The mechanics of jumping versus steady hopping in yellow-footed rock wallabies

Elastic pinch biomechanisms can yield consistent launch speeds regardless of projectile mass

Energetic trade-offs are particularly pertinent to bio-ballistic systems which impart energy to projectiles exclusively during launch. We investigated such trade-offs in the spring-propelled seeds of Loropetalum chinense, Hamamelis virginiana and Fortunearia sinensis. Using similar seed-shooting mechanisms, fruits of these confamilial plants (Hamamelidaceae) span an order of magnitude in spring and seed mass. We expected that as seed mass increases, launch speed decreases. Instead, launch speed was relatively constant regardless of seed mass. We tested if fruits shoot larger seeds by storing more elastic potential energy (PE). Spring mass and PE increased as seed mass increased (in order of increasing seed mass: L. chinense, H. virginiana, F. sinensis). As seed mass to spring mass ratio increased (ratios: H. virginiana = 0.50, F. sinensis = 0.65, L. chinense = 0.84), mass-specific PE storage increased. The conversion efficiency of PE to seed kinetic energy (KE) decreased with increasing fruit mass. Therefore, similar launch speeds across scales occurred because (i) larger fruits stored more PE and (ii) smaller fruits had higher mass-specific PE storage and improved PE to KE conversion. By examining integrated spring and projectile mechanics in our focal species, we revealed diverse, energetic scaling strategies relevant to spring-propelled systems navigating energetic trade-offs.

Understanding Australia’s unique hopping species: a comparative review of the musculoskeletal system and locomotor biomechanics in Macropodoidea

Kangaroos and other macropodoids stand out among mammals for their unusual hopping locomotion and body shape. This review examines the scaling of hind- and forelimb bones, and the primary ankle extensor muscles and tendons. We find that the scaling of the musculoskeletal system is sensitive to the phylogenetic context. Tibia length increases with positive allometry among most macropodoids, but negative allometry in eastern grey kangaroos and isometry in red kangaroos. Femur length decreases with stronger negative allometry in eastern grey and red kangaroos than among other macropodoids. Muscle masses scale with negative allometry in western grey kangaroos and with isometry in red kangaroos, compared to positive allometry in other macropodoids. We further summarise the work on the hopping gait, energetics in macropodoids, and stresses in the musculoskeletal system in an evolutionary context, to determine what trade-offs may limit locomotor performance in macropodoids. When large kangaroos hop, they do not increase oxygen consumption with speed, unlike most mammals, including small hopping species. We conclude that there is not enough information to isolate the biomechanical factors that make large kangaroos so energy efficient. We identify key areas for further research to fill these gaps.

Predictive Simulations of Musculoskeletal Function and Jumping Performance in a Generalized Bird

Jumping is a common, but demanding, behavior that many animals employ during everyday activity. In contrast to jump-specialists such as anurans and some primates, jumping biomechanics and the factors that influence performance remains little studied for generalized species that lack marked adaptations for jumping. Computational biomechanical modeling approaches offer a way of addressing this in a rigorous, mechanistic fashion. Here, optimal control theory and musculoskeletal modeling are integrated to generate predictive simulations of maximal height jumping in a small ground-dwelling bird, a tinamou. A three-dimensional musculoskeletal model with 36 actuators per leg is used, and direct collocation is employed to formulate a rapidly solvable optimal control problem involving both liftoff and landing phases. The resulting simulation raises the whole-body center of mass to over double its standing height, and key aspects of the simulated behavior qualitatively replicate empirical observations for other jumping birds. However, quantitative performance is lower, with reduced ground forces, jump heights, and muscle–tendon power. A pronounced countermovement maneuver is used during launch. The use of a countermovement is demonstrated to be critical to the achievement of greater jump heights, and this phenomenon may only need to exploit physical principles alone to be successful; amplification of muscle performance may not necessarily be a proximate reason for the use of this maneuver. Increasing muscle strength or contractile velocity above nominal values greatly improves jump performance, and interestingly has the greatest effect on more distal limb extensor muscles (i.e., those of the ankle), suggesting that the distal limb may be a critical link for jumping behavior. These results warrant a re-evaluation of previous inferences of jumping ability in some extinct species with foreshortened distal limb segments, such as dromaeosaurid dinosaurs.

Simulations prédictives de la fonction musculo-squelettique et des performances de saut chez un oiseau généralisé Sauter est un comportement commun, mais exigeant, que de nombreux animaux utilisent au cours de leurs activités quotidiennes. Contrairement aux spécialistes du saut tels que les anoures et certains primates, la biomécanique du saut et les facteurs qui influencent la performance restent peu étudiés pour les espèces généralisées qui n’ont pas d’adaptations marquées pour le saut. Les approches de modélisation biomécanique computationnelle offrent un moyen d’aborder cette question de manière rigoureuse et mécaniste. Ici, la théorie du contrôle optimal et la modélisation musculo-squelettique sont intégrées pour générer des simulations prédictives du saut en hauteur maximal chez un petit oiseau terrestre, le tinamou. Un modèle musculo-squelettique tridimensionnel avec 36 actionneurs par patte est utilisé, et une méthode numérique nommée “direct collocation” est employée pour formuler un problème de contrôle optimal rapidement résoluble impliquant les phases de décollage et d’atterrissage. La simulation qui en résulte élève le centre de masse du corps entier à plus du double de sa hauteur debout, et les aspects clés du comportement simulé reproduisent qualitativement les observations empiriques d’autres oiseaux sauteurs. Cependant, les performances quantitatives sont moindres, avec une réduction des forces au sol, des hauteurs de saut et de la puissance musculo-tendineuse. Une manœuvre de contre-mouvement prononcée est utilisée pendant le lancement. Il a été démontré que l’utilisation d’un contre-mouvement est essentielle à l’obtention de hauteurs de saut plus importantes, et il se peut que ce phénomène doive exploiter uniquement des principes physiques pour réussir; l’amplification de la performance musculaire n’est pas nécessairement une raison immédiate de l’utilisation de cette manœuvre. L’augmentation de la force musculaire ou de la vitesse de contraction au-dessus des valeurs nominales améliore grandement la performance de saut et, fait intéressant, a le plus grand effet sur les muscles extenseurs des membres plus distaux (c'est-à-dire ceux de la cheville), ce qui suggère que le membre distal peut être un lien critique pour le comportement de saut. Ces résultats justifient une réévaluation des déductions précédentes de la capacité de sauter chez certaines espèces éteintes avec des segments de membres distaux raccourcis, comme les dinosaures droméosauridés.

Voorspellende simulaties van musculoskeletale functie en springprestaties bij een gegeneraliseerde vogel Springen is een veel voorkomend, maar veeleisend, gedrag dat veel dieren toepassen tijdens hun dagelijkse bezigheden. In tegenstelling tot de springspecialisten zoals de anura en sommige primaten, is de biomechanica van het springen en de factoren die de prestaties beïnvloeden nog weinig bestudeerd voor algemene soorten die geen uitgesproken adaptaties voor het springen hebben. Computationele biomechanische modelbenaderingen bieden een manier om dit op een rigoureuze, mechanistische manier aan te pakken. Hier worden optimale controle theorie en musculoskeletale modellering geïntegreerd om voorspellende simulaties te genereren van maximale hoogtesprong bij een kleine grondbewonende vogel, een tinamou. Een driedimensionaal musculoskeletaal model met 36 actuatoren per poot wordt gebruikt, en directe collocatie wordt toegepast om een snel oplosbaar optimaal controleprobleem te formuleren dat zowel de opstijg-als de landingsfase omvat. De resulterende simulatie verhoogt het lichaamszwaartepunt tot meer dan het dubbele van de stahoogte, en belangrijke aspecten van het gesimuleerde gedrag komen kwalitatief overeen met empirische waarnemingen voor andere springende vogels. De kwantitatieve prestaties zijn echter minder, met verminderde grondkrachten, spronghoogtes en spierpeeskracht. Tijdens de lancering wordt een uitgesproken tegenbewegingsmanoeuvre gebruikt. Aangetoond is dat het gebruik van een tegenbeweging van cruciaal belang is voor het bereiken van grotere spronghoogten, en dit fenomeen hoeft alleen op fysische principes te berusten om succesvol te zijn; versterking van de spierprestaties hoeft niet noodzakelijk een proximate reden te zijn voor het gebruik van deze manoeuvre. Het verhogen van de spierkracht of van de contractiesnelheid boven de nominale waarden verbetert de sprongprestatie aanzienlijk, en heeft interessant genoeg het grootste effect op de meer distale extensoren van de ledematen (d.w.z. die van de enkel), wat suggereert dat de distale ledematen een kritieke schakel kunnen zijn voor het springgedrag. Deze resultaten rechtvaardigen een herevaluatie van eerdere conclusies over springvermogen bij sommige uitgestorven soorten met voorgekorte distale ledematen, zoals dromaeosauride dinosauriërs.

Prädiktive Simulationen der muskuloskelettalen Funktion und Sprungleistung bei einem generalisierten Vogel Springen ist ein übliches jedoch anstrengendes Verhalten, das viele Tiere bei ihren täglichen Aktivitäten einsetzen. Im Gegensatz zu Springspezialisten, wie Fröschen und einigen Primaten, sind bei allgemeinen Arten, welche keine ausgeprägten Anpassung für Sprungverhalten aufweisen, die Biomechanik beim Springen und die Faktoren, welche die Leistungsfähigkeit beeinflussen, noch wenig untersucht. Computergestützte biomechanische Modellierungsverfahren bieten hier eine Möglichkeit, dies in einer gründlichen, mechanistischen Weise anzugehen. In dieser Arbeit werden die optimale Steuerungstheorie und Muskel-Skelett-Modellierung zusammen eingesetzt, um die maximale Sprunghöhe eines kleinen bodenlebenden Vogels, eines Perlsteisshuhns, zu simulieren und zu prognostizieren. Es wird ein dreidimensionales Muskel-Skelett-Modell mit 36 Aktuatoren pro Bein verwendet, und durch direkte Kollokation wird ein schnell lösbares optimales Steuerungsproblem formuliert, das sowohl die Abstoss- als auch die Landephase umfasst. Die daraus folgende Simulation bringt den Ganzkörperschwerpunkt auf mehr als das Doppelte seiner Standhöhe und entscheidende Aspekte des simulierten Verhaltens entsprechen qualitativ empirischen Beobachtungen für andere springende Vögel. Allerdings ist die quantitative Leistungsfähigkeit geringer, mit reduzierten Bodenkräften, Sprunghöhen und Muskel-Sehnen-Kräften. Beim Abstossen wird ein ausgeprägtes Gegenbewegungsmanöver durchgeführt. Die Durchführung einer Gegenbewegung ist nachweislich entscheidend für das Erreichen grösserer Sprunghöhen, wobei dieses Phänomen möglicherweise nur physikalische Prinzipien auszuschöpfen braucht, um erfolgreich zu sein. Die Verstärkung der Muskelleistung ist daher möglicherweise nicht zwingend ein unmittelbarer Grund für die Verwendung dieses Manövers. Eine Erhöhung der Muskelkraft oder der Kontraktionsgeschwindigkeit über die Nominalwerte hinaus führt zu einer erheblichen Zunahme der Sprungleistung und hat interessanterweise den grössten Effekt bei den weiter distal gelegenen Streckmuskeln der Beine (d.h. bei denjenigen des Sprunggelenks), was darauf hindeutet, dass die distale Gliedmasse ein entscheidendes Element für das Sprungverhalten sein könnte. Diese Ergebnisse geben Anlass zur Überprüfung früherer Schlussfolgerungen hinsichtlich der Sprungfähigkeit einiger ausgestorbener Arten mit verkürzten distalen Gliedmassen, wie beispielsweise bei dromaeosauriden Dinosauriern.

How spiders hunt heavy prey: the tangle web as a pulley and spider's lifting mechanics observed and quantified in the laboratory

The spiders of Theridiidae's family display a peculiar behaviour when they hunt extremely large prey. They lift the quarry, making it unable to escape, by attaching pre-tensioned silk threads to it. In this work, we analysed for the first time in the laboratory the lifting hunting mechanism and, in order to quantify the phenomenon, we applied the lifting mechanics theory. The comparison between the experiments and the theory suggests that, during the process, spiders do not stretch the silk too much by keeping it in the linear elastic regime. We thus report here further evidence for the strong role of silk in spiders' evolution, especially how spiders can stretch and use it as an external tool to overcome their muscles' limits and capture prey with large mass, e.g. 50 times the spider's mass.

Design of Tendon-Driven Mechanism Using Geometrical Condition

A tendon-driven robot offers many advantages, such as easy designs for mass distribution that facilitate dexterous motion. A procedure to design such a robot using a single actuator to achieve the desired force direction and magnitude on an endpoint is presented herein. The force on the endpoint is generated by the single actuator and a wire that passes through pulleys attached on links. To set the pulley position for the desired force direction and magnitude, a geometrical condition is proposed. To evaluate the proposed method, a physical monopod robot was developed. We compared the calculated and physical forces on the endpoint of the physical robot for the desired directions. Finally, we confirmed that the proposed method provided the desired force on the endpoint without iterative trials.

Functional morphology of the ankle extensor muscle-tendon units in the springhare Pedetes capensis shows convergent evolution with macropods for bipedal hopping locomotion

This study assesses the functional morphology of the ankle extensor muscle-tendon units of the springhare Pedetes capensis, an African bipedal hopping rodent, to test for convergent evolution with the Australian bipedal hopping macropods. We dissect and measure the gastrocnemius, soleus, plantaris, and flexor digitorum longus in 10 adult springhares and compare them against similar-sized macropods using phylogenetically informed scaling analyses. We show that springhares align reasonably well with macropod predictions, being statistically indistinguishable with respect to the ankle extensor mean weighted muscle moment arm (1.63 vs. 1.65 cm, respectively), total muscle mass (41.1 vs. 29.2 g), total muscle physiological cross-sectional area (22.9 vs. 19.3 cm² ), mean peak tendon stress (26.2 vs. 35.2 MPa), mean tendon safety factor (4.7 vs. 3.6), and total tendon strain energy return capacity (1.81 vs. 1.82 J). However, total tendon cross-sectional area is significantly larger in springhares than predicted for a similar-sized macropod (0.26 vs. 0.17 cm² , respectively), primarily due to a greater plantaris tendon thickness (0.084 vs. 0.048 cm² ), and secondarily because the soleus muscle-tendon unit is present in springhares but is vestigial in macropods. The overall similarities between springhares and macropods indicate that evolution has favored comparable lower hindlimb body plans for bipedal hopping locomotion in the two groups of mammals that last shared a common ancestor ~160 million years ago. The springhare's relatively thick plantaris tendon may facilitate rapid transfer of force from muscle to skeleton, enabling fast and accelerative hopping, which could help to outpace and outmaneuver predators.

Limb dynamics in agility jumps of beginner and advanced dogs

A considerable body of work has examined the dynamics of different dog gaits, but there are no studies that have focused on limb dynamics in jumping. Jumping is an essential part of dog agility, a dog sport in which handlers direct their dogs through an obstacle course in a limited time. We hypothesized that limb parameters like limb length and stiffness indicate the skill level of dogs. We analyzed global limb parameters in jumping for 10 advanced and 10 beginner dogs. In experiments, we collected 3D kinematics and ground reaction forces during dog jumping at high forward speeds. Our results revealed general strategies of limb control in jumping and highlighted differences between advanced and beginner dogs. In take-off, the spatially leading forelimb was 75% (P<0.001) stiffer than the trailing forelimb. In landing, the trailing forelimb was 14% stiffer (P<0.001) than the leading forelimb. This indicates a strut-like action of the forelimbs to achieve jumping height in take-off and to transfer vertical velocity into horizontal velocity in landing (with switching roles of the forelimbs). During landing, the more (24%) compliant forelimbs of beginner dogs (P=0.005) resulted in 17% (P=0.017) higher limb compression during the stance phase. This was associated with a larger amount of eccentric muscle contraction, which might in turn explain the soft tissue injuries that frequently occur in the shoulder region of beginner dogs. For all limbs, limb length at toe-off was greater for advanced dogs. Hence, limb length and stiffness might be used as objective measures of skill.

External power amplification drives prey capture in a spider web

Power amplification allows animals to produce movements that exceed the physiological limits of muscle power and speed, such as the mantis shrimp's ultrafast predatory strike and the flea's jump. However, all known examples of nonhuman, muscle-driven power amplification involve anatomical structures that store energy from a single cycle of muscular contraction. Here, we describe a nonhuman example of external power amplification using a constructed device: the web of the triangle-weaver spider, Hyptiotes cavatus, which uses energy stored in the silk threads to actively tangle prey from afar. Hyptiotes stretches its web by tightening a separate anchor line over multiple cycles of limb motion, and then releases its hold on the anchor line when insects strike the web. Both spider and web spring forward 2 to 3 cm with a peak acceleration of up to 772.85 m/s² so that up to four additional adhesive capture threads contact the prey while jerking caused by the spider's sudden stop subsequently wraps silk around the prey from all directions. Using webs as external "tools" to store energy offers substantial mechanical advantages over internal tissue-based power amplification due to the ability of Hyptiotes to load the web over multiple cycles of muscular contraction and thus release more stored energy during prey capture than would be possible with muscle-driven anatomical elastic-energy systems. Elastic power amplification is an underappreciated component of silk's function in webs and shows remarkable convergence to the fundamental mechanical advantages that led humans to engineer power-amplifying devices such as catapults and ballistae.

External mechanical work in the galloping racehorse

Horse locomotion is remarkably economical. Here, we measure external mechanical work of the galloping horse and relate it to published measurements of metabolic cost. Seven Thoroughbred horses were galloped (ridden) over force plates, under a racing surface. Twenty-six full strides of force data were recorded and used to calculate the external mechanical work of galloping. The mean sum of decrements of mechanical energy was -876 J (±280 J) per stride and increments were 2163 J (±538 J) per stride as horses were accelerating. Combination with published values for internal work and metabolic costs for galloping yields an apparent muscular efficiency of 37-46% for galloping, which would be reduced by energy storage in leg tendons. Knowledge about external work of galloping provides further insight into the mechanics of galloping from both an evolutionary and performance standpoint.

Three-Dimensional Takeoff Step Kinetics of Long Jumpers with and without a Transtibial Amputation

PURPOSE

The loads applied on the musculoskeletal system during the long jump takeoff step are not well established for nonamputee athletes or athletes with a lower extremity amputation. Information on joint loading and potential injury mechanisms is important for improving training or rehabilitation protocols, prosthetic design, and the general understanding of the long jump.

METHODS

Three-dimensional takeoff step kinematics and kinetics were used for inverse dynamic model calculations on three male athletes with and seven male athletes without a below the knee amputation (BKA). Athletes with BKA used their affected leg as their takeoff leg.

RESULTS

Despite equivalent long jump performance, ground reaction force application characteristics were widely different, and calculated joint loads were significantly lower in athletes with BKA compared with nonamputee athletes during the takeoff step. The takeoff step of the long jump for athletes with BKA seems to be dominated by sagittal plane movements, whereas it involves sagittal plane movement and compensatory joint work in the frontal plane for nonamputee athletes.

CONCLUSIONS

Coaches and athletes should adapt training protocols to the unique musculoskeletal loading patterns of long jumpers with or without a BKA. Specifically, nonamputee athletes should strengthen the muscles responsible for hip and knee extension, as well as for frontal plane stabilization, early in the season to avoid injuries. The presented data enable clinicians to identify potential causes of pain or injury more differentially in both groups of athletes and might stimulate future research in the field of robotics and prosthetic components. Furthermore, the altered joint mechanics of athletes with BKA versus nonamputees serves as an explanation for their previously described more effective takeoff step.

Jumping mechanics of desert kangaroo rats

Kangaroo rats are small bipedal desert rodents that use erratic vertical jumps to escape predator strikes. In this study we examined how individual hind limb joints of desert kangaroo rats (Dipodomys deserti) power vertical jumps across a range of heights. We hypothesized that increases in net work would be equally divided across hind limb joints with increases in jump height. To test this hypothesis, we used an inverse dynamics analysis to quantify the mechanical output from the hind limb joints of kangaroo rats jumping vertically over a wide range of heights. The kangaroo rats in this study reached maximal jump heights up to ∼9-times hip height. Net joint work increased significantly with jump height at the hip, knee and ankle, and decreased significantly at the metatarsal-phalangeal joint. The increase in net work generated by each joint was not proportional across joints but was dominated by the ankle, which ranged from contributing 56% of the work done on the center of mass at low jumps to 70% during the highest jumps. Therefore, the results of this study did not support our hypothesis. However, using an anatomical model, we estimated that a substantial proportion of the work delivered at the ankle (48%) was transferred from proximal muscles via the biarticular ankle extensors.

Limb bone scaling in hopping macropods and quadrupedal artiodactyls

Bone adaptation is modulated by the timing, direction, rate and magnitude of mechanical loads. To investigate whether frequent slow, or infrequent fast, gaits could dominate bone adaptation to load, we compared scaling of the limb bones from two mammalian herbivore clades that use radically different high-speed gaits, bipedal hopping (suborder Macropodiformes; kangaroos and kin) and quadrupedal galloping (order Artiodactyla; goats, deer and kin). Forelimb and hindlimb bones were collected from 20 artiodactyl and 15 macropod species (body mass M 1.05-1536 kg) and scanned in computed tomography or X-ray microtomography. Second moment of area (I _max) and bone length (l) were measured. Scaling relations (y = ax^b ) were calculated for l versus M for each bone and for I _max versus M and I _max versus l for every 5% of length. I _max versus M scaling relationships were broadly similar between clades despite the macropod forelimb being nearly unloaded, and the hindlimb highly loaded, during bipedal hopping. I _max versus l and l versus M scaling were related to locomotor and behavioural specializations. Low-intensity loads may be sufficient to maintain bone mass across a wide range of species. Occasional high-intensity gaits might not break through the load sensitivity saturation engendered by frequent low-intensity gaits.

Why do mammals hop? Understanding the ecology, biomechanics and evolution of bipedal hopping

Bipedal hopping is a specialized mode of locomotion that has arisen independently in at least five groups of mammals. We review the evolutionary origins of these groups, examine three of the most prominent hypotheses for why bipedal hopping may have arisen, and discuss how this unique mode of locomotion influences the behavior and ecology of modern species. While all bipedal hoppers share generally similar body plans, differences in underlying musculoskeletal anatomy influence what performance benefits each group may derive from this mode of locomotion. Based on a review of the literature, we conclude that the most likely reason that bipedal hopping evolved is associated with predator avoidance by relatively small species in forested environments. Yet, the morphological specializations associated with this mode of locomotion have facilitated the secondary acquisition of performance characteristics that enable these species to be highly successful in ecologically demanding environments such as deserts. We refute many long-held misunderstandings about the origins of bipedal hopping and identify potential areas of research that would advance the understanding of this mode of locomotion.

Elite long jumpers with below the knee prostheses approach the board slower, but take-off more effectively than non-amputee athletes

The use of technological aids to improve sport performance ('techno doping') and inclusion of Paralympic athletes in Olympic events are matters of ongoing debate. Recently, a long jumper with a below the knee amputation (BKA) achieved jump distances similar to world-class athletes without amputations, using a carbon fibre running-specific prosthesis (RSP). We show that athletes with BKA utilize a different, more effective take-off technique in the long jump, which provided the best athlete with BKA a performance advantage of at least 0.13 m compared to non-amputee athletes. A maximum speed constraint imposed by the use of RSPs would indicate a performance disadvantage for the long jump. We found slower maximum sprinting speeds in athletes with BKA, but did not find a difference in the overall vertical force from both legs of athletes with BKA compared to non-amputees. Slower speeds might originate from intrinsically lower sprinting abilities of athletes with BKA or from more complex adaptions in sprinting mechanics due to the biomechanical and morphological differences induced by RSPs. Our results suggest that due to different movement strategies, athletes with and without BKA should likely compete in separate categories for the long jump.

Scaling of the ankle extensor muscle-tendon units and the biomechanical implications for bipedal hopping locomotion in the post-pouch kangaroo Macropus fuliginosus

Bipedal hopping is used by macropods, including rat-kangaroos, wallabies and kangaroos (superfamily Macropodoidea). Interspecific scaling of the ankle extensor muscle-tendon units in the lower hindlimbs of these hopping bipeds shows that peak tendon stress increases disproportionately with body size. Consequently, large kangaroos store and recover more strain energy in their tendons, making hopping more efficient, but their tendons are at greater risk of rupture. This is the first intraspecific scaling analysis on the functional morphology of the ankle extensor muscle-tendon units (gastrocnemius, plantaris and flexor digitorum longus) in one of the largest extant species of hopping mammal, the western grey kangaroo Macropus fuliginosus (5.8-70.5 kg post-pouch body mass). The effective mechanical advantage of the ankle extensors does not vary with post-pouch body mass, scaling with an exponent not significantly different from 0.0. Therefore, larger kangaroos balance rotational moments around the ankle by generating muscle forces proportional to weight-related gravitational forces. Maximum force is dependent upon the physiological cross-sectional area of the muscle, which we found scales geometrically with a mean exponent of only 0.67, rather than 1.0. Therefore, larger kangaroos are limited in their capacity to oppose large external forces around the ankle, potentially compromising fast or accelerative hopping. The strain energy return capacity of the ankle extensor tendons increases with a mean exponent of ~1.0, which is much shallower than the exponent derived from interspecific analyses of hopping mammals (~1.4-1.9). Tendon safety factor (ratio of rupture stress to estimated peak hopping stress) is lowest in the gastrocnemius (< 2), and it decreases with body mass with an exponent of -0.15, extrapolating to a predicted rupture at 160 kg. Extinct giant kangaroos weighing 250 kg could therefore not have engaged in fast hopping using 'scaled-up' lower hindlimb morphology of extant western grey kangaroos.

Vertical leaping mechanics of the Lesser Egyptian Jerboa reveal specialization for maneuverability rather than elastic energy storage

BACKGROUND

Numerous historical descriptions of the Lesser Egyptian jerboa, Jaculus jaculus, a small bipedal mammal with elongate hindlimbs, make special note of their extraordinary leaping ability. We observed jerboa locomotion in a laboratory setting and performed inverse dynamics analysis to understand how this small rodent generates such impressive leaps. We combined kinematic data from video, kinetic data from a force platform, and morphometric data from dissections to calculate the relative contributions of each hindlimb muscle and tendon to the total movement.

RESULTS

Jerboas leapt in excess of 10 times their hip height. At the maximum recorded leap height (not the maximum observed leap height), peak moments for metatarso-phalangeal, ankle, knee, and hip joints were 13.1, 58.4, 65.1, and 66.9 Nmm, respectively. Muscles acting at the ankle joint contributed the most work (mean 231.6 mJ / kg Body Mass) to produce the energy of vertical leaping, while muscles acting at the metatarso-phalangeal joint produced the most stress (peak 317.1 kPa). The plantaris, digital flexors, and gastrocnemius tendons encountered peak stresses of 25.6, 19.1, and 6.0 MPa, respectively, transmitting the forces of their corresponding muscles (peak force 3.3, 2.0, and 3.8 N, respectively). Notably, we found that the mean elastic energy recovered in the primary tendons of both hindlimbs comprised on average only 4.4% of the energy of the associated leap.

CONCLUSIONS

The limited use of tendon elastic energy storage in the jerboa parallels the morphologically similar heteromyid kangaroo rat, Dipodomys spectabilis. When compared to larger saltatory kangaroos and wallabies that sustain hopping over longer periods of time, these small saltatory rodents store and recover less elastic strain energy in their tendons. The large contribution of muscle work, rather than elastic strain energy, to the vertical leap suggests that the fitness benefit of rapid acceleration for predator avoidance dominated over the need to enhance locomotor economy in the evolutionary history of jerboas.

Walking on five legs: investigating tail use during slow gait in kangaroos and wallabies

Pentapedal locomotion is the use of the tail as a fifth leg during the slow gait of kangaroos. Although previous studies have informally noted that some smaller species of macropodines do not engage in pentapedal locomotion, a systematic comparative analysis of tail use during slow gait across a wide range of species in this group has not been done. Analysis of relative movement of the pelvis, tail, and joint angles of the lower limbs during slow gait, using 2D landmark techniques on video recordings, was carried out on 16 species of Macropodinae. We also compared the relative lengthening of the tibia using crural index (CI) to test whether hindlimb morphology was associated with pentapedal locomotion. Pentapedal locomotion was characterised by three features: the presence of the ‘tail repositioning phase’, the constant height of the pelvis and the stationary placement of the distal tail on the ground during the hindlimb swing phase. The mean CI of pentapedal species was significantly greater than that of non-pentapedal species (1.71 versus 1.36; P < 0.001). This lends support to the hypothesis that the use of pentapedal locomotion is associated with the relative lengthening of the hindlimb, which in turn is associated with body size and habitat preference within the Macropodinae.

Compensations for increased rotational inertia during human cutting turns

Locomotion in a complex environment is often not steady state, but unsteady locomotion (stability and maneuverability) is not well understood. We investigated the strategies used by humans to perform sidestep cutting turns when running. Previous studies have argued that because humans have small yaw rotational moments of inertia relative to body mass, deceleratory forces in the initial velocity direction that occur during the turning step, or 'braking' forces, could function to prevent body over-rotation during turns. We tested this hypothesis by increasing body rotational inertia and testing whether braking forces during stance decreased. We recorded ground reaction force and body kinematics from seven participants performing 45 deg sidestep cutting turns and straight running at five levels of body rotational inertia, with increases up to fourfold. Contrary to our prediction, braking forces remained consistent at different rotational inertias, facilitated by anticipatory changes to body rotational speed. Increasing inertia revealed that the opposing effects of several turning parameters, including rotation due to symmetrical anterior-posterior forces, result in a system that can compensate for fourfold changes in rotational inertia with less than 50% changes to rotational velocity. These results suggest that in submaximal effort turning, legged systems may be robust to changes in morphological parameters, and that compensations can involve relatively minor adjustments between steps to change initial stance conditions.

Task-level strategies for human sagittal-plane running maneuvers are consistent with robotic control policies

The strategies that humans use to control unsteady locomotion are not well understood. A “spring-mass” template comprised of a point mass bouncing on a sprung leg can approximate both center of mass movements and ground reaction forces during running in humans and other animals. Legged robots that operate as bouncing, “spring-mass” systems can maintain stable motion using relatively simple, distributed feedback rules. We tested whether the changes to sagittal-plane movements during five running tasks involving active changes to running height, speed, and orientation were consistent with the rules used by bouncing robots to maintain stability. Changes to running height were associated with changes to leg force but not stance duration. To change speed, humans primarily used a “pogo stick” strategy, where speed changes were associated with adjustments to fore-aft foot placement, and not a “unicycle” strategy involving systematic changes to stance leg hip moment. However, hip moments were related to changes to body orientation and angular speed. Hip moments could be described with first order proportional-derivative relationship to trunk pitch. Overall, the task-level strategies used for body control in humans were consistent with the strategies employed by bouncing robots. Identification of these behavioral strategies could lead to a better understanding of the sensorimotor mechanisms that allow for effective unsteady locomotion.

Control of position and movement is simplified by combined muscle spindle and Golgi tendon organ feedback

Whereas muscle spindles play a prominent role in current theories of human motor control, Golgi tendon organs (GTO) and their associated tendons are often neglected. This is surprising since there is ample evidence that both tendons and GTOs contribute importantly to neuromusculoskeletal dynamics. Using detailed musculoskeletal models, we provide evidence that simple feedback using muscle spindles alone results in very poor control of joint position and movement since muscle spindles cannot sense changes in tendon length that occur with changes in muscle force. We propose that a combination of spindle and GTO afferents can provide an estimate of muscle-tendon complex length, which can be effectively used for low-level feedback during both postural and movement tasks. The feasibility of the proposed scheme was tested using detailed musculoskeletal models of the human arm. Responses to transient and static perturbations were simulated using a 1-degree-of-freedom (DOF) model of the arm and showed that the combined feedback enabled the system to respond faster, reach steady state faster, and achieve smaller static position errors. Finally, we incorporated the proposed scheme in an optimally controlled 2-DOF model of the arm for fast point-to-point shoulder and elbow movements. Simulations showed that the proposed feedback could be easily incorporated in the optimal control framework without complicating the computation of the optimal control solution, yet greatly enhancing the system's response to perturbations. The theoretical analyses in this study might furthermore provide insight about the strong physiological couplings found between muscle spindle and GTO afferents in the human nervous system.

Combining forces and kinematics for calculating consistent centre of mass trajectories

The motion of centre of mass (CoM) is a fundamental object of investigation in biomechanical analysis. In principle, the CoM motion can either be calculated from force data (dynamic method) or motion capture data (kinematic method). In both approaches, the accuracy of the calculated trajectories depends on the quality of the original signals. Interestingly, the inaccuracies in each method are related to different parts of the Fourier spectrum. Here, we present a new approach to compute CoM motion based on the reliable frequency range of force and kinematic measurements. As a result we obtain physically consistent CoM and force signals, i.e. the second derivative of the CoM trajectory equals the force. The algorithm is verified on simulation data and applied to selected experimental data. We show that the new algorithm can eliminate typical inaccuracies inherent in kinematic and force signals. Also, we discuss the biological and technical origins of these findings.

The effect of substrate compliance on the biomechanics of gibbon leaps

The storage and recovery of elastic strain energy in the musculoskeletal systems of locomoting animals has been extensively studied, yet the external environment represents a second potentially useful energy store that has often been neglected. Recent studies have highlighted the ability of orangutans to usefully recover energy from swaying trees to minimise the cost of gap crossing. Although mechanically similar mechanisms have been hypothesised for wild leaping primates, to date no such energy recovery mechanisms have been demonstrated biomechanically in leapers. We used a setup consisting of a forceplate and two high-speed video cameras to conduct a biomechanical analysis of captive gibbons leaping from stiff and compliant poles. We found that the gibbons minimised pole deflection by using different leaping strategies. Two leap types were used: slower orthograde leaps and more rapid pronograde leaps. The slower leaps used a wider hip joint excursion to negate the downward movement of the pole, using more impulse to power the leap, but with no increase in work done on the centre of mass. Greater hip excursion also minimised the effective leap distance during orthograde leaps. The more rapid leaps conversely applied peak force earlier in stance where the pole was effectively stiffer, minimising deflection and potential energy loss. Neither leap type appeared to usefully recover energy from the pole to increase leap performance, but the gibbons demonstrated an ability to best adapt their leap biomechanics to counter the negative effects of the compliant pole.

Exploring the mechanical basis for acceleration: pelvic limb locomotor function during accelerations in racing greyhounds (Canis familiaris)

Animals in their natural environments are confronted with a regular need to perform rapid accelerations (for example when escaping from predators or chasing prey). Such acceleration requires net positive mechanical work to be performed on the centre of mass by skeletal muscle. Here we determined how pelvic limb joints contribute to the mechanical work and power that are required for acceleration in galloping quadrupeds. In addition, we considered what, if any, biomechanical strategies exist to enable effective acceleration to be achieved. Simultaneous kinematic and kinetic data were collected for racing greyhounds undergoing a range of low to high accelerations. From these data, joint moments and joint powers were calculated for individual hindlimb joints. In addition, the mean effective mechanical advantage (EMA) of the limb and the ;gear ratio' of each joint throughout stance were calculated. Greatest increases in joint work and power with acceleration appeared at the hip and hock joints, particularly in the lead limb. Largest increases in absolute positive joint work occurred at the hip, consistent with the hypothesis that quadrupeds power locomotion by torque about the hip. In addition, hindlimb EMA decreased substantially with increased acceleration - a potential strategy to increase stance time and thus ground impulses for a given peak force. This mechanism may also increase the mechanical advantage for applying the horizontal forces necessary for acceleration.

Integration within and between muscles during terrestrial locomotion: effects of incline and speed

Animals must continually adapt to varying locomotor demands when moving in their natural habitat. Despite the dynamic nature of locomotion, little is known about how multiple muscles, and different parts of a muscle, are functionally integrated as demand changes. In order to determine the extent to which synergist muscles are functionally heterogeneous, and whether this heterogeneity is altered with changes in demand, we examined the in vivo function of the lateral (LG) and medial (MG) gastrocnemius muscles of helmeted guinea fowl (Numida meleagris) during locomotion on different inclines (level and uphill at 14 degrees ) and at different speeds (0.5 and 2.0 m s(-1)). We also quantified function in the proximal (pMG) and distal (dMG) regions of the MG to examine the extent to which a single muscle is heterogeneous. We used electromyography, sonomicrometry and tendon force buckles to quantify activation, length change and force patterns of both muscles, respectively. We show that the LG and MG exhibited an increase in force and stress with a change in gait and an increase in locomotor speed, but not with changes in incline. While the LG and MG exhibited similar levels of stress when walking at 0.5 m s(-1), stress in the LG was 1.8 times greater than in the MG when running at 2.0 m s(-1). Fascicle shortening increased with an increase in speed on both inclines for the LG, but only on the level for the pMG. Positive work performed by the LG exceeded that of the pMG and dMG for all conditions, and this difference was magnified when locomotor speed increased. Within the MG, the pMG shortened more, and at a faster rate than the dMG, resulting in a greater amount of positive work performed by the pMG. Mean spike amplitude of the electromyogram (EMG) bursts increased for all muscle locations with an increase in speed, but changes with incline were more variable. The functional differences between the LG and MG are likely due to the different moments each exerts at the knee, as well as differences in motor unit recruitment. The differences within the MG are likely due to motor unit recruitment differences, but also differences in architecture. Fascicles within the dMG insert into an extensive aponeurosis, which results in a higher apparent dynamic stiffness relative to fascicles operating within the pMG. On the level surface, the greater compliance of the pMG leads to increased stretch of its fascicles at the onset of force, further enhancing force production. Our results demonstrate the capacity for functional diversity between and within muscle synergists, which occur with changes in gait, speed and grade.

Mechanics of cutting maneuvers by ostriches (Struthio camelus)

We studied the strategies used by cursorial bipeds (ostriches) to maneuver during running. Eight ostriches were induced to run along a trackway and execute turns. Ground reaction forces and three-dimensional kinematics of the body and leg joints were simultaneously recorded, allowing calculation of joint angles and quasi-static net joint torques. Sidesteps, where the leg on the outside of the turn changes the movement direction, and crossovers using the inside leg, occurred with nearly equal frequency. Ostriches executed maneuvers using a simple control strategy that required minimal changes to leg kinematics or net torque production at individual joints. Although ostriches did use acceleration or braking forces to control body rotation, their morphology allowed for both crossovers and sidesteps to be accomplished with minimal net acceleratory/braking force production. Moreover, body roll and ab/adduction of the leg shifted the foot position away from the turn direction, reducing the acceleratory/braking forces required to prevent under-or over-rotation and aligning the leg with the ground reaction force.

Scaling of the axial morphology and gap-bridging ability of the brown tree snake, Boiga irregularis

Networks of branches in arboreal environments create many functional challenges for animals, including traversing gaps between perches. Many snakes are arboreal and their elongate bodies are theoretically well suited for bridging gaps. However, only two studies have previously investigated gap bridging in snakes, and the effects of size are poorly understood. Thus, we videotaped and quantified maximal gap-bridging ability in a highly arboreal species of snake (Boiga irregularis), for which we were able to obtain a large range in snout–vent length (SVL=43–188 cm)and mass (10–1391 g). We expected smaller snakes to bridge relatively larger gaps than larger individuals because of their proportionately higher ratio of muscle cross-sectional area to mass. The maximal length of the gaps spanned by B. irregularis had negative allometry, indicating that smaller snakes could span a greater proportion of their length than larger snakes. The greatest relative gap distance spanned (64% SVL) was by the smallest individual. The majority of snakes (85%) simply crawled slowly to cross a gap. Most of the suspended portion of the body and the path traveled by the head were below the perch that supported the posterior body, which may decrease the tendency of the snake to roll. Some (15%) of the snakes used another behavior in which the neck inclined as much as 45° and then rapidly lunged towards the anterior perch, and this enabled them to cross larger gaps than those using the crawling behavior. Perhaps the launching behavior of the gliding tree snakes (Chrysopelea sp.) evolved from an ancestral behavior of lunging to bridge gaps analogous to that of the brown tree snakes. An estimate of the muscle strain required to prevent the body of the snake from buckling suggests that, despite being light-bodied, brown tree snakes bridging a gap may be at the limit of the physiological capacity of their epaxial muscles.

Functional specialisation of the pelvic limb of the hare (Lepus europeus)

We provide quantitative anatomical data on the muscle-tendon architecture of the hare pelvic limb (specifically muscle mass, fascicle length, pennation angle, tendon mass and length). In addition, moment arms of major pelvic limb muscles were measured. Maximum isometric force and power of muscles, the moment of force about a joint, and tendon stress and strain were estimated. Data are compared with published data for other cursorial mammals such as the horse and dog, and a non-specialised Lagamorph, the rabbit. The pelvic limb of the hare was found to contain substantial amounts of hip extensor and adductor/abductor muscle volume, which is likely to be required for power production and stability during rapid turning. A proximal to distal reduction in muscle volume and fascicle length was also observed, as is the case in other cursorial quadrupeds, along with a reduction in distal limb mass via the replacement of muscle volume by long distal limb tendons, capable of storing large amounts of elastic energy. The majority of hare pelvic limb muscle moment arms varied with joint position, giving the hare the capacity to vary muscle function with limb posture and presumably different locomotor activities.