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.
Fascia is a highly organized collagenous tissue that is ubiquitous in the body, but whose function is not well understood. Because fascia has a sheet-like structure attaching to muscles and bones at multiple sites, it is exposed to different states of multi- or biaxial strain. In order to measure how biaxial strain affects fascia material behavior, planar biaxial tests with strain control were performed on longitudinal and transversely oriented samples of goat fascia lata (FL). Cruciform samples were cycled to multiple strain levels while the perpendicular direction was held at a constant strain. Structural differences among FL layers were examined using histology and SEM. Results show that FL stiffness, hysteresis, and strain energy density are greater in the longitudinal vs. transverse direction. Increased stiffness in the longitudinal layer is likely due to its greater thickness and greater average fibril diameter compared to the transverse layer(s). Perpendicular strain did not affect FL material behavior. Differential loading in the longitudinal vs. transverse directions may lead to structural changes, enhancing the ability of the longitudinal FL to transmit force, store energy, or stabilize the limb during locomotion. The relative compliance of the transverse fibers may allow expansion of underlying muscles when they contract.
We review here the use and reliability of Hill-type muscle models to predict muscle performance under varying conditions, ranging from in situ production of isometric force to in vivo dynamics of muscle length change and force in response to activation. Muscle models are frequently used in musculoskeletal simulations of movement, particularly when applied to studies of human motor performance in which surgically implanted transducers have limited use. Musculoskeletal simulations of different animal species also are being developed to evaluate comparative and evolutionary aspects of locomotor performance. However, such models are rarely validated against direct measures of fascicle strain or recordings of muscle-tendon force. Historically, Hill-type models simplify properties of whole muscle by scaling salient properties of single fibers to whole muscles, typically accounting for a muscle's architecture and series elasticity. Activation of the model's single contractile element (assigned the properties of homogenous fibers) is also simplified and is often based on temporal features of myoelectric (EMG) activation recorded from the muscle. Comparison of standard one-element models with a novel two-element model and with in situ and in vivo measures of EMG, fascicle strain, and force recorded from the gastrocnemius muscles of goats shows that a two-element Hill-type model, which allows independent recruitment of slow and fast units, better predicts temporal patterns of in situ and in vivo force. Recruitment patterns of slow/fast units based on wavelet decomposition of EMG activity in frequency-time space are generally correlated with the intensity spectra of the EMG signals, the strain rates of the fascicles, and the muscle-tendon forces measured in vivo, with faster units linked to greater strain rates and to more rapid forces. Using direct measures of muscle performance to further test Hill-type models, whether traditional or more complex, remains critical for establishing their accuracy and essential for verifying their applicability to scientific and clinical studies of musculoskeletal function.
Animals modulate the power output needed for different locomotor tasks by changing muscle forces and fascicle strain rates. To generate the necessary forces, appropriate motor units must be recruited. Faster motor units have faster activation-deactivation rates than slower motor units, and they contract at higher strain rates; therefore, recruitment of faster motor units may be advantageous for tasks that involve rapid movements or high rates of work. This study identified motor unit recruitment patterns in the gastrocnemii muscles of goats and examined whether faster motor units are recruited when locomotor speed is increased. The study also examined whether locomotor tasks that elicit faster (or slower) motor units are associated with increased (or decreased) in vivo tendon forces, force rise and relaxation rates, fascicle strains and/or strain rates. Electromyography (EMG), sonomicrometry and muscle-tendon force data were collected from the lateral and medial gastrocnemius muscles of goats during level walking, trotting and galloping and during inclined walking and trotting. EMG signals were analyzed using wavelet and principal component analyses to quantify changes in the EMG frequency spectra across the different locomotor conditions. Fascicle strain and strain rate were calculated from the sonomicrometric data, and force rise and relaxation rates were determined from the tendon force data. The results of this study showed that faster motor units were recruited as goats increased their locomotor speeds from level walking to galloping. Slow inclined walking elicited EMG intensities similar to those of fast level galloping but different EMG frequency spectra, indicating that recruitment of the different motor unit types depended, in part, on characteristics of the task. For the locomotor tasks and muscles analyzed here, recruitment patterns were generally associated with in vivo fascicle strain rates, EMG intensity and tendon force. Together, these data provide new evidence that changes in motor unit recruitment have an underlying mechanical basis, at least for certain locomotor tasks.
Hill-type models are commonly used to estimate muscle forces during human and animal movement-yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation-deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with "differential" activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r(2), was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r(2)=0.26-0.51), and all exhibited some errors (RMSE=9.63-32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.
Goats and other quadrupeds must modulate the work output of their muscles to accommodate the changing mechanical demands associated with locomotion in their natural environments. This study examined which hindlimb joint moments goats use to generate and absorb mechanical energy on level and sloped surfaces over a range of locomotor speeds. Ground reaction forces and the three-dimensional locations of joint markers were recorded as goats walked, trotted and galloped over 0, +15 and -15 deg sloped surfaces. Net joint moments, powers and work were estimated at the goats' hip, knee, ankle and metatarsophalangeal joints throughout the stance phase via inverse dynamics calculations. Differences in locomotor speed on the level, inclined and declined surfaces were characterized and accounted for by fitting regression equations to the joint moment, power and work data plotted versus non-dimensionalized speed. During level locomotion, the net work generated by moments at each of the hindlimb joints was small (less than 0.1 J kg(-1) body mass) and did not vary substantially with gait or locomotor speed. During uphill running, by contrast, mechanical energy was generated at the hip, knee and ankle, and the net work at each of these joints increased dramatically with speed (P<0.05). The greatest increases in positive joint work occurred at the hip and ankle. During downhill running, mechanical energy was decreased in two main ways: goats generated larger knee extension moments in the first half of stance, absorbing energy as the knee flexed, and goats generated smaller ankle extension moments in the second half of stance, delivering less energy. The goats' hip extension moment in mid-stance was also diminished, contributing to the decrease in energy. These analyses offer new insight into quadrupedal locomotion, clarifying how the moments generated by hindlimb muscles modulate mechanical energy at different locomotor speeds and grades, as needed to accommodate the demands of variable terrain.
Biomechanical models of whole muscles commonly used in simulations of musculoskeletal function and movement typically assume that the muscle generates force as a scaled-up muscle fiber. However, muscles are comprised of motor units that have different intrinsic properties and that can be activated at different times. This study tested whether a muscle model comprised of motor units that could be independently activated resulted in more accurate predictions of force than traditional Hill-type models. Forces predicted by the models were evaluated by direct comparison with the muscle forces measured in situ from the gastrocnemii in goats. The muscle was stimulated tetanically at a range of frequencies, muscle fiber strains were measured using sonomicrometry, and the activation patterns of the different types of motor unit were calculated from electromyographic recordings. Activation patterns were input into five different muscle models. Four models were traditional Hill-type models with different intrinsic speeds and fiber-type properties. The fifth model incorporated differential groups of fast and slow motor units. For all goats, muscles and stimulation frequencies the differential model resulted in the best predictions of muscle force. The in situ muscle output was shown to depend on the recruitment of different motor units within the muscle.
This study explored the muscle strain and activation patterns of several key flight muscles of the pigeon (Columba livia) during takeoff and landing flight. Using electromyography (EMG) to measure muscle activation, and sonomicrometry to quantify muscle strain, we evaluated the muscle function patterns of the pectoralis, biceps, humerotriceps and scapulotriceps as pigeons flew between two perches. These recordings were analyzed in the context of three-dimensional wing kinematics. To understand the different requirements of takeoff, midflight and landing, we compared the activity and strain of these muscles among the three flight modes. The pectoralis and biceps exhibited greater fascicle strain rates during takeoff than during midflight or landing. However, the triceps muscles did not exhibit notable differences in strain among flight modes. All observed strain, activation and kinematics were consistent with hypothesized muscle functions. The biceps contracted to stabilize and flex the elbow during the downstroke. The humerotriceps contracted to extend the elbow at the upstroke-downstroke transition, followed by scapulotriceps contraction to maintain elbow extension during the downstroke. The scapulotriceps also appeared to contribute to humeral elevation. Greater muscle activation intensity was observed during takeoff, compared with mid-flight and landing, in all muscles except the scapulotriceps. The timing patterns of muscle activation and length change differed among flight modes, yet demonstrated that pigeons do not change the basic mechanical actions of key flight muscles as they shift from flight activities that demand energy production, such as takeoff and midflight, to maneuvers that require absorption of energy, such as landing. Similarly, joint kinematics were consistent among flight modes. The stereotypy of these neuromuscular and joint kinematic patterns is consistent with previously observed stereotypy of wing kinematics relative to the pigeon's body (in the local body frame) across these flight behaviors. Taken together, these observations suggest that the control of takeoff and landing flight primarily involves modulation of overall body pitch to effect changes in stroke plane angle and resulting wing aerodynamics.
Hummingbirds (Trochilidae) are widely known for their insect-like flight strokes characterized by high wing beat frequency, small muscle strains and a highly supinated wing orientation during upstroke that allows for lift production in both halves of the stroke cycle. Here, we show that hummingbirds achieve these functional traits within the limits imposed by a vertebrate endoskeleton and muscle physiology by accentuating a wing inversion mechanism found in other birds and using long-axis rotational movement of the humerus. In hummingbirds, long-axis rotation of the humerus creates additional wing translational movement, supplementing that produced by the humeral elevation and depression movements of a typical avian flight stroke. This adaptation increases the wing-to-muscle-transmission ratio, and is emblematic of a widespread scaling trend among flying animals whereby wing-to-muscle-transmission ratio varies inversely with mass, allowing animals of vastly different sizes to accommodate aerodynamic, biomechanical and physiological constraints on muscle-powered flapping flight.
Turning is crucial for animals, particularly during predator-prey interactions and to avoid obstacles. For flying animals, turning consists of changes in (i) flight trajectory, or path of travel, and (ii) body orientation, or 3D angular position. Changes in flight trajectory can only be achieved by modulating aerodynamic forces relative to gravity. How birds coordinate aerodynamic force production relative to changes in body orientation during turns is key to understanding the control strategies used in avian maneuvering flight. We hypothesized that pigeons produce aerodynamic forces in a uniform direction relative to their bodies, requiring changes in body orientation to redirect those forces to turn. Using detailed 3D kinematics and body mass distributions, we examined net aerodynamic forces and body orientations in slowly flying pigeons (Columba livia) executing level 90 degrees turns. The net aerodynamic force averaged over the downstroke was maintained in a fixed direction relative to the body throughout the turn, even though the body orientation of the birds varied substantially. Early in the turn, changes in body orientation primarily redirected the downstroke aerodynamic force, affecting the bird's flight trajectory. Subsequently, the pigeon mainly reacquired the body orientation used in forward flight without affecting its flight trajectory. Surprisingly, the pigeon's upstroke generated aerodynamic forces that were approximately 50% of those generated during the downstroke, nearly matching the relative upstroke forces produced by hummingbirds. Thus, pigeons achieve low speed turns much like helicopters, by using whole-body rotations to alter the direction of aerodynamic force production to change their flight trajectory.
Recruitment patterns and activation dynamics of different motor units greatly influence the temporal pattern and magnitude of muscle force development, yet these features are not often considered in muscle models. The purpose of this study was to characterize the recruitment and activation dynamics of slow and fast motor units from electromyographic (EMG) recordings and twitch force profiles recorded directly from animal muscles. EMG and force data from the gastrocnemius muscles of seven goats were recorded during in vivo tendon-tap reflex and in situ nerve stimulation experiments. These experiments elicited EMG signals with significant differences in frequency content (p<0.001). The frequency content was characterized using wavelet and principal components analysis, and optimized wavelets with centre frequencies, 149.94 Hz and 323.13 Hz, were obtained. The optimized wavelets were used to calculate the EMG intensities and, with the reconstructed twitch force profiles, to derive transfer functions for slow and fast motor units that estimate the activation state of the muscle from the EMG signal. The resulting activation-deactivation time constants gave r values of 0.98-0.99 between the activation state and the force profiles. This work establishes a framework for developing improved muscle models that consider the intrinsic properties of slow and fast fibres within a mixed muscle, and that can more accurately predict muscle force output from EMG.
Collision-based expenditure of mechanical energy and the compliance and geometry of the leg are fundamental, interrelated considerations in the mechanical design of legged runners. This article provides a basic context and rationale for experiments designed to inform each of these key areas in Boston Dynamic's BigDog robot. Although these principles have been investigated throughout the past few decades within different academic disciplines, BigDog required that they be considered together and in concert with an impressive set of control algorithms that are not discussed here. Although collision reduction is an important strategy for reducing mechanical cost of transport in the slowest and fastest quadrupedal gaits, walking and galloping, BigDog employed an intermediate-speed trotting gait without collision reduction. Trotting, instead, uses a spring-loaded inverted pendulum mechanism with potential for storage and return of elastic strain energy in appropriately compliant structures. Rather than tuning BigDog's built-in leg springs according to a spring-mass model-based virtual leg-spring constant , a much stiffer distal leg spring together with actuation of the adjacent joint provided good trotting dynamics and avoided functional limitations that might have been imposed by too much compliance in real-world terrain. Adjusting the directional compliance of the legs by adopting a knee-forward, elbow-back geometry led to more robust trotting dynamics by reducing perturbations about the pitch axis of the robot's center of mass (CoM). BigDog is the most successful large-scale, all-terrain trotting machine built to date and it continues to stimulate our understanding of legged locomotion in comparative biomechanics as well as in robotics.
The analysis of terrestrial locomotion over the past half century has focused largely on strategies of mechanical energy recovery used during walking and running. In contrast, we describe the underlying mechanics of legged locomotion as a collision-like interaction that redirects the centre of mass (CoM). We introduce the collision angle, determined by the angle between the CoM force and velocity vectors, and show by computing the collision fraction, a ratio of actual to potential collision, that the quadrupedal walk and gallop employ collision-reduction strategies while the trot permits greater collisions. We provide the first experimental evidence that a collision-based approach can differentiate quadrupedal gaits and quantify interspecific differences. Furthermore, we show that this approach explains the physical basis of a commonly used locomotion metric, the mechanical cost of transport. Collision angle and collision fraction provide a unifying analysis of legged locomotion which can be applied broadly across animal size, leg number and gait.