The dynamics of quadrupedal locomotion

The Functional and Anatomical Impacts of Healthy Muscle Ageing

Even "healthy" muscle ageing is often associated with substantial changes in muscle form and function and can lead to increased injury risks and significant negative impacts on quality of life. However, the impacts of healthy muscle ageing on the fibre architecture and microstructure of different muscles and muscle groups throughout the lower limb, and how these are related to their functional capabilities, are not fully understood. Here, a previously established framework of magnetic resonance and diffusion tensor imaging was used to measure the muscle volumes, intramuscular fat, fibre lengths and physiological cross-sectional areas of 12 lower limb muscles in a cohort of healthily aged individuals, which were compared to the same data from a young population. Maximum muscle forces were also measured from an isokinetic dynamometer. The more substantial interpopulation differences in architecture and functional performance were located within the knee extensor muscles, while the aged muscles were also more heterogeneous in muscle fibre type and atrophy. The relationships between architecture and muscle strength were also more significant in the knee extensors compared to other functional groups. These data highlight the importance of the knee extensors as a potential focus for interventions to negate the impacts of muscle ageing.

Peak vertical ground force of hand–knee crawling in human adults

[Purpose] Fall risk is immanent in humans because they are bipedal. Bipedalism has transited from quadrupedalism in both evolutional and developmental contexts. Past studies have measured the peak vertical ground force of forelimbs and hindlimbs in quadrupedalism; and revealed that load dominancy shifted from forelimbs to hindlimbs during evolution. The dominance of hindlimb peak vertical ground force allows forelimb freedom and is considered important for locomotor evolution toward bipedalism. With this consideration, we hypothesize that hindlimb peak vertical ground force is dominant in human adults when they designedly crawl in a quadrupedal manner. [Participants and Methods] Six healthy human adults crawled on their hands and knees over a pressure platform. We calculated the peak vertical ground force of their hands and knees by integrating the pressure of the contact area of each limb. [Results] The mean knee peak vertical ground force at 0.694 (per body weight) was significantly higher than that of the hand at 0.372 (per body weight). The mean hand/knee peak vertical ground force ratio was 0.536; therefore, it was -0.624 on the natural logarithmic scale. [Conclusions] Our findings on human adults are compatible with existing considerations on locomotor evolution toward bipedalism. Our findings contribute to the comprehensive understanding of human locomotion.

Control of Mammalian Locomotion by Somatosensory Feedback

When animals walk overground, mechanical stimuli activate various receptors located in muscles, joints, and skin. Afferents from these mechanoreceptors project to neuronal networks controlling locomotion in the spinal cord and brain. The dynamic interactions between the control systems at different levels of the neuraxis ensure that locomotion adjusts to its environment and meets task demands. In this article, we describe and discuss the essential contribution of somatosensory feedback to locomotion. We start with a discussion of how biomechanical properties of the body affect somatosensory feedback. We follow with the different types of mechanoreceptors and somatosensory afferents and their activity during locomotion. We then describe central projections to locomotor networks and the modulation of somatosensory feedback during locomotion and its mechanisms. We then discuss experimental approaches and animal models used to investigate the control of locomotion by somatosensory feedback before providing an overview of the different functional roles of somatosensory feedback for locomotion. Lastly, we briefly describe the role of somatosensory feedback in the recovery of locomotion after neurological injury. We highlight the fact that somatosensory feedback is an essential component of a highly integrated system for locomotor control. © 2021 American Physiological Society. Compr Physiol 11:1-71, 2021.

Forelimb joints contribute to locomotor performance in reindeer (Rangifer tarandus) by maintaining stability and storing energy

Reindeer (Rangifer tarandus) have lengthy seasonal migrations on land and their feet possess excellent locomotor characteristics that can adapt to complex terrains. In this study, the kinematics and vertical ground reaction force (GRF) of reindeer forelimb joints (interphalangeal joint b, metacarpophalangeal joint c, and wrist joint d) under walk, trot 1, and trot 2 were measured using a motion tracking system and Footscan pressure plates. Significant differences among different locomotor activities were observed in the joint angles, but not in changes of the joint angles (α_b, α_c, α_d) during the stance phase. Peak vertical GRF increased as locomotor speed increased. Net joint moment, power, and work at the forelimb joints were calculated via inverse dynamics. The peak joint moment and net joint power related to the vertical GRF increased as locomotor speed increased. The feet absorbed and generated more energy at the joints. During different locomotor activities, the contribution of work of the forelimbs changed with both gait and speed. In the stance phase, the metacarpophalangeal joint absorbed more energy than the other two joints while trotting and thus performed better in elastic energy storage. The joint angles changed very little (∼5°) from 0 to 75% of the stance phase, which reflected the stability of reindeer wrist joints. Compared to typical ungulates, reindeer toe joints are more stable and the stability and energy storage of forelimb joints contribute to locomotor performance in reindeer.

Sheep Quickstep while the Floor Rock and Rolls: Visuomotor Lateralization during Simulated Sea Travel

Unpredictable floor motions during transport disturbs animals' balance, requiring stepping to move the centre of gravity in the direction of body movement. When repeated regularly, this may be stressful, requiring involvement of the right brain hemisphere, hence we investigated the existence of behavioral laterality in sheep during prolonged floor motions. Six sheep were restrained in pairs on a programmable rocking platform, in which they were unable to turn around. They were exposed to three continuous rocking motion treatments (roll, pitch or both) in a regular or irregular pattern for 1 h periods in a changeover design. Right forelimb and left hindlimb diagonal stepping was more frequent in response to the motion treatment of irregular roll and pitch, which previous research has suggested to be the most stressful from heart rate measurements. An overall strategy to maintain balance appeared to be the use of the right hindlimb as a stabilizer, which was repositioned least often of all limbs until towards the end of the hour of experimental treatment. Of each tested pair, sheep restrained on the left side of the rocking floor stepped significantly often than its partner restrained on the right side, and we postulate the existence of visuomotor lateralization as left restrained sheep were unable to view their partner within the field of view of their left eye. We also investigated which side sheep lie down on, which if left lateralized could explain our observed bipedal diagonal control of sheep balance under stress. From the observation of 412 web-based images of sheep, there was an overall left-sided laterality to their lying, as has been observed in cattle. We conclude that stepping activity in sheep in response to a motion stressor is lateralized, providing evidence that floor motion experienced in transport may induce stress responses.

Goats decrease hindlimb stiffness when walking over compliant surfaces

Leg stiffness, commonly estimated as the 'compression' of a defined leg element in response to a load, has long been used to characterize terrestrial locomotion. This study investigated how goats adjust the stiffness of their hindlimbs to accommodate surfaces of different stiffness. Goats provide a compelling animal model for studying leg stiffness modulation, because they skillfully ambulate over a range of substrates that vary in compliance. To investigate the adjustments that goats make when walking over such substrates, ground reaction forces and three-dimensional trajectories of hindlimb markers were recorded as goats walked on rigid, rubber and foam surfaces. Net joint moments, power and work at the hip, knee, ankle and metatarsophalangeal joints were estimated throughout stance via inverse dynamics. Hindlimb stiffness was estimated from plots of total leg force versus total leg length, and individual joint stiffness was estimated from plots of joint moment versus joint angle. Our results support the hypothesis that goats modulate hindlimb stiffness in response to surface stiffness; specifically, hindlimb stiffness decreased on the more compliant surfaces (P<0.002). Estimates of joint stiffness identified hip and ankle muscles as the primary drivers of these adjustments. When humans run on compliant surfaces, they generally increase leg stiffness to preserve their center-of-mass mechanics. We did not estimate center-of-mass mechanics in this study; nevertheless, our estimates of hindlimb stiffness suggest that goats exhibit a different behavior. This study offers new insight into mechanisms that allow quadrupeds to modulate their gait mechanics when walking on surfaces of variable compliance.

A Dynamic Simulation of Musculoskeletal Function in the Mouse Hindlimb During Trotting Locomotion

Mice are often used as animal models of various human neuromuscular diseases, and analysis of these models often requires detailed gait analysis. However, little is known of the dynamics of the mouse musculoskeletal system during locomotion. In this study, we used computer optimization procedures to create a simulation of trotting in a mouse, using a previously developed mouse hindlimb musculoskeletal model in conjunction with new experimental data, allowing muscle forces, activation patterns, and levels of mechanical work to be estimated. Analyzing musculotendon unit (MTU) mechanical work throughout the stride allowed a deeper understanding of their respective functions, with the rectus femoris MTU dominating the generation of positive and negative mechanical work during the swing and stance phases. This analysis also tested previous functional inferences of the mouse hindlimb made from anatomical data alone, such as the existence of a proximo-distal gradient of muscle function, thought to reflect adaptations for energy-efficient locomotion. The results do not strongly support the presence of this gradient within the mouse musculoskeletal system, particularly given relatively high negative net work output from the ankle plantarflexor MTUs, although more detailed simulations could test this further. This modeling analysis lays a foundation for future studies of the control of vertebrate movement through the development of neuromechanical simulations.

Fitting unanchored puzzle pieces in the skeleton: appropriate 3D scapular positions for the quadrupedal support in tetrapods

Deducing the scapular positions of extinct tetrapod skeletons remains difficult, because the scapulae and rib cage are connected with each other not directly by skeletal joint, but by thoracic muscles. In extant non-testudine quadrupedal tetrapods, the top positions of the scapulae/suprascapulae occur at the anterior portion of the rib cage, above the vertebral column and near the median plane. The adequacy of this position was tested using three-dimensional mechanical models of Felis, Rattus and Chamaeleo that assumed stances on a forelimb on a single side and the hindlimbs. The net moment about the acetabulum generated by the gravity force and the contractive forces of the anti-gravity thoracic muscles, and the resistance of the rib to vertical compression between the downward gravity and upward lifting force from the anti-gravity thoracic muscle depend on the scapular position. The scapular position common among quadrupeds corresponds to the place at which the roll and yaw moments of the uplifted portion of the body are negligible, where the pitch moment is large enough to lift the body, and above the ribs having high strength against vertical compression. These relationships between scapular position and rib cage morphology should allow reliable reconstruction of limb postures of extinct taxa.

The locomotor kinematics and ground reaction forces of walking giraffes

Giraffes (Giraffa camelopardalis Linnaeus 1758) possess specialised anatomy. Their disproportionately elongate limbs and neck confer recognised feeding advantages, but little is known about how their morphology affects locomotor function. In this study, we examined the stride parameters and ground reaction forces from three adult giraffes in a zoological park, across a range of walking speeds. The patterns of GRFs during walking indicate that giraffes, similar to other mammalian quadrupeds, maintain a forelimb-biased weight distribution. The angular excursion of the neck has functional links with locomotor dynamics in giraffes, and was exaggerated at faster speeds. The horizontal accelerations of the neck and trunk were out of phase, compared with the vertical accelerations which were intermediate between in and out of phase. Despite possessing specialised morphology, giraffes’ stride parameters were broadly predicted from dynamic similarity, facilitating the use of other quadrupedal locomotion models to generate testable hypotheses in giraffes.

Strategies for obstacle avoidance during walking in the cat

Avoiding obstacles is essential for successful navigation through complex environments. This study aimed to clarify what strategies are used by a typical quadruped, the cat, to avoid obstacles during walking. Four cats walked along a corridor 2.5 m long and 25 or 15 cm wide. Obstacles, small round objects 2.5 cm in diameter and 1 cm in height, were placed on the floor in various locations. Movements of the paw were recorded with a motion capture and analysis system (Visualeyez, PTI). During walking in the wide corridor, cats' preferred strategy for avoiding a single obstacle was circumvention, during which the stride direction changed while stride duration and swing-to-stride duration ratio were preserved. Another strategy, stepping over the obstacle, was used during walking in the narrow corridor, when lateral deviations of walking trajectory were restricted. Stepping over the obstacle involved changes in two consecutive strides. The stride preceding the obstacle was shortened, and swing-to-stride ratio was reduced. The obstacle was negotiated in the next stride of increased height and normal duration and swing-to-stride ratio. During walking on a surface with multiple obstacles, both strategies were used. To avoid contact with the obstacle, cats placed the paw away from the object at a distance roughly equal to the diameter of the paw. During obstacle avoidance cats prefer to alter muscle activities without altering the locomotor rhythm. We hypothesize that a choice of the strategy for obstacle avoidance is determined by minimizing the complexity of neuro-motor processes required to achieve the behavioral goal.NEW & NOTEWORTHY In a study of feline locomotor behavior we found that the preferred strategy to avoid a small obstacle is circumvention. During circumvention, stride direction changes but length and temporal structure are preserved. Another strategy, stepping over the obstacle, is used in narrow walkways. During overstepping, two strides adjust. A stride preceding the obstacle decreases in length and duration. The following stride negotiating the obstacle increases in height while retaining normal temporal structure and nearly normal length.

The Mechanics of Quadrupedal Galloping and the Future of Legged Vehicles

Previous studies have noted that biological quadrupeds adjust their gaits when encountering drag in their locomotion. This paper investigates the hypothesis that these gait adjustments allow the legs to operate at an optimal working length when generating thrust. A 5-DoF dynamic model of a quadruped having a rigid trunk and massless legs is formulated. This model reflects the dimensions and inertial properties of a galloping machine the authors are designing. The constrained, steady-state motion equations governing the transverse and rotary gallops of the model are solved numerically for various levels of drag. The footfall phasing solutions for both forms of the gallop approach a partially in-phase gait, the half-bound, as drag increases. These gait transitions are the result of constraints requiring the legs to operate at their optimal working length when in contact with the terrain. Thus, the behavior of the model supports the original hypothesis. This paper also includes a discussion of future research directions in the field of artificial legged locomotion.

System Design of a Quadrupedal Galloping Machine

In this paper we present the system design of a machine that we have constructed to study a quadrupedal gallop gait. The gallop gait is the preferred high-speed gait of most cursorial quadrupeds. To gallop, an animal must generate ballistic trajectories with characteristic strong impacts, coordinate leg movements with asymmetric footfall phasing, and effectively use compliant members, all the while maintaining dynamic stability. In this paper we seek to further understand the primary biological features necessary for galloping by building and testing a robotic quadruped similar in size to a large goat or antelope. These features include high-speed actuation, energy storage, on-line learning control, and high-performance attitude sensing. Because body dynamics are primarily influenced by the impulses delivered by the legs, the successful design and control of single leg energetics is a major focus of this work. The leg stores energy during flight by adding tension to a spring acting across an articulated knee. During stance, the spring energy is quickly released using a novel capstan design. As a precursor to quadruped control, two intelligent strategies have been developed for verification on a one-legged system. The Levenberg-Marquardt on-line learning method is applied to a simple heuristic controller and provides good control over height and forward velocity. Direct adaptive fuzzy control, which requires no system modeling but is more computationally expensive, exhibits better response. Using these techniques we have been successful in operating one leg at speeds necessary for a dynamic gallop of a machine of this scale. Another necessary component of quadruped locomotion is high-resolution and high-bandwidth attitude sensing. The large ground impact accelerations, which cause problems for any single traditional sensor, are overcome through the use of an inertial sensing approach using updates from optical sensors and vehicle kinematics.

Effects of reinnervation of the biarticular shoulder-elbow muscles on joint kinematics and electromyographic patterns of the feline forelimb during downslope walking

Full recovery of the forelimb kinematics during level and upslope walking following reinnervation of the biarticular elbow extensor suggests that the proprioceptive loss is compensated by other sensory sources or altered central drive, yet these findings have not been explored in downslope walking. Kinematics and muscle activity of the shoulder and elbow during downslope locomotion following reinnervation of the feline long head of the triceps brachii (TLo) and biceps brachii (Bi) were evaluated (1) during paralysis and (2) after the motor function was recovered but the proprioceptive feedback was permanently disrupted. The step cycle was examined in three walking conditions: level (0%), -25% grade (-14° downslope) and -50% grade (-26.6° downslope). Measurements were taken prior to and at three time points (2 weeks, and 1 and 12+ months) after transecting and suturing the radial and musculocutaneous nerves. There was an increase in the yield (increased flexion) at the elbow and less extensor activity duration of flexion during stance as the downslope grade increased. There were two notable periods of eccentric contractions (active lengthening) providing an apparent 'braking' action. Paralysis of the TLo and the Bi resulted in uncompensated alterations in shoulder-elbow kinematics and motor activity during the stance phase. However, unlike the case for the level and upslope conditions, during both paralysis and reinnervation, changes in interjoint coordination persisted for the downslope condition. The lack of complete recovery in the long term suggests that the autogenic reflexes contribute importantly to muscle and joint stiffness during active lengthening.

Effects of reinnervation of the triceps brachii on joint kinematics and electromyographic patterns of the feline forelimb during level and upslope walking

Nerve injury in the hindlimb of the cat results in locomotor changes, yet these findings have not been explored in a more multifunctional forelimb. Kinematics and muscle activity of the shoulder and elbow during level and upslope locomotion following reinnervation of the feline long head of the triceps brachii (TLo) were evaluated (1) during paralysis [none to minimum motor activity (short-term effects)] and (2) after the motor function was recovered but the proprioceptive feedback was permanently disrupted (long-term effects). The step cycle was examined in three walking conditions: level (0%), 25% grade (14° upslope) and 50% grade (26.6° upslope). Measurements were taken prior to and at three time points (2 weeks, 1 month and 12+ months) after transecting and suturing the radial nerve of TLo. There was less of a yield (increased flexion) at the elbow joint and more extensor activity during elbow flexion during stance (E2) as the grade of walking increased. Substantial short-term effects were observed at the elbow joint (increased flexion during E2) as well as increased motor activity by the synergistic elbow extensors, and greater shoulder extension at paw contact, leading to altered interjoint coordination during stance. Forelimb shoulder and elbow kinematics during level and upslope locomotion progressed back to baseline at 12 months. The short-term effects can be explained by both mechanical and neural factors that are altered by the functional elimination of the TLo. Full recovery of the forelimb kinematics during level and upslope walking suggests that the proprioceptive length feedback loss is compensated by other sensory sources or altered central drive.

A Critical Characteristic in the Transverse Galloping Pattern

Transverse gallop is a common gait used by a large number of quadrupeds. This paper employs the simplified dimensionless quadrupedal model to discuss the underlying mechanism of the transverse galloping pattern. The model is studied at different running speeds and different values of leg stiffness, respectively. If the horizontal running speed reaches up to a critical value at a fixed leg stiffness, or if the leg stiffness reaches up to a critical value at a fixed horizontal speed, a key property would emerge which greatly reduces the overall mechanical forces of the dynamic system in a proper range of initial pitch angular velocities. Besides, for each horizontal speed, there is an optimal stiffness of legs that can reduce both the mechanical loads and the metabolic cost of transport. Furthermore, different body proportions and landing distance lags of a pair of legs are studied in the transverse gallop. We find that quadrupeds with longer length of legs compared with the length of the body are more suitable to employ the transverse galloping pattern, and the landing distance lag of a pair of legs could reduce the cost of transport and the locomotion frequency.

Forelimb muscle activity during equine locomotion

Few quantitative data exist to describe the activity of the distal muscles of the equine forelimb during locomotion, and there is an incomplete understanding of the functional roles of the majority of the forelimb muscles. Based on morphology alone it would appear that the larger proximal muscles perform the majority of work in the forelimb, whereas the smaller distal muscles fulfil supplementary roles such as stabilizing the joints and positioning the limb for impact with the ground. We measured the timing and amplitude of the electromyographic activity of the intrinsic muscles of the forelimb in relation to the phase of gait (stance versus swing) and the torque demand placed on each joint during walking, trotting and cantering. We found that all forelimb muscles, except the extensor carpi radialis (ECR), were activated just prior to hoof-strike and deactivated during stance. Only the ECR was activated during swing. The amplitudes of muscle activation typically increased as gait speed increased. However, the amplitudes of muscle activation were not proportional to the net joint torques, indicating that passive structures may also contribute significantly to torque generation. Our results suggest that the smaller distal muscles help to stabilize the forelimb in early stance, in preparation for the passive structures (tendons and ligaments) to be stretched. The distal forelimb muscles remain active throughout stance only during canter, when the net torques acting about the distal forelimb joints are highest. The larger proximal muscles activate in a complex coordination to position and stabilize the shoulder and elbow joints during ground contact.

A stance period approach for simplified observation of galloping as applied to canines

The gallop is the preferred gait by mammals for agile traversal through terrain. This motion is intrinsically complex as the feet are used individually and asymmetrically. Simple models provide a conceptual framework for understanding this gait. In this light, this paper considers the footfall projections as suggested by an impulse model for galloping as a measurement simplifying strategy. Instead of concentrating on forces and inverse dynamics, this view focuses observations on leg motion (footfalls and stance periods) for subsequent gallop analysis and parameter estimation. In practice, this eases experiments (particularly for IR-based motion capture) by extending the experimental workspace, removing the need for single-leg contact force-plate measurements, and reducing the marker set. This provides shorter setup times, and it reduces postprocessing as data are less likely to suffer from occlusion, errant correspondence, and tissue flexion. This approach is tested using with three canine subjects (ranging from 8 to 24 kg) performing primarily rotary gallops down a 15 m runway. Normalized results are in keeping with insights from previous animal and legged robot studies and are consistent with motions suggested by said impulse model.

Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop

Mammals use two distinct gallops referred to as the transverse (where landing and take-off are contralateral) and rotary (where landing and take-off are ipsilateral). These two gallops are used by a variety of mammals, but the transverse gallop is epitomized by the horse and the rotary gallop by the cheetah. In this paper, we argue that the fundamental difference between these gaits is determined by which set of limbs, fore or hind, initiates the transition of the centre of mass from a downward-forward to upward-forward trajectory that occurs between the main ballistic (non-contact) portions of the stride when the animal makes contact with the ground. The impulse-mediated directional transition is a key feature of locomotion on limbs and is one of the major sources of momentum and kinetic energy loss, and a main reason why active work must be added to maintain speed in locomotion. Our analysis shows that the equine gallop transition is initiated by a hindlimb contact and occurs in a manner in some ways analogous to the skipping of a stone on a water surface. By contrast, the cheetah gallop transition is initiated by a forelimb contact, and the mechanics appear to have much in common with the human bipedal run. Many mammals use both types of gallop, and the transition strategies that we describe form points on a continuum linked even to functionally symmetrical running gaits such as the tölt and amble.

Compliance, actuation, and work characteristics of the goat foreleg and hindleg during level, uphill, and downhill running

We model the action of muscle-tendon system(s) about a given joint as a serial actuator and spring. By this technique, the experimental joint moment is imposed while the combined angular deflection of the actuator and spring are constrained to match the experimental joint angle throughout the stance duration. The same technique is applied to the radial leg (i.e., shoulder/hip-to-foot). The spring constant that minimizes total actuator work is considered optimal, and this minimum work is expressed as a fraction of total joint/radial leg work, yielding an actuation ratio (AR; 1 = pure actuation and 0 = pure compliance). To address work modulation, we determined the specific net work (SNW), the absolute value of net divided by total work. This ratio is unity when only positive or negative work is done and zero when equal energy is absorbed and returned. Our proximodistal predictions of joint function are supported during level and 15 degrees grade running. The greatest AR and SNW are found in the proximal leg joints (elbow and knee). The ankle joint is the principal spring of the hindleg and shows no significant change in SNW with grade, reflecting the true compliance of the common calcaneal tendon. The principal foreleg spring is the metacarpophalangeal joint. The observed pattern of proximal actuation and distal compliance, as well as the substantial SNW at proximal joints, minimal SNW at intermediate joints, and variable energy absorption at distal joints, may emerge as general principles in quadruped limb mechanics and help to inform the leg designs of highly capable running robots.

Modulation of proximal muscle function during level versus incline hopping in tammar wallabies (Macropus eugenii)

We examined the functional role of two major proximal leg extensor muscles of tammar wallabies during level and inclined hopping (12 degrees, 21.3% grade). Previous in vivo studies of hopping wallabies have revealed that, unlike certain avian bipeds, distal hindlimb muscles do not alter their force-length behavior to contribute positive work during incline hopping. This suggests that proximal muscles produce the increased mechanical work associated with moving up an incline. Based on relative size and architectural anatomy, we hypothesized that the biceps femoris (BF), primarily a hip extensor, and the vastus lateralis (VL), the main knee extensor, would exhibit changes in muscle strain and activation patterns consistent with increased work production during incline versus level hopping. Our results clearly support this hypothesis. The BF experienced similar activation patterns during level and incline hopping but net fascicle shortening increased (-0.5% for level hopping versus -4.2% for incline hopping) during stance when the muscle likely generated force. Unlike the BF, the VL experienced active net lengthening during stance, indicating that it absorbs energy during both level and incline hopping. However, during incline hopping, net lengthening was reduced (8.3% for level hopping versus 3.9% for incline hopping), suggesting that the amount of energy absorbed by the VL was reduced. Consequently, the changes in contractile behavior of these two muscles are consistent with a net production of work by the whole limb. A subsidiary aim of our study was to explore possible regional variation within the VL. Although there was slightly higher fascicle strain in the proximal VL compared with the distal VL, regional differences in strain were not significant, suggesting that the overall pattern of in vivo strain is fairly uniform throughout the muscle. Estimates of muscle work based on inverse dynamics calculations support the conclusion that both the BF and VL contribute to the additional work required for incline hopping. However, on a muscle mass-specific basis, these two muscles appear to contribute less than their share. This indicates that other hindlimb muscles, or possibly trunk and back muscles, must contribute substantial work during incline hopping.

Running stability is enhanced by a proximo-distal gradient in joint neuromechanical control

We currently know little about how animals achieve dynamic stability when running over uneven and unpredictable terrain, often characteristic of their natural environment. Here we investigate how limb and joint mechanics of an avian biped, the helmeted guinea fowl Numida meleagris, respond to an unexpected drop in terrain during running. In particular, we address how joint mechanics are coordinated to achieve whole limb dynamics. Based on muscle-tendon architecture and previous studies of steady and incline locomotion, we hypothesize a proximo-distal gradient in joint neuromechanical control. In this motor control strategy, (1) proximal muscles at the hip and knee joints are controlled primarily in a feedforward manner and exhibit load-insensitive mechanical performance, and (2) distal muscles at the ankle and tarsometatarso-phalangeal (TMP) joints are highly load-sensitive, due to intrinsic mechanical effects and rapid, higher gain proprioceptive feedback. Limb kinematics and kinetics during the unexpected perturbation reveal that limb retraction, controlled largely by the hip, remains similar to level running throughout the perturbed step, despite altered limb loading. Individual joints produce or absorb energy during both level and perturbed running steps, such that the net limb work depends on the balance of energy among the joints. The hip maintains the same mechanical role regardless of limb loading, whereas the ankle and TMP switch between spring-like or damping function depending on limb posture at ground contact. Initial knee angle sets limb posture and alters the balance of work among the joints, although the knee contributes little work itself. This distribution of joint function results in posture-dependent changes in work performance of the limb, which allow guinea fowl to rapidly produce or absorb energy in response to the perturbation. The results support the hypothesis that a proximo-distal gradient exists in limb neuromuscular performance and motor control. This control strategy allows limb cycling to remain constant, whereas limb posture, loading and energy performance are interdependent. We propose that this control strategy provides simple, rapid mechanisms for managing energy and controlling velocity when running over rough terrain.

External forces on the limbs of jumping lemurs at takeoff and landing

Ground reaction forces were recorded for jumps of three individuals each of Lemur catta and Eulemur fulvus. Animals jumped back and forth between a ground-mounted force plate and a 0.5-m elevated platform, covering horizontal distances of 0.5-2 m. In total, 190 takeoffs and 263 landings were collected. Animals typically jumped from a run up and into a run out, during which they gained or into which they carried horizontal impulse. Correspondingly, vertical impulses dominated takeoffs and landings. Peak forces were moderate in magnitude and not much higher than forces reported for quadrupedal gaits. This is in contrast to the forces for standing jumps of specialized leapers that considerably exceed forces associated with quadrupedal gaits. Force magnitudes for the lemur jumps are more comparable to peak forces reported for other quadrupeds performing running jumps. Takeoffs are characterized by higher hindlimb than forelimb peak forces and impulses. L. catta typically landed with the hindlimbs making first contact, and the hindlimb forces and impulses were higher than the forelimb forces and impulses at landing. E. fulvus typically landed with the forelimbs striking first and also bearing the higher forces. This pattern does not fully conform to the paradigm of primate limb force distribution, with higher hindlimb than forelimb forces. However, the absolute highest forces in E. fulvus also occur at the hindlimbs, during acceleration for takeoff.

Quantification of motor cortex activity and full-body biomechanics during unconstrained locomotion

Recent progress in the understanding of motor cortex function has been achieved primarily by simultaneously recording motor cortex neuron activity and the movement kinematics of the corresponding limb. We have expanded this approach by combining high-quality cortical single-unit activity recordings with synchronized recordings of full-body kinematics and kinetics in the freely behaving cat. The method is illustrated by selected results obtained from two cats tested while walking on a flat surface. Using this method, the activity of 43 pyramidal tract neurons (PTNs) was recorded, averaged over 10 bins of a locomotion cycle, and compared with full-body mechanics by means of principal component and multivariate linear regression analyses. Patterns of 24 PTNs (56%) and 219 biomechanical variables (73%) were classified into just four groups of inter-correlated variables that accounted for 91% of the total variance, indicating that many of the recorded variables had similar patterns. The ensemble activity of different groups of two to eight PTNs accurately predicted the 10-bin patterns of all biomechanical variables (neural decoding) and vice versa; different small groups of mechanical variables accurately predicted the 10-bin pattern of each PTN (neural encoding). We conclude that comparison of motor cortex activity with full-body biomechanics may be a useful tool in further elucidating the function of the motor cortex.

New technique for studying reaction forces during primate behaviors on vertical substrates

Recording reaction forces from primates during behaviors on vertical substrates, such as leaping, climbing, or biting trees, typically requires the design and construction of customized recording devices or mounting commercially available force platforms in a vertical position. The technical difficulties imposed by either option have hindered in vivo research on the kinetics of primate behaviors on vertical substrates. We describe a simple, inexpensive apparatus for recording forces from primate behaviors on vertical substrates. The apparatus includes an instrumented beam fastened directly to a horizontal force platform and a surrounding vertical substrate that does not contact the instrumented beam or platform. The contact piece at the end of the instrumented beam is positioned flush with the noninstrumented vertical substrate, and reaction forces elicited on this instrumented section are directed to the force platform. Because most of the vertical substrate is not instrumented, we can isolate and record forces from a single limb or jaw during a behavior. Biewener and Full ([1992] Biomechanics Structures and Positions: A Practical Approach; New York: Oxford University press, p. 45-73) gave seven criteria to consider when designing a customized force-recording device. Where appropriate, we tested if our apparatus met their criteria. The apparatus accurately records forces in three orthogonal directions, has low cross-talk, maintains a high frequency response, exhibits a linear response up to at least 200 Newtons, and displays a uniform response to a given force across the instrumented contact piece. Our design does not easily facilitate the identification of the point of force application. Therefore, joint moments cannot be easily calculated. This limitation, however, does not affect the apparatus's ability to accurately record the magnitude and direction of a force (as shown by other tests). We developed this apparatus to measure jaw forces during tree gouging in common marmosets (Callithrix jacchus), but the general design can be readily modified to study a variety of primate behaviors on vertical substrates.

Dynamics of leg muscle function in tammar wallabies (M. eugenii) during level versus incline hopping

The goal of our study was to examine whether the in vivo force-length behavior, work and elastic energy savings of distal muscle-tendon units in the legs of tammar wallabies (Macropus eugenii) change during level versus incline hopping. To address this question, we obtained measurements of muscle activation (via electromyography), fascicle strain (via sonomicrometry) and muscle-tendon force (via tendon buckles) from the lateral gastrocnemius (LG) and plantaris (PL) muscles of tammar wallabies trained to hop on a level and an inclined (10 degrees, 17.4% grade) treadmill at two speeds (3.3 m s(-1) and 4.2 m s(-1)). Similar patterns of muscle activation, force and fascicle strain were observed under both level and incline conditions. This also corresponded to similar patterns of limb timing and movement (duty factor, limb contact time and hopping frequency). During both level and incline hopping, the LG and PL exhibited patterns of fascicle stretch and shortening that yielded low levels of net fascicle strain [LG: level, -1.0+/-4.6% (mean +/- S.E.M.) vs incline, 0.6+/-4.5%; PL: level, 0.1+/-1.0% vs incline, 0.4+/-1.6%] and muscle work (LG: level, -8.4+/-8.4 J kg(-1) muscle vs incline, -6.8+/-7.5 J kg(-1) muscle; PL: level, -2.0+/-0.6 J kg(-1) muscle vs incline, -1.4+/-0.7 J kg(-1) muscle). Consequently, neither muscle significantly altered its contractile dynamics to do more work during incline hopping. Whereas electromyographic (EMG) phase, duration and intensity did not differ for the LG, the PL exhibited shorter but more intense periods of activation, together with reduced EMG phase (P<0.01), during incline versus level hopping. Our results indicate that design for spring-like tendon energy savings and economical muscle force generation is key for these two distal muscle-tendon units of the tammar wallaby, and the need to accommodate changes in work associated with level versus incline locomotion is achieved by more proximal muscles of the limb.

Substrate alters forelimb to hindlimb peak force ratios in primates

It is often claimed that the walking gaits of primates are unusual because, unlike most other mammals, primates appear to have higher vertical peak ground reaction forces on their hindlimbs than on their forelimbs. Many researchers have argued that this pattern of ground reaction force distribution is part of a general adaptation to arboreal locomotion. This argument is frequently used to support models of primate locomotor evolution. Unfortunately, little is known about the force distribution patterns of primates walking on arboreal supports, nor do we completely understand the mechanisms that regulate weight distribution in primates. We collected vertical peak force data for seven species of primates walking quadrupedally on instrumented terrestrial and arboreal supports. Our results show that, when walking on arboreal vs. terrestrial substrates, primates generally have lower vertical peak forces on both limbs but the difference is most extreme for the forelimb. We found that force reduction occurs primarily by decreasing forelimb and, to a lesser extent, hindlimb stiffness. As a result, on arboreal supports, primates experience significantly greater functional differentiation of the forelimb and hindlimb than on the ground. These data support long-standing theories that arboreal locomotion was a critical factor in the differentiation of the forelimbs and hindlimbs in primates. This change in functional role of the forelimb may have played a critical role in the origin of primates and facilitated the evolution of more specialized locomotor behaviors.

Effects of mass distribution on the mechanics of level trotting in dogs

The antero-posterior mass distribution of quadrupeds varies substantially amongst species, yet the functional implications of this design characteristic remain poorly understood. During trotting, the forelimb exerts a net braking force while the hindlimb exerts a net propulsive force. Steady speed locomotion requires that braking and propulsion of the stance limbs be equal in magnitude. We predicted that changes in body mass distribution would alter individual limb braking-propulsive force patterns and we tested this hypothesis by adding 10% body mass near the center of mass, at the pectoral girdle, or at the pelvic girdle of trotting dogs. Two force platforms in series recorded fore- and hindlimb ground reaction forces independently. Vertical and fore-aft impulses were calculated by integrating individual force-time curves and Fourier analysis was used to quantify the braking-propulsive (b-p) bias of the fore-aft force curve. We predicted that experimental manipulation of antero-posterior mass distribution would (1) change the fore-hind distribution of vertical impulse when the limb girdles are loaded, (2) decrease the b-p bias of the experimentally loaded limb and (3) increase relative contact time of the experimentally loaded limb, while (4) the individual limb mean fore-aft forces (normalized to body weight + added weight) would be unaffected. All four of these results were observed when mass was added at the pelvic girdle, but only 1, 3 and 4 were observed when mass was added at the pectoral girdle. We propose that the observed relationship between antero-posterior mass distribution and individual limb function may be broadly applicable to quadrupeds with different body types. In addition to the predicted results, our data show that the mechanical effects of adding mass to the trunk are much more complex than would be predicted from mass distribution alone. Effects of trunk moments due to loading were evident when mass was added at the center of mass or at the pelvic girdle. These results suggest a functional link between appendicular and axial mechanics via action of the limbs as levers.

Muscle force-length dynamics during level versus incline locomotion: a comparison of in vivo performance of two guinea fowl ankle extensors

For a terrestrial animal to move in the complex natural environment, the limb muscles must modulate force and work performance to meet changing mechanical requirements; however, it is not clear whether this is accomplished via a collective shift in function by all limb muscles, or a division of labor among limb muscles. Do muscles differ in their ability to modulate force-length contractile function to meet the mechanical demands of different locomotor tasks? We explore this question by examining the in vivo force-length performance of the guinea fowl Numida meleagris lateral gastrocnemius (LG) and digital flexor-IV (DF-IV), during level and incline locomotion. During level locomotion, the LG and DF-IV exhibit differing muscle fascicle strain patterns: the LG shortens by 10-15% while developing force, whereas the DF-IV undergoes a stretch-shorten cycle with large strain amplitudes and small net strains of 1-8%. Furthermore, the DF-IV operates at higher muscle stresses (92-130 kPa, compared to 23-39 kPa for LG) and possesses a longer tendon, which allows the DF-IV tendon to recover greater elastic energy than the LG tendon. During incline locomotion, these muscles contribute only one-third of the energy expected for their mass, with the DF-IV exhibiting high stride-to-stride variability in work output. While the stretch-shorten cycle of the DF-IV muscle may allow more economic force production, it also leads to large changes in work output with small changes in the relative timing of force and strain. Thus, while the primary determinants of LG work are net strain and mean force, the primary determinant of DF-IV work is the phase relationship between force and strain. Our results suggest that, in addition to influencing a muscle's mechanical performance during steady level locomotion, morphology also affects its capacity and mechanism for altering work output for different locomotor tasks.

Modelisation of an unspecialized quadruped walking mammal

Kinematics and structural analyses were used as basic data to elaborate a dynamic quadruped model that may represent an unspecialized mammal. Hedgehogs were filmed on a treadmill with a cinefluorographic system providing trajectories of skeletal elements during locomotion. Body parameters such as limb segments mass and length, and segments centre of mass were checked from cadavers. These biological parameters were compiled in order to build a virtual quadruped robot. The robot locomotor behaviour was compared with the actual hedgehog to improve the model and to disclose the necessary changes. Apart from use in robotics, the resulting model may be useful to simulate the locomotion of extinct mammals.

Loading conditions and cortical bone construction of an artiodactyl calcaneus

Customary nonuniform distributions of physiological bone strains are thought to evoke heterogeneous material adaptation in diaphyseal cortices of some limb bones. Recent studies of artiodactyl calcanei have suggested that the regional prevalence of specific mechanical strain features such as mode and magnitude correlate with specific variations in cortical bone ultrastructure, microstructure and mineralization. These data are also consistent with predictions of current algorithms of mechanically induced bone adaptation. However, detailed characterization of the customary functional strain environment of these bones is needed to understand better the mechanisms of these adaptations. An in vitro loading method and rosette strain gauges were used to record principal strains, maximum shear strains and principal strain angles at multiple locations on ten calcanei of adult male mule deer (Odocoileus hemionus hemionus). Each hind limb was fixed in an apparatus to mimic the mid-support phase of the gait and loaded via the Achilles tendon over a broad range of functional loads (0 to 2943 N). Strains were recorded on the craniolateral, craniomedial, caudal, medial and lateral cortices at mid-diaphysis. Loading variations included the progressive elimination of the ligament and tendon along the caudal calcaneus. The results showed that the cranial cortex experiences longitudinal compressive strains that are nearly equal to the principal minimum strains and that the caudal cortex receives longitudinal tensile strains that are nearly equal to the principal maximum strains. With a 981 N load, the mean principal compressive strain on the cranial cortex was −636+/−344 micro(ε) (mean +/− s.d., N=9) and the mean principal tensile strain on the caudal cortex was 1112+/−68 micro;(ε)x (N=9). In contrast to the cranial and caudal cortices, principal strains in the medial and lateral cortices displayed relatively large deviations from the longitudinal axis (medial, 24 degrees cranial; lateral, 27 degrees caudal). Although shear strains predominated at all gauge sites, variations in maximum shear strains showed no apparent regional pattern or consistent regional predominance. The plantar ligament and tendon of the superficial digital flexor muscle were shown to have important load-sharing functions. These results demonstrate that the functionally loaded artiodactyl calcaneus generally behaves like a cantilevered beam with longitudinal compression and tension strains predominating in opposing cranial and caudal cortices, respectively. Differences in osteon remodeling rates, osteon morphology and mineral content reported previously between the cranial and caudal cortices correlate, in part, with the magnitudes of the principal compressive and tensile strains, respectively. However, material differences that distinguish the medial and lateral cortices from the cranial and caudal cortices could not be primarily attributed to locally increased shear strains as previously suggested. Variations in osteon and/or collagen fiber orientation may correlate more strongly with principal strain direction.

Takeoff and landing forces of leaping strepsirhine primates

Knowledge of the forces animals generate and are exposed to during locomotion is an important prerequisite for understanding the musculoskeletal correlates of locomotor modes. We recorded takeoff and landing forces for 14 animals representing seven species of strepsirhine primates with a compliant force pole. Our sample included both specialized vertical clingers and leapers and more generalized species. Takeoff forces are higher than landing forces. Peak forces during acceleration for takeoff ranged from 6 to 12 times body weight, and the peak impact forces at landing are between 5 and 9 times body weight. There is a size-related trend in peak force magnitudes. Both takeoff and landing forces decrease with increasing body size in our sample of animals from 1 kg to over 5 kg. Peak forces increase with distance leapt. The distance effect is less clear, probably due to the narrow range of distances represented in our sample. A comparison of subadult and adult animals of two species of sifakas reveals a tendency for the young animals to exert relatively higher peak forces in comparison to their adult conspecifics. Finally, Lemur catta and Eulemur rubriventer, the "generalists" in our sample, tend to generate higher forces for equal tasks than the specialized vertical clingers and leapers (i.e., the indriids and Hapalemur).A broad-scale comparison of peak leaping forces and peak forces for quadrupedal and bipedal walking and running shows that leaping at small body size is associated with exceptionally high forces. Whereas relative forces (i.e., forces divided by body weight) decrease with increasing body mass for leaping, forces for walking and running do not change much with size. Leaping forces in our sample scale to (mass)(-1/3), which is consistent with expectations derived from geometric similarity models. Forces associated with other locomotor activities do not appear to follow this pattern. The very high forces found in strepsirhine leapers do not seem to be matched by bone robusticity beyond that documented for quadrupedal species.

Patterns of strain in the macaque ulna during functional activity

In vivo bone strain experiments were performed on the ulnae of three female rhesus macaques to test how the bone deforms during locomotion. The null hypothesis was that, in an animal moving its limbs predominantly in sagittal planes, the ulna experiences anteroposterior bending. Three rosette strain gauges were attached around the circumference of the bone slightly distal to midshaft. They permit a complete characterization of the ulna's loading environment. Strains were recorded during walking and galloping activities. Principal strains and strain directions relative to the long axis of the bone were calculated for each gauge site. In all three animals, the lateral cortex experienced higher tensile than compressive principal strains during the stance phase of walking. Compressive strains predominated at the medial cortex of two animals (the gauge on this cortex of the third animal did not function). The posterior cortex was subject to lower strains; the nature of the strain was highly dependent on precise gauge position. The greater principal strains were aligned closely with the long axis of the bone in two animals, whereas they deviated up to 45 degrees from the long axis in the third animal. A gait change from walk to gallop was recorded for one animal. It was not accompanied by an incremental change in strain magnitudes. Strains are at the low end of the range of strain magnitudes recorded for walking gaits of nonprimate mammals. The measured distribution of strains in the rhesus monkey ulna indicates that mediolateral bending, rather than anteroposterior bending, is the predominant loading regime, with the neutral axis of bending running from anterior and slightly medial to posterior and slightly lateral. A variable degree of torsion was superimposed over this bending regime. Ulnar mediolateral bending is apparently caused by a ground reaction force vector that passes medial to the forearm. The macaque ulna is not reinforced in the plane of bending. The lack of buttressing in the loaded plane and the somewhat counterintuitive bending direction recommend caution with regard to conventional interpretations of long bone cross-sectional geometry.

The design and performance of an experimental external fixation device with load transducers

It is becoming increasingly common that fracture healing is modelled in the laboratory with an osteotomy in the diaphysis of the ovine tibia. External fixation is often used to hold the bones in these models, presenting the problem that the loads on such devices are poorly understood. To help investigate this, a unilateral device has been developed which is capable of measuring the two components of load considered to be the most important, that of axial compression and bending in the plane of the fixator. The device was found to be a rigid system and easy to apply, with the in-vivo measurements being straightforward. The estimated limits of error of the compression transducer are +37.9 N and -21.4 N and those of the bending transducer are +3.6 Nm and -4.2 Nm. Preliminary measurements showed the maximum load during normal walking to 345 N compression and 28 Nm in-plane bending.

Energy comparison between trot, bound, and gallop using a simple model

In this paper, the dynamics of quadruped trot, gallop, and bound will be examined using a simple model for the quadruped. The body of the quadruped is modeled as a uniform bar and the legs are modeled by massless springs. It will be shown that symmetry can be used to study the locomotion of this system. Using symmetry, a technique will be developed to obtain periodic solutions for each of the gaits of the quadruped model. These periodic solutions will be computed at various speeds. The energy levels will be compared for each of the gaits. The exchange of energy between its different forms will be shown for different gaits. It will be shown that even without body flexibility, there are significant savings in energy due to gait transition from trot to gallop. The energy levels will be used to predict the trot-gallop transition speed. These results will be compared with the experimental results for horses and dogs.

Electromyography of back muscles during quadrupedal and bipedal walking in primates

Despite the extensive electromyographic research that has addressed limb muscle function during primate quadrupedalism, the role of the back muscles in this locomotor behavior has remained undocumented. We report here the results of an electromyographic (EMG) analysis of three intrinsic back muscles (multifidus, longissimus, and iliocostalis) in the baboon (Papio anubis), chimpanzee (Pan troglodytes), and orangutan (Pongo pygmaeus) during quadrupedal walking. The recruitment patterns of these three back muscles are compared to those reported for the same muscles during nonprimate quadrupedalism. In addition, the function of the back muscles during quadrupedalism and bipedalism in the two hominoids is compared. Results indicate that the back muscles restrict trunk movements during quadrupedalism by contracting with the touchdown of one or both feet, with more consistent activity associated with touchdown of the contralateral foot. Moreover, despite reported differences in their gait preferences and forelimb muscle EMG patterns, primates and nonprimate mammals recruit their back muscles in an essentially similar fashion during quadrupedal walking. These quadrupedal EMG patterns also resemble those reported for chimpanzees, gibbons and humans (but not orangutans) walking bipedally. The fundamental similarity in back muscle function across species and locomotor behaviors is consistent with other data pointing to conservatism in the evolution of the neural control of tetrapod limb movement, but does not preclude the suggestion (based on forelimb muscle EMG and spinal lesion studies) that some aspects of primate neural circuitry are unique.