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.

Latch-mediated spring actuation (LaMSA): the power of integrated biomechanical systems.

Across the tree of life - from fungi to frogs - organisms wield small amounts of energy to generate fast and potent movements. These movements are propelled with elastic structures, and their loading and release are mediated by latch-like opposing forces. They comprise a class of elastic mechanisms termed latch-mediated spring actuation (LaMSA). Energy flow through LaMSA begins when an energy source loads elastic element(s) in the form of elastic potential energy. Opposing forces, often termed latches, prevent movement during loading of elastic potential energy. As the opposing forces are shifted, reduced or removed, elastic potential energy is transformed into kinetic energy of the spring and propelled mass. Removal of the opposing forces can occur instantaneously or throughout the movement, resulting in dramatically different outcomes for consistency and control of the movement. Structures used for storing elastic potential energy are often distinct from mechanisms that propel the mass: elastic potential energy is often distributed across surfaces and then transformed into localized mechanisms for propulsion. Organisms have evolved cascading springs and opposing forces not only to serially reduce the duration of energy release, but often to localize the most energy-dense events outside of the body to sustain use without self-destruction. Principles of energy flow and control in LaMSA biomechanical systems are emerging at a rapid pace. New discoveries are catalyzing remarkable growth of the historic field of elastic mechanisms through experimental biomechanics, synthesis of novel materials and structures, and high-performance robotics systems.

Developing elastic mechanisms: ultrafast motion and cavitation emerge at the millimeter scale in juvenile snapping shrimp.

Organisms such as jumping froghopper insects and punching mantis shrimp use spring-based propulsion to achieve fast motion. Studies of elastic mechanisms have primarily focused on fully developed and functional mechanisms in adult organisms. However, the ontogeny and development of these mechanisms can provide important insights into the lower size limits of spring-based propulsion, the ecological or behavioral relevance of ultrafast movement, and the scaling of ultrafast movement. Here, we examined the development of the spring-latch mechanism in the bigclaw snapping shrimp, Alpheus heterochaelis (Alpheidae). Adult snapping shrimp use an enlarged claw to produce high-speed strikes that generate cavitation bubbles. However, until now, it was unclear when the elastic mechanism emerges during development and whether juvenile snapping shrimp can generate cavitation at this size. We reared A. heterochaelis from eggs, through their larval and postlarval stages. Starting 1 month after hatching, the snapping shrimp snapping claw gradually developed a spring-actuated mechanism and began snapping. We used high-speed videography (300,000 frames s-1) to measure juvenile snaps. We discovered that juvenile snapping shrimp generate the highest recorded accelerations (5.8×105±3.3×105 m s-2) for repeated-use, underwater motion and are capable of producing cavitation at the millimeter scale. The angular velocity of snaps did not change as juveniles grew; however, juvenile snapping shrimp with larger claws produced faster linear speeds and generated larger, longer-lasting cavitation bubbles. These findings establish the development of the elastic mechanism and cavitation in snapping shrimp and provide insights into early life-history transitions in spring-actuated mechanisms.

Geometric latches enable tuning of ultrafast, spring-propelled movements.

The smallest, fastest, repeated-use movements are propelled by power-dense elastic mechanisms, yet the key to their energetic control may be found in the latch-like mechanisms that mediate transformation from elastic potential energy to kinetic energy. Here, we tested how geometric latches enable consistent or variable outputs in ultrafast, spring-propelled systems. We constructed a reduced-order mathematical model of a spring-propelled system that uses a torque reversal (over-center) geometric latch. The model was parameterized to match the scales and mechanisms of ultrafast systems, specifically snapping shrimp. We simulated geometric and energetic configurations that enabled or reduced variation of strike durations and dactyl rotations given variation of stored elastic energy and latch mediation. Then, we collected an experimental dataset of the energy storage mechanism and ultrafast snaps of live snapping shrimp (Alpheus heterochaelis) and compared our simulations with their configuration. We discovered that snapping shrimp deform the propodus exoskeleton prior to the strike, which may contribute to elastic energy storage. Regardless of the amount of variation in spring loading duration, strike durations were far less variable than spring loading durations. When we simulated this species' morphological configuration in our mathematical model, we found that the low variability of strike duration is consistent with their torque reversal geometry. Even so, our simulations indicate that torque reversal systems can achieve either variable or invariant outputs through small adjustments to geometry. Our combined experiments and mathematical simulations reveal the capacity of geometric latches to enable, reduce or enhance variation of ultrafast movements in biological and synthetic systems.

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.

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.

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.

Context-dependent scaling of kinematics and energetics during contests and feeding in mantis shrimp.

Measurements of energy use, and its scaling with size, are critical to understanding how organisms accomplish myriad tasks. For example, energy budgets are central to game theory models of assessment during contests and underlie patterns of feeding behavior. Clear tests connecting energy to behavioral theory require measurements of the energy use of single individuals for particular behaviors. Many species of mantis shrimp (Stomatopoda: Crustacea) use elastic energy storage to power high-speed strikes that they deliver to opponents during territorial contests and to hard-shelled prey while feeding. We compared the scaling of strike kinematics and energetics between feeding and contests in the mantis shrimp Neogonodactylus bredini We filmed strikes with high-speed video, measured strike velocity and used a mathematical model to calculate strike energy. During contests, strike velocity did not scale with body size but strike energy scaled positively with size. Conversely, while feeding, strike velocity decreased with increasing size and strike energy did not vary according to body size. Individuals most likely achieved this strike variation through differential compression of their exoskeletal spring prior to the strike. Post hoc analyses found that N. bredini used greater velocity and energy when striking larger opponents, yet variation in prey size was not accompanied by varying strike velocity or energetics. Our estimates of energetics inform prior tests of contest and feeding behavior in this species. More broadly, our findings elucidate the role behavioral context plays in measurements of animal performance.

Adhesive latching and legless leaping in small, worm-like insect larvae.

Jumping is often achieved using propulsive legs, yet legless leaping has evolved multiple times. We examined the kinematics, energetics and morphology of long-distance jumps produced by the legless larvae of gall midges (Asphondylia sp.). They store elastic energy by forming their body into a loop and pressurizing part of their body to form a transient 'leg'. They prevent movement during elastic loading by placing two regions covered with microstructures against each other, which likely serve as a newly described adhesive latch. Once the latch releases, the transient 'leg' launches the body into the air. Their average takeoff speeds (mean: 0.85 m s-1; range: 0.39-1.27 m s-1) and horizontal travel distances (up to 36 times body length or 121 mm) rival those of legged insect jumpers and their mass-specific power density (mean: 910 W kg-1; range: 150-2420 W kg-1) indicates the use of elastic energy storage to launch the jump. Based on the forces reported for other microscale adhesive structures, the adhesive latching surfaces are sufficient to oppose the loading forces prior to jumping. Energetic comparisons of insect larval crawling versus jumping indicate that these jumps are orders of magnitude more efficient than would be possible if the animals had crawled an equivalent distance. These discoveries integrate three vibrant areas in engineering and biology - soft robotics, small, high-acceleration systems, and adhesive systems - and point toward a rich, and as-yet untapped area of biological diversity of worm-like, small, legless jumpers.

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

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

The effect of size-scale on the kinematics of elastic energy release.

Elastically-driven motion has been used as a strategy to achieve high speeds in small organisms and engineered micro-robotic devices. We examine the size-scaling relations determining the limit of elastic energy release from elastomer bands that efficiently cycle mechanical energy with minimal loss. The maximum center-of-mass velocity of the elastomer bands was found to be size-scale independent, while smaller bands demonstrated larger accelerations and shorter durations of elastic energy release. Scaling relationships determined from these measurements are consistent with the performance of small organisms and engineered devices which utilize elastic elements to power motion.

Mutual assessment during ritualized fighting in mantis shrimp (Stomatopoda).

Safe and effective conflict resolution is critical for survival and reproduction. Theoretical models describe how animals resolve conflict by assessing their own and/or their opponent's ability (resource holding potential, RHP), yet experimental tests of these models are often inconclusive. Recent reviews have suggested this uncertainty could be alleviated by using multiple approaches to test assessment models. The mantis shrimp Neogonodactylus bredini presents visual displays and ritualistically exchanges high-force strikes during territorial contests. We tested how N. bredini contest dynamics were explained by any of three assessment models-pure self-assessment, cumulative assessment and mutual assessment-using correlations and a novel, network analysis-based sequential behavioural analysis. We staged dyadic contests over burrow access between competitors matched either randomly or based on body size. In both randomly and size-matched contests, the best metric of RHP was body mass. Burrow residency interacted with mass to predict outcome. Correlations between contest costs and RHP rejected pure self-assessment, but could not fully differentiate between cumulative and mutual assessment. The sequential behavioural analysis ruled out cumulative assessment and supported mutual assessment. Our results demonstrate how multiple analyses provide strong inference to tests of assessment models and illuminate how individual behaviours constitute an assessment strategy.

Smashing mantis shrimp strategically impact shells.

Many predators fracture strong mollusk shells, requiring specialized weaponry and behaviors. The current shell fracture paradigm is based on jaw- and claw-based predators that slowly apply forces (high impulse, low peak force). However, predators also strike shells with transient intense impacts (low impulse, high peak force). Toward the goal of incorporating impact fracture strategies into the prevailing paradigm, we measured how mantis shrimp (Neogonodactylus bredini) impact snail shells, tested whether they strike shells in different locations depending on prey shape (Nerita spp., Cenchritis muricatus, Cerithium spp.) and deployed a physical model (Ninjabot) to test the effectiveness of strike locations. We found that, contrary to their formidable reputation, mantis shrimp struck shells tens to hundreds of times while targeting distinct shell locations. They consistently struck the aperture of globular shells and changed from the aperture to the apex of high-spired shells. Ninjabot tests revealed that mantis shrimp avoid strike locations that cause little damage and that reaching the threshold for eating soft tissue is increasingly difficult as fracture progresses. Their ballistic strategy requires feed-forward control, relying on extensive pre-strike set-up, unlike jaw- and claw-based strategies that can use real-time neural feedback when crushing. However, alongside this pre-processing cost to impact fracture comes the ability to circumvent gape limits and thus process larger prey. In sum, mantis shrimp target specific shell regions, alter their strategy depending on shell shape, and present a model system for studying the physics and materials of impact fracture in the context of the rich evolutionary history of predator-prey interactions.

Mechanical sensitivity and the dynamics of evolutionary rate shifts in biomechanical systems.

The influence of biophysical relationships on rates of morphological evolution is a cornerstone of evolutionary theory. Mechanical sensitivity-the correlation strength between mechanical output and the system's underlying morphological components-is thought to impact the evolutionary dynamics of form-function relationships, yet has rarely been examined. Here, we compare the evolutionary rates of the mechanical components of the four-bar linkage system in the raptorial appendage of mantis shrimp (Order Stomatopoda). This system's mechanical output (kinematic transmission (KT)) is highly sensitive to variation in its output link, and less sensitive to its input and coupler links. We found that differential mechanical sensitivity is associated with variation in evolutionary rate: KT and the output link exhibit faster rates of evolution than the input and coupler links to which KT is less sensitive. Furthermore, for KT and, to a lesser extent, the output link, rates of evolution were faster in 'spearing' stomatopods than 'smashers', indicating that mechanical sensitivity may influence trait-dependent diversification. Our results suggest that mechanical sensitivity can impact morphological evolution and guide the process of phenotypic diversification. The connection between mechanical sensitivity and evolutionary rates provides a window into the interaction between physical rules and the evolutionary dynamics of morphological diversification.

Competing influences on morphological modularity in biomechanical systems: a case study in mantis shrimp.

Related species that share similar biomechanical systems and segmentation patterns may exhibit different patterns of morphological covariation. We examined morphological covariation of the potent prey capture appendage of two mantis shrimp (Stomatopoda) species-a spearer (Squilla empusa) and smasher (Gonodactylaceus falcatus). We assessed three frameworks for modularity, two based on the biomechanics of the appendage and one based on its segmentation as a proxy for shared developmental pathways. We collected morphometric data from S. empusa, and compared morphological covariation patterns across the raptorial appendage with patterns from a new analysis of previously published morphometric data from G. falcatus. The relative importance of the different hypothetical influences differed between the two species, and was dependent on whether specimens were analyzed all together or subdivided based on sex or sub-populations, including one particularly distinct population in the Gulf of Mexico. We also found an intriguing handedness pattern in which right-hand appendages had a variable number of spines, whereas the left had a constant number of spines. Overall, our findings highlight the importance of testing multiple, alternative frameworks for morphological covariation and suggest that mantis shrimp experience contrasting influences on covariation depending on their feeding mechanisms.

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.

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 comparative hydrodynamics of rapid rotation by predatory appendages.

Countless aquatic animals rotate appendages through the water, yet fluid forces are typically modeled with translational motion. To elucidate the hydrodynamics of rotation, we analyzed the raptorial appendages of mantis shrimp (Stomatopoda) using a combination of flume experiments, mathematical modeling and phylogenetic comparative analyses. We found that computationally efficient blade-element models offered an accurate first-order approximation of drag, when compared with a more elaborate computational fluid-dynamic model. Taking advantage of this efficiency, we compared the hydrodynamics of the raptorial appendage in different species, including a newly measured spearing species, Coronis scolopendra The ultrafast appendages of a smasher species (Odontodactylus scyllarus) were an order of magnitude smaller, yet experienced values of drag-induced torque similar to those of a spearing species (Lysiosquillina maculata). The dactyl, a stabbing segment that can be opened at the distal end of the appendage, generated substantial additional drag in the smasher, but not in the spearer, which uses the segment to capture evasive prey. Phylogenetic comparative analyses revealed that larger mantis shrimp species strike more slowly, regardless of whether they smash or spear their prey. In summary, drag was minimally affected by shape, whereas size, speed and dactyl orientation dominated and differentiated the hydrodynamic forces across species and sizes. This study demonstrates the utility of simple mathematical modeling for comparative analyses and illustrates the multi-faceted consequences of drag during the evolutionary diversification of rotating appendages.