice because yield occurred in the material, causing plastic buckling. The legs of bees have a non-circular cross section due to a pollen-carrying feature (the corbicula). We found that this did not significantly affect their resistance to buckling. Our results imply that buckling is the dominant failure mode in the tibia of insects; it likely to be a significant consideration for other arthropods and any organisms with stiff exoskeletons. The interactions displayed here between material properties and cross sectional geometry may provide insights for the biomimetic design of engineering structures using thin walled tubes.

Why are there no long distance jumpers among click-beetles (Elateridae)?

Click-beetles jump from an inverted position without using their legs. This unique mechanism results in high vertical jumps with the jump angle restricted by the rigid morphology of the exoskeleton. We explored the option to exploit this jumping mechanism for application to small mechanical devices having to extricate themselves from rough terrain. We combined experiments on a biomimetic jumping device with a physical-mathematical model of the jump to assess the effect of morphological variation on the jumping performance. We found that through morphological change of two non-dimensional (size independent) parameters, the propulsive force powering the jump can be directed at angles as small as 40°. However, in practice jumping at such angles is precluded by loss of traction with the ground during the push-off phase. This limitation to steep jump angles is inherent to the jumping mechanism which is based on rotation of body parts about a single hinge. Such a rotation dictates a curvilinear trajectory for the center of mass during takeoff so that the vertical and horizontal accelerations occur out of phase, implying loss of traction with the ground before substantial horizontal acceleration can be reached. Thus click-beetle inspired jumping is effective mainly for making steep-angle righting jumps.

Direct look from a predator shortens the risk-assessment time by prey

Decision making process is an important component of information use by animals and has already been studied in natural situations. Decision making takes time, which is expressed as a cost in evolutionary explanations of decision making abilities of animals. However, the duration of information assessment and decision making process has not been measured in a natural situation. Here, we use responses of wild magpies (Pica pica) to predictably approaching humans to demonstrate that, regardless of whether the bird perceived high (decided to fly away) or low (resumed foraging) threat level, the bird assessed the situation faster when approaching humans looked directly at it than when the humans were not directly looking at it. This indicates that prey is able to extract more information about the predator's intentions and to respond sooner when the predator is continuously ("intently") looking at the prey. The results generally illustrate how an increase of information available to an individual leads to a shorter assessment and decision making process, confirming one of central tenets of psychology of information use in a wild bird species in its natural habitat.

Jumping from the surface of water by the long-legged fly Hydrophorus (Diptera, Dolichopodidae)

The fly, Hydrophorus that is 4 mm long and has a mass of 4.7 mg moves around upon and jumps from water without its tarsi penetrating the surface. All 6 tarsi have a surface area of 1.3 mm-2 in contact with the water but did not dimple its surface when standing. Jumping was propelled by depression of the trochantera and extension of the tibiae of both hind and middle legs which are 40% longer than the front legs and 170% longer than the body. As these four legs progressively propelled the insect to take-off, they each created dimples on the water surface that expanded in depth and area. No dimples were associated with the front legs, which were not moved in a consistent sequence. The wings opened while the legs were moving and then flapped at a frequency of 148 Hz. The body was accelerated in a mean time of 21 ms to a mean take-off velocity of 0.7 m s-1. The best jumps reached velocities of 1.6 m s-1, required an energy output of 7 µJ and a power output of 0.6 mW, with the fly experiencing a force of 140 g. The required power output indicates that direct muscle contractions could propel the jump without the need for elaborate mechanisms for energy storage. Take-off trajectories were steep with a mean of 87 degrees to the horizontal. Take-off velocity fell if a propulsive tarsus penetrated the surface of the water. If more tarsi became submerged, take-off was not successful. A second strategy for take-off was powered only by the wings and was associated with slower (1 degree ms-1 compared with 10 degrees ms-1 when jumping) and less extensive movements of the propulsive joints of the middle and hind legs. No dimples were then created on the surface of the water. When jumping was combined with wing flapping, the acceleration time to take-off was reduced by 84 % and the take-off velocity was increased by 168 %. Jumping can potentially therefore enhance survival when threatened by a potential predator.

Fatigue of insect cuticle

Many parts of the insect exoskeleton experience repeated cyclic loading. Although the cuticle of insects and other arthropods is the second most common natural composite material in the world, so far nothing is known about its fatigue properties, despite the fact that fatigue undoubtedly limits the durability of body parts in vivo. For the first time, we here present experimental fatigue data of insect cuticle. Using force-controlled cyclic loading, we determined the number of cycles to failure for hind legs (tibiae) and hind wings of the locust Schistocerca gregaria, as a function of the applied cyclic stress. Our results show that, although both made from cuticle, these two body parts behaved very differently. Wing samples failed after 100,000 cycles when we applied 46% of the stress needed for instantaneous failure (the UTS). Legs, in contrast, were able to sustain a stress of 76% of UTS for the same number of cycles to failure. This can be explained by the difference in the composition and structure of the material and related to the well-known behaviour of engineering composites. Final failure of the tibiae occurred via one of two different failure modes - crack propagation in tension or buckling in compression - indicating that the tibia is evolutionary optimized to resist both failure modes equally. These results are further discussed in relation to the evolution and normal use of these two body parts.

Shape optimization in exoskeletons and endoskeletons: a biomechanics analysis

This paper addresses the question of strength and mechanical failure in exoskeletons and endoskeletons. We developed a new, more sophisticated model to predict failure in bones and other limb segments, modelled as hollow tubes of radius r and thickness t. Five failure modes were considered: transverse fracture; buckling (of three different kinds) and longitudinal splitting. We also considered interactions between failure modes. We tested the hypothesis that evolutionary adaptation tends towards an optimum value of r/t, this being the value which gives the highest strength (i.e. load-carrying capacity) for a given weight. We analysed two examples of arthropod exoskeletons: the crab merus and the locust tibia, using data from the literature and estimating the stresses during typical activities. In both cases, the optimum r/t value for bending was found to be different from that for axial compression. We found that the crab merus experiences similar levels of bending and compression in vivo and that its r/t value represents an ideal compromise to resist these two types of loading. The locust tibia, however, is loaded almost exclusively in bending and was found to be optimized for this loading mode. Vertebrate long bones were found to be far from optimal, having much lower r/t values than predicted, and in this respect our conclusions differ from those of previous workers. We conclude that our theoretical model, though it has some limitations, is useful for investigating evolutionary development of skeletal form in exoskeletons and endoskeletons.

Fracture toughness of locust cuticle

Insect cuticle is one of the most common biological materials, yet very little is known about its mechanical properties. Many parts of the insect exoskeleton, such as the jumping legs of locusts, have to withstand high and repeated loading without failure. This paper presents the first measurements of fracture toughness for insect cuticle using a standard engineering approach. Our results show that the fracture toughness of cuticle in locust hind legs is 4.12 MPa m(1/2) and decreases with desiccation of the cuticle. Stiffness and strength of the tibia cuticle were measured using buckling and cantilever bending and increased with desiccation. A combination of the cuticle's high toughness with a relatively low stiffness of 3.05 GPa results in a work of fracture of 5.56 kJ m(-2), which is amongst the highest of any biological material, giving the insect leg an exceptional ability to tolerate defects such as cracks and damage. Interestingly, insect cuticle achieves these unique properties without using reinforcement by a mineral phase, which is often found in other biological composite materials. These findings thus might inspire the development of new biomimetic composite materials.

Jumping mechanisms of treehopper insects (Hemiptera, Auchenorrhyncha, Membracidae)

The kinematics and jumping performance of treehoppers (Hemiptera, Auchenorrhyncha, Membracidae) were analysed from high speed images. The 8 species analysed had an 11 fold range of body mass (3.8 mg to 41 mg) and a 2 fold range of body lengths (4.1 to 8.4 mm). Body shape was dominated by a prothoracic helmet that projected dorsally and posteriorly over the body, and in some species forwards to form a protruding horn. Jumping was propelled by rapid depression of the trochantera of the hind legs. The hind legs were only 30 – 60 % longer than the front and middle legs, and 47 – 94% the length of the body in different species. They were slung beneath the body and moved together in the same plane. In preparation for a jump, the hind legs were initially levated and rotated forwards so that the femora were pressed into indentations of the coxae. The tibiae were flexed about the femora and the tarsi were placed on the ground directly beneath the lateral edges of the abdomen. Movements of the front and middle legs adjusted the angle of the body relative to the ground, but for most treehoppers this angle was small so that the body was almost parallel to the ground. The rapid depression of the hind legs accelerated the body to take-off in 1.2 ms in the lighter treehoppers and 3.7 ms in the heavier ones. Take-off velocities of 2.1 – 2.7 m s-1 were achieved and were not correlated with body mass. In the best jumps, these performances involved accelerations of 560 – 2450 m s-2 (g forces of 47- 250), an energy expenditure of 13.5 – 101 µJ, a power output of 12 – 32 mW and exerted a force or 9.5 – 29 mN. The power output per mass of muscle far exceeds the maximum active contractile limit of normal muscle. Such requirements indicate that treehoppers must be using a power amplification mechanism in a catapult-like action. Some jumps were preceded by flapping movements of the wings, but the propulsive movements of the hind legs were critical in achieving take-off.

Jumping mechanisms and performance of snow fleas (Mecoptera, Boreidae)

Flightless snow fleas (snow scorpion flies, Mecoptera, Boreidae) live as adults during northern hemisphere winters, often jumping and walking on the surface of snow. Their jumping mechanisms and performance were analysed with high speed imaging. Jumps were propelled by simultaneous movements of both the middle and hind pairs of legs, as judged by the 0.2 ms resolution afforded by image rates of 5000 frames s(-1). The middle legs of males represent 140% and the hindlegs 187% of the body length (3.4 mm), and the ratio of leg lengths is 1:1.3:1.7 (front:middle:hind). In preparation for a jump the middle legs and hindlegs were rotated forwards at their coxal joints with the fused mesothorax and metathorax. The first propulsive movement of a jump was the rotation of the trochantera about the coxae, powered by large depressor muscles within the thorax. The acceleration time was 6.6 ms. The fastest jump by a male had a take-off velocity of 1 m s(-1), which required 1.1 μJ of energy and a power output of 0.18 mW, and exerted a force about 16 times its body weight. Jump distances of about 100 mm were unaffected by temperature. This, and the power per mass of muscle requirement of 740 W kg(-1), suggests that a catapult mechanism is used. The elastic protein resilin was revealed in four pads at the articulation of the wing hinge with the dorsal head of the pleural ridge of each middle leg and hindleg. By contrast, fleas, which use just their hindlegs for jumping, have only two pads of resilin. This, therefore, provides a functional reference point for considerations about the phylogenetic relationships between snow fleas and true fleas.

Biomechanics of jumping in the flea

It has long been established that fleas jump by storing and releasing energy in a cuticular spring, but it is not known how forces from that spring are transmitted to the ground. One hypothesis is that the recoil of the spring pushes the trochanter onto the ground, thereby generating the jump. A second hypothesis is that the recoil of the spring acts through a lever system to push the tibia and tarsus onto the ground. To decide which of these two hypotheses is correct, we built a kinetic model to simulate the different possible velocities and accelerations produced by each proposed process and compared those simulations with the kinematics measured from high-speed images of natural jumping. The in vivo velocity and acceleration kinematics are consistent with the model that directs ground forces through the tibia and tarsus. Moreover, in some natural jumps there was no contact between the trochanter and the ground. There were also no observable differences between the kinematics of jumps that began with the trochanter on the ground and jumps that did not. Scanning electron microscopy showed that the tibia and tarsus have spines appropriate for applying forces to the ground, whereas no such structures were seen on the trochanter. Based on these observations, we discount the hypothesis that fleas use their trochantera to apply forces to the ground and conclude that fleas jump by applying forces to the ground through the end of the tibiae.

Control of tumbling during the locust jump

Locust can jump precisely to a target, yet they can also tumble during the trajectory. We propose two mechanisms that would allow the locust to control tumbling during the jump. The first is that prior to the jump, locusts adjust the pitch of their body to move the center of mass closer to the intended thrust vector. The second is that contraction of the dorsolongitudinal muscles during the jump will produce torques that counter the torque produced by thrust. We found that locusts increased their take-off angle as the initial body pitch increased, and that little tumbling occurred for jumps that observed this relationship. Simulations of locust jumping demonstrated that a pitch versus take-off angle relationship that minimized tumbling in simulated jumps was similar to the relationship observed in live locusts. Locusts were strongly biased to pitch head-upward, and performed dorsiflexions far more often than ventral flexions. The direction and magnitude of tumbling could be controlled in simulations by adjusting the tension in the dorsolongitudinal muscles. These mechanisms allowed the simulations to match the data from the live animals. Control of tumbling was also found to influence the control of jump elevation. The bias to pitch head-upwards may have an evolutionary advantage when evading a predator and so make control of tumbling important for the locust.

Ballistic movements of jumping legs implemented as variable components of cricket behaviour

Ballistic accelerations of a limb or the whole body require special joint mechanisms in many animals. Specialized joints can be moved by stereotypic or variable motor control during motor patterns with and without ballistic components. As a model of variable motor control, the specialized femur-tibia (knee) joints of cricket (Acheta domesticus) hindlegs were studied during ballistic kicking, jumping and swimming and in non-ballistic walking. In this joint the tendons of the antagonistic flexor and the extensor muscles attach at different distances from the pivot and the opposed lever arms form an angle of 120 deg. A 10:1 ratio of their effective lever arms at full knee flexion helps to prepare for most ballistic extensions: the tension of the extensor can reach its peak while it is restrained by flexor co-contraction. In kicks, preparatory flexion is rapid and the co-contraction terminates just before knee extensions. Therefore, mainly the stored tension of the extensor muscle accelerates the small mass of the tibia. Jumps are prepared with slower extensor-flexor co-contractions that flex both knees simultaneously and then halt to rotate both legs outward to a near horizontal level. From there, catapult extension of both knees accelerates the body, supported by continued high frequency motor activity to their tibia extensor muscles during the ongoing push-off from the substrate. Premature extension of one knee instantly takes load from the lagging leg that extends and catches up, which finally results in a straight jump. In swimming, synchronous ballistic power strokes of both hindlegs drive the tibiae on a ventral-to-posterior trajectory through the water, well coordinated with the swimming patterns of all legs. In walking, running and climbing the steps of the hindlegs range between 45 deg flexion and 125 deg extension and use non-ballistic, alternating activity of knee flexor and extensor muscles. Steep climbing requires longer bursts from the extensor tibiae muscles when they support the extended hindlegs against gravity forces when the body hangs over. All ballistic movements of cricket knees are elicited by a basic but variable motor pattern: knee flexions by co-contraction of the antagonists prepare catapult extensions with speeds and forces as required in the different behaviours.

Escapes with and without preparation: the neuroethology of visual startle in locusts

Locusts respond to the images of approaching (looming) objects with responses that include gliding while in flight and jumping while standing. For both of these responses there is good evidence that the DCMD neuron (descending contralateral movement detector), which carries spike trains from the brain to the thoracic ganglia, is involved. Sudden glides during flight, which cause a rapid loss of height, are last-chance manoeuvres without prior preparation. Jumps from standing require preparation over several tens of milliseconds because of the need to store muscle-derived energy in a catapult-like mechanism. Locusts' DCMD neurons respond selectively to looming stimuli, and make connections with some motor neurons and interneurons known to be involved in flying and jumping. For glides, a burst of high-frequency DCMD spikes is a key trigger. For jumping, a similar burst can influence timing, but neither the DCMD nor any other single interneuron has been shown to be essential for triggering any stage in preparation or take-off. Responses by the DCMD to looming stimuli can alter in different behavioural contexts: in a flying locust, arousal ensures a high level of both DCMD responsiveness and glide occurrence; and there are significant differences in DCMD activity between locusts in the gregarious and the solitarious phase.

Neuromechanical simulation of the locust jump

The neural circuitry and biomechanics of kicking in locusts have been studied to understand their roles in the control of both kicking and jumping. It has been hypothesized that the same neural circuit and biomechanics governed both behaviors but this hypothesis was not testable with current technology. We built a neuromechanical model to test this and to gain a better understanding of the role of the semi-lunar process (SLP) in jump dynamics. The jumping and kicking behaviors of the model were tested by comparing them with a variety of published data, and were found to reproduce the results from live animals. This confirmed that the kick neural circuitry can produce the jump behavior. The SLP is a set of highly sclerotized bands of cuticle that can be bent to store energy for use during kicking and jumping. It has not been possible to directly test the effects of the SLP on jump performance because it is an integral part of the joint, and attempts to remove its influence prevent the locust from being able to jump. Simulations demonstrated that the SLP can significantly increase jump distance, power, total energy and duration of the jump impulse. In addition, the geometry of the joint enables the SLP force to assist leg flexion when the leg is flexed, and to assist extension once the leg has begun to extend.

Jumping mechanisms and performance of pygmy mole crickets (Orthoptera, Tridactylidae)

Pygmy mole crickets live in burrows at the edge of water and jump powerfully to avoid predators such as the larvae and adults of tiger beetles that inhabit the same microhabitat. Adults are 5–6 mm long and weigh 8 mg. The hind legs are dominated by enormous femora containing the jumping muscles and are 131% longer than the body. The ratio of leg lengths is: 1:2.1:4.5 (front:middle:hind, respectively). The hind tarsi are reduced and their role is supplanted by two pairs of tibial spurs that can rotate through 180 deg. During horizontal walking the hind legs are normally held off the ground. Jumps are propelled by extension of the hind tibiae about the femora at angular velocities of 68,000 deg s−1 in 2.2 ms, as revealed by images captured at rates of 5000 s−1. The two hind legs usually move together but can move asynchronously, and many jumps are propelled by just one hind leg. The take-off angle is steep and once airborne the body rotates backwards about its transverse axis (pitch) at rates of 100 Hz or higher. The take-off velocity, used to define the best jumps, can reach 5.4 m s−1, propelling the insect to heights of 700 mm and distances of 1420 mm with an acceleration of 306 g. The head and pronotum are jerked rapidly as the body is accelerated. Jumping on average uses 116 μJ of energy, requires a power output of 50 mW and exerts a force of 20 mN. In jumps powered by one hind leg the figures are about 40% less.

The mechanics of azimuth control in jumping by froghopper insects

Many animals move so fast that there is no time for sensory feedback to correct possible errors. The biomechanics of the limbs participating in such movements appear to be configured to simplify neural control. To test this general principle, we analysed how froghopper insects control the azimuth direction of their rapid jumps, using high speed video of the natural movements and modelling to understand the mechanics of the hind legs. We show that froghoppers control azimuth by altering the initial orientation of the hind tibiae; their mean angle relative to the midline closely predicts the take-off azimuth. This applies to jumps powered by both hind legs, or by one hind leg. Modelling suggests that moving the two hind legs at different times relative to each other could also control azimuth, but measurements of natural jumping showed that the movements of the hind legs were synchronised to within 32 mus of each other. The maximum timing difference observed (67 micros) would only allow control of azimuth over 0.4 deg. to either side of the midline. Increasing the timing differences between the hind legs is also energetically inefficient because it decreases the energy available and causes losses of energy to body spin; froghoppers with just one hind leg spin six times faster than intact ones. Take-off velocities also fall. The mechanism of azimuth control results from the mechanics of the hind legs and the resulting force vectors of their tibiae. This enables froghoppers to have a simple transform between initial body position and motion trajectory, therefore potentially simplifying neural control.

Energy storage and synchronisation of hind leg movements during jumping in planthopper insects (Hemiptera, Issidae)

The hind legs of Issus (Hemiptera, Issidae) move in the same plane underneath the body, an arrangement that means they must also move synchronously to power jumping. Moreover, they move so quickly that energy must be stored before a jump and then released suddenly. High speed imaging and analysis of the mechanics of the proximal joints of the hind legs show that mechanical mechanisms ensure both synchrony of movements and energy storage. The hind trochantera move first in jumping and are synchronised to within 30 micros. Synchrony is achieved by mechanical interactions between small protrusions from each trochantera which fluoresce bright blue under specific wavelengths of ultra-violet light and which touch at the midline when the legs are cocked before a jump. In dead Issus, a depression force applied to a cocked hind leg, or to the tendon of its trochanteral depressor muscle causes a simultaneous depression of both hind legs. The protrusion of the hind leg that moves first nudges the other hind leg so that both move synchronously. Contractions of the trochanteral depressor muscles that precede a jump bend the metathoracic pleural arches of the internal skeleton. Large areas of these bow-shaped structures fluoresce bright blue in ultraviolet light, and the intensity of this fluorescence depends on the pH of the bathing saline. These are key signatures of the rubber-like protein resilin. The remainder of a pleural arch consists of stiff cuticle. Bending these composite structures stores energy and their recoil powers jumping.

Visually mediated motor planning in the escape response of Drosophila

A key feature of reactive behaviors is the ability to spatially localize a salient stimulus and act accordingly. Such sensory-motor transformations must be particularly fast and well tuned in escape behaviors, in which both the speed and accuracy of the evasive response determine whether an animal successfully avoids predation [1]. We studied the escape behavior of the fruit fly, Drosophila, and found that flies can use visual information to plan a jump directly away from a looming threat. This is surprising, given the architecture of the pathway thought to mediate escape [2, 3]. Using high-speed videography, we found that approximately 200 ms before takeoff, flies begin a series of postural adjustments that determine the direction of their escape. These movements position their center of mass so that leg extension will push them away from the expanding visual stimulus. These preflight movements are not the result of a simple feed-forward motor program because their magnitude and direction depend on the flies' initial postural state. Furthermore, flies plan a takeoff direction even in instances when they choose not to jump. This sophisticated motor program is evidence for a form of rapid, visually mediated motor planning in a genetically accessible model organism.