The musculoskeletal configuration of the mammalian pectoral limb has been heralded as a key anatomical feature leading to the adaptive radiation of mammals, but limb function in the non‐mammaliaform cynodont outgroup remains unresolved. Conflicting reconstructions of abducted and adducted posture are based on mutually incompatible interpretations of ambiguous osteology. We reconstruct the pectoral limb of the Triassic non‐mammaliaform cynodont Massetognathus pascuali in three dimensions, by combining skeletal morphology from micro‐computed tomography with muscle anatomy from an extended extant phylogenetic bracket. Conservative tests of maximum range of motion suggest a degree of girdle mobility, as well as substantial freedom at the shoulder and the elbow joints. The glenoid fossa supports a neutral pose in which the distal end of the humerus points 45° posterolaterally from the body wall, intermediate between classically ‘sprawling’ and ‘parasagittal’ limb postures. Massetognathus pascuali is reconstructed as having a near‐mammalian complement of shoulder muscles, including an incipient rotator cuff (m. subscapularis, m. infraspinatus, m. supraspinatus, and m. teres minor). Based on close inspection of the morphology of the glenoid fossa, we hypothesize a posture‐driven scenario for the evolution of the therian ball‐and‐socket shoulder joint. The musculoskeletal reconstruction presented here provides the anatomical scaffolding for more detailed examination of locomotor evolution in the precursors to mammals.
Traditional Hill-type muscle models, parameterized using high-quality experimental data, are often “too weak” to reproduce the joint torques generated by healthy adults during rapid, high force tasks. This study investigated whether the failure of these models to account for different types of motor units contributes to this apparent weakness; if so, muscle-driven simulations may rely on excessively high muscle excitations to generate a given force. We ran a series of forward simulations that reproduced measured ankle mechanics during cycling at five cadences ranging from 60 to 140 RPM. We generated both “nominal” simulations, in which an abstract ankle model was actuated by a 1-element Hill-type plantar flexor with a single contractile element (CE), and “test” simulations, in which the same model was actuated by a 2-element plantar flexor with two CEs that accounted for the force-generating properties of slower and faster motor units. We varied the total excitation applied to the 2-element plantar flexor between 60 and 105% of the excitation from each nominal simulation, and we varied the amount distributed to each CE between 0 and 100% of the total. Within this test space, we identified the excitation level and distribution, at each cadence, that best reproduced the plantar flexor forces generated in the nominal simulations. Our comparisons revealed that the 2-element model required substantially less total excitation than the 1-element model to generate comparable forces, especially at higher cadences. For instance, at 140 RPM, the required excitation was reduced by 23%. These results suggest that a 2-element model, in which contractile properties are “tuned” to represent slower and faster motor units, can increase the apparent strength and perhaps improve the fidelity of simulations of tasks with varying mechanical demands.
Existing "off-the-shelf" musculoskeletal models are problematic when simulating movements that involve substantial hip and knee flexion, such as the upstroke of pedalling, because they tend to generate excessive passive fibre force. The goal of this study was to develop a refined musculoskeletal model capable of simulating pedalling and fast running, in addition to walking, which predicts the activation patterns of muscles better than existing models. Specifically, we tested whether the anomalous co-activation of antagonist muscles, commonly observed in simulations, could be resolved if the passive forces generated by the underlying model were diminished. We refined the OpenSim™ model published by Rajagopal et al. (IEEE Trans Biomed Eng 63:1-1, 2016) by increasing the model's range of knee flexion, updating the paths of the knee muscles, and modifying the force-generating properties of eleven muscles. Simulations of pedalling, running and walking based on this model reproduced measured EMG activity better than simulations based on the existing model-even when both models tracked the same subject-specific kinematics. Improvements in the predicted activations were associated with decreases in the net passive moments; for example, the net passive knee moment during the upstroke of pedalling decreased from 36.9 N m (existing model) to 6.3 N m (refined model), resulting in a dramatic decrease in the co-activation of knee flexors. The refined model is available from SimTK.org and is suitable for analysing movements with up to 120° of hip flexion and 140° of knee flexion.
Birds have highly mobile necks, but neither the details of how they realize complex poses nor the evolution of this complex musculoskeletal system is well-understood. Most previous work on avian neck function has focused on dorsoventral flexion, with few studies quantifying lateroflexion or axial rotation. Such data are critical for understanding joint function, as musculoskeletal movements incorporate motion around multiple degrees of freedom simultaneously. Here we use biplanar X-rays on wild turkeys to quantify three-dimensional cervical joint range of motion in an avian neck to determine patterns of mobility along the cranial-caudal axis.
Range of motion can be generalized to a three-region model: cranial joints are ventroflexed with high axial and lateral mobility, caudal joints are dorsiflexed with little axial rotation but high lateroflexion, and middle joints show varying amounts axial rotation and a low degree of lateroflexion. Nonetheless, variation within and between regions is high. To attain complex poses, substantial axial rotation can occur at joints caudal to the atlas/axis complex and zygapophyseal joints can reduce their overlap almost to osteological disarticulation. Degrees of freedom interact at cervical joints; maximum lateroflexion occurs at different dorsoventral flexion angles at different joints, and axial rotation and lateroflexion are strongly coupled. Further, patterns of joint mobility are strongly predicted by cervical morphology.
Birds attain complex neck poses through a combination of mobile intervertebral joints, coupled rotations, and highly flexible zygapophyseal joints. Cranial-caudal patterns of joint mobility are tightly linked to cervical morphology, such that function can be predicted by form. The technique employed here provides a repeatable protocol for studying neck function in a broad array of taxa that will be directly comparable. It also serves as a foundation for future work on the evolution of neck mobility along the line from non-avian theropod dinosaurs to birds.
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Birds fly effectively and maneuver nimbly by dynamically changing the shape of their wings during each wingbeat. These shape changes have yet to be quantified automatically at high temporal and spatial resolution. Therefore, we developed a custom 3D surface reconstruction method, which uses a high-speed camera to identify spatially encoded binary striped patterns that are projected on a flying bird. This non-invasive structured-light method allows automated 3D reconstruction of each stand-alone frame and can be extended to multiple views. We demonstrate this new technique by automatically reconstructing the dorsal surface of a parrotlet wing at 3200 fps during flapping flight. From this shape we analyze key parameters such as wing twist and angle of attack distribution. While our binary ‘single-shot’ algorithm is demonstrated by quantifying dynamic shape changes of a flying bird, it is generally applicable to moving animals, plants and deforming objects.
Digit reduction is a major trend that characterizes horse evolution, but its causes and consequences have rarely been quantitatively tested. Using beam analysis on fossilized centre metapodials, we tested how locomotor bone stresses changed with digit reduction and increasing body size across the horse lineage. Internal bone geometry was captured from 13 fossil horse genera that covered the breadth of the equid phylogeny and the spectrum of digit reduction and body sizes, from Hyracotherium to Equus. To account for the load-bearing role of side digits, a novel, continuous measure of digit reduction was also established—toe reduction index (TRI). Our results show that without accounting for side digits, three-toed horses as late as Parahippus would have experienced physiologically untenable bone stresses. Conversely, when side digits are modelled as load-bearing, species at the base of the horse radiation through Equus probably maintained a similar safety factor to fracture stress. We conclude that the centre metapodial compensated for evolutionary digit reduction and body mass increases by becoming more resistant to bending through substantial positive allometry in internal geometry. These results lend support to two historical hypotheses: that increasing body mass selected for a single, robust metapodial rather than several smaller ones; and that, as horse limbs became elongated, the cost of inertia from the side toes outweighed their utility for stabilization or load-bearing.
Hill-type models are ubiquitous in the field of biomechanics, providing estimates of a muscle’s force as a function of its activation state and its assumed force-length and force-velocity properties. However, despite their routine use, the accuracy with which Hill-type models predict the forces generated by muscles during submaximal, dynamic tasks remains largely unknown. This study compared human gastrocnemii forces predicted by Hill-type models to the forces estimated from ultrasound-based measures of tendon length changes and stiffness during cycling, over a range of loads and cadences. We tested both a traditional model, with one contractile element, and a differential model, with two contractile elements that accounted for independent contributions of slow and fast muscle fibres. Both models were driven by subject-specific, ultrasound-based measures of fascicle lengths, velocities, and pennation angles and by activation patterns of slow and fast muscle fibres derived from surface electromyographic recordings. The models predicted on average, 54 % the time-varying gastrocnemii forces estimated from the ultrasound-based methods. However, differences between predicted and estimated forces were smaller under low speed-high activation conditions, with models able to predict nearly 80 % of the gastrocnemii force over a complete pedal cycle. Additionally, the predictions from the Hill-type muscle models tested here showed that a similar pattern of force production could be achieved for most conditions with and without accounting for the independent contributions of different muscle fibre types.
Flying animals must successfully contend with obstacles in their natural environments. Inspired by the robust manoeuvring abilities of flying animals, unmanned aerial systems are being developed and tested to improve flight control through cluttered environments. We previously examined steering strategies that pigeons adopt to fly through an array of vertical obstacles (VOs). Modelling VO flight guidance revealed that pigeons steer towards larger visual gaps when making fast steering decisions. In the present experiments, we recorded three-dimensional flight kinematics of pigeons as they flew through randomized arrays of horizontal obstacles (HOs). We found that pigeons still decelerated upon approach but flew faster through a denser array of HOs compared with the VO array previously tested. Pigeons exhibited limited steering and chose gaps between obstacles most aligned to their immediate flight direction, in contrast to VO navigation that favoured widest gap steering. In addition, pigeons navigated past the HOs with more variable and decreased wing stroke span and adjusted their wing stroke plane to reduce contact with the obstacles. Variability in wing extension, stroke plane and wing stroke path was greater during HO flight. Pigeons also exhibited pronounced head movements when negotiating HOs, which potentially serve a visual function. These head-bobbing-like movements were most pronounced in the horizontal (flight direction) and vertical directions, consistent with engaging motion vision mechanisms for obstacle detection. These results show that pigeons exhibit a keen kinesthetic sense of their body and wings in relation to obstacles. Together with aerodynamic flapping flight mechanics that favours vertical manoeuvring, pigeons are able to navigate HOs using simple rules, with remarkable success.
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.
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.
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.
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Mechanistically linking movement behaviors and ecology is key to understanding the adaptive evolution of locomotion. Predator evasion, a behavior that enhances fitness, may depend upon short bursts or complex patterns of locomotion. However, such movements are poorly characterized by existing biomechanical metrics. We present methods based on the entropy measure of randomness from Information Theory to quantitatively characterize the unpredictability of non-steady-state locomotion. We then apply the method by examining sympatric rodent species whose escape trajectories differ in dimensionality. Unlike the speed-regulated gait use of cursorial animals to enhance locomotor economy, bipedal jerboa (family Dipodidae) gait transitions likely enhance maneuverability. In field-based observations, jerboa trajectories are significantly less predictable than those of quadrupedal rodents, likely increasing predator evasion ability. Consistent with this hypothesis, jerboas exhibit lower anxiety in open fields than quadrupedal rodents, a behavior that varies inversely with predator evasion ability. Our unpredictability metric expands the scope of quantitative biomechanical studies to include non-steady-state locomotion in a variety of evolutionary and ecologically significant contexts.
While prior studies of swallow manoeuvering have focused on slow-speed flight and obstacle avoidance in still air, swallows survive by foraging at high speeds in windy environments. Recent advances in field-portable, high-speed video systems, coupled with precise anemometry, permit measures of high-speed aerial performance of birds in a natural state. We undertook the present study to test: (i) the manner in which barn swallows (Hirundo rustica) may exploit wind dynamics and ground effect while foraging and (ii) the relative importance of flapping versus gliding for accomplishing high-speed manoeuvers. Using multi-camera videography synchronized with wind-velocity measurements, we tracked coursing manoeuvers in pursuit of prey. Wind speed averaged 1.3–2.0 m s−1 across the atmospheric boundary layer, exhibiting a shear gradient greater than expected, with instantaneous speeds of 0.02–6.1 m s−1. While barn swallows tended to flap throughout turns, they exhibited reduced wingbeat frequency, relying on glides and partial bounds during maximal manoeuvers. Further, the birds capitalized on the near-earth wind speed gradient to gain kinetic and potential energy during both flapping and gliding turns; providing evidence that such behaviour is not limited to large, fixed-wing soaring seabirds and that exploitation of wind gradients by small aerial insectivores may be a significant aspect of their aeroecology.
Flying birds rely on visual cues for retinal image stabilization by negating rotation-induced optic flow, the motion of the visual panorama across the retina, through corrective eye and head movements. In combination with vestibular and proprioceptive feedback, birds may also use visual cues to stabilize their body during flight. Here, we test whether artificially induced wide-field motion generated through projected visual patterns elicits maneuvers in body orientation and flight position, in addition to stabilizing vision. To test this hypothesis, we present hummingbirds flying freely within a 1.2 m cylindrical visual arena with a virtual surround rotated at different speeds about its vertical axis. The birds responded robustly to these visual perturbations by rotating their heads and bodies with the moving visual surround, and by adjusting their flight trajectories, following the surround. Thus, similar to insects, hummingbirds appear to use optic flow cues to control flight maneuvers as well as to stabilize their visual inputs.
Skeletal muscles share many common, highly conserved features of organization at the molecular and myofilament levels, giving skeletal muscle fibers generally similar and characteristic mechanical and energetic properties; properties well described by classical studies of muscle mechanics and energetics. However, skeletal muscles can differ considerably in architectural design (fiber length, pinnation, and connective tissue organization), as well as fiber type, and how they contract in relation to the timing of neuromotor activation and in vivo length change. The in vivo dynamics of muscle contraction is, therefore, crucial to assessing muscle design and the roles that muscles play in animal movement. Architectural differences in muscle–tendon organization combined with differences in the phase of activation and resulting fiber length changes greatly affect the time-varying force and work that muscles produce, as well as the energetic cost of force generation. Intrinsic force–length and force–velocity properties of muscles, together with their architecture, also play important roles in the control of movement, facilitating rapid adjustments to changing motor demands. Such adjustments complement slower, reflex-mediated neural feedback control of motor recruitment. Understanding how individual fiber forces are integrated to whole-muscle forces, which are transmitted to the skeleton for producing and controlling locomotor movement, is therefore essential for assessing muscle design in relation to the dynamics of movement.
Airflow conditions close to the Earth's surface are often complex, posing challenges to flight stability and control for volant taxa. Relatively little is known about how well flying animals can contend with complex, adverse air flows, or about the flight-control mechanisms employed by animals to mitigate wind disturbances. Several recent studies have examined flight in the unsteady von Karman vortex streets that form behind cylinders, generating flow disturbances that are predictable in space and time; these structures are relatively rare in nature, as they occur only the immediate, downstream vicinity of an object. In contrast, freestream turbulence is characterized by rapid, unpredictable flow disturbances across a wide range of spatial and temporal scales, and is nearly ubiquitous in natural habitats. Hummingbirds are ideal organisms for studying the influence of freestream turbulence on flight, as they forage in a variety of aerial conditions and are powerful flyers. We filmed ruby-throated hummingbirds (A. colubris) maintaining position at a feeder in laminar and strongly turbulent (intensity approximately 15%) airflow environments within a wind tunnel, and compared their mean head, body, tail and wing kinematics, as well as variability in these parameters. Hummingbirds exhibited remarkably stable head position and orientation in both smooth and turbulent flow while maintaining position at the feeder. However, the hummingbird's body was less stable in turbulent flow and appeared to be most sensitive to disturbances along the mediolateral axis, displaying large lateral accelerations, translations, and rolling motions during flight. The hummingbirds mitigated these disturbances by increasing mean wing stroke amplitude and stroke plane angle, and by varying these parameters asymmetrically between the wings, and from one stroke to the next. They also actively varied the orientation and fan angle of the tail, maintaining a larger mean fan angle when flying in turbulent flow; this may improve their passive stability, but likely incurs an energetic cost due to increased drag. Overall, we observed many of the same kinematic changes noted previously for hummingbirds flying in a von Karman vortex street, but we also observed kinematic changes associated with high force production, similar to those seen during load-lifting or high-speed flight. These findings suggest that flight may be particularly costly in fully mixed, freestream turbulence, the flow condition that hummingbirds are likely to encounter most frequently in natural habitats.
The complexity of low speed maneuvering flight is apparent from the combination of two critical aspects of this behavior: high power and precise control. To understand how such control is achieved, we examined the underlying kinematics and resulting aerodynamic mechanisms of low speed turning flight in the pigeon (Columba livia). Three birds were trained to perform 90 deg level turns in a stereotypical fashion and detailed three-dimensional (3D) kinematics were recorded at high speeds. Applying the angular momentum principle, we used mechanical modeling based on time-varying 3D inertia properties of individual sections of the pigeon's body to separate angular accelerations of the torso based on aerodynamics from those based on inertial effects. Directly measured angular accelerations of the torso were predicted by aerodynamic torques, justifying inferences of aerodynamic torque generation based on inside wing versus outside wing kinematics. Surprisingly, contralateral asymmetries in wing speed did not appear to underlie the 90 deg aerial turns, nor did contralateral differences in wing area, angle of attack, wingbeat amplitude or timing. Instead, torso angular accelerations into the turn were associated with the outside wing sweeping more anteriorly compared with a more laterally directed inside wing. In addition to moving through a relatively more retracted path, the inside wing was also more strongly pronated about its long axis compared with the outside wing, offsetting any difference in aerodynamic angle of attack that might arise from the observed asymmetry in wing trajectories. Therefore, to generate roll and pitch torques into the turn, pigeons simply reorient their wing trajectories toward the desired flight direction. As a result, by acting above the center of mass, the net aerodynamic force produced by the wings is directed inward, generating the necessary torques for turning.
Individuals traversing challenging obstacles are faced with a decision: they can adopt traversal strategies that minimally disrupt their normal locomotion patterns or they can adopt strategies that substantially alter their gait, conferring new advantages and disadvantages. We flew pigeons (Columba livia) through an array of vertical obstacles in a flight arena, presenting them with this choice. The pigeons selected either a strategy involving only a slight pause in the normal wing beat cycle, or a wings-folded posture granting reduced efficiency but greater stability should a misjudgment lead to collision. The more stable but less efficient flight strategy was not used to traverse easy obstacles with wide gaps for passage but came to dominate the postures used as obstacle challenge increased with narrower gaps and there was a greater chance of a collision. These results indicate that birds weigh potential obstacle negotiation strategies and estimate task difficulty during locomotor pattern selection.
In this paper we propose a constitutive model to analyze in-plane extension of goat fascia lata. We first perform a histological analysis of the fascia that shows a well-organized bi-layered arrangement of undulated collagen fascicles oriented along two well defined directions. To develop a model consistent with the tissue structure we identify the absolute and relative thickness of each layer and the orientation of the preferred directions. New data are presented showing the mechanical response in uniaxial and planar biaxial extension. The paper proposes a constitutive relation to describe the mechanical response. We provide a summary of the main ingredients of the nonlinear theory of elasticity and introduce a suitable strain-energy function to describe the anisotropic response of the fascia. We validate the model by showing good fit of the numerical results and the experimental data. Comments are included about differences and analogies between goat fascia lata and the human iliotibial band.
Various flight navigation strategies for birds have been identified at the large spatial scales of migratory and homing behaviours. However, relatively little is known about close-range obstacle negotiation through cluttered environments. To examine obstacle flight guidance, we tracked pigeons (Columba livia) flying through an artificial forest of vertical poles. Interestingly, pigeons adjusted their flight path only approximately 1.5 m from the forest entry, suggesting a reactive mode of path planning. Combining flight trajectories with obstacle pole positions, we reconstructed the visual experience of the pigeons throughout obstacle flights. Assuming proportional-derivative control with a constant delay, we searched the relevant parameter space of steering gains and visuomotor delays that best explained the observed steering. We found that a pigeon's steering resembles proportional control driven by the error angle between the flight direction and the desired opening, or gap, between obstacles. Using this pigeon steering controller, we simulated obstacle flights and showed that pigeons do not simply steer to the nearest opening in the direction of flight or destination. Pigeons bias their flight direction towards larger visual gaps when making fast steering decisions. The proposed behavioural modelling method converts the obstacle avoidance behaviour into a (piecewise) target-aiming behaviour, which is better defined and understood. This study demonstrates how such an approach decomposes open-loop free-flight behaviours into components that can be independently evaluated.
The output of skeletal muscle can be varied by selectively recruiting different motor units. However, our knowledge of muscle function is largely derived from muscle in which all motor units are activated. This discrepancy may limit our understanding of in vivo muscle function. Hence, this study aimed to characterize the mechanical properties of muscle with different motor unit activation. We determined the isometric properties and isotonic force-velocity relationship of rat plantaris muscles in situ with all of the muscle active, 30% of the muscle containing predominately slower motor units active or 20% of the muscle containing predominately faster motor units active. There was a significant effect of active motor unit type on isometric force rise time (p < 0.001) and the force-velocity relationship (p < 0.001). Surprisingly, force rise time was longer and maximum shortening velocity higher when all motor units were active than when either fast or slow motor units were selectively activated. We propose this is due to the greater relative effects of factors such as series compliance and muscle resistance to shortening during sub-maximal contractions. The findings presented here suggest that recruitment according to the size principle, where slow motor units are activated first and faster ones recruited as demand increases, may not pose a mechanical paradox, as has been previously suggested.
Trotting, bipedal running, and especially hopping have long been considered the principal bouncing gaits of legged animals. We use the radial-leg spring constant [Formula: see text] to quantify the stiffness of the physical leg during bouncing gaits. The radial-leg is modeled as an extensible strut between the hip and the ground and [Formula: see text] is determined from the force and deflection of this strut in each instance of stance. A Hookean spring is modeled in-series with a linear actuator and the stiffness of this spring [Formula: see text] is determined by minimizing the work of the actuator while reproducing the measured force-deflection dynamics of an individual leg during trotting or running, and of the paired legs during hopping. Prior studies have estimated leg stiffness using [Formula: see text], a metric that imagines a virtual-leg connected to the center of mass. While [Formula: see text] has been applied extensively in human and comparative biomechanics, we show that [Formula: see text] more accurately models the spring in the leg when actuation is allowed, as is the case in biological and robotic systems. Our allometric analysis of [Formula: see text] in the kangaroo rat, tammar wallaby, dog, goat, and human during hopping, trotting, or running show that [Formula: see text] scales as body mass to the two-third power, which is consistent with the predictions of dynamic similarity and with the scaling of [Formula: see text]. Hence, two-third scaling of locomotor spring constants among mammals is supported by both the radial-leg and virtual-leg models, yet the scaling of [Formula: see text] emerges from work-minimization in the radial-leg model instead of being a defacto result of the ratio of force to length used to compute [Formula: see text]. Another key distinction between the virtual-leg and radial-leg is that [Formula: see text] is substantially greater than [Formula: see text], as indicated by a 30-37% greater scaling coefficient for [Formula: see text]. We also show that the legs of goats are on average twice as stiff as those of dogs of the same mass and that goats increase the stiffness of their legs, in part, by more nearly aligning their distal limb-joints with the ground reaction force vector. This study is the first allometric analysis of leg spring constants in two decades. By means of an independent model, our findings reinforce the two-third scaling of spring constants with body mass, while showing that springs in-series with actuators are stiffer than those predicted by energy-conservative models of the leg.