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

A Tunable, Simplified Model for Biological Latch Mediated Spring Actuated Systems

We develop a model of latch-mediated spring actuated (LaMSA) systems relevant to comparative biomechanics and bioinspired design. The model contains five components: two motors (muscles), a spring, a latch, and a load mass. One motor loads the spring to store elastic energy and the second motor subsequently removes the latch, which releases the spring and causes movement of the load mass. We develop freely available software to accompany the model, which provides an extensible framework for simulating LaMSA systems. Output from the simulation includes information from the loading and release phases of motion, which can be used to calculate kinematic performance metrics that are important for biomechanical function. In parallel, we simulate a comparable, directly actuated system that uses the same motor and mass combinations as the LaMSA simulations. By rapidly iterating through biologically relevant input parameters to the model, simulated kinematic performance differences between LaMSA and directly actuated systems can be used to explore the evolutionary dynamics of biological LaMSA systems and uncover design principles for bioinspired LaMSA systems. As proof of principle of this concept, we compare a LaMSA simulation to a directly actuated simulation that includes either a Hill-type force-velocity trade-off or muscle activation dynamics, or both. For the biologically-relevant range of parameters explored, we find that the muscle force-velocity trade-off and muscle activation have similar effects on directly actuated performance. Including both of these dynamic muscle properties increases the accelerated mass range where a LaMSA system outperforms a directly actuated one.

On springtails (Hexapoda: Collembola): a morphofunctional study of the jumping apparatus

Background

Springtails (Hexapoda: Collembola) are tiny organisms that lead a hidden life, mostly occuring deep in the soil and on leaf litter. They have a variety of interesting body morphology patterns, the most famous of which is the catapult-like structure that enables them to jump and flee from predators. This highly specialized jumping apparatus consists of a mobile furca, which when at rest fits into a trigger, "the retinaculum" on the ventral side of the abdomen. Despite the many studies that have attempted to investigate the jumping apparatus, the actual mechanisms involved in the jump, for example the way in which the furca is released by the retinaculum, how and where the mechanisms of spring and hydrostatic pressure originate, are still not properly understood. The morphology of the jumping apparatus of Orchesella cincta was investigated in detail using confocal laser scanning microscopy and MicroCT techniques for 3D reconstruction.

Results

The morphology of O. cincta with both flexed and extended furca is analysed and described. The abdominal musculature involved in the jumping mechanism and relevant structures of the exoskeleton of retinaculum and furca are described in detail. With the data obtained in this study, hypotheses can be made about (1) where and how the spring and hydrostatic pressure mechanisms originate; (2) which muscles act on the extension and flexion of the furca; (3) which muscles act on the retinaculum and (4) how the retinaculum is released from the furca.

Conclusions

The comparative morphological study proved informative, and shows how springtail jumping involves mechanisms unique to this taxon. Hydrostatic pressure regulation possibly varies between animals with distinct segmentation, and those with fused segmentation. Interesting cuticular characters were revealed, such as basal plates and sclerites related to the construction of the spring mechanism. The present study establishes itself as a model option for future morphofunctional studies on springtail’s jumping. Analysis of videos and images using a high speed camera will be useful for understanding how the jump develops through take-off, aerial and landing phases.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12983-022-00463-y.

Theory of Fast Walking With Human-Driven Load-Carrying Robot Exoskeletons

Reaching and maintaining high walking speeds is challenging for a human when carrying extra weight, such as walking with a heavy backpack. Robotic limbs can support a heavy backpack when standing still, but accelerating a backpack within a couple of steps to race-walking speeds requires limb force and energy beyond natural human ability. Here, we conceive a human-driven robot exoskeleton that could accelerate a heavy backpack faster and maintain top speeds higher than what the human alone can when not carrying a backpack. The key components of the exoskeleton are the mechanically adaptive but energetically passive spring limbs. We show that by optimally adapting the stiffness of the limbs, the robot can achieve near-horizontal center of mass motion to emulate the load-bearing mechanics of the bicycle. We find that such an exoskeleton could enable the human to accelerate one extra body weight up to top race-walking speeds in ten steps. Our finding predicts that human-driven mechanically adaptive robot exoskeletons could extend human weight-bearing and fast-walking ability without using external energy.

Dual spring force couples yield multifunctionality and ultrafast, precision rotation in tiny biomechanical systems

Small organisms use propulsive springs rather than muscles to repeatedly actuate high acceleration movements, even when constrained to tiny displacements and limited by inertial forces. Through integration of a large kinematic dataset, measurements of elastic recoil, energetic math modeling and dynamic math modeling, we tested how trap-jaw ants (Odontomachus brunneus) utilize multiple elastic structures to develop ultrafast and precise mandible rotations at small scales. We found that O. brunneus develops torque on each mandible using an intriguing configuration of two springs: their elastic head capsule recoils to push and the recoiling muscle-apodeme unit tugs on each mandible. Mandibles achieved precise, planar, circular trajectories up to 49,100 rad s-1 (470,000 rpm) when powered by spring propulsion. Once spring propulsion ended, the mandibles moved with unconstrained and oscillatory rotation. We term this mechanism a 'dual spring force couple', meaning that two springs deliver energy at two locations to develop torque. Dynamic modeling revealed that dual spring force couples reduce the need for joint constraints and thereby reduce dissipative joint losses, which is essential to the repeated use of ultrafast, small systems. Dual spring force couples enable multifunctionality: trap-jaw ants use the same mechanical system to produce ultrafast, planar strikes driven by propulsive springs and for generating slow, multi-degrees of freedom mandible manipulations using muscles, rather than springs, to directly actuate the movement. Dual spring force couples are found in other systems and are likely widespread in biology. These principles can be incorporated into microrobotics to improve multifunctionality, precision and longevity of ultrafast systems.

Muscle fatigue in the latch-mediated spring actuated mandibles of trap-jaw ants

Muscle fatigue can reduce performance potentially affecting an organism's fitness. However, some aspects of fatigue could be overcome by employing a latch-mediated spring actuated system (LaMSA) where muscle activity is decoupled from movement. We estimated the effects of muscle fatigue on different aspects of mandible performance in six species of ants, two whose mandibles are directly actuated by muscles and four that have LaMSA "trap-jaw" mandibles. We found evidence that the LaMSA system of trap-jaw ants may prevent some aspects of performance from declining with repeated use, including duration, acceleration and peak velocity. However, inter-strike interval increased with repeated strikes suggesting that muscle fatigue still comes into play during the spring loading phase. In contrast, one species with directly actuated mandibles showed a decline in bite force over time. These results have implications for design principles aimed at minimizing the effects of fatigue on performance in spring and motor actuated systems.

Mathematical model and nanoindentation properties of the claws of Cyrtotrachelus buqueti Guer (Coleoptera: Curculionidae)

Scanning electron microscopy (SEM) was used to observe the macroscopic, microscopic, and cross‐sectional structures of the claws of Cyrtotrachelus buqueti Guer (Coleoptera: Curculionidae), and a mathematical model of a claw was used to investigate the structure–function relationships. To improve the quality of the SEM images, a non‐local means (NLM) algorithm and an improved NLM algorithm were applied. After comparison and analysis of five classical edge‐detection algorithms, the boundaries of the structural features of the claw were extracted based on a B‐spline wavelet algorithm, and the results showed that the variable curvature of the beetle claw enhances its adhesion force and improves its strength. Adhesion models of the claw were established, and the mechanical properties of its biomaterials were measured using nanoindentation. Considering that the presence of water can affect the hardness and Young's modulus, both ‘dry’ and ‘wet’ samples were examined. For the dry samples, the hardness and Young's modulus were 0.197 ± 0.074 GPa and 1.105 ± 0.197 GPa, respectively, whereas the respective values for the wet samples were both lower at 0.071 ± 0.030 GPa and 0.693 ± 0.163 GPa. This study provides data that can inform the design of climbing robots.

Engineered jumpers overcome biological limits via work multiplication

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

Power Amplification for Jumping Soft Robots Actuated by Artificial Muscles

Robots composed of soft materials can passively adapt to constrained environments and mitigate damage due to impact. Given these features, jumping has been explored as a mode of locomotion for soft robots. However, for mesoscale jumping robots, lightweight and compact actuation are required. Previous work focused on systems powered by fluids, combustion, smart materials, electromagnetic, or electrostatic motors, which require one or more of the following: large rigid components, external power supplies, components of specific, pre-defined sizes, or fast actuation. In this work, we propose an approach to design and fabricate an electrically powered soft amplification mechanism to enable untethered mesoscale systems with continuously tunable performance. We used the tunable geometry of a liquid crystal elastomer actuator, an elastic hemispherical shell, and a pouch motor for active latching to achieve rapid motions for jumping despite the slow contraction rate of the actuator. Our system amplified the power output of the LCE actuator by a factor of 8.12 × 10³ with a specific power of 26.4 W/kg and jumped to a height of 55.6 mm (with a 20 g payload). This work enables future explorations for electrically untethered soft systems capable of rapid motions (e.g., jumping).

Use of compliant actuators for throwing rigid projectiles

Muscles and tendons, actuators in robotics, and various sports implements are examples that exploit elasticity to accelerate objects. Tuning the mechanical properties of elastic elements connecting objects can greatly enhance the transfer of mechanical energy between the objects. Here, we study experimentally the throw of rigid projectiles by an actuator, which has a soft elastic element added to the distal end. We vary the thickness of the elastic layer and suggest a simple mass-spring chain model to find the properties of the elastic layer, which will maximize the energy transfer from the actuator to the projectile. The insertion of a soft layer, impedance matched to the ejection frequency of the projectile mass, can increase the throwing efficiency by over 400%. Finally, we identify that very thick and very soft compliant layers could potentially lead to high efficiency and flexibility simultaneously.

Analyzing Modeled Torque Profiles to Understand Scale-Dependent Active Muscle Responses in the Hip Joint

Animal locomotion is influenced by a combination of constituent joint torques (e.g., due to limb inertia and passive viscoelasticity), which determine the necessary muscular response to move the limb. Across animal size-scales, the relative contributions of these constituent joint torques affect the muscular response in different ways. We used a multi-muscle biomechanical model to analyze how passive torque components change due to an animal’s size-scale during locomotion. By changing the size-scale of the model, we characterized emergent muscular responses at the hip as a result of the changing constituent torque profile. Specifically, we found that activation phases between extensor and flexor torques to be opposite between small and large sizes for the same kinematic motion. These results suggest general principles of how animal size affects neural control strategies. Our modeled torque profiles show a strong agreement with documented hindlimb torque during locomotion and can provide insights into the neural organization and muscle activation behavior of animals whose motion has not been extensively documented.

Elastic energy storage across speeds during steady-state hopping of desert kangaroo rats (Dipodomys deserti)

Small bipedal hoppers, including kangaroo rats, are thought to not benefit from substantial elastic energy storage and return during hopping. However, recent species-specific material properties research suggests that, despite relative thickness, the ankle extensor tendons of these small hoppers are considerably more compliant than had been assumed. With faster locomotor speeds demanding higher forces, a lower tendon stiffness suggests greater tendon deformation and thus a greater potential for elastic energy storage and return with increasing speed. Using the elastic modulus values specific to kangaroo rat tendons, we sought to determine how much elastic energy is stored and returned during hopping across a range of speeds. In vivo techniques were used to record tendon force in the ankle extensors during steady-speed hopping. Our data support the hypothesis that the ankle extensor tendons of kangaroo rats store and return elastic energy in relation to hopping speed, storing more at faster speeds. Despite storing comparatively less elastic energy than larger hoppers, this relationship between speed and energy storage offer novel evidence of a functionally similar energy storage mechanism, operating irrespective of body size or tendon thickness, across the distal muscle-tendon units of both small and large bipedal hoppers.

Materials for Smart Soft Actuator Systems

In contrast to conventional hard actuators, soft actuators offer many vivid advantages, such as improved flexibility, adaptability, and reconfigurability, which are intrinsic to living systems. These properties make them particularly promising for different applications, including soft electronics, surgery, drug delivery, artificial organs, or prosthesis. The additional degree of freedom for soft actuatoric devices can be provided through the use of intelligent materials, which are able to change their structure, macroscopic properties, and shape under the influence of external signals. The use of such intelligent materials allows a substantial reduction of a device's size, which enables a number of applications that cannot be realized by externally powered systems. This review aims to provide an overview of the properties of intelligent synthetic and living/natural materials used for the fabrication of soft robotic devices. We discuss basic physical/chemical properties of the main kinds of materials (elastomers, gels, shape memory polymers and gels, liquid crystalline elastomers, semicrystalline ferroelectric polymers, gels and hydrogels, other swelling polymers, materials with volume change during melting/crystallization, materials with tunable mechanical properties, and living and naturally derived materials), how they are related to actuation and soft robotic application, and effects of micro/macro structures on shape transformation, fabrication methods, and we highlight selected applications.

Tuned muscle and spring properties increase elastic energy storage

Elastic recoil drives some of the fastest and most powerful biological movements. For effective use of elastic recoil, the tuning of muscle and spring force capacity is essential. Although studies of invertebrate organisms that use elastic recoil show evidence of increased force capacity in their energy loading muscle, changes in the fundamental properties of such muscles have yet to be documented in vertebrates. Here, we used three species of frogs (Cuban tree frogs, bullfrogs and cane toads) that differ in jumping power to investigate functional shifts in muscle-spring tuning in systems using latch-mediated spring actuation (LaMSA). We hypothesized that variation in jumping performance would result from increased force capacity in muscles and relatively stiffer elastic structures, resulting in greater energy storage. To test this, we characterized the force-length property of the plantaris longus muscle-tendon unit (MTU), and quantified the maximal amount of energy stored in elastic structures for each species. We found that the plantaris longus MTU of Cuban tree frogs produced higher mass-specific energy and mass-specific forces than the other two species. Moreover, we found that the plantaris longus MTU of Cuban tree frogs had higher pennation angles than the other species, suggesting that muscle architecture was modified to increase force capacity through packing of more muscle fibers. Finally, we found that the elastic structures were relatively stiffer in Cuban tree frogs. These results provide a mechanistic link between the tuned properties of LaMSA components, energy storage capacity and whole-system performance.

Muscle Actuators, Not Springs, Drive Maximal Effort Human Locomotor Performance

The current investigation examined muscle-tendon unit kinematics and kinetics in human participants asked to perform a hopping task for maximal performance with variational preceding milieu. Twenty-four participants were allocated post-data collection into those participants with an average hop height of higher (HH) or lower (LH) than 0.1 m. Participants were placed on a customized sled at a 20º angle while standing on a force plate. Participants used their dominant ankle for all testing and their knee was immobilized and thus all movement involved only the ankle joint and corresponding propulsive unit (triceps surae muscle complex). Participants were asked to perform a maximal effort during a single dynamic countermovement hop (CMH) and drop hops from 10 cm (DH10) and 50 cm (DH50). Three-dimensional motion analysis was performed by utilizing an infrared camera VICON motion analysis system and a corresponding force plate. An ultrasound probe was placed on the triceps surae muscle complex for muscle fascicle imaging. HH hopped significantly higher in all hopping tasks in comparison to LH. In addition, the HH group concentric ankle work was significantly higher in comparison to LH during all of the hopping tasks. Active muscle work was significantly higher in HH in comparison to LH as well. Tendon work was not significantly different between HH and LH. Active muscle work was significantly correlated with hopping height (r = 0.97) across both groups and hopping tasks and contributed more than 50% of the total work. The data indicates that humans primarily use a motor-driven system and thus it is concluded that muscle actuators and not springs maximize performance in hopping locomotor tasks in humans.

Autonomous snapping and jumping polymer gels

Snap-through buckling is commonly used in nature for power-amplified movements. While natural examples such as Utricularia and Dionaea muscipula can autonomously reset their snapping structures, bio-inspired analogues require external mediation for sequential snap events. Here we report the design principles for self-repeating, snap-based polymer jumping devices. Transient shape changes during the drying of a polymer gel are exploited to generate mechanical constraint and an internal driving force for snap-through buckling. Snap-induced shape changes alter environmental interactions to realize multiple, self-repeating snap events. The underlying mechanisms are understood through controlled experiments and numerical modelling. Using these lessons, we create snap-induced jumping devices with power density outputs (specific power ≈ 312 W kg^-1) that are similar to high-performing jumping organisms and engineered robots. These results provide the demonstration of an autonomous, self-repeating, high-speed movement, marking an important advance in the development of environmental energy harvesting, high-power motion that is important for microscale robots and actuated devices.

Jumping in lantern bugs (Hemiptera, Fulgoridae)

Lantern bugs are amongst the largest of the jumping hemipteran bugs, with body lengths reaching 44 mm and masses reaching 0.7 g. They are up to 600 times heavier than smaller hemipterans that jump powerfully using catapult mechanisms to store energy. Does a similar mechanism also propel jumping in these much larger insects? The jumping performance of two species of lantern bugs (Hemiptera, Auchenorrhyncha, family Fulgoridae) from India and Malaysia was therefore analysed from high-speed videos. The kinematics showed that jumps were propelled by rapid and synchronous movements of both hind legs, with their trochantera moving first. The hind legs were 20–40% longer than the front legs, which was attributable to longer tibiae. It took 5–6 ms to accelerate to take-off velocities reaching 4.65 m s⁻¹ in the best jumps by female Kalidasa lanata. During these jumps, adults experienced an acceleration of 77 g, required an energy expenditure of 4800 μJ and a power output of 900 mW, and exerted a force of 400 mN. The required power output of the thoracic jumping muscles was 21,000 W kg⁻¹, 40 times greater than the maximum active contractile limit of muscle. Such a jumping performance therefore required a power amplification mechanism with energy storage in advance of the movement, as in their smaller relatives. These large lantern bugs are near isometrically scaled-up versions of their smaller relatives, still achieve comparable, if not higher, take-off velocities, and outperform other large jumping insects such as grasshoppers.

Summary: Lantern bugs are large insects that jump at high-take-off velocities using a catapult mechanism that matches the performance of their much smaller planthopper relatives

Phase transformation-driven artificial muscle mimics the multifunctionality of avian wing muscle

Skeletal muscle provides a compact solution for performing multiple tasks under diverse operational conditions, a capability lacking in many current engineered systems. Here, we evaluate if shape memory alloy (SMA) components can serve as artificial muscles with tunable mechanical performance. We experimentally impose cyclic stimuli, electric and mechanical, to an SMA wire and demonstrate that this material can mimic the response of the avian humerotriceps, a skeletal muscle that acts in the dynamic control of wing shapes. We next numerically evaluate the feasibility of using SMA springs as artificial leg muscles for a bipedal walking robot. Altering the phase offset between mechanical and electrical stimuli was sufficient for both synthetic and natural muscle to shift between actuation, braking and spring-like behaviour.

Plasticity of the gastrocnemius elastic system in response to decreased work and power demand during growth

Elastic energy storage and release can enhance performance that would otherwise be limited by the force-velocity constraints of muscle. Although functional influence of a biological spring depends on tuning between components of an elastic system (the muscle, spring-driven mass and lever system), we do not know whether elastic systems systematically adapt to functional demand. To test whether altering work and power generation during maturation alters the morphology of an elastic system, we prevented growing guinea fowl (Numida meleagris) from jumping. We compared the jump performance of our treatment group at maturity with that of controls and measured the morphology of the gastrocnemius elastic system. We found that restricted birds jumped with lower jump power and work, yet there were no significant between-group differences in the components of the elastic system. Further, subject-specific models revealed no difference in energy storage capacity between groups, though energy storage was most sensitive to variations in muscle properties (most significantly operating length and least dependent on tendon stiffness). We conclude that the gastrocnemius elastic system in the guinea fowl displays little to no plastic response to decreased demand during growth and hypothesize that neural plasticity may explain performance variation.

The ultrafast snap of a finger is mediated by skin friction

The snap of a finger has been used as a form of communication and music for millennia across human cultures. However, a systematic analysis of the dynamics of this rapid motion has not yet been performed. Using high-speed imaging and force sensors, we analyse the dynamics of the finger snap. We discover that the finger snap achieves peak angular accelerations of 1.6 × 10⁶° s^-2 in 7 ms, making it one of the fastest recorded angular accelerations the human body produces (exceeding professional baseball pitches). Our analysis reveals the central role of skin friction in mediating the snap dynamics by acting as a latch to control the resulting high velocities and accelerations. We evaluate the role of this frictional latch experimentally, by covering the thumb and middle finger with different materials to produce different friction coefficients and varying compressibility. In doing so, we reveal that the compressible, frictional latch of the finger pads likely operates in a regime optimally tuned for both friction and compression. We also develop a soft, compressible friction-based latch-mediated spring actuated model to further elucidate the key role of friction and how it interacts with a compressible latch. Our mathematical model reveals that friction plays a dual role in the finger snap, both aiding in force loading and energy storage while hindering energy release. Our work reveals how friction between surfaces can be harnessed as a tunable latch system and provides design insight towards the frictional complexity in many robotic and ultra-fast energy-release structures.

A physical model of mantis shrimp for exploring the dynamics of ultrafast systems

Efficient and effective generation of high-acceleration movement in biology requires a process to control energy flow and amplify mechanical power from power density-limited muscle. Until recently, this ability was exclusive to ultrafast, small organisms, and this process was largely ascribed to the high mechanical power density of small elastic recoil mechanisms. In several ultrafast organisms, linkages suddenly initiate rotation when they overcenter and reverse torque; this process mediates the release of stored elastic energy and enhances the mechanical power output of extremely fast, spring-actuated systems. Here we report the discovery of linkage dynamics and geometric latching that reveals how organisms and synthetic systems generate extremely high-acceleration, short-duration movements. Through synergistic analyses of mantis shrimp strikes, a synthetic mantis shrimp robot, and a dynamic mathematical model, we discover that linkages can exhibit distinct dynamic phases that control energy transfer from stored elastic energy to ultrafast movement. These design principles are embodied in a 1.5-g mantis shrimp scale mechanism capable of striking velocities over 26 m [Formula: see text] in air and 5 m [Formula: see text] in water. The physical, mathematical, and biological datasets establish latching mechanics with four temporal phases and identify a nondimensional performance metric to analyze potential energy transfer. These temporal phases enable control of an extreme cascade of mechanical power amplification. Linkage dynamics and temporal phase characteristics are easily adjusted through linkage design in robotic and mathematical systems and provide a framework to understand the function of linkages and latches in biological systems.

Mechanical evaluation of 3D printed biomimetic non-Euclidean saddle geometries mimicking the mantis shrimp

Engineering design has drawn inspiration from naturally occurring structures to advance manufacturing processes and products, termed biomimetics. For example, the mantis shrimp, orderStomatopoda, is capable of producing one of the fastest appendage strikes in the world with marginal musculoskeletal displacement. The extreme speed of the mantis shrimp's raptorial appendage is due to the non-Euclidean hyperbolic paraboloid (i.e. saddle) shape within the dorsal region of the merus, which allows substantial energy storage through compression in the sagittal plane. Here, investigation of 3D printed synthetic geometries inspired by the mantis shrimp saddle geometry has revealed insights for elastic energy storage (i.e. spring-like) applications. Saddles composed of either astiffor aflexibleresin were investigated for spring response to explore the geometric effects. By modulating the saddle geometry and testing the spring response, it was found that, for thestiffresin, the spring constant was improved as the curvature of the contact and orthogonal faces were maximized and minimized, respectively. For theflexibleresin, it was found that the spring constant increased by less than 250 N mm^-1as the saddle geometry changed, substantiating that the flexible component of mantis saddles does not contribute to energy storage capabilities. The geometries of two saddles from the mantis shrimp speciesO. scyllaruswere estimated and exhibited similar trends to manufactured saddles, suggesting that modulating saddle geometry can be used for tailored energy storage moduli in spatially constrained engineering applications.

Thermal sensitivity of Axolotl feeding behaviors

Musculoskeletal movement results from muscle contractions, recoil of elastic tendons, aponeuroses, and ligaments, or combinations thereof. Muscular and elastic contributions can vary both across behaviors and with changes in temperature. Skeletal muscles reach peak contraction speed at a temperature optimum with performance declining away from that optimum by approximately 50% per 10 °C, following the Q10 principle. Elastic recoil action, however, is less temperature sensitive. We subjected Axolotls (Ambystoma mexicanum) to changes from warm (23 °C), via medium (14 °C), to cold (6 °C) temperature across most of their thermal tolerance range, and recorded jaw kinematics during feeding on crickets. We sought to determine if suction feeding strikes and food processing chews involve elastic mechanisms and, specifically, if muscular versus elastic contribution vary with temperature for gape opening and closing. Measurements of peak and mean speed for gape opening and closing during strikes and chews across temperature treatments were compared to Q10-based predictions. We found that strike gape speed decreased significantly from warm and medium to cold treatments, indicating low thermal robustness, and no performance-enhancement due to elastic recoil. For chews, peak and mean gape closing speeds, as well as peak gape opening speed, also decreased significantly from warm to cold treatments. However, peak gape opening and closing speeds for chews showed performance-enhancement, consistent with a previously demonstrated presence of elastic action in the Axolotl jaw system. Our results add to a relatively small body of evidence suggesting that elastic recoil plays significant roles in aquatic vertebrate feeding systems, and in cyclic food processing mechanisms.

Complexity and diversity of motion amplification and control strategies in motile carnivorous plant traps

Similar to animals, plants have evolved mechanisms for elastic energy storage and release to power and control rapid motion, yet both groups have been largely studied in isolation. This is exacerbated by the lack of consistent terminology and conceptual frameworks describing elastically powered motion in both groups. Iconic examples of fast movements can be found in carnivorous plants, which have become important models to study biomechanics, developmental processes, evolution and ecology. Trapping structures and processes vary considerably between different carnivorous plant groups. Using snap traps, suction traps and springboard-pitfall traps as examples, we illustrate how traps mix and match various mechanisms to power, trigger and actuate motions that contribute to prey capture, retention and digestion. We highlight a fundamental trade-off between energetic investment and movement control and discuss it in a functional-ecological context.

Rapid frequency modulation in a resonant system: aerial perturbation recovery in hawkmoths

Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.

A new species group of Strumigenys (Hymenoptera, Formicidae) from Ecuador, with a description of its mandible morphology

Strumigenys is one of the most diverse ant genera in the world and arguably the most morphologically diverse, exhibiting an exceptional range of mandible shape and function. A new species, Strumigenysayerstheysp. nov., discovered in the Chocó region of Ecuador is described. With two morphological characters, this species is shown to be a morphologically unique outlier among Strumigenys globally, having predominately smooth and shining cuticle surface sculpturing and long trap-jaw mandibles. Using µCT scans, we produced 3D images of the worker ant and static images to examine and compare mandible articular morphologies with most morphologically similar members of the mandibularis species group. Cuticular, pilosity, and articular mandible morphological differences supports placing the new species in its own new species group.

Scaling and development of elastic mechanisms: the tiny strikes of larval mantis shrimp

Latch-mediated spring actuation (LaMSA) is used by small organisms to produce high acceleration movements. Mathematical models predict that acceleration increases as LaMSA systems decrease in size. Adult mantis shrimp use a LaMSA mechanism in their raptorial appendages to produce extremely fast strikes. Until now, however, it was unclear whether mantis shrimp at earlier life-history stages also strike using elastic recoil and latch mediation. We tested whether larval mantis shrimp (Gonodactylaceus falcatus) use LaMSA and, because of their smaller size, achieve higher strike accelerations than adults of other mantis shrimp species. Based on microscopy and kinematic analyses, we discovered that larval G. falcatus possess the components of, and actively use, LaMSA during their fourth larval stage, which is the stage of development when larvae begin feeding. Larvae performed strikes at high acceleration and speed (mean: 4.133×105 rad s-2, 292.7 rad s-1; 12 individuals, 25 strikes), which are of the same order of magnitude as for adults - even though adult appendages are up to two orders of magnitude longer. Larval strike speed (mean: 0.385 m s-1) exceeded the maximum swimming speed of similarly sized organisms from other species by several orders of magnitude. These findings establish the developmental timing and scaling of the mantis shrimp LaMSA mechanism and provide insights into the kinematic consequences of scaling limits in tiny elastic mechanisms.

Body-catapult mechanism of the sandhopper jump and its biomimetic implications

Power amplification with catapult-like structures in arthropods is well studied, including the jump mechanism of natural organisms and biomimetic applications in robotics. Most catapult jump mechanisms have been developed based on animals that use legs to jump. However, jumps of some arthropods that use body parts other than legs and that show outstanding performance have been less studied until now. Here, we experimentally studied the jumping behavior of the sandhopper Talitrus saltator to determine whether they jump through the catapult mechanism and identify its critical catapult structures. The results showed that the sandhopper jumps through a body-catapult mechanism (muscle-specific power output: 1.7-5.7 kW/kg, 3.4-11.4 times the power output limit of arthropod muscle). The arch-shaped structures at the fore margin of the five posterior segments can provide a large amount of strain energy storage and account for more than 80% of the total kinetic energy demand. In addition, we build a biomimetic bi-segment device whose extension movement is actuated by sandhopper-inspired spring units. The results indicate that a multi-segmented robotic configuration can achieve rapid jumps based on the same principles of the body-catapult mechanism of the sandhopper.

Pendulum-based measurements reveal impact dynamics at the scale of a trap-jaw ant

Small organisms can produce powerful, sub-millisecond impacts by moving tiny structures at high accelerations. We developed and validated a pendulum device to measure the impact energetics of microgram-sized trap-jaw ant mandibles accelerated against targets at 10⁵ m s^-2 Trap-jaw ants (Odontomachus brunneus; 19 individuals, 212 strikes) were suspended on one pendulum and struck swappable targets that were either attached to an opposing pendulum or fixed in place. Mean post-impact kinetic energy (energy from a strike converted to pendulum motion) was higher with a stiff target (21.0-21.5 µJ) than with a compliant target (6.4-6.5 µJ). Target mobility had relatively little influence on energy transfer. Mean contact duration of strikes against stiff targets was shorter (3.9-4.5 ms) than against compliant targets (6.2-7.9 ms). Shorter contact duration was correlated with higher post-impact kinetic energy. These findings contextualize and provide an energetic explanation for the diverse, natural uses of trap-jaw ant strikes such as impaling prey, launching away threats and performing mandible-powered jumps. The strong effect of target material on energetic exchange suggests material interactions as an avenue for tuning performance of small, high acceleration impacts. Our device offers a foundation for novel research into the ecomechanics and evolution of tiny biological impacts and their application in synthetic systems.

Functional innovation promotes diversification of form in the evolution of an ultrafast trap-jaw mechanism in ants

Evolutionary innovations underlie the rise of diversity and complexity-the 2 long-term trends in the history of life. How does natural selection redesign multiple interacting parts to achieve a new emergent function? We investigated the evolution of a biomechanical innovation, the latch-spring mechanism of trap-jaw ants, to address 2 outstanding evolutionary problems: how form and function change in a system during the evolution of new complex traits, and whether such innovations and the diversity they beget are repeatable in time and space. Using a new phylogenetic reconstruction of 470 species, and X-ray microtomography and high-speed videography of representative taxa, we found the trap-jaw mechanism evolved independently 7 to 10 times in a single ant genus (Strumigenys), resulting in the repeated evolution of diverse forms on different continents. The trap mechanism facilitates a 6 to 7 order of magnitude greater mandible acceleration relative to simpler ancestors, currently the fastest recorded acceleration of a resettable animal movement. We found that most morphological diversification occurred after evolution of latch-spring mechanisms, which evolved via minor realignments of mouthpart structures. This finding, whereby incremental changes in form lead to a change of function, followed by large morphological reorganization around the new function, provides a model for understanding the evolution of complex biomechanical traits, as well as insights into why such innovations often happen repeatedly.

Torque-dense photomechanical actuation

Contactless actuation powered using light is shown to generate torque densities approaching 10 N m kg-1 at angular velocities ∼102 rad s-1: metrics that compare favorably against tethered electromechanical systems. This is possible even though the extinction of actinic light limits the characteristic thickness of photoresponse in polymers to tens of μm. Confinement of molecularly patterned developable shells fabricated from azobenzene-functionalized liquid crystalline polymers encodes torque-dense photoactuation. Photostrain gradients from unstructured irradiation segment this geometry into two oppositely curved regions connected by a curved crease. A monolithic curved shell spontaneously bifurcates into a jointed, arm-like mechanism that generates flexure over sweep angles exceeding a radian. Strain focusing at the crease is hierarchical: an integral crease nucleates at smaller magnitudes of the prebiased curvature, while a crease decorated with point-like defects emerges at larger curvatures. The phase-space of morphogenesis is traceable to the competition between stretch and bending energies and is parameterizable as a function of the geometry. The framework for generating repetitive torque-dense actuation from slender light-powered actuators holds broader implications for the design of soft, remotely operated machines. Here, it is harnessed in illustrative mechanisms including levers, lifters and grabbers that are powered and regulated exclusively using light.

Snaps of a tiny amphipod push the boundary of ultrafast, repeatable movement

Surprisingly, the fastest motions are not produced by large animals or robots. Rather, small organisms or structures, including cnidarian stinging cells, fungal shooting spores, and mandible strikes of ants, termites, and spiders, hold the world acceleration records.^1-5 These diverse systems share common features: they rapidly convert potential energy - stored in deformed material or fluid - into kinetic energy when a latch is released.^4-6 However, the fastest of these are not repeatable, because mechanical components are broken or ejected.^5,6 Furthermore, some of these systems must overcome the added challenge of moving in water, where high density and viscosity constrain acceleration at small sizes. Here we report the kinematics of repeatable, ultrafast snaps by tiny marine amphipods (Dulichiella cf. appendiculata). Males use their enlarged major claw, which can exceed 30% of body mass, to snap a 1 mm-long dactyl with a diameter equivalent to a human hair (184 μm). The claw snaps closed extremely rapidly, averaging 93 μs, 17 m s^-1, and 2.4 x 10⁵ m s^-2. These snaps are among the smallest and fastest of any documented repeatable movement, and are sufficiently fast to operate in the inertial hydrodynamic regime (Reynolds number (Re) >10,000). They generate audible pops and rapid water jets, which occasionally yield cavitation, and may be used for defense. These amphipod snaps push the boundaries of acceleration and size for repeatable movements, particularly in water, and exemplify how new biomechanical insights can arise from unassuming animals. VIDEO ABSTRACT.

Nonlinear elasticity and damping govern ultrafast dynamics in click beetles

Many small animals use springs and latches to overcome the mechanical power output limitations of their muscles. Click beetles use springs and latches to bend their bodies at the thoracic hinge and then unbend extremely quickly, resulting in a clicking motion. When unconstrained, this quick clicking motion results in a jump. While the jumping motion has been studied in depth, the physical mechanisms enabling fast unbending have not. Here, we first identify and quantify the phases of the clicking motion: latching, loading, and energy release. We detail the motion kinematics and investigate the governing dynamics (forces) of the energy release. We use high-speed synchrotron X-ray imaging to observe and analyze the motion of the hinge's internal structures of four Elater abruptus specimens. We show evidence that soft cuticle in the hinge contributes to the spring mechanism through rapid recoil. Using spectral analysis and nonlinear system identification, we determine the equation of motion and model the beetle as a nonlinear single-degree-of-freedom oscillator. Quadratic damping and snap-through buckling are identified to be the dominant damping and elastic forces, respectively, driving the angular position during the energy release phase. The methods used in this study provide experimental and analytical guidelines for the analysis of extreme motion, starting from motion observation to identifying the forces causing the movement. The tools demonstrated here can be applied to other organisms to enhance our understanding of the energy storage and release strategies small animals use to achieve extreme accelerations repeatedly.

The strike of the dragonfly larvae

The predatory strike of dragonfly larvae can inspire the design of fast robotic movement with enhanced control and precision.

A controllable dual-catapult system inspired by the biomechanics of the dragonfly larvae's predatory strike

The biomechanics underlying the predatory strike of dragonfly larvae is not yet understood. Dragonfly larvae are aquatic ambush predators, capturing their prey with a strongly modified extensible mouthpart. The current theory of hydraulic pressure being the driving force of the predatory strike can be refuted by our manipulation experiments and reinterpretation of former studies. Here, we report evidence for an independently loaded synchronized dual-catapult system. To power the ballistic movement of a single specialized mouthpart, two independently loaded springs simultaneously release and actuate two separate joints in a kinematic chain. Energy for the movement is stored by straining an elastic structure at each joint and, possibly, the surrounding cuticle, which is preloaded by muscle contraction. As a proof of concept, we developed a bioinspired robotic model resembling the morphology and functional principle of the extensible mouthpart. Understanding the biomechanics of the independently loaded synchronized dual-catapult system found in dragonfly larvae can be used to control the extension direction and, thereby, thrust vector of a power-modulated robotic system.

Survey of biomechanical aspects of arthropod terrestrialisation - Substrate bound legged locomotion

Arthropods are the most diverse clade on earth with regard to both species number and variability of body plans. Their general body plan is characterised by variable numbers of legs, and many-legged locomotion is an essential aspect of many aquatic and terrestrial arthropod species. Moreover, arthropods belong to the first groups of animals to colonise subaerial habitats, and they did so repeatedly and independently in a couple of clades. Those arthropod clades that colonised land habitats were equipped with highly variable body plans and locomotor apparatuses. Proceeding from their respective specific anatomies, they were challenged with strongly changing environmental conditions as well as altered physical and physiological constraints. This review explores the transitions from aquatic to terrestrial habitats across the different arthropod body plans and explains the major mechanisms and principles that constrain design and function of a range of locomotor apparatuses. Important aspects of movement physiology addressed here include the effects of different numbers of legs, different body sizes, miniaturisation and simplification of body plans and different ratios of inertial and damping forces. The article's focus is on continuous legged locomotion, but related ecological and behavioural aspects are also taken into account.

Form, Structure, and Function: How Plants vs. Animals Solve Physical Problems

Plants and animals have evolved solutions for a wide range of mechanical problems, such as adhesion and dispersal. Several of these solutions have been sources for bio-inspiration, like the Lotus Effect for self-cleaning surfaces or Velcro for adhesion. This symposium brought together plant and animal biomechanics researchers who tackle similar problems in different systems under the unifying theme of structure-function relations with relevance to bio-inspiration. For both communities it holds true that the structural systems, which have evolved in the respective organisms to address the mechanical challenges mentioned above, are often highly complex. This requires interdisciplinary research involving "classical" experimental biology approaches in combination with advanced imaging methods and computational modeling. The transfer of such systems into biomimetic technical materials and structures comes with even more challenges, like scalability issues and applicability. Having brought all these topics under one umbrella, this symposium presented the forefront of biophysical basic and application-oriented international research with the goal of facilitation knowledge transfer across systems and disciplines.

Achieving High-Speed Retraction in Stretchable Hydrogels

Hydrogels mimicking elastomeric biopolymers such as resilin, responsible for power-amplified activities in biological species necessary for locomotion, feeding, and defense have applications in soft robotics and prosthetics. Here, we report a bioinspired hydrogel synthesized through a free-radical polymerization reaction. By maintaining a balance between the hydrophilic and hydrophobic components, we obtain gels with an elastic modulus as high as 100 kPa, stretchability up to 800%, and resilience up to 98%. Such properties enable these gels to catapult projectiles. Furthermore, these gels achieve a retraction velocity of 16 m s^-1 with an acceleration of 4 × 10³ m s^-2 when released from a stretched state, and these values are comparable to those observed in many biological species during a power amplification process. By utilizing and tuning the simple synthetic strategy used here, these gels can be used in soft robotics, prosthetics, and engineered devices where power amplification is desired.

Programming Impulsive Deformation with Mechanical Metamaterials

Impulsive deformation is widely observed in biological systems to generate movement with high acceleration and velocity. By storing elastic energy in a quasistatic loading and releasing it through an impulsive elastic recoil, organisms circumvent the intrinsic trade-off between force and velocity and achieve power amplified motion. However, such asymmetry in strain rate in loading and unloading often results in reduced efficiency in converting elastic energy to kinetic energy for homogeneous materials. Here, we demonstrate that specific internal structural designs can offer the ability to tune quasistatic and high-speed recoil independently to control energy storage and conversion processes. Experimental demonstrations with mechanical metamaterials reveal that certain internal structures optimize energy conversion far beyond unstructured materials under the same conditions. Our results provide the first quantitative model and experimental demonstration for tuning energy conversion processes through internal structures of metamaterials.

Ultrafast launch of slingshot spiders using conical silk webs

In the Theridiosomatidae spider family, at least three genera (Epeirotypus, Naatlo and Theridiosoma) use their three-dimensional cone-shaped webs as ultrafast slingshots that catapult both the spider and the web towards prey [1-3]. Also known as slingshot spiders, theridiosomatids build three-dimensional conical webs with a tension line directly attached to the center of the web. In 1932, Hingston [1] hypothesized that the slingshot spider releases the tension line using its front legs, while holding the web with its rear legs. Coddington [2] detailed how female spiders meticulously build their webs line-by-line. But lacking to date has been quantification of spider kinematics, such as displacement, velocity and acceleration. Here we report the first quantification of theridiosomatid motion, revealing that slingshot spiders generate the fastest arachnid full body motion through use of their webs for external latch-mediated spring actuation [4].

Morphology and performance of the 'trap-jaw' cheliceral strikes in spiders (Araneae, Mecysmaucheniidae)

Mecysmaucheniidae spiders have evolved ultra-fast cheliceral strikes 4 times independently. The mechanism for producing these high-speed strikes is likely due to a latch/spring system that allows for stored energy to be rapidly released. This study examined two different sister lineages: Zearchaea has ultra-fast cheliceral strikes and Aotearoa, based on external morphology of the clypeus, is hypothesized to have slower strikes. Using high-speed videography, I first gathered kinematic data on each taxon. Then, using histology and data from micro-computed tomography scanning, I examined internal cheliceral muscle morphology to test whether shifts in muscle anatomy correspond to performance differences in cheliceral strike. Results from high-speed video analysis revealed that Zearchaea achieves peak angular velocities of 25.0×103±4.8×103 rad s-1 (mean±s.d.) in durations of 0.0843±0.017 ms. The fastest recorded strike had a peak angular and linear velocity of 30.8×103 rad s-1 and 18.2 m s-1, respectively. The slower striking sister species, Aotearoa magna, was three orders of magnitude slower in velocity and longer in duration. Histology revealed sarcomere length differences, with some muscles optimized for force, and other muscles for speed. 3D printed models revealed structural differences that explain how the chelicerae hinge open and close. Combining all of this evidence, I put forth a hypothesis for the ultra-fast trap-jaw mechanism. This research documents the morphological shifts that accompany ultra-fast movements that result in increased rotation in joints and increased muscle specialization.

Latch-based control of energy output in spring actuated systems

The inherent force-velocity trade-off of muscles and motors can be overcome by instead loading and releasing energy in springs to power extreme movements. A key component of this paradigm is the latch that mediates the release of spring energy to power the motion. Latches have traditionally been considered as switches; they maintain spring compression in one state and allow the spring to release energy without constraint in the other. Using a mathematical model of a simplified contact latch, we reproduce this instantaneous release behaviour and also demonstrate that changing latch parameters (latch release velocity and radius) can reduce and delay the energy released by the spring. We identify a critical threshold between instantaneous and delayed release that depends on the latch, spring, and mass of the system. Systems with stiff springs and small mass can attain a wide range of output performance, including instantaneous behaviour, by changing latch release velocity. We validate this model in both a physical experiment as well as with data from the Dracula ant, Mystrium camillae, and propose that latch release velocity can be used in both engineering and biological systems to control energy output.

The Mechanical Power of Titin Folding

The delivery of mechanical power, a crucial component of animal motion, is constrained by the universal compromise between the force and the velocity of its constituent molecular systems. While the mechanisms of force generation have been studied at the single molecular motor level, there is little understanding of the magnitude of power that can be generated by folding proteins. Here, we use single-molecule force spectroscopy techniques to measure the force-velocity relation of folding titin domains that contain single internal disulfide bonds, a common feature throughout the titin I-band. We find that formation of the disulfide regulates the peak power output of protein folding in an all-or-none manner, providing at 6.0 pN, for example, a boost from 0 to 6,000 zW upon oxidation. This mechanism of power generation from protein folding is of great importance for muscle, where titin domains may unfold and refold with each extension and contraction of the sarcomere.

Eckels et al. use single-molecule magnetic tweezers to simultaneously probe the folding dynamics of titin Ig domains and monitor the redox status of single disulfides within the Ig fold. Oxidation of the disulfide bond greatly increases both the folding force and the magnitude of power delivered by protein folding.

"Simple" Biomechanical Model for Ants Reveals How Correlated Evolution among Body Segments Minimizes Variation in Center of Mass as Heads Get Larger

The field of comparative biomechanics strives to understand the diversity of the biological world through the lens of physics. To accomplish this, researchers apply a variety of modeling approaches to explore the evolution of form and function ranging from basic lever models to intricate computer simulations. While advances in technology have allowed for increasing model complexity, insight can still be gained through the use of low-parameter "simple" models. All models, regardless of complexity, are simplifications of reality and must make assumptions; "simple" models just make more assumptions than complex ones. However, "simple" models have several advantages. They allow individual parameters to be isolated and tested systematically, can be made applicable to a wide range of organisms and make good starting points for comparative studies, allowing for complexity to be added as needed. To illustrate these ideas, we perform a case study on body form and center of mass stability in ants. Ants show a wide diversity of body forms, particularly in terms of the relative size of the head, petiole(s), and gaster (the latter two make-up the segments of the abdomen not fused to thorax in hymenopterans). We use a "simple" model to explore whether balance issues pertaining to the center of mass influence patterns of segment expansion across major ant clades. Results from phylogenetic comparative methods imply that the location of the center of mass in an ant's body is under stabilizing selection, constraining the center of mass to the middle segment (thorax) over the legs. This is potentially maintained by correlated rates of evolution between the head and gaster on either end. While these patterns arise from a model that makes several assumptions/simplifications relating to shape and materials, they still offer intriguing insights into the body plan of ants across ∼68% of their diversity. The results from our case study illustrate how "simple," low-parameter models both highlight fundamental biomechanical trends and aid in crystalizing specific questions and hypotheses for more complex models to address.

Ladybird beetle–inspired compliant origami

Origami can enable structures that are compact and lightweight. The facets of an origami structure in traditional designs, however, are essentially nondeformable rigid plates. Therefore, implementing energy storage and robust self-locking in these structures can be challenging. We note that the intricately folded wings of a ladybird beetle can be deployed rapidly and effectively sustain aerodynamic forces during flight; these abilities originate from the geometry and deformation of a specialized vein in the wing of this insect. We report compliant origami inspired by the wing vein in ladybird beetles. The deformation and geometry of the compliant facet enables both large energy storage and self-locking in a single origami joint. On the basis of our compliant origami, we developed a deployable glider module for a multimodal robot. The glider module is compactly foldable, is rapidly deployable, and can effectively sustain aerodynamic forces. We also apply our compliant origami to enhance the energy storage capacity of the jumping mechanism in a jumping robot.

Modeling the Determinants of Mechanical Advantage During Jumping: Consequences for Spring- and Muscle-Driven Movement

Systems powered by elastic recoil need a latch to prevent motion while a spring is loaded but allow motion during spring recoil. Some jumping animals that rely on elastic recoil use the increasing mechanical advantage of limb extensor muscles to accomplish latching. We examined the ways in which limb morphology affects latching and the resulting performance of an elastic-recoil mechanism. Additionally, because increasing mechanical advantage is a consequence of limb extension that may be found in many systems, we examined the mechanical consequences for muscle in the absence of elastic elements. By simulating muscle contractions against a simplified model of an extending limb, we found that increasing mechanical advantage can limit the work done by muscle by accelerating muscle shortening during limb extension. The inclusion of a series elastic element dramatically improves mechanical output by allowing for additional muscle work that is stored and released from the spring. This suggests that elastic recoil may be beneficial for more animals than expected when assuming peak isotonic power output from muscle during jumping. The mechanical output of elastic recoil depends on limb morphology; long limbs moving small loads maximize total work, but it is done at a low power, whereas shorter limbs moving larger loads do less work at a higher power. This work-power trade-off of limb morphology is true with or without an elastic element. Systems with relatively short limbs may have performance that is robust to variable conditions such as body mass or muscle activation, while long-limbed systems risk complete failure with relatively minor perturbations. Finally, a changing mechanical advantage latch allows for muscle work to be done simultaneously with spring recoil, changing the predictions for spring mechanical properties. Overall, the design constraints revealed by considering the mechanics of this particular latch will inform our understanding of the evolution of elastic-recoil mechanisms and our attempts to engineer similar systems.

Thermodynamics of the Bladderwort Feeding Strike-Suction Power from Elastic Energy Storage

The carnivorous plant bladderwort exemplifies the use of accumulated elastic energy to power motion: respiration-driven pumps slowly load the walls of its suction traps with elastic energy (∼1 h). During a feeding strike, this energy is released suddenly to accelerate water (∼1 ms). However, due to the traps' small size and concomitant low Reynolds number, a significant fraction of the stored energy may be dissipated as viscous friction. Such losses and the mechanical reversibility of Stokes flow are thought to degrade the feeding success of other suction feeders in this size range, such as larval fish. In contrast, triggered bladderwort traps are generally successful. By mapping the energy budget of a bladderwort feeding strike, we illustrate how this smallest of suction feeders can perform like an adult fish.

The Power of Mantis Shrimp Strikes: Interdisciplinary Impacts of an Extreme Cascade of Energy Release

In the course of a single raptorial strike by a mantis shrimp (Stomatopoda), the stages of energy release span six to seven orders of magnitude of duration. To achieve their mechanical feats of striking at the outer limits of speeds, accelerations, and impacts among organisms, they use a mechanism that exemplifies a cascade of energy release-beginning with a slow and forceful, spring-loading muscle contraction that lasts for hundreds of milliseconds and ending with implosions of cavitation bubbles that occur in nanoseconds. Mantis shrimp use an elastic mechanism built of exoskeleton and controlled with a latching mechanism. Inspired by both their mechanical capabilities and evolutionary diversity, research on mantis shrimp strikes has provided interdisciplinary and fundamental insights to the fields of elastic mechanisms, fluid dynamics, evolutionary dynamics, contest dynamics, the physics of fast, small systems, and the rapidly-expanding field of bioinspired materials science. Even with these myriad connections, numerous discoveries await, especially in the arena of energy flow through materials actuating and controlling fast, impact fracture resistant systems.

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

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