Mechanics of locomotion and jumping in the forelimb of the horse (Equus): in vivo stress developed in the radius and metacarpus

Principal stresses acting in the midshafts of the radius and metacarpus of the horse were determined from in vivo strain recordings during locomotion and jumping. Ground forces and limb position were also recorded. Over a range of speed and gait the radius was subjected to considerable bending, whereas the metacarpus was loaded primarily in axial compression. As a result, peak stresses acting in the radius (maximum: –45 MN/m²) were consistently 50% greater than those acting in the metacarpus (maximum: –31 MN/m²). The increase in peak bone stress (radius: 119% and metacarpus; 114%) with increasing speed was matched by a 103% increase in the mass-specific vertical force ( A _v) exerted on the limb and a 55% decline in duty factor of the limb. The forelimb was closely aligned with the direction of ground force during the support phase (<9° when peak force acted) to minimize bending forces exerted on the distal limb bones. Hence, bending of the radius resulted mainly from axial forces acting about its longitudinal curvature. This was in contrast to the metacarpus, which is a much straighter bone.
Significantly greater stresses were recorded in each bone during jumping: –81 MN/m² in the radius and –53 MN/m² in the metacarpus. While the distribution of loading in the radius was similar to that during steady state locomotion, greater variability in the magnitude and/or distribution of metacarpal loading was observed between animals, largely due to differences in the orientation of the limb during takeoff and landing. These data demonstrate that the horse, despite its large size, maintains a safety factor of nearly 3–4 during peak performance.     

Increased SCE levels in Mediterranean Italian buffaloes affected by limb malformation (transversal hemimelia)

In recent years some buffalo farms in Campania have reported the birth of calves with limb malformation, especially with transversal hemimelia. We investigated 20 Mediterranean Italian buffaloes (8 males and 12 females) from one day to six months of age, of which 10 were affected by transversal hemimelia (group 1) and 10 were healthy controls (group 2). The following clinical and radiological patterns were observed in the malformed animals: hind limbs amputated, the right amputated off the second tarsus bones and the left amputated off the proximal epiphysis metatarsus, and the right thoracic limb hypoplasic (1 female); left hind limb amputated off the proximal epiphysis metatarsus (2 females and 1 male); left hind limb amputated off the third tarsus bones (1 female); left hind limb amputated off the tibia (1 female and 1 male); left hind limb amputated off the distal epiphysis metatarsus (1 female); left hind limb amputated off the first phalanx (1 male); right hind limb amputated off the proximal epiphysis metatarsus (1 male). In their malformed limbs all the animals presented more or less developed outlines of claws. The mean rate of SCE/cell in animals with transversal hemimelia was 8.80 +/- 3.19, that of the controls 6.61 +/- 2.73. The difference was statistically significant (P < 0.001).     

Optimum stiffness for leg bones

A limb bone will be lighter if it is made thinner. However, thinner bones are more flexible (for given length and shape of cross-section) so their muscles must shorten more to move the distal end of the bone against a resisting force. To shorten more, a muscle needs longer muscle fibres and so must be heavier. Thus a particular thickness for the bone will enable the combined mass of bone plus muscle to be minimized. Peak stresses due to bending moments, in bones that were optimized according to this criterion, would be about ±70 MPa. Stresses of about this magnitude have been found in leg bones of various mammals, in strenuous activities such as running and jumping. However, similar stresses might be predicted on grounds of strength requirements, to give adequate factors of safety.     

Scaling of the appendicular skeleton of the giraffe (Giraffa camelopardalis)

Giraffes have remarkably long and slender limb bones, but it is unknown how they grow with regard to body mass, sex, and neck length. In this study, we measured the length, mediolateral (ML) diameter, craniocaudal (CC) diameter and circumference of the humerus, radius, metacarpus, femur, tibia, and metatarsus in 10 fetuses, 21 females, and 23 males of known body masses. Allometric exponents were determined and compared. We found the average bone length increased from 340 ± 50 mm at birth to 700 ± 120 mm at maturity, while average diameters increased from 30 ± 3 to 70 ± 11 mm. Fetal bones increased with positive allometry in length (relative to body mass) and in diameter (relative to body mass and length). In postnatal giraffes bone lengths and diameters increased iso‐ or negatively allometric relative to increases in body mass, except for the humerus CC diameter which increased with positive allometry. Humerus circumference also increased with positive allometry, that of the radius and tibia isometrically and the femur and metapodials with negative allometry. Relative to increases in bone length, both the humerus and femur widened with positive allometry. In the distal limb bones, ML diameters increased isometrically (radius, metacarpus) or positively allometric (tibia, metatarsus) while the corresponding CC widths increased with negative allometry and isometrically, respectively. Except for the humerus and femur, exponents were not significantly different between corresponding front and hind limb segments. We concluded that the patterns of bone growth in males and females are identical. In fetuses, the growth of the appendicular skeleton is faster than it is after birth which is a pattern opposite to that reported for the neck. Allometric exponents seemed unremarkable compared to the few species described previously, and pointed to the importance of neck elongation rather than leg elongation during evolution. Nevertheless, the front limb bones and especially the humerus may show adaptation to behaviors such as drinking posture. J. Morphol. 276:503–516, 2015. © 2014 Wiley Periodicals, Inc.     

Symmetrical gaits of Cebus apella: implications for the functional significance of diagonal sequence gait in primates

Quadrupedal locomotion of primates is distinguished from the quadrupedalism of many other mammals by several features, including a diagonal sequence (DS) footfall used in symmetrical gaits. This presumably unique feature of primate locomotion has been attributed to an ancestral adaptation for cautious arboreal quadrupedalism on thin, flexible branches. However, the functional significance of DS gait remains largely hypothetical. The study presented here tests hypotheses about the functional significance of DS gait by analyzing the gait mechanics of a primate that alternates between DS and lateral sequence (LS) gaits, Cebus apella. Kinematic and kinetic data were gathered from two subjects as they moved across both terrestrial and simulated arboreal substrates. These data were used to test four hypotheses: (1) locomotion on arboreal supports is associated with increased use of DS gait, (2) DS gait is associated with lower peak vertical substrate reaction forces than LS gait, (3) DS gait is associated with greater forelimb/hind limb differentiation in force magnitudes, and (4) DS gait offers increased stability. Our results indicate that animals preferred DS gait on the arboreal substrate, and LS gait while on the ground. Peak vertical substrate reaction forces showed a tendency to be lower in DS gait, but not consistently so. Pole ("arboreal") forces were lower than ground forces in DS gait, but not in LS gait. The preferred symmetrical gait on both substrates was a grounded run or amble, with the body supported by only one limb throughout most of the stride. During periods of bilateral support, the DS gait had predominantly diagonal support couplets. This benefit for stability on an arboreal substrate is potentially outweighed by overstriding, its associated ipsilateral limb interference in DS gait and hind foot positioning in front of the hand on untested territory. DS gait also did not result in an optimal anchoring position of the hind foot under the center of mass of the body at forelimb touchdown. In sum, the results are mixed regarding the superiority of DS gait in an arboreal setting. Consequently, the notion that DS gait is an ancestral adaptation of primates, conditioned by the selection demands of an arboreal environment, remains largely hypothetical.     

An application of cineradiography to the study of locomotion in primates

The cineradiographic technique, whereby, at 64 frames/second, the successive positions of every bone segment of animals in motion can be accurately analyzed, was used to study the vertical leap of a Galago alleni from the ground position. This jump, 13 to 14 times the body length of the animal excluding the tail, is a record among primates challenged only by the tarsier. Such vertical leaps from the ground are a common mode of locomotion for the galago. Two different patterns were observed, a symmetrical and an asymmetrical jump. In the former, the two hind limbs move in the same manner and simultaneously; and the propulsive force is equally distributed in both limbs. In the latter (more frequent in our records), the animal shifts its weight onto one foot during the preparatory phase and lifts the other; thus, only one of the hind limbs is responsible for the launching. The angular variations of every knee and ankle articulation and the successive positions of the hind limb bones were measured and diagrammatically analyzed frame by frame. A short film was made to illustrate the cineradiographic technique; it cinematographically and cineradiographically records in successive sequence the galago's leap from the ground. The symmetrical and asymmetrical jumps are also schematically presented.     

The role of hind limb flexor muscles during swimming in the toad, Bufo marinus

Most work examining muscle function during anuran locomotion has focused largely on the roles of major hind limb extensors during jumping and swimming. Nevertheless, the recovery phase of anuran locomotion likely plays a critical role in locomotor performance, especially in the aquatic environment, where flexing limbs can increase drag on the swimming animal. In this study, I use kinematic and electromyographic analyses to explore the roles of four anatomical flexor muscles in the hind limb of Bufo marinus during swimming: m. iliacus externus, a hip flexor; mm. iliofibularis and semitendinosus, knee flexors; and m. tibialis anticus longus, an ankle flexor. Two general questions are addressed: (1) What role, if any, do these flexors play during limb extension? and (2) How do limb flexors control limb flexion? Musculus iliacus externus exhibits a large burst of EMG activity early in limb extension and shows low levels of activity during recovery. Both m. iliofibularis and m. semitendinosus are biphasically active, with relatively short but intense bursts during limb extension followed by longer and typically weaker secondary bursts during recovery. Musculus tibialis anticus longus becomes active mid way through recovery and remains active through the start of extension in the next stroke. In conclusion, flexors at all three joints exhibit some activity during limb extension, indicating that they play a role in mediating limb movements during propulsion. Further, recovery is controlled by a complex pattern of flexor activation timing, but muscle intensities are generally lower, suggesting relatively low force requirements during this phase of swimming.     

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).     

Functional differentiation of long bones in lorises

The external dimensions of the limb bones and the geometry of their midshaft cross-sections were determined for Loris tardigradus and Nycticebus coucang. Relative cortical thickness, cortical area, and second moment of area were calculated and contrasted with locomotor stresses. The difference in shape-related strength of the bones between the smaller- and the larger-bodied species is more pronounced than can be expected from stresses acting during normal locomotion. The Nycticebus skeleton has a much higher safety margin overall and seems to be dimensioned for infrequent but critical stresses of high magnitude. Lorisine gaits in general are characterized by low ground reaction forces, great mobility in all joints, and a nearly equal share in propulsion and weight-bearing by the fore- and hindlimb. Accordingly, the long bones of lorises (especially those of L. tardigradus) tend to be less rigid than those of other mammalian species (including other primates), they lack a preferential plane of higher bending strength, and femur and humerus do not differ markedly in their capacity to withstand mechanical stresses. External dimensions of the humerus and femur of the two African lorisine species parallel and corroborate these results. Some more general implications for the relationships between bone shape and locomotor stresses are also discussed.     

Skeletal growth and function in the California gull (Larus californicus)

Although the bones of rapidly growing animals are composed of weak tissue, they often must function in locomotor activity. We address the conflict between development and skeletal function by analysing the ontogeny of skeletal strength in the California gull, Larus californicus. Changes in shape and mechanical properties of the femur, tibia, tarsometatarsus, humerus, ulna and carpometacarpus were analysed in a complete post-hatching growth series. During post-hatching growth, strength and stiffness of the skeletal tissue increases six- to ten-fold. At hatching, long bones of the wing are relatively weak and they remain so throughout the major portion of the growth period. However, in the hind limb, relatively thick bones in juveniles compensate for the weak tissue such that the force required to break the bones remains constant relative to body mass. This difference between hind limb and wing parallels the development of locomotor function; young gulls begin to walk within a day or two of hatching, but they do not fly until they are fully grown. Thus, in the bones of the hind limb, the conflict between rapid growth and skeletal function is solved by negative allometry of bone thickness.
After young gulls reach adult size, the breaking strength of the wing bones increases three- to four-fold, the mass of the pectoralis muscle triples and the surface area of the wing doubles. The one aspect of wing development that is not delayed until shortly before fledging is linear growth of the bones. Bones of the wing increase in length at a rapid and relatively constant rate from the time of hatching to the attainment of adult size. Relatively early initiation of linear growth of the wing bones suggests that the rate at which bones grow in length may be the rate limiting factor in wing development.     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

A possible energy-saving role for the major fascia of the thigh in running quadrupedal mammals

Experiments were performed to determine the mechanical importance of the fascia lata in stopping the hind limb during its rearward extension and reversing the direction of leg swing. Samples of fascia lata from a number of different mammals were subjected to tensile tests. Tangent Young's moduli reached about 0.5 GPa and stresses at failure about 50 MPa for fascia from each of the species examined. Energy losses incurred in a loading-unloading cycle were generally about 20%. The moment arms of the fascia lata, in combination with its muscle, about the hip and knee joints were determined and the extension of the fascia lata while its muscle is active was estimated. Calculations suggest that the fascia lata could help to reverse the backward swing of the hind limb by recoiling elastically shortly after the foot leaves the ground. Substantial savings of internal kilnetic energy could be made.     

A cockroach that jumps

We report on a newly discovered cockroach (Saltoblattella montistabularis) from South Africa, which jumps and therefore differs from all other extant cockroaches that have a scuttling locomotion. In its natural shrubland habitat, jumping and hopping accounted for 71 per cent of locomotory activity. Jumps are powered by rapid and synchronous extension of the hind legs that are twice the length of the other legs and make up 10 per cent of the body weight. In high-speed images of the best jumps the body was accelerated in 10 ms to a take-off velocity of 2.1 m s(-1) so that the cockroach experienced the equivalent of 23 times gravity while leaping a forward distance of 48 times its body length. Such jumps required 38 μJ of energy, a power output of 3.4 mW and exerted a ground reaction force through both hind legs of 4 mN. The large hind legs have grooved femora into which the tibiae engage fully in advance of a jump, and have resilin, an elastic protein, at the femoro-tibial joint. The extensor tibiae muscles contracted for 224 ms before the hind legs moved, indicating that energy must be stored and then released suddenly in a catapult action to propel a jump. Overall, the jumping mechanisms and anatomical features show remarkable convergence with those of grasshoppers with whom they share their habitat and which they rival in jumping performance.     

Torsion and Antero-Posterior Bending in the In Vivo Human Tibia Loading Regimes during Walking and Running

Bending, in addition to compression, is recognized to be a common loading pattern in long bones in animals. However, due to the technical difficulty of measuring bone deformation in humans, our current understanding of bone loading patterns in humans is very limited. In the present study, we hypothesized that bending and torsion are important loading regimes in the human tibia. In vivo tibia segment deformation in humans was assessed during walking and running utilizing a novel optical approach. Results suggest that the proximal tibia primarily bends to the posterior (bending angle: 0.15°–1.30°) and medial aspect (bending angle: 0.38°–0.90°) and that it twists externally (torsion angle: 0.67°–1.66°) in relation to the distal tibia during the stance phase of overground walking at a speed between 2.5 and 6.1 km/h. Peak posterior bending and peak torsion occurred during the first and second half of stance phase, respectively. The peak-to-peak antero-posterior (AP) bending angles increased linearly with vertical ground reaction force and speed. Similarly, peak-to-peak torsion angles increased with the vertical free moment in four of the five test subjects and with the speed in three of the test subjects. There was no correlation between peak-to-peak medio-lateral (ML) bending angles and ground reaction force or speed. On the treadmill, peak-to-peak AP bending angles increased with walking and running speed, but peak-to-peak torsion angles and peak-to-peak ML bending angles remained constant during walking. Peak-to-peak AP bending angle during treadmill running was speed-dependent and larger than that observed during walking. In contrast, peak-to-peak tibia torsion angle was smaller during treadmill running than during walking. To conclude, bending and torsion of substantial magnitude were observed in the human tibia during walking and running. A systematic distribution of peak amplitude was found during the first and second parts of the stance phase.     

Load transfer mechanics between trans-tibial prosthetic socket and residual limb--dynamic effects

The effects of inertial loads on the interface stresses between trans-tibial residual limb and prosthetic socket were investigated. The motion of the limb and prosthesis was monitored using a Vicon motion analysis system and the ground reaction force was measured by a force platform. Equivalent loads at the knee joint during walking were calculated in two cases with and without consideration of the material inertia. A 3D nonlinear finite element (FE) model based on the actual geometry of residual limb, internal bones and socket liner was developed to study the mechanical interaction between socket and residual limb during walking. To simulate the friction/slip boundary conditions between the skin and liner, automated surface-to-surface contact was used. The prediction results indicated that interface pressure and shear stress had the similar double-peaked waveform shape in stance phase. The average difference in interface stresses between the two cases with and without consideration of inertial forces was 8.4% in stance phase and 20.1% in swing phase. The maximum difference during stance phase is up to 19%. This suggests that it is preferable to consider the material inertia effect in a fully dynamic FE model.     

Stresses exerted in the hindlimb muscles of common chimpanzees (Pan troglodytes) during bipedal locomotion

Recent studies have indicated that chimpanzee bipedality is mechanically inefficient and dynamically unlike that of humans, thus undermining the chimpanzee analogy for mechanical aspects of the early evolution of hominid bipedalism. This paper continues this theme by measuring the forces and stresses engendered by the muscles during bipedal locomotion, for an untrained chimpanzee and for data from chimpanzees which have been encouraged to walk bipedally, presented in the literature. Peak stresses in the triceps surae were lower for the untrained chimpanzee than for the trained subjects because during the late stance phase, when peak ankle moments occur, the centre of pressure of the ground reaction force on the foot of the untrained chimpanzee stayed close to the ankle joint. In contrast, for the trained subjects it moved closer to the toes, as in human bipedalism. Quadriceps and hip extensor stresses are approximately 30% larger for the untrained chimpanzee than for the trained subjects, because the trained chimpanzees walked with a more erect posture. These results may reflect the way in which muscles can develop in response to training, since research on humans has shown that muscle physiological cross-sectional area increases as a result of exercise, resulting in smaller stresses for a given muscle force. During a slow walk, untrained chimpanzees were found to exert far greater muscle stresses than humans do when running at moderate speed, particularly in the muscles that extend the hip, because of the bent-hip, bent-knee posture.     

Functional differentiation of trailing and leading forelimbs during locomotion on the ground and on a horizontal branch in the European red squirrel (Sciurus vulgaris, Rodentia)

Mammalian locomotion is characterized by the frequent use of in-phase gaits in which the footfalls of the left and right fore- or hindlimbs are unevenly spaced in time. Although previous studies have identified a functional differentiation between the first limb (trailing limb) and the second limb (leading limb) to touch the ground during terrestrial locomotion, the influence of a horizontal branch on limb function has never been explored. To determine the functional differences between trailing and leading forelimbs during locomotion on the ground and on a horizontal branch, X-ray motion analysis and force measurements were carried out in two European red squirrels (Sciurus vulgaris, Rodentia). The differences observed between trailing and leading forelimbs were minimal during terrestrial locomotion, where both limbs fulfill two functions and go through a shock-absorbing phase followed by a generating phase. During locomotion on a horizontal branch, European red squirrels reduce speed and all substrate reaction forces transmitted may be due to the reduction of vertical oscillation of the center of mass. Further adjustments during locomotion on a horizontal branch differ significantly between trailing and leading forelimbs and include limb flexion, lead intervals, limb protraction and vertical displacement of the scapular pivot. Consequently, trailing and leading forelimbs perform different functions. Trailing forelimbs function primarily as shock-absorbing elements, whereas leading forelimbs are characterized by a high level of stiffness. This functional differentiation indicates that European red squirrels ‘test’ the substrate for stability with the trailing forelimb, while the leading forelimb responds to or counteracts swinging or snapping branches.     

Ontogeny of limb force distribution in squirrel monkeys (Saimiri boliviensis): insights into the mechanical bases of primate hind limb dominance

The distribution of peak vertical forces between the forelimbs and the hind limbs is one of the key traits distinguishing primate quadrupedal locomotion from that of other mammals. Whereas most mammals generate greater peak vertical forelimb forces, primates generate greater peak vertical hind limb forces. At the ultimate level, hind limb dominance in limb force distribution is typically interpreted as an adaptation to facilitate fine-branch arboreality. However, the proximate biomechanical bases for primate limb force distribution remain controversial. Three models have been previously proposed. The Center of Mass (COM) Position model attributes primates’ unique mode of limb loading to differences in the position of the whole-body COM relative to the hands and feet. The Active Weight Shift model asserts that primates actively redistribute body weight to their hind limbs by pitching the trunk up via the activation of hind limb retractor muscles. Finally, the Limb Compliance model argues that primates selectively mitigate forelimb forces by maintaining a compliant forelimb and a flat shoulder trajectory. Here, a detailed dataset of ontogenetic changes in morphology and locomotor mechanics in Bolivian squirrel monkeys (Saimiri boliviensis) was employed as a model system to evaluate each of these proposed models in turn. Over the first 10 months of life, squirrel monkeys transitioned from forelimb dominant infants to hind limb dominant juveniles, a change that was precipitated by decreases in peak vertical forelimb forces and increases in peak vertical hind limb forces. Results provided some support for all three of the models, although the COM Position and Active Weight Shift models were most strongly supported by the data. Overall, this study suggests that primates may use a variety of biomechanical strategies to achieve hind limb dominance in limb force distribution.     

The mechanics of jumping by a dog (Canis familiaris)

A force platform has been used to obtain records of the forces exerted on the ground by an Alsatian dog, during take-off for running long jumps and standing scale jumps. The records have been analysed in conjunction with cinematograph film, taken simultaneously, and anatomical data. Stresses in the principal muscles of the hind limb, and in the triceps, have been calculated and the values obtained are compared with the stresses found by other investigators in isometric experiments with excised mammal muscles. Stresses in certain tendons and bones have been calculated, and the values obtained are compared with published values for the strength of tendon and bone. Evidence is presented that the gastrocnemius and plantaris muscles behave, in take-off for a jump, essentially as passive elastic bodies. Most of the elastic energy is probably stored in their tendons. A tendency for distal limb muscles to be pinnate, with much shorter fibres than proximal limb muscles, is noted and discussed.