SummaryElastic mechanisms in the invertebrates are fantastically diverse, yet much of this diversity can be captured by examining just a few fundamental physical principles. Our goals for this commentary are threefold. First, we aim to synthesize and simplify the fundamental principles underlying elastic mechanisms and show how different configurations of basic building blocks can be used for different functions. Second, we compare single rapid movements and rhythmic movements across six invertebrate examples -ranging from poisonous cnidarians to high-jumping froghoppers -and identify remarkable functional properties arising from their underlying elastic systems. Finally, we look to the future of this field and find two prime areas for exciting new discoveries -the evolutionary dynamics of elastic mechanisms and biomimicry of invertebrate elastic materials and mechanics.

SUMMARYElastic mechanisms are fundamental to fast and efficient movements. Mantis shrimp power their fast raptorial appendages using a conserved network of exoskeletal springs, linkages and latches. Their appendages are fantastically diverse, ranging from spears to hammers. We measured the spring mechanics of 12 mantis shrimp species from five different families exhibiting hammershaped, spear-shaped and undifferentiated appendages. Across species, spring force and work increase with size of the appendage and spring constant is not correlated with size. Species that hammer their prey exhibit significantly greater spring resilience compared with species that impale evasive prey (ʻspearersʼ); mixed statistical results show that species that hammer prey also produce greater work relative to size during spring loading compared with spearers. Disabling part of the spring mechanism, the ʻsaddleʼ, significantly decreases spring force and work in three smasher species; cross-species analyses show a greater effect of cutting the saddle on the spring force and spring constant in species without hammers compared with species with hammers. Overall, the study shows a more potent spring mechanism in the faster and more powerful hammering species compared with spearing species while also highlighting the challenges of reconciling within-species and cross-species mechanical analyses when different processes may be acting at these two different levels of analysis. The observed mechanical variation in spring mechanics provides insights into the evolutionary history, morphological components and mechanical behavior, which were not discernible in prior single-species studies. The results also suggest that, even with a conserved spring mechanism, spring behavior, potency and component structures can be varied within a clade with implications for the behavioral functions of power-amplified devices. Supplementary material available online at

SUMMARYThe geometry of an animalʼs skeleton governs the transmission of force to its appendages. Joints and rigid elements that create a relatively large output displacement per unit input displacement have been considered to be geared for speed, but the relationship between skeletal geometry and speed is largely untested. The present study explored this subject with experiments and mathematical modeling to evaluate how morphological differences in the raptorial appendage of a mantis shrimp (Gonodactylus smithii) affect the speed of its predatory strike. Based on morphological measurements and material testing, we computationally simulated the transmission of the stored elastic energy that powers a strike and the drag that resists this motion. After verifying the modelʼs predictions against measurements of strike impulse, we conducted a series of simulations that varied the linkage geometry, but were provided with a fixed amount of stored elastic energy. We found that a skeletal geometry that creates a large output displacement achieves a slower maximum speed of rotation than a low-displacement system. This is because a large displacement by the appendage causes a relatively large proportion of its elastic energy to be lost to the generation of drag. Therefore, the efficiency of transmission from elastic to kinetic energy mediates the relationship between the geometry and the speed of a skeleton. We propose that transmission efficiency plays a similar role in form-function relationships for skeletal systems in a diversity of animals.

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.

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.