The kinematics and neural control of high-speed kicking movements in the locust

Intelligent ankle-foot prosthesis based on human structure and motion bionics

The ankle-foot prosthesis aims to compensate for the missing motor functions by fitting the motion characteristics of the human ankle, which contributes to enabling the lower-limb amputees to take care of themselves and improve mobility in daily life. To address the problems of poor bionic motion of the ankle-foot prosthesis and the lack of natural interaction among the patient, prosthesis, and the environment, we developed a complex reverse-rolling conjugate joint based on the human ankle-foot structure and motion characteristics, the rolling joint was used to simulate the rolling-sliding characteristics of the knee joint. Meanwhile, we established a segmental dynamics model of the prosthesis in the stance phase, and the prosthetic structure parameters were obtained with the optimal prosthetic structure dimensions and driving force. In addition, a carbon fiber energy-storage foot was designed based on the human foot profile, and the dynamic response of its elastic strain energy at different thicknesses was simulated and analyzed. Finally, we integrated a bionic ankle-foot prosthesis and experiments were conducted to verify the bionic nature of the prosthetic joint motion and the energy-storage characteristics of the carbon fiber prosthetic foot. The proposed ankle-foot prosthesis provides ambulation support to assist amputees in returning to social life normally and has the potential to help improve clinical viability to reduce medical rehabilitation costs.

Bionic intelligent ankle-foot prosthesis based on the conjugate curved surface

Given the poor biomimetic motion of traditional ankle-foot prostheses, it is of great significance to develop an intelligent prosthesis that can realize the biomimetic mechanism of human feet and ankles. To this end, we presented a bionic intelligent ankle-foot prosthesis based on the complex conjugate curved surface. The proposed prosthesis is mainly composed of the rolling conjugated joints with a bionic design and the carbon fiber energy-storage foot. We investigated the flexibility of the prosthetic ankle joint movement, and the ability of the prosthetic foot to absorb ground impact during the gait cycle. Experimental results showed the matching of the ankle/toe position relationship of the human foot during simulated walking, which is helpful to realize the biomimetic motion of the human foot and ankle. It can also help therapists and clinicians provide better rehabilitation for lower-limb amputees.

Roles of muscle activities in foreleg movements during predatory strike of the mantis

Foreleg trajectory in the mantis strike varies depending on prey distance. To examine how muscle activities affect foreleg trajectory, we recorded strike behaviours of the Chinese mantis with a high-speed camera and electromyograms of the foreleg trochanteral extensor and flexor. At the approach phase of the mantis strike, the prothorax-coxa (P-C) joint elevated and the femur-tibia (F-T) joint extended. At the sweep phase, the coxa-trochanter (C-T) joint rapidly extended, then, the F-T joint rapidly flexed to capture the prey. At capture initiation, the C-T joint extended more with greater prey distance. After cutting the tendon of the trochanteral flexor, the C-T joint extended similarly to that of the intact foreleg but did not flex after it reached its peak angle. After cutting the tendon of the trochanteral extensor, the C-T joint did not extend as much as that of the intact foreleg. During rapid extension of the C-T joint, a burst of spikes from the coxal trochanteral extensor was observed in electromyograms. Among several parameters, burst duration was the best predictor of C-T joint angular change during strike. Unexpectedly, trochanteral flexor activity was also observed during rapid extension of the C-T joint. These results indicated that the coxal trochanteral extensor mainly contributed to the rapid C-T extension during strike, but other muscles also contributed at the beginning of extension. The trochanteral flexor appeared to contribute to C-T flexion by countering the rapid extension.

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.

Filtration-processed biomass nanofiber electrodes for flexible bioelectronics

An increasing demand for bioelectronics that interface with living systems has driven the development of materials to resolve mismatches between electronic devices and biological tissues. So far, a variety of different polymers have been used as substrates for bioelectronics. Especially, biopolymers have been investigated as next-generation materials for bioelectronics because they possess interesting characteristics such as high biocompatibility, biodegradability, and sustainability. However, their range of applications has been restricted due to the limited compatibility of classical fabrication methods with such biopolymers. Here, we introduce a fabrication process for thin and large-area films of chitosan nanofibers (CSNFs) integrated with conductive materials. To this end, we pattern carbon nanotubes (CNTs), silver nanowires, and poly (3,4-ethylenedioxythiophene):poly (styrenesulfonate) (PEDOT:PSS) by a facile filtration process that uses polyimide masks fabricated via laser ablation. This method yields feedlines of conductive material on nanofiber paper and demonstrates compatibility with conjugated and high-aspect-ratio materials. Furthermore, we fabricate a CNT neural interface electrode by taking advantage of this fabrication process and demonstrate peripheral nerve stimulation to the rapid extensor nerve of a live locust. The presented method might pave the way for future bioelectronic devices based on biopolymer nanofibers.

Temperature effects on the jumping performance of house crickets

Insect jumping and other explosive animal movements often make use of elastic-recoil mechanisms to enhance performance. These mechanisms circumvent the intrinsic rate limitations on muscle shortening, allowing for greater power production as well as thermal robustness of the associated movements. Here we examine the performance and temperature effects on jumping in the house cricket, Acheta domesticus, using high-speed imaging and inverse dynamics analysis. We find that adult house crickets jumped with greater performance than would be possible using direct muscle shortening, generating a peak power of over 2000 W/kg of muscle mass and maintaining high performance across the entire tested range of body temperatures (12-32°C). Performance declined at the lowest temperature (12°C), yet jump power still exceeds available muscle power. These results reveal that Acheta domesticus makes use of an elastic-recoil mechanism that enhances both the performance and thermal robustness of jumping.

A neuromechanical model exploring the role of the common inhibitor motor neuron in insect locomotion

In this work, we analyze a simplified, dynamical, closed-loop, neuromechanical simulation of insect joint control. We are specifically interested in two elements: (1) how slow muscle fibers may serve as temporal integrators of sensory feedback and (2) the role of common inhibitory (CI) motor neurons in resetting this integration when the commanded position changes, particularly during steady-state walking. Despite the simplicity of the model, we show that slow muscle fibers increase the accuracy of limb positioning, even for motions much shorter than the relaxation time of the fiber; this increase in accuracy is due to the slow dynamics of the fibers; the CI motor neuron plays a critical role in accelerating muscle relaxation when the limb moves to a new position; as in the animal, this architecture enables the control of the stance phase speed, independent of swing phase amplitude or duration, by changing the gain of sensory feedback to the stance phase muscles. We discuss how this relates to other models, and how it could be applied to robotic control.

Muscle-spring dynamics in time-limited, elastic movements

Muscle contractions that load in-series springs with slow speed over a long duration do maximal work and store the most elastic energy. However, time constraints, such as those experienced during escape and predation behaviours, may prevent animals from achieving maximal force capacity from their muscles during spring-loading. Here, we ask whether animals that have limited time for elastic energy storage operate with springs that are tuned to submaximal force production. To answer this question, we used a dynamic model of a muscle-spring system undergoing a fixed-end contraction, with parameters from a time-limited spring-loader (bullfrog: Lithobates catesbeiana) and a non-time-limited spring-loader (grasshopper: Schistocerca gregaria). We found that when muscles have less time to contract, stored elastic energy is maximized with lower spring stiffness (quantified as spring constant). The spring stiffness measured in bullfrog tendons permitted less elastic energy storage than was predicted by a modelled, maximal muscle contraction. However, when muscle contractions were modelled using biologically relevant loading times for bullfrog jumps (50 ms), tendon stiffness actually maximized elastic energy storage. In contrast, grasshoppers, which are not time limited, exhibited spring stiffness that maximized elastic energy storage when modelled with a maximal muscle contraction. These findings demonstrate the significance of evolutionary variation in tendon and apodeme properties to realistic jumping contexts as well as the importance of considering the effect of muscle dynamics and behavioural constraints on energy storage in muscle-spring systems.

Increased muscular volume and cuticular specialisations enhance jump velocity in solitarious compared with gregarious desert locusts, Schistocerca gregaria

The desert locust, Schistocerca gregaria, shows a strong phenotypic plasticity. It can develop, depending upon population density, into either a solitarious or gregarious phase that differs in many aspects of behaviour, physiology and morphology. Prominent amongst these differences is that solitarious locusts have proportionately longer hind femora than gregarious locusts. The hind femora contain the muscles and energy-storing cuticular structures that propel powerful jumps using a catapult-like mechanism. We show that solitarious locusts jump on average 23% faster and 27% further than gregarious locusts, and attribute this improved performance to three sources: first, a 17.5% increase in the relative volume of their hind femur, and hence muscle volume; second, a 24.3% decrease in the stiffness of the energy-storing semi-lunar processes of the distal femur; and third, a 4.5% decrease in the stiffness of the tendon of the extensor tibiae muscle. These differences mean that solitarious locusts can generate more power and store more energy in preparation for a jump than can gregarious locusts. This improved performance comes at a cost: solitarious locusts expend nearly twice the energy of gregarious locusts during a single jump and the muscular co-contraction that energises the cuticular springs takes twice as long. There is thus a trade-off between achieving maximum jump velocity in the solitarious phase against the ability to engage jumping rapidly and repeatedly in the gregarious phase.

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.

Development and deposition of resilin in energy stores for locust jumping

Locusts jump by using a catapult mechanism in which energy produced by slow contractions of the extensor tibiae muscles of the hind legs is stored in distortions of the exoskeleton, most notably (1) the two semi-lunar processes at each knee joint and (2) the tendons of the extensor muscles themselves. The energy is then suddenly released from these stores to power the rapid, propulsive movements of the hind legs. The reliance on the mechanical storage of energy is likely to impact on jumping because growth occurs by a series of five moults, at each of which the exoskeleton is replaced by a new one. All developmental stages (instars) nevertheless jump as a means of forward locomotion, or as an escape movement. Here, I show that in each instar, resilin is added to the semi-lunar processes and to the core of the extensor tendons so that their thickness increases. As the next moult approaches, a new exoskeleton forms within the old one, with resilin already present in the new semi-lunar processes. The old exoskeleton, the tendons and their resilin are discarded at moulting. The resilin of the semi-lunar processes and tendons of the new instar is initially thin, but a similar pattern of deposition results in an increase of their thickness. In adults, resilin continues to be deposited so that at 4 weeks old the thickness in the semi-lunar processes has increased fourfold. These changes in the energy stores accompany changes in jumping ability and performance during each moulting cycle.

Feed-forward motor control of ultrafast, ballistic movements

To circumvent the limits of muscle, ultrafast movements achieve high power through the use of springs and latches. The time scale of these movements is too short for control through typical neuromuscular mechanisms, thus ultrafast movements are either invariant or controlled prior to movement. We tested whether mantis shrimp (Stomatopoda: Neogonodactylus bredini) vary their ultrafast smashing strikes and, if so, how this control is achieved prior to movement. We collected high-speed images of strike mechanics and electromyograms of the extensor and flexor muscles that control spring compression and latch release. During spring compression, lateral extensor and flexor units were co-activated. The strike initiated several milliseconds after the flexor units ceased, suggesting that flexor activity prevents spring release and determines the timing of strike initiation. We used linear mixed models and Akaike's information criterion to serially evaluate multiple hypotheses for control mechanisms. We found that variation in spring compression and strike angular velocity were statistically explained by spike activity of the extensor muscle. The results show that mantis shrimp can generate kinematically variable strikes and that their kinematics can be changed through adjustments to motor activity prior to the movement, thus supporting an upstream, central-nervous-system-based control of ultrafast movement. Based on these and other findings, we present a shishiodoshi model that illustrates alternative models of control in biological ballistic systems. The discovery of feed-forward control in mantis shrimp sets the stage for the assessment of targets, strategic variation in kinematics and the role of learning in ultrafast animals.

The mechanics of elastic loading and recoil in anuran jumping

Many animals use catapult mechanisms to produce extremely rapid movements for escape or prey capture, resulting in power outputs far beyond the limits of muscle. In these catapults, muscle contraction loads elastic structures, which then recoil to release the stored energy extremely rapidly. Many arthropods employ anatomical ‘catch mechanisms’ to lock the joint in place during the loading period, which can then be released to allow joint motion via elastic recoil. Jumping vertebrates lack a clear anatomical catch, yet face the same requirement to load the elastic structure prior to movement. There are several potential mechanisms to allow loading of vertebrate elastic structures, including the gravitational load of the body, a variable mechanical advantage, and moments generated by the musculature of proximal joints. To test these hypothesized mechanisms, we collected simultaneous 3D kinematics via X-ray Reconstruction of Moving Morphology (XROMM) and single-foot forces during the jumps of three Rana pipiens. We calculated joint mechanical advantage, moment and power using inverse dynamics at the ankle, knee, hip and ilio-sacral joints. We found that the increasing proximal joint moments early in the jump allowed for high ankle muscle forces and elastic pre-loading, and the subsequent reduction in these moments allowed the ankle to extend using elastic recoil. Mechanical advantage also changed throughout the jump, with the muscle contracting against a poor mechanical advantage early in the jump during loading and a higher mechanical advantage late in the jump during recoil. These ‘dynamic catch mechanisms’ serve to resist joint motion during elastic loading, then allow it during elastic recoil, functioning as a catch mechanism based on the balance and orientation of forces throughout the limb rather than an anatomical catch.

Jumping mechanisms in flatid planthoppers (Hemiptera, Flatidae)

The jumping performance of three species of hemipterans from Australia and Europe belonging to the family Flatidae, were analysed from images captured at a rate of 5000 s-1. The shape of a flatid was dominated by large triangular or wedge-shaped front wings which, when folded, covered and extended above and behind the body to give a laterally compressed and possibly streamlined appearance. Body length of the three species of adults ranged from 7 to 9 mm and their mass from 8 to 19 mg. The propulsive hind legs were 30% longer than the front legs but only 36-54% of body length. Jumps with the fastest take-off velocities of 2.8-3.2 m s-1 had acceleration times of 1.4-1.8 ms. During such jumps adults experienced an acceleration of 174 - 200 g. These jumps required an energy expenditure of 76-225 μJ, a power output of 13-60 mW and exerted a force of 9-37 mN. The required power output per mass of jumping muscle in adults ranged from 24,000 to 27,000 W kg-1 muscle, 100 times greater than the maximum active contractile limit of normal muscle. The free-living nymphs were also proficient jumpers, reaching take-off velocities of 2.2 m s-1. To achieve such a jumping performance requires a power amplification mechanism. The energy store for such a mechanism was identified as the internal skeleton linking a hind coxa to the articulation of a hind wing. These pleural arches fluoresced bright blue when illuminated with ultraviolet light indicating the presence of the elastic protein resilin. The energy generated by the prolonged contractions of the trochanteral depressor muscles was stored in distortions of these structures and their rapid elastic recoil powered the synchronous propulsive movements of the hind legs.

Passive joint forces are tuned to limb use in insects and drive movements without motor activity

Background

Limb movements are generally driven by active muscular contractions working with and against passive forces arising in muscles and other structures. In relatively heavy limbs, the effects of gravity and inertia predominate, whereas in lighter limbs, passive forces intrinsic to the limb are of greater consequence. The roles of passive forces generated by muscles and tendons are well understood, but there has been little recognition that forces originating within joints themselves may also be important, and less still that these joint forces may be adapted through evolution to complement active muscle forces acting at the same joint.

Results

We examined the roles of passive joint forces in insect legs with different arrangements of antagonist muscles. We first show that passive forces modify actively generated movements of a joint across its working range, and that they can be sufficiently strong to generate completely passive movements that are faster than active movements observed in natural behaviors. We further demonstrate that some of these forces originate within the joint itself. In legs of different species adapted to different uses (walking, jumping), these passive joint forces complement the balance of strength of the antagonist muscles acting on the joint. We show that passive joint forces are stronger where they assist the weaker of two antagonist muscles.

Conclusions

In limbs where the dictates of a key behavior produce asymmetry in muscle forces, passive joint forces can be coadapted to provide the balance needed for the effective generation of other behaviors.

•

Limb movements are assisted by passive forces arising within joints

•

Functional cyclic movements can be generated by a single motor neuron

•

Joint forces are matched to the strength of antagonist muscles across species

•

Passive joint properties can transfer force from a stronger to a weaker muscle

Jumping mechanisms in jumping plant lice (Hemiptera, Sternorrhyncha, Psyllidae)

Jumping mechanisms and performance were analysed in three species of psyllids (Hemiptera, Sternorrhyncha) that ranged from 2 to 4 mm in body length and from 0.7 to 2.8 mg in mass. Jumping was propelled by rapid movements of the short hind legs, which were only 10-20% longer than the other legs and 61-77% of body length. Power was provided by large thoracic muscles that depressed the trochantera so that the two hind legs moved in parallel planes on either side of the body. These movements accelerated the body to take-off in 0.9 ms in the smallest psyllid and 1.7 ms in the largest, but in all species imparted a rapid forward rotation so that at take-off the head pointed downwards, subtending angles of approximately -60 deg relative to the ground. The front legs thus supported the body just before take-off and either lost contact with the ground at the same time as, or even after, the hind legs. In the best jumps from the horizontal, take-off velocity reached 2.7 m s(-1) and the trajectory was steep at 62-80 deg. Once airborne, the body spun rapidly at rates of up to 336 Hz in the pitch plane. In many jumps, the wings did not open to provide stabilisation, but some jumps led directly to sustained flight. In their best jumps, the smallest species experienced a force of 637 g. The largest species had an energy requirement of 13 μJ, a power output of 13 mW and exerted a force of nearly 10 mN. In a rare jumping strategy seen in only two of 211 jumps analysed, the femoro-tibial joints extended further and resulted in the head pointing upwards at take-off and the spin rate being greatly reduced.

A buckling region in locust hindlegs contains resilin and absorbs energy when jumping or kicking goes wrong

If a hindleg of a locust slips during jumping, or misses its target during kicking, energy generated by the two extensor tibiae muscles is no longer expended in raising the body or striking a target. How, then, is the energy in a jump (4100-4800 μJ) or kick (1700 μJ) dissipated? A specialised buckling region found in the proximal hind-tibia where the bending moment is high, but not present in the other legs, buckled and allowed the distal part of the tibia to extend. In jumps when a hindleg slipped, it bent by a mean of 23±14 deg at a velocity of 13.4±9.5 deg ms(-1); in kicks that failed to contact a target it bent by 32±16 deg at a velocity of 32.9±9.5 deg ms(-1). It also buckled 8.5±4.0 deg at a rate of 0.063±0.005 deg ms(-1) when the tibia was prevented from flexing fully about the femur in preparation for both these movements. By experimentally buckling this region through 40 deg at velocities of 0.001-0.65 deg ms(-1), we showed that one hindleg could store about 870 μJ on bending, of which 210 μJ was dissipated back to the leg on release. A band of blue fluorescence was revealed at the buckling region under UV illumination that had the two key signatures of the elastic protein resilin. A group of campaniform sensilla 300 μm proximal to the buckling region responded to imposed buckling movements. The features of the buckling region show that it can act as a shock absorber as proposed previously when jumping and kicking movements go wrong.

A system identification analysis of neural adaptation dynamics and nonlinear responses in the local reflex control of locust hind limbs

Nonlinear type system identification models coupled with white noise stimulation provide an experimentally convenient and quick way to investigate the often complex and nonlinear interactions between the mechanical and neural elements of reflex limb control systems. Previous steady state analysis has allowed the neurons in such systems to be categorised by their sensitivity to position, velocity or acceleration (dynamics) and has improved our understanding of network function. These neurons, however, are known to adapt their output amplitude or spike firing rate during repetitive stimulation and this transient response may be more important than the steady state response for reflex control. In the current study previously used system identification methods are developed and applied to investigate both steady state and transient dynamic and nonlinear changes in the neural circuit responsible for controlling reflex movements of the locust hind limbs. Through the use of a parsimonious model structure and Monte Carlo simulations we conclude that key system dynamics remain relatively unchanged during repetitive stimulation while output amplitude adaptation is occurring. Whilst some evidence of a significant change was found in parts of the systems nonlinear response, the effect was small and probably of little physiological relevance. Analysis using biologically more realistic stimulation reinforces this conclusion.

Locusts use a composite of resilin and hard cuticle as an energy store for jumping and kicking

Locusts jump and kick by using a catapult mechanism in which energy is first stored and then rapidly released to extend the large hind legs. The power is produced by a slow contraction of large muscles in the hind femora that bend paired semi-lunar processes in the distal part of each femur and store half the energy needed for a kick. We now show that these energy storage devices are composites of hard cuticle and the rubber-like protein resilin. The inside surface of a semi-lunar process consists of a layer of resilin, particularly thick along an inwardly pointing ridge and tightly bonded to the external, black cuticle. From the outside, resilin is visible only as a distal and ventral triangular area that tapers proximally. High-speed imaging showed that the semi-lunar processes were bent in all three dimensions during the prolonged muscular contractions that precede a kick. To reproduce these bending movements, the extensor tibiae muscle was stimulated electrically in a pattern that mimicked the normal sequence of its fast motor spikes recorded in natural kicking. Externally visible resilin was compressed and wrinkled as a semi-lunar process was bent. It then sprung back to restore the semi-lunar process rapidly to its original natural shape. Each of the five nymphal stages jumped and kicked and had a similar distribution of resilin in their semi-lunar processes as adults; the resilin was shed with the cuticle at each moult. It is suggested that composite storage devices that combine the elastic properties of resilin with the stiffness of hard cuticle allow energy to be stored by bending hard cuticle over only a small distance and without fracturing. In this way all the stored energy is returned and the natural shape of the femur is restored rapidly so that a jump or kick can be repeated.

Collision detection as a model for sensory-motor integration

Visually guided collision avoidance is critical for the survival of many animals. The execution of successful collision-avoidance behaviors requires accurate processing of approaching threats by the visual system and signaling of threat characteristics to motor circuits to execute appropriate motor programs in a timely manner. Consequently, visually guided collision avoidance offers an excellent model with which to study the neural mechanisms of sensory-motor integration in the context of a natural behavior. Neurons that selectively respond to approaching threats and brain areas processing them have been characterized across many species. In locusts in particular, the underlying sensory and motor processes have been analyzed in great detail: These animals possess an identified neuron, called the LGMD, that responds selectively to approaching threats and conveys that information through a second identified neuron, the DCMD, to motor centers, generating escape jumps. A combination of behavioral and in vivo electrophysiological experiments has unraveled many of the cellular and network mechanisms underlying this behavior.

Design and Realization of a Flexible Claw of Rough Wall Climbing Robot

Based on the research of foot characteristics of insecta, a climbing robot’s mechanical structure and kinematics are analyzed, and the main crawling institutions was designed by a kind of bionic four-bar linkage. Claws are made of sharp spines, claws are composed of a number of toes which are flexible structure with local degrees of freedom, they have a grate adaptivity to the rough wall. We have studied the characteristics of the rough wall climbing, and made analysis affection of reliability with the angle perched on. The experimental study indicates spine planning and structure design, material selection are reasonable.

A comparison of models of the isometric force of locust skeletal muscle in response to pulse train inputs

Muscle models are an important tool in the development of new rehabilitation and diagnostic techniques. Many models have been proposed in the past, but little work has been done on comparing the performance of models. In this paper, seven models that describe the isometric force response to pulse train inputs are investigated. Five of the models are from the literature while two new models are also presented. Models are compared in terms of their ability to fit to isometric force data, using Akaike's and Bayesian information criteria and by examining the ability of each model to describe the underlying behaviour in response to individual pulses. Experimental data were collected by stimulating the locust extensor tibia muscle and measuring the force generated at the tibia. Parameters in each model were estimated by minimising the error between the modelled and actual force response for a set of training data. A separate set of test data, which included physiological kick-type data, was used to assess the models. It was found that a linear model performed the worst whereas a new model was found to perform the best. The parameter sensitivity of this new model was investigated using a one-at-a-time approach, and it found that the force response is not particularly sensitive to changes in any parameter.

There is no trade-off between speed and force in a dynamic lever system

Lever systems within a skeleton transmit force with a capacity determined by the mechanical advantage, A. A is the distance from input force to a joint, divided by the distance from the joint to the output force. A lever with a relatively high A in static equilibrium has a great capacity to generate force but moves a load over a small distance. Therefore, the geometry of a skeletal lever presents a trade-off between force and speed under quasi-static conditions. The present study considers skeletal dynamics that do not assume static equilibrium by modelling kicking by a locust leg, which is powered by stored elastic energy. This model predicts that the output force of this lever is proportional to A, but its maximum speed is independent of A. Therefore, no trade-off between force and velocity exists in a lever system with spring-mass dynamics. This demonstrates that the motion of a skeleton depends on the major forces that govern its dynamics and cannot be inferred from skeletal geometry alone.

Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle

An improved model of locust skeletal muscle will inform on the general behaviour of invertebrate and mammalian muscle with the eventual aim of improving biomedical models of human muscles, embracing prosthetic construction and muscle therapy. In this article, the isometric response of the locust hind leg extensor muscle to input pulse trains is investigated. Experimental data was collected by stimulating the muscle directly and measuring the force at the tibia. The responses to constant frequency stimulus trains of various frequencies and number of pulses were decomposed into the response to each individual stimulus. Each individual pulse response was then fitted to a model, it being assumed that the response to each pulse could be approximated as an impulse response and was linear, no assumption were made about the model order. When the interpulse frequency (IPF) was low and the number of pulses in the train small, a second-order model provided a good fit to each pulse. For moderate IPF or for long pulse trains a linear third-order model provided a better fit to the response to each pulse. The fit using a second-order model deteriorated with increasing IPF. When the input comprised higher IPFs with a large number of pulses the assumptions that the response was linear could not be confirmed. A generalised model is also presented. This model is second-order, and contains two nonlinear terms. The model is able to capture the force response to a range of inputs. This includes cases where the input comprised of higher frequency pulse trains and the assumption of quasi-linear behaviour could not be confirmed.

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.

A predictive model of the isometric force response of the locust extensor muscle

A predictive model that can be used to estimate the isometric force response of the locust hind leg extensor muscle is presented. The model consists of two first order coupled differential equations. The first of these equations is linear and relates an input pulse train to the calcium concentration in muscle filaments. The second is non-linear and relates the calcium concentration to muscle force. Experimental data was collected by stimulating the extensor muscle and measuring the force generated at the tibia. Model parameters were estimated by minimising the error between the modelled and actual force response in a set of training data. These parameters were then used to predict the isometric response when the neural activity recorded during a kick was used as an input to the model. The model was found to accurately predict the isometric force response of the locust hind leg extensor muscle.

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.

Isometric force generated by locust skeletal muscle: responses to single stimuli

A mathematical model of the locust hind leg extensor muscle is described. The model accounts for the force response of the muscle to well-separated input stimuli under isometric conditions. Experimental data was collected by stimulating the extensor muscle and measuring the force generated at the tibia. In developing a model it was assumed that the response to a single isolated stimulus was linear. A linear model was found to fit well to the response to an isolated stimulus. No assumptions were made about the model order and models of various order were fitted to data in the frequency domain, using a least squares fit. The stimulus can be approximated as an impulse, with the response to each stimulus well described by a linear second-order system. Using a third-order model provided a better fit to data, but the improvement in fit was marginal and the model uses one extra parameter. A fourth-order model, which is often used to describe the behaviour of isometric muscle was found to overfit the data. Using a second-order model provides a simpler way of describing the behaviour of an isometric twitch.

Resilin and chitinous cuticle form a composite structure for energy storage in jumping by froghopper insects

Background

Many insects jump by storing and releasing energy in elastic structures within their bodies. This allows them to release large amounts of energy in a very short time to jump at very high speeds. The fastest of the insect jumpers, the froghopper, uses a catapult-like elastic mechanism to achieve their jumping prowess in which energy, generated by the slow contraction of muscles, is released suddenly to power rapid and synchronous movements of the hind legs. How is this energy stored?

Results

The hind coxae of the froghopper are linked to the hinges of the ipsilateral hind wings by pleural arches, complex bow-shaped internal skeletal structures. They are built of chitinous cuticle and the rubber-like protein, resilin, which fluoresces bright blue when illuminated with ultra-violet light. The ventral and posterior end of this fluorescent region forms the thoracic part of the pivot with a hind coxa. No other structures in the thorax or hind legs show this blue fluorescence and it is not found in larvae which do not jump. Stimulating one trochanteral depressor muscle in a pattern that simulates its normal action, results in a distortion and forward movement of the posterior part of a pleural arch by 40 μm, but in natural jumping, the movement is at least 100 μm.

Conclusion

Calculations showed that the resilin itself could only store 1% to 2% of the energy required for jumping. The stiffer cuticular parts of the pleural arches could, however, easily meet all the energy storage needs. The composite structure therefore, combines the stiffness of the chitinous cuticle with the elasticity of resilin. Muscle contractions bend the chitinous cuticle with little deformation and therefore, store the energy needed for jumping, while the resilin rapidly returns its stored energy and thus restores the body to its original shape after a jump and allows repeated jumping.

Preparing for escape: an examination of the role of the DCMD neuron in locust escape jumps

Many animals begin to escape by moving away from a threat the instant it is detected. However, the escape jumps of locusts take several hundred milliseconds to produce and the locust must therefore be prepared for escape before the jumping movement can be triggered. In this study we investigate a locust's preparations to escape a looming stimulus and concurrent spiking activity in its pair of uniquely identifiable looming-detector neurons (the descending contralateral movement detectors; DCMDs). We find that hindleg flexion in preparation for a jump occurs at the same time as high frequency DCMD spikes. However, spikes in a DCMD are not necessary for triggering hindleg flexion, since this hindleg flexion still occurs when the connective containing a DCMD axon is severed or in response to stimuli that cause no high frequency DCMD spikes. Such severing of the connective containing a DCMD axon does, however, increase the variability in flexion timing. We therefore propose that the DCMD contributes to hindleg flexion in preparation for an escape jump, but that its activity affects only flexion timing and is not necessary for the occurrence of hindleg flexion.

Anatomy of the hind legs and actions of their muscles during jumping in leafhopper insects

The rapid and simultaneous depression of the trochantera about the coxae of both hind legs of leafhoppers are the key joint movements powering a jump. The present study analyses the structure of these joints and the actions of the muscles that move them. The hind coxae are huge and are linked to each other at the midline by a protrusion from one coxa that inserts in a socket of the other and acts like a press-stud (popper) fastener. This asymmetry is not reflected in any left- or right-handed preference either within one species or between species. The movements of the joints in a jump are monitored by a number of possible proprioceptors that should be activated when a hind leg is fully levated in preparation for a jump: a hair row and two hair plates on the coxa, a hair plate on a trochanteral pivot with a coxa, and femoral spines at the femoro-tibial joint. The depressor and levator muscles that move the trochanter are of similar size and together occupy the greater part of the metathorax. Their lever arms are similar when the leg is fully levated, but the lever arm of the depressor increases with initial depression of the coxo-trochanteral joint while that of the levator declines. A jump is preceded by activity in the trochanteral depressor and levator muscles, which results in a forward movement of the coxa and metathorax with the trochanter fully levated. This period of co-contraction could result in storage of energy in skeletal structures in the thorax. Just before the rapid depression of the trochanter in the jump movement the frequency of depressor spikes increases while that in the levator declines, releasing any force stored by the preceding muscle contractions. These bursts of depressor spikes occur at the same time in the left and right muscles but none of the individual motor spikes appeared to be synchronous on the two sides.

Morphology and action of the hind leg joints controlling jumping in froghopper insects

The morphology and movements of key joints of the hind legs that generate the rapid jumping of froghoppers were analysed. The movements of an individual hind leg during a jump occur in three phases. First, the trochanter is slowly levated about the coxa so that the femur moves anteriorly and engages with a lateral protrusion on the coxa. Second, both hind legs are held in this fully levated (cocked) position without moving for a few seconds. Third, both hind legs depress and extend completely in less than 1 ms. The critical,power-generating movement underlying a jump is the rapid and simultaneous depression of the trochantera about the coxae.

The lever arm of the hind trochanteral depressor muscle is smallest at the cocked position, but does not appear to go over the centre of the pivot. It then increases to a maximum after some 80° of depression movement. By contrast, the lever arm of the trochanteral levator tendon is similar over the range of joint movements and is exceeded by that of the depressor only after 40° of depression. Three prominent arrays of hairs on the trochantin, coxa and trochanter are appropriately positioned to act as proprioceptors signalling key movements in jumping.

In the fully levated position, a protrusion on the dorsal, proximal surface of a hind femur engages with a protrusion from the ventral and lateral part of a coxa. These structures are not present on the front and middle legs. Both protrusions are covered with a dense array of small projections (microtrichia)that both increase the surface area and may interlock with each other. To depress rapidly in a jump these protrusions must disengage. If the hind leg of a dead froghopper is forcibly levated, it will lock in its cocked position,from which it can depress rapidly by movement of the coxo-trochanteral joint and disengagement of the femoral and coxal protrusions. A prominent click sound occurs at the start of a jump that results either from the initial movements of the coxo-trochanteral joint, or from the disengagement of the microtrichia on the coxa and femur. Larval Philaenus, which do not jump, lack a femoral protrusion and have no microtrichia in equivalent positions on either the coxa or femur.

Neural control and coordination of jumping in froghopper insects

The thrust for jumping in froghopper insects is produced by a rapid, synchronous depression of both hind legs generated by huge, multipartite trochanteral depressor muscles in the thorax and smaller levator muscles in the coxae. A three-phase motor pattern activates these muscles in jumping. First, a levation phase lasts a few hundred milliseconds, in which a burst of spikes in the trochanteral levator motor neurons moves the hind legs into their fully cocked position and thus engages a mechanical lock between a coxa and a femur. Second, a cocked phase lasts a few seconds, in which a trochanteral depressor motor neuron spikes continuously at a frequency gradually rising to 50 Hz, although the hind legs remain stationary. Levator motor spikes are sporadic. Third, the jump movement lasts <1 ms, in which the spikes in the depressors stop abruptly and the legs rapidly depress. This pattern may vary in the speed of the initial levation and in the duration of the cocked phase. Recordings from the depressor muscles on both sides showed remarkable synchrony of their motor spikes. In one 4.9-long cocked phase all 174 spikes were synchronous and in another 27 s period of continuous spiking all but one of 1,176 spikes were synchronous. When a single hind leg moves rapidly, these depressor spikes are nevertheless independent of those of the other leg. These features of the motor pattern and the coupling between motor neurons to the two hind legs ensure powerful movements to propel rapid jumping.

Storage and recovery of elastic potential energy powers ballistic prey capture in toads

Ballistic tongue projection in toads is a remarkably fast and powerful movement. The goals of this study were to: (1) quantify in vivo power output and activity of the depressor mandibulae muscles that are responsible for ballistic mouth opening, which powers tongue projection; (2) quantify the elastic properties of the depressor mandibulae muscles and their series connective tissues using in situ muscle stimulation and force-lever studies; and (3) develop and test an elastic recoil model, based on the observed elastic properties of the depressor mandibulae muscles and series connective tissues, that accounts for displacement, velocity, acceleration and power output during ballistic mouth opening in toads. The results demonstrate that the depressor mandibulae muscles of toads are active for up to 250 ms prior to mouth opening. During this time, strains of up to 21.4% muscle resting length (ML) develop in the muscles and series connective tissues. At maximum isometric force, series connective tissues develop strains up to 14% ML, and the muscle itself develops strains up to 17.5% ML. When the mouth opens rapidly, the peak instantaneous power output of the depressor mandibulae muscles and series connective tissues can reach 9600 W kg(-1). The results suggest that: (1) elastic recoil of muscle itself can contribute significantly to the power of ballistic movements; (2) strain in series elastic elements of the depressor mandibulae muscle is too large to be borne entirely by the cross bridges and the actin-myosin filament lattice; and (3) central nervous control of ballistic tongue projection in toads likely requires the specification of relatively few parameters.

Motor activity and trajectory control during escape jumping in the locust Locusta migratoria

We investigated the escape jumps that locusts produce in response to approaching objects. Hindleg muscular activity during an escape jump is similar to that during a defensive kick. Locusts can direct their escape jumps up to 50 degrees either side of the direction of their long axis at the time of hindleg flexion, allowing them to consistently jump away from the side towards which an object is approaching. Variation in jump trajectory is achieved by rolling and yawing movements of the body that are controlled by the fore- and mesothoracic legs. During hindleg flexion, a locust flexes the foreleg ipsilateral to its eventual jump trajectory and then extends the contralateral foreleg. These foreleg movements continue throughout co-contraction of the hindleg tibial muscles, pivoting the locust's long axis towards its eventual jump trajectory. However, there are no bilateral differences in the motor programs of the left and right hindlegs that correlate with jump trajectory. Foreleg movements enable a locust to control its jump trajectory independent of the hindleg motor program, allowing a decision on jump trajectory to be made after the hindlegs have been cocked in preparation for a jump.

The locust jump: an integrated laboratory investigation

The locust is well known for its ability to jump large distances to avoid predation. This class sets out a series of investigations into the mechanisms underlying the jump enabling students to bring together information from biomechanics, muscle physiology, and anatomy. The nature of the investigation allows it to be undertaken at a number of levels of complexity from relatively simple comparative observations to detailed analysis of the properties of the muscles and the energy storage systems involved in powering the jump. The relative size and robustness of the locust make it simple to handle and ideal for such investigations.

High-speed video analysis of wing-snapping in two manakin clades (Pipridae: Aves)

Basic kinematic and detailed physical mechanisms of avian, non-vocal sound production are both unknown. Here, for the first time, field-generated high-speed video recordings and acoustic analyses are used to test numerous competing hypotheses of the kinematics underlying sonations, or non-vocal communicative sounds, produced by two genera of Pipridae, Manacus and Pipra (Aves). Eleven behaviorally and acoustically distinct sonations are characterized, five of which fall into a specific acoustic class of relatively loud, brief, broad-frequency sound pulses, or snaps. The hypothesis that one kinematic mechanism of snap production is used within and between birds in general, and manakins specifically, is rejected. Instead, it is verified that three of four competing hypotheses of the kinematic mechanisms used for producing snaps, namely: (1). above-the-back wing-against-wing claps, (2). wing-against-body claps and (3). wing-into-air flicks, are employed between these two clades, and a fourth mechanism, (4). wing-against-tail feather interactions, is discovered. The kinematic mechanisms used to produce snaps are invariable within each identified sonation, despite the fact that a diversity of kinematic mechanisms are used among sonations. The other six sonations described are produced by kinematic mechanisms distinct from those used to create snaps, but are difficult to distinguish from each other and from the kinematics of flight. These results provide the first detailed kinematic information on mechanisms of sonation in birds in general, and the Pipridae specifically. Further, these results provide the first evidence that acoustically similar avian sonations, such as brief, broad frequency snaps, can be produced by diverse kinematic means, both among and within species. The use of high-speed video recordings in the field in a comparative manner documents the diversity of kinematic mechanisms used to sonate, and uncovers a hidden, sexually selected radiation of behavioral and communicative diversity in the Pipridae.

Jumping and kicking in bush crickets

Bush crickets have long, thin hind legs but jump and kick rapidly. The mechanisms underlying these fast movements were analysed by correlating the activity of femoral muscles in a hind leg with the movements of the legs and body captured in high-speed images. A female Pholidoptera griseoaptera weighing 600 mg can jump a horizontal distance of 300 mm from a takeoff angle of 34 degrees and at a velocity of 2.1 m s(-1), gaining 1350 microJ of kinetic energy. The body is accelerated at up to 114 m s(-2), and the tibiae of the hind legs extend fully within 30 ms at maximal rotational velocities of 13500 deg. s(-1). Such performance requires a minimal power output of 40 mW. Ruddering movements of the hind legs may contribute to the stability of the body once the insect is airborne. During kicking, a hind tibia is extended completely within 10 ms with rotational velocities three times higher at 41800 deg. s(-1). Before a kick, high-speed images show no distortions of the hind femoro-tibial joints or of the small semi-lunar groove in the distal femur. Both kicks and jumps can be generated without full flexion of the hind tibiae. Some kicks involve a brief, 40-90 ms, period of co-contraction between the extensor and flexor tibiae muscles, but others can be generated by contraction of the extensor without a preceding co-contraction with the flexor. In the latter kicks, the initial flexion of the tibia is generated by a burst of flexor spikes, which then stop before spikes occur in the fast extensor tibiae (FETi) motor neuron. The rapid extension of the tibia can follow directly upon these spikes or can be delayed by as long as 40 ms. The velocity of tibial movement is positively correlated with the number of FETi spikes. The hind legs are 1.5 times longer than the body and more than four times longer than the front legs. The mechanical advantage of the hind leg flexor muscle over the extensor is greater at flexed joint angles and is enhanced by a pad of tissue on its tendon that slides over a protuberance in the ventral wall of the distal femur. The balance of forces in the extensor and flexor muscles, coupled with their changing lever ratio at different joint positions, appears to determine the point of tibial release and to enable rapid movements without an obligatory co-contraction of the two muscles.

Proprioceptors monitoring forces in a locust hind leg during kicking form negative feedback loops with flexor tibiae motor neurons

In preparation for jumping and kicking, a locust slowly generates large forces in the femoral muscles of its hind legs and stores them in elastic distortions of the tendons and femoral cuticle. At the femoro-tibial joints, the semi-lunar processes are bent, the cuticle of the dorsal distal femur is crumpled, and the femur is expanded in a mediolateral direction. We have analysed whether these distortions are monitored by sense organs and whether the information they provide is used to limit the forces generated and thus prevent structural damage to the joint. The two sensory neurons comprising the lump receptor lie in a groove in the ventral part of the distal femur. The sensory neurons spike if force is applied to the flexor tendon when the joint is fully flexed, but not when it is extended. They also spike as the tendon of the flexor muscle slides into the ventral femoral groove when the tibia is fully flexed during the co-contraction phase of kicking. Their spike frequency correlates with the extent of bending of a semi-lunar process that provides a quantifiable measure of the joint distortions. If the tibia is not fully flexed, however, then muscle contractions still cause distortions of the joint but these are not signalled by sensory spikes from the lump receptor. The lump receptor, therefore, does not respond primarily to the joint distortions but to the movements or force in the flexor tendon. Contractions of the flexor tibiae muscle caused by spikes in individual flexor motor neurons can evoke spikes in sensory neurons from the lump receptor when the joint is fully flexed. In turn, the sensory neurons cause a hyperpolarisation in particular flexor motor neurons in a polysynaptic negative feedback loop. The lump receptor could, therefore, regulate the output of the flexor motor neurons and, thus, limit the amount of force generated during co-contraction. It may also contribute to the inhibition of the flexors at the end of co-contraction that allows rapid kicking movements to occur.

Jumping in a winged stick insect

The Thailand winged stick insect (Sipyloidea sp.) flees rapidly from a disturbance by jumping forwards when stimulated on the abdomen and backwards when stimulated on the head. The mechanisms underlying these fast movements were analysed by measuring movements of the body and legs from images captured at 250 Hz.

A forward jump of both adults and nymphs involves movements of the abdomen and the middle and hind pairs of legs. The abdomen is raised and swung forwards by flexion at the joint with the metathorax and at the joint between the meso- and metathorax. At the same time, the tibiae of the hind and middle legs are extended and their femora depressed. The femoro-tibial joints of the legs are not fully flexed before a jump, and no structures in these joints appear to store muscular energy. The whole jumping sequence takes approximately 100 ms and results in take-off angles of 10-35° at velocities of 0.6-0.8 m s-1 and with an acceleration of 10 m s-2. The abdominal angular velocity was 2000° s-1and the tip of the abdomen moved at linear velocities of some 1 m s-1, while the maximum rate of tibial extension was 4000°s-1.

Rapid backward movements result either in the collapse of the body onto the ground, with a displacement away from the stimulus of approximately half a body length, or in the propulsion of the insect off its perch. Neither movement involves curling of the abdomen.

From a horizontal posture, the forward jumps result in a displacement of a few body lengths. More lift can be generated in adults by elevating the hind wings as the abdomen is swung forwards and depressing them as the legs lose contact with the ground. In this way, jumps can lead directly to flapping flight. Take-off into flight can, however, be achieved without the abdominal movements seen during jumping.

From a vertical posture, a forward jump propels the insect upwards and backwards before it falls to the ground horizontally displaced from its perch. Backward movements result in the insect falling with little horizontal displacement from its perch.

Jumping and kicking in the false stick insectProsarthria teretrirostris: kinematics and motor control

The false stick insect Prosarthria teretrirostris looks and behaves like a real stick insect but can jump and kick rapidly and powerfully like a locust, to which it is more closely related. It has an elongated body with slender hind legs that are some 2.5 times longer than the front and middle legs. A male with a body 67 mm long and weighing 0.28 g can jump 90 cm with a take-off angle of 40° and velocity of 2.5 ms-1,requiring an energy expenditure of 850 μJ. The body is accelerated at 165 ms-2 for only 30 ms. The larger and heavier females (mean body length 104 mm and weighing 1.5 g) can jump on average a distance of 49 cm.

During jumping, the tibiae of the hind legs are extended in 30 ms with maximum rotational velocities of 11.5° per ms, but during kicking, when there is no body weight to support, extension is complete in 7 ms with rotational velocities as high as 48° per ms. The short time available to accelerate the body indicates that the movements are not powered by direct muscle contractions and that there must be storage of elastic energy in advance. The motor patterns responsible for generating the necessary forces in the hind legs for jumping and kicking are similar and consist of three phases;an initial flexion of the tibia is followed by a co-contraction of the small flexor and large extensor tibiae muscles lasting several hundred milliseconds while the tibia remains fully flexed. Finally, the flexor motor neurons stop spiking so that the tibia is able to extend rapidly. The small semi-lunar processes at the femoro-tibial joints are not distorted, so that they cannot act as energy stores. Some 7% of the energy is stored transiently by bending the thin tibiae during the initial acceleration phase of a jump and releasing it just before take-off.

The jumping and kicking mechanisms of Prosarthria teretrirostrishave features in common with those used by locusts but also have their own characteristics. The evolution of jumping in Orthoptera is discussed in this context.