Emanuel Andrada

Kinematics and Center of Mass Mechanics During Terrestrial Locomotion in Northern Lapwings (Vanellus vanellus, Charadriiformes)

Avian bipedalism is best studied in derived walking/running specialists. Here, we use kinematics and center of mass (CoM) mechanical energy patterns to investigate gait transitions of lapwings-migratory birds that forage on the ground, and therefore may need a trade-off between the functional demands of terrestrial locomotion and long distance flights. The animals ran on a treadmill while high-speed X-ray videos were recorded within the sustainable speed range. Instantaneous CoM mechanics were computed from integrating kinematics and body segment properties. Lapwings exhibit similar locomotor characteristics to specialized walking/running birds, but have less distinct gaits. At slow speeds no clear separation between vaulting (i.e., walking) and bouncing (i.e., running) energy patterns exists. Mechanical energy recovery of non-bouncing gaits correlates poorly with speed and suggests inefficient use of the inverted pendulum mechanism. Speed ranges of gaits overlap considerably, especially those of grounded running, a gait with CoM mechanics indicative of running but without an aerial phase, and aerial phase running, with no preferential gait at most speeds. Compliant limb morphology and grounded running in birds can be regarded as an evolutionary constraint, but lapwings effectively make use of advantages offered by this gait for a great fraction of their speed range. Thus, effective usage of grounded running during terrestrial locomotion is suggested generally to be a part of striding avian bipedalism-even in species not specialized in walking/running locomotion.

Adjustments of global and hindlimb local properties during the terrestrial locomotion of the common quail (Coturnix coturnix)

SUMMARY Previous research has resulted in increasing insight into neuro-mechanical control strategies during perturbed locomotion. In contrast, more general analyses on simple model (template)-related parameters during avian terrestrial locomotion are still rare. Quail kinematic data obtained using X-ray videography combined with ground reaction force measurements were used as a basis to investigate how ‘global’ template and ‘local’ leg joint parameters in this small, predominantly terrestrial bird change with speed and gait. Globally, quail locomotion approximates a spring-like behavior in all investigated gaits. However, ground reaction forces are more vertically oriented, which may help to balance the trunk. At the joint level, practically all the spring-like work was found to occur in the intertarsal joint (ITJ). From walking to grounded running, the local stiffness of the ITJ decreases similarly to the reduction observed in global leg stiffness. Thus, in gaits without aerial phases the quails may modulate ITJ stiffness to regulate global leg stiffness, and therefore gait changes, to a significant degree. At higher speeds both global leg compression and stiffness are increased (the latter to values not significantly different to those obtained during walking). This enables the animals to shorten contact time and to generate aerial phases (running). However, we did not observe a change in the stiffness in the ITJ with a change of gait from grounded running to running. We hypothesize that a more extended leg at touch-down, controlled by the joint angles in the knee and ITJ, has an important influence in the leg stiffness adjustment process during running.

Trunk orientation causes asymmetries in leg function in small bird terrestrial locomotion.

In contrast to the upright trunk in humans, trunk orientation in most birds is almost horizontal (pronograde). It is conceivable that the orientation of the heavy trunk strongly influences the dynamics of bipedal terrestrial locomotion. Here, we analyse for the first time the effects of a pronograde trunk orientation on leg function and stability during bipedal locomotion. For this, we first inferred the leg function and trunk control strategy applied by a generalized small bird during terrestrial locomotion by analysing synchronously recorded kinematic (three-dimensional X-ray videography) and kinetic (three-dimensional force measurement) quail locomotion data. Then, by simulating quail gaits using a simplistic bioinspired numerical model which made use of parameters obtained in in vivo experiments with real quail, we show that the observed asymmetric leg function (left-skewed ground reaction force and longer leg at touchdown than at lift-off) is necessary for pronograde steady-state locomotion. In addition, steady-state locomotion becomes stable for specific morphological parameters. For quail-like parameters, the most common stable solution is grounded running, a gait preferred by quail and most of the other small birds. We hypothesize that stability of bipedal locomotion is a functional demand that, depending on trunk orientation and centre of mass location, constrains basic hind limb morphology and function, such as leg length, leg stiffness and leg damping.

Grounded running in quails: Simulations indicate benefits of observed fixed aperture angle between legs before touch-down

Many birds use grounded running (running without aerial phases) in a wide range of speeds. Contrary to walking and running, numerical investigations of this gait based on the BSLIP (bipedal spring loaded inverted pendulum) template are rare. To obtain template related parameters of quails (e.g. leg stiffness) we used x-ray cinematography combined with ground reaction force measurements of quail grounded running. Interestingly, with speed the quails did not adjust the swing legs angle of attack with respect to the ground but adapted the angle between legs (which we termed aperture angle), and fixed it about 30ms before touchdown. In simulations with the BSLIP we compared this swing leg alignment policy with the fixed angle of attack with respect to the ground typically used in the literature. We found symmetric periodic grounded running in a simply connected subset comprising one third of the investigated parameter space. The fixed aperture angle strategy revealed improved local stability and surprising tolerance with respect to large perturbations. Starting with the periodic solutions, after step-down step-up or step-up step-down perturbations of 10% leg rest length, in the vast majority of cases the bipedal SLIP could accomplish at least 50 steps to fall. The fixed angle of attack strategy was not feasible. We propose that, in small animals in particular, grounded running may be a common gait that allows highly compliant systems to exploit energy storage without the necessity of quick changes in the locomotor program when facing perturbations.

A mechanical link model of two-toed sloths: no pendular mechanics during suspensory locomotion

Sloths are morphologically specialized in suspensory quadrupedal locomotion and posture. During steady-state locomotion they utilize a trot-like footfall sequence. Contrasting the growing amount of published accounts of the functional morphology and kinematics of sloth locomotion, no study concerned with the dynamics of their quadrupedal suspensory locomotion has been conducted. Brachiating primates have been shown to travel at low mechanical costs using pendular mechanics, but this is associated with considerable dynamic forces exerted onto the support. To test whether sloth locomotion can be described by simple connected pendulum mechanics, we analyzed the dynamics of sloth locomotion with use of a mechanical segment link model. The model integrates the body segment parameters and is driven by kinematic data with both segment parameters and kinematic data obtained from the same sloth individual. No simple pendular mechanics were present. We then used the model to carry out an inverse dynamic analysis. The analysis allowed us to estimate net limb joint torques and substrate reaction forces during the contact phases. Predominant flexing limb joint torque profiles in the shoulder, elbow, hip, and knee are in stark contrast to published dominant extensor torques in the limb joints of pronograde quadrupedal mammals. This dissimilarity likely reflects the inverse orientation of the sloth towards the gravity vector. Nevertheless, scapular pivot and shoulder seem to provide the strongest torque for progression as expected based on unchanged basic kinematic pattern previously described. Our model predicts that sloths actively reduce the dynamical forces and moments that are transmitted onto the support. We conclude that these findings reflect the need to reduce the risk of breaking supports because in this case sloths would likely be unable to react quickly enough to prevent potentially lethal falls. To achieve this, sloths seem to avoid the dynamical consequences of effective pendular mechanics.

Positioning the hip with respect to the COM: Consequences for leg operation

In bipedal runners and hoppers the hip is not located at the center of mass in the sagittal projection. This displacement influences operation and energetics of the leg attached to the hip. To investigate this influence in a first step a simple conservative bouncing template is developed in which a heavy trunk is suspended to a massless spring at a pivot point above the center of mass. This model describes the orientation of the ground reaction forces observed in experiments on running birds. In a second step it is assumed that an effective telescope leg with its hip fixed to the trunk remote from the COM generates the same ground reaction forces as those predicted by the template. For this effective leg the influence of hip placement on leg operation and energetics is investigated. Placing the hip directly below, at, or above the pivot point results in high axial energy storage. Posterior placement increases axial losses and hip work whereas anterior placement would require axial work and absorption at the hip. Shifting the hip far posteriorly as observed in some birds can lead to the production of pure extension torques throughout the stance phase. It is proposed that the relative placement of the hip with respect to the center of mass is an important measure to modify effective leg operation with possible implications for balancing the trunk and the control of legged motion systems.

Bridging “Romer’s Gap”: Limb Mechanics of an Extant Belly-Dragging Lizard Inform Debate on Tetrapod Locomotion During the Early Carboniferous

Devonian stem tetrapods are thought to have used ‘crutching’ on land, a belly-dragging form of synchronous forelimb action-powered locomotion. During the Early Carboniferous, early tetrapods underwent rapid radiation, and the terrestrial locomotion of crown-group node tetrapods is believed to have been hindlimb-powered and ‘raised’, involving symmetrical gaits similar to those used by modern salamanders. The fossil record over this period of evolutionary transition is remarkably poor (Romer’s Gap), but we hypothesize a phase of belly-dragging sprawling locomotion combined with symmetrical gaits. Since belly-dragging sprawling locomotion has differing functional demands from ‘raised’ sprawling locomotion, we studied the limb mechanics of the extant belly-dragging blue-tongued skink. We used X-ray reconstruction of moving morphology to quantify the three-dimensional kinematic components, and simultaneously recorded single limb substrate reaction forces (SRF) in order to calculate SRF moment arms and the external moments acting on the proximal limb joints. In the hindlimbs, stylopodal long-axis rotation is more emphasized than in the forelimbs, and much greater vertical and propulsive forces are exerted. The SRF moment arm acting on the shoulder is at a local minimum at the instant of peak force. The hindlimbs display patterns that more closely resemble ‘raised’ sprawling species. External moment at the shoulder of the skink is smaller than in ‘raised’ sprawlers. We propose an evolutionary scenario in which the locomotor mechanics of belly-dragging early tetrapods were gradually modified towards hindlimb-powered, raised terrestrial locomotion with symmetrical gait. In accordance with the view that limb evolution was an exaptation for terrestrial locomotion, the kinematic pattern of the limbs for the generation of propulsion preceded, in our scenario, the evolution of permanent body weight support.

Grounded Running: An Overlooked Strategy for Robots

In this paper, the possible advantages of using grounded running, a running gait without aerial phases, for fast robot locomotion are discussed. Extended fields of fixed points for grounded running, obtained using dimensionless numerical modeling, are presented. They can be used to find global parameters for the design and operation of robots. The use of self-stable (for steady-state locomotion) or weak unstable (to improve maneuverability-stability trade-off) gait-modes as a design parameter could represent a strategy to reduce the still existing gap between animals and mimicking machines with respect to elegance and performance.

FROM BIOMECHANICS OF RATS' INCLINED LOCOMOTION TO A CLIMBING ROBOT

The base of the design and construction of an adaptive light-weight climbing robot is an understanding of the adaptive nature of small mammals’ motion on sloped supports. In the present study, the locomotor generalist Rattus norvegicus (the rat) served as the main biological paragon. Experiments were performed under X-ray high-speed videography with synchronized substrate reaction force (SRF) measurements, to allow calculation of inverse dynamics. Statistical analyses were performed to examine the effects of different substrate orientations on the kinematic variables. We obtained SRFs, torque and power patterns in the extremities and trunk of rats moving on simulated arboreal substrates at different substrate orientations (0°, 30°, 60°). During locomotion on horizontal substrates, rats prefer symmetrical gaits and switch to synchronous gaits at 60° inclination. Surprisingly, horizontal locomotion and locomotion on moderately inclined substrates (30°) differ only in the power invested in locomotion. Our results suggest that the trunk seems to play a more important role during locomotion at steeper inclines where rats switch to the more quasi-static in-phase gait. We conclude that this may be an indication of a change from a grounded to a climbing gait. Via bionic transfer we derived main basic principles, which we applied to the design of the robot Rat-Nic.

Mixed gaits in small avian terrestrial locomotion.

Scientists have historically categorized gaits discretely (e.g. regular gaits such as walking, running). However, previous results suggest that animals such as birds might mix or regularly or stochastically switch between gaits while maintaining a steady locomotor speed. Here, we combined a novel and completely automated large-scale study (over one million frames) on motions of the center of mass in several bird species (quail, oystercatcher, northern lapwing, pigeon, and avocet) with numerical simulations. The birds studied do not strictly prefer walking mechanics at lower speeds or running mechanics at higher speeds. Moreover, our results clearly display that the birds in our study employ mixed gaits (such as one step walking followed by one step using running mechanics) more often than walking and, surprisingly, maybe as often as grounded running. Using a bio-inspired model based on parameters obtained from real quails, we found two types of stable mixed gaits. In the first, both legs exhibit different gait mechanics, whereas in the second, legs gradually alternate from one gait mechanics into the other. Interestingly, mixed gaits parameters mostly overlap those of grounded running. Thus, perturbations or changes in the state induce a switch from grounded running to mixed gaits or vice versa.