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Quadrupedal Mechanics - Anatomy & Physiology (view source)
Revision as of 09:48, 1 May 2013
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There is a safety factor that limits the rate of limb movement in larger animals. In order to support static loads, both the tissues supporting the animal, and the tissues propelling it, have no need for disproportionate development.
There is a safety factor that limits the rate of limb movement in larger animals. In order to support static loads, both the tissues supporting the animal, and the tissues propelling it, have no need for disproportionate development.
=='''The design of the vertebral trunk'''==
==='''The trunk is a horizontal beam
The body of the dog shown in Fig. 9.1 a is represented mechanically by a beam, the vertebral column A–D, 45 cm long with a uniformly distributed load of 0.2 kg.cm–2 (the neck and trunk), and a concentrated load cranially of 2 kg (the head). The total weight is therefore 11 kg. With the fore and hindlimbs each represented each by one simple strut and placed as shown at B and C, the opposing reaction forces can be calculated as 7.9 kg for the forelimbs and 3.1 kg for the hindlimbs. This turns out to be approximately the situation in a real dog in which the weight borne by the forelimb is about twice that borne by the hindlimb. Since the weight of the hindlimb of the dog is about the same as that of the forelimb, one must conclude that the weight of hindlimb in excess of what is needed for postural support is available for propulsion; in other words the forelimb and the hindlimb of the dog differ in their postural and propulsive roles. The forelimb supports and balances, the hindlimb pushes.
In Fig. 9.1c, muscles preventing bending include (a) the epaxial muscles of the neck and thorax, (b) the hypaxial muscles of the thorax, and (c), the hypaxial muscles of the lumbar region. Props assisting the action of these muscles and the ligaments shown are (p) the spinous process of the axis, (q) the spinous process of the first thoracic vertebra (together with adjacent spinous processes), (r) the spinous process of the anticlinal vertebra (eleventh thoracic), (s) the sacrum and (t) the costal arch.
(u) and (v) are the forelimb and hindlimb respectively. Note that the shape of the vertebral column is opposite to that of the bending moments shown in Fig. 9.1b for the horizontal beam A — D.
:::::'''Fig 9.1 Bending in the vertebral column'''
:::::The trunk of a dog is represented in Fig. 9.1a by a horizontal beam A — D, 45 cm long with a uniformly distributed load of 0.2 kg.cm-1, together with a concentrated load cranially of 2 kg (the head). The total weight is 11 kg. With the limbs placed as shown, the opposing reaction forces are 7.9 kg in the forelimb and 3.1 kg in the hindlimb. Bending moments along the vertebral column are shown graphically in Fig. 9.1b.
==='''Forces along the beam'''===
The skeleton of the trunk is a row of separate bones, the vertebral column, on its own hardly a stable bridge. Its rigidity is maintained to a large extent by a compressive force produced in the massive muscle surrounding the column (Fig. 9.2). As a bridge, therefore, this structure is comparable to prestressed concrete. We have already seen that the trabecular network is oriented axially within the vertebral bodies, to resist the tensile stress (Fig. 3.2). When the axial muscles are relaxed as during anesthesia, the vertebral column is no longer rigid.
Rigidity of the vertebral column is attained also by the supraspinous and dorsal and ventral longitudinal ligaments (Figs. 9.2 and 9.3) and by the shape of the synovial intervertebral (zygapophyseal) joints.
:::::'''Fig 9.2 Transverse section of a pig at the thoracolumbar junction'''
:::::Caudal aspect, showing the intervertebral joint and the structures supporting the vertebral column.
==='''The effect of gravity on the beam'''===
Opposing this rigidity are bending moments that are a parabolic function of x, the distance in cm from A along the horizontal beam, and can be calculated for any value of x (Fig. 9.1 b). The bending moment in a ventrally concave sense is maximal at B, and the bending in a dorsally concave sense is maximal at about two-thirds the distance between B and C. The beam is subjected to no bending at two points between B and C. At some points, bending is not as much a problem as it is in others. This is compensated for in several ways, depending on the location.
==='''Improving the beam with good engineering'''===
Bending in a ventrally concave sense is opposed by first altering the shape of the beam to produce a dorsally concave curve at B (Fig. 9.1 c), and secondly by providing a system of struts, the spinous processes of the cervical and thoracic vertebrae at B and the sacrum at C, with stays, the nuchal ligament and the dorsal muscles of the neck at B and the sacro-tuberous ligament at C. Bending in a dorsally concave sense is opposed again by altering the shape of the beam, by providing a ventrally concave curve in the thoracolumbar region, and a series of struts, the costal arch, with stays, the ventral thoracic and abdominal muscles.
==='''Inclined spinous processes'''===
We can tell the direction of the forces on the spinous processes of the vertebrae by the way they lean, as you can easily tell in which direction the contestants in a tug-of-war are pulling, and resisting being pulled. Mechanical struts are more effective when a force is applied to them at an acute angle rather than a right angle. Therefore, the tall spines of the cranial thoracic vertebrae slope caudally. In the cat, this occurs as far caudally as the tenth thoracic vertebrae (Fig. 8.2), and the eleventh in the dog (Fig. 9.1 c).
:::::'''Fig 9.3 Median section of an intervertebral joint in the thoracic region'''
:::::Structures are shown which resist bending or hydrostatically distribute a uniform compression stress on the vertebral bodies.
==='''Flexibility of the vertebral column'''===
Apart from the joint between the first two cervical vertebrae, the intervertebral joints are not synovial joints. It is important that joints in a column under compression should be able to distribute pressure evenly over the opposing surfaces of the vertebral bodies, regardless of the angle of the joint. Intervertebral movement and even pressure distribution are achieved hydrostatically by the nucleus pulposus between each body (Figs. 9.2, 9.3). The change in shape of this mucoprotein gel with movement of the joint is accommodated by the annulus fibrosis, a lamellar arrangement of collagen fibres. The lamellae pass from vertebra to vertebra with their fibres crossing each other obliquely. They are therefore constructed to withstand the tensile stress imposed by the bending of the vertebral column, and also to prevent rupture of the nucleus pulposus. The mechanical and morphological concept suggested by the term intervertebral disc is misleading.
==='''This rigid beam can be flexible'''
In the dog, the maximum movement occurs between the segments around the tenth and the eleventh thoracic vertebrae. These segments are the most vulnerable to the injury of intervertebral structures. This is especially so in dogs with short legs which must use their vertebral column to a greater extent for propulsion than long legged dogs.
The flexibility of the vertebral column varies between species. A galloping horse maintains an almost rigid back (Fig. 9.4 a). This is also true for some of the fastest terrestrial animals, the gazelles and antelopes, some of which are small (Fig. 9.4 b). This is in contrast with the cheetah (Fig. 9.4 c). The big cats, which have flexible vertebral columns, spend little of their time standing, as compared with herbivores of equivalent size, which have more rigid columns. The axial muscles of herbivores are presumably more postural in function than those of carnivores and the smaller animals.
:::::'''Fig 9.4 Flexibility of the vertebral column in galloping animals'''
:::::The diagrams on the left represent full extension and the right side, full flexion of the vertebral column. The horse (a) and the gazelle (b) do not flex their backs appreciably, in contrast with the cheetah, (c).
==='''The vertebral column in locomotion'''===
The locomotory apparatus of the trunk is driven by the caudal epaxial muscles, notably the longissimus muscle (Fig. 9.2) and its attachments. In the species in which the apparatus is well developed, such as rodents, felids and canids, the attachments of the longissimus muscle to the spinous and transverse processes of the caudal thoracic and lumbar vertebrae are functionally strengthened by an angling of these processes away from the direction of tension. Thus, the transverse processes of the lumbar vertebrae slope cranially and ventrally. For the spinous processes, the effect is opposite to that seen in the cranial segments of the vertebral column where they slope caudally against the tension in the dorsal stays of the cervicothoracic region (Fig. 9.1 c). There is therefore an anticlinal vertebra, which represents the changing point (Fig. 8.2). In species that presumably do not use their vertebral column effectively to lengthen the hindlimb pendulum in locomotion, an anticlinal vertebra is absent.
We can now proceed to consider the action of the trunk and limbs as used by quadrupeds in performing unusual tasks.
=='''Locomotion'''==
==='''The standing quadruped'''===
The location of the centre of gravity of a horse is shown in Fig. 10.1. In the horse, 55% of the weight of the body is supported by the forelimbs and 45% by the hindlimbs. A horse usually rests one hindlimb while standing, but can do so for a forelimb only with difficulty. Relatively more weight is presumably supported by the forelimb of the bison and by the hindlimb of the rabbit (Fig. 10.2). The dog carries two thirds of its weight on its forelimbs and one third on its hindlimbs (Fig. 9.1).
:::::'''Fig 10.1 Location of the centre of gravity of a horse'''
:::::This is found in a transverse plane immediately caudal to the xiphoid process, and in a dorsal plane between the ventral and middle thirds of the trunk.
:::::'''Fig 10.2 Species differences in the location of the centre of gravity'''
:::::Compare these probable locations in the bison (a) and rabbit (b) with that determined for the horse in Fig. 10.1.
==='''Using the head to change the centre of gravity'''===
The function of the limbs as struts in supporting the trunk, and the function of the trunk as a supporting beam, have already been discussed. The remaining major bulk of the body, the head and neck, is also important in the standing quadruped because of its influence on the centre of gravity. Raising the head will bring it nearer to the trunk in the dorsal plane, and lowering it to bring the neck parallel to the trunk axis will increase this distance. Thus raising the head moves the centre of gravity caudally, removing weight from the forelimbs, and lowering it moves the centre of gravity cranially, increasing weight on the forelimbs (Fig. 10.3). Thus when a lame forelimb takes weight, the head is raised to relieve it. When one wishes to lift a forefoot of a horse or ox, its head should be raised and move laterally away from the foot to be lifted. On the other hand, it should be lowered with a hindfoot is to be lifted. An animal can be prevented from kicking with its hindlimb by holding its head high.
:::::'''Fig 10.3 Use of the head and neck to alter the centre of gravity'''
:::::The horse can lift a forefoot when the head is raised (a), and a hindfoot when the head is lowered.
:::::'''Fig 10.4 Curvature of the vertebral column in the sitting cat'''
:::::The shape of the thoracic cage (doted outline) is maintained by bending the vertebral column predominantly near the thoracolumbar junction.
==='''Motion without change of location'''===
The natural manner in which each species moves into a sitting or lying position and back to a standing position should be observed in normal animals. Assistance to animals incapacitated by disease or narcosis should be given in such a way as to enable the animal to complete its task in its natural manner.
'''Sitting down:''' Only animals with a vertebral column flexible enough normally adopt a sitting position. It is a usual position for the dog and cat (Fig. 10.4), an occasional one for the pig, and a possible although a very unusual one for cattle.
'''Lying down:''' From the standing position, the dog, cat and pig adopt a sitting position first. They lie in ventral recumbency with all four limbs tucked underneath or the hindlimbs placed to one side. Cattle and sheep first raise their head to shift the centre of gravity caudally, and then flex their carpal joints one after the other while bringing the centre of gravity cranially by lowering the head. The cranial part of the trunk is now supported with the carpal joints on the ground. The hindlimbs are now placed as far as possible under the trunk, and the caudal part of the trunk is dropped to the ground with the hindlimbs to one side. Finally, the carpal joints and elbows are flexed to lower the sternum to the ground. The horse arches its back, brings its four limbs underneath the trunk, lowers its head, flexes its limbs and drops heavily to one side.
'''Standing up:''' The smaller the animal, the more easily it can spring to its feet with a sudden back movement, but even horses can manage to do this. A slower, more deliberate movement is, for the dog, cat and pig, essentially the reverse process of lying down. Cattle and sheep raise themselves up on to their hindlimbs first, then on to their flexed carpuses. The horse rolls its trunk to sternal recumbency, collects its four legs underneath, and then protracts and extends its forelimbs, raising its cranial trunk before its caudal trunk, by pushing its weight over its forelimbs with a thrust from the hindlimbs.
'''Standing on hindlimbs:''' In order to achieve this, the centre of gravity must lie vertically above the hindfeet (Fig. 10.5 a, b). This is easier for horses than cattle. Horses can prance and kick with their forelimbs, but cattle cannot. A copulating bull can maintain the position only briefly, and uses the cow for support. Standing on hindlimbs is especially easy for animals with a more caudally located centre of gravity (Fig. 10.2 b).
:::::'''Fig 10.5 Stable positions for the horse on its hindlimbs'''
:::::Both in rearing (a) and in the levade (b), the centre of gravity of the horse lies over the hindfeet.
:::::'''Fig 10.6 Propulsion and friction forces'''
:::::The insertion of a plate between the hose and the ground enables the forces acting on the body during a propulsive movement of the hindlimbs during the gallop to be visualised.
==='''Propulsive force'''===
A propulsive force, applied to the limb to retract it, propels the animal over the ground. Opposing the propulsive force is friction force, acting between the animal body and the ground. It is the friction force that acts in the direction of movement. This is best visualised by interposing a plate between the animal and the ground (Fig. 10.6). When there is no friction between the plate and the ground, the propulsive force accelerates the plate and not the animal body. If the friction force equals the propulsion force, the plate remains at rest, and the animal is accelerated. Friction, which is usually thought to oppose motion, is essential for locomotion. The construction of the surface contact with the ground is vitally important and is often a source of breakdown in running animals, just as it is for motor vehicles.
In animals that use their vertebral column in running, the fore and hindlimb pendulums swing about a pivot near the thoracolumbar junction (Fig. 10.7). Axial muscles and extrinsic limb muscles acting over this pivot produce the propulsive thrust.
:::::'''Fig 10.7 The propulsive apparatus of the greyhound'''
:::::(a) Hindlimb. Retraction is brought about by the extensors of the vertebral column (x, m. longissimus and its dorsal aponeurosis) and the extensors of the hip (y, the middle gluteal muscle and z, the caudal thigh muscles).
:::::(b) Forelimb. Retraction is brought about by the flexors of the vertebral column (w, the external abdominal oblique muscle and x, rectus abdominis), and suitably placed muscles of the forelimb (y, latissimus dorsi and z, the deep pectoral muscle).
==='''Gaits'''===
Any continued movement of a quadruped over the ground necessitates a pattern of limb movement. Such a pattern is called a gait. There are obviously many possible ways of moving four limbs in relation to one another. Several of these may be exploited by a single species, and quadrupeds use many different gaits as a whole. When it is realised that 27 gait formulas have been recorded for the walk of the horse, and that this is not the only gait used by this species, the complexity of this subject is apparent. This account is limited to a description of the simple extremes of gait types, in the belief that these can be used to interpret the locomotory patterns of animals in real situations.
==='''Symmetrical gaits'''===
In considering a pair of forelimbs or hindlimbs, the sequence of footfalls may be symmetrical, that is, the interval between footfalls of right and left feet, and left and right feet, is the same. A human in normal walking uses such a symmetrical gait. Alternatively, the sequence of footfalls may be asymmetrical; the interval between footfalls of right and left feet, and left and right feet, is unequal. A child while “skipping” uses such an asymmetrical gait.
Symmetrical gaits of quadrupeds include the walk, trot, and pace. Asymmetrical gaits include the various types of gallop.
==='''The slow walk'''===
For one limb to be lifted slowly, the centre of gravity must lie within a triangle formed by the remaining three feet (Fig. 10.8). The most stable form of progression will therefore have three feet on the ground at any one time, and the centre of gravity shifts with the limb movement. The animal can stop at any instant without falling over. In animals in which the centre of gravity lies cranial to the transverse plane midway between the fore and hindlimbs, (Figs. 10.1 and 10.2 a), either hindlimb can be lifted without lateral change in the centre of gravity. However, such lateral movement is necessary to lift the forelimbs, and will be assisted by alternating movements of the head, neck and trunk (Fig. 10.9).
All animals use the slow walk at times when stability is important, for example when walking over rough terrain and by animals bearing awkward loads. It is visualised by a gait diagram in Fig. 10.10 a.
:::::'''Fig 10.8 Support triangles'''
:::::When a horse stands on all four feet, its centre of gravity lies as shown diagrammatically in dorsal view (a), cranial to the diagonals between the feet. Either hindfoot can now be lifted without change in weight distribution, because the centre of gravity lies within the triangle of support formed by the other three feet (b, c). Raising the head as in Fig.10.3 a directs the centre of gravity caudally. In (d), either forefoot can now be lifted. The centre of gravity need not be directed so far caudally if the head deviates to the side; if it deviates to the left, the right forefoot can be lifted (e).
:::::'''Fig 10.9 Head, neck, trunk and tail movements during the slow walk'''
:::::If protraction of the left hind limb in (a) produces the axial displacement shown in (b), the left forefoot can be lifted and the limb protracted. Forelimb protraction straightens the body axis and prepares it for the same movement on the opposite side of the body (c, d). Using this slow gait, even a highly adapted cursorial animal uses to some extent the same axial movements for locomotion as an animal with only rudimentary limbs.
==='''The fast walk'''===
If the sequence in the slow walk is speeded up to any extent, the next foot in the sequence will be off the ground before the previous limb moved has contacted the ground. Thus, for a time, there are only two feet left on the ground (Fig. 10.10 b). The animal would fall over if stopped at certain stages of the cycle. Stability is achieved by a dynamic rather than a static equilibrium. For the heaviest quadrupeds, such as elephants, the fast walk represents the greatest degree of static instability allowable, and it is their fastest gait. Horses, and in particular some breeds such as the Tennessee Walking Horse, can be trained to perform a variety of styles of fast walk with names such as "paso", "slow gait", "running walk", "rack" and "plantation gait", useful because of the smoothness for the rider.
:::::'''Fig 10.10 Extreme forms of symmetrical gaits of the horse'''
:::::From a, b to c or a, b to d there are progressively shorter periods of contact of each foot with the ground.
:::::All these gaits are symmetrical because the time interval between footfalls of pairs of forefeet or hindfeet is always one half of a stride interval. Thus there is symmetry between right and left sides of the body. Pale blue horseshoe = left footfall; Dark blue horseshoe = right footfall.
==='''Two–beat symmetrical gaits'''===
The walk is a four–beat gait because the limb movements are unpaired; each foot hits the ground separately. Two–beat symmetrical gaits are possible if a forefoot and hindfoot pair hit the ground together. These pairs can be either contralateral or ipsilateral. The two–beat symmetrical gait in which a forefoot contact the ground at the same time as a contralateral hindfoot is the trot. A trot can be derived from a fast walk by lengthening the period of diagonal support to such an extent that there is no period of unilateral support (Fig. 10.10 c).
==='''The trot'''===
In the trot, there is no contact with the ground between footfalls. The whole trunk therefore rises at the changeover, making it an uncomfortable gait for the rider. The vertebral column remains straight, and the head and neck move vertically in the median plane. The trot is preferred to the other two–beat symmetrical gait, the pace, by animals that have short legs and heavy heads. It is a natural gait for all horses and other ungulates as well as carnivores use it extensively. Longer legged dogs can still trot if they avoid interference between their ipsilateral forefeet and hindfeet by turning the axis of the body slightly from the direction of travel.
==='''The pace'''===
A pace is derived from a fast walk by lengthening the period of unilateral support until there is no period of diagonal support (Fig. 10.10 d). Ipsilateral feet then meet the ground together. Of the few animals that pace, all are long legged, and thence avoid the interference with their limbs that would occur if they trotted. The pace is natural to the giraffe the camel and to long legged breeds of dogs. In horses, it is generally not a natural gait but is acquired by training for harness racing. Pacing horses run slightly faster than trotters.
==='''Asymmetrical gaits'''===
When the footfalls of a pair of forefeet or hindfeet are unevenly spaced in time, the gait is asymmetrical. Symmetrical gaits are all some variant of the gallop, which is a general term. The beat is therefore composed of couplets, separated by pauses, and one foot is a leading foot. For the horse at least, the leading foot for the forelimbs is conventionally the second foot of the couplet to strike the ground (Fig. 10.11 c: 6th stage). The leading forelimb is always on the inside of a turn (Fig. 10.12). A galloping horse changes its lead during the stage when both forelimbs are off the ground (Fig. 10.11: 2nd stage). It may be necessary for a horse to change lead during a jump in order to prepare for a turn immediately on landing.
:::::'''Fig 10.11 Forms of asymmetrical gaits'''
:::::All these gaits are asymmetrical because the left forefoot and the left hindfoot contact the ground before the right foot, as a couplet. The sides of the body therefore behave differently in relation to one another. In terms of common usage, each of the gait patterns represented here has a "right lead". Note that for a very slow gallop, there are no periods of suspension. The slow gallop becomes a canter when diagonal pairs of limbs contact the ground together. The fast gallop as shown here for the horse has one period of gathered suspension. The springing gallop of the greyhound has two periods of suspension, gathered and extended. All the gaits shown here are transverse; the left feet contact the ground first in each forelimb and hindlimb couplet.
:::::Pale blue footprint = left footfall;
:::::Dark blue footprint = right footfall.
:::::'''Fig 10.12 Limb sequencing at a galloping turn'''
:::::The zebra is turning to its left. The right forefoot contacts the ground first and the leading (left) limb is on the inside of the turn.
==='''Transverse and rotary sequence'''===
Since in an asymmetrical gait we can define a leading foot for forelimbs and hindlimbs, it is possible for the lead to be on the same side of the body for forefeet and hindfeet (Fig. 10.13). This is the transverse sequence of footfalls shown by the horse and carnivores (Fig. 10.11 c, d). Alternatively, the lead may be on the opposite side of the body for forefeet and hindfeet (Fig. 10.13). This is the rotary sequence of footfalls shown by the fastest artiodactyls, the gazelles and antelopes. It is also seen when a galloping horse becomes tired and changes lead with its forelimbs but not its hindlimbs. The gallop in this instance is termed "disunited".
==='''Extended and gathered suspension'''===
Asymmetrical gaits are generally a faster form of locomotion than symmetrical gaits. While at some stages of a slow gallop three feet may be in contact with the ground, during many types of gallop there may be support from only one limb, and no feet are in contact with the ground at some stages. A stage with no ground support is called a period of suspension. In galloping this may occur, either when the forelimbs are protracted and the hindlimbs retracted (extended suspension in Fig. 10.11 d: 4th stage), or when the forelimbs are retracted and the hindlimbs protracted (gathered suspension shown in Fig. 10.11 c, d: 8th stage).
There are thus four possibilities for the gallop in terms of suspension periods:
1.There may be no periods of suspension. The body is always supported by at least one foot, as in the very slow gallop of the horse (Fig. 10.11 b).
2.Gathered suspension only may occur. When the larger animals gallop, they run in this way. It occurs in the fast gallop of the horse and camel (Fig. 10.11 c).
3.Extended suspension only may occur. This is characteristic of the gallop of some deer and rodents.
4.Finally, both extended and gathered suspension occurs in the fast springing gallop of the rabbit, carnivores (Fig. 10.11 d) and some artiodactyls.
:::::'''Fig 10.13 Basic patterns of footfalls in asymmetric gaits'''
:::::The canter is a transverse gallop, modified to a three beat gait.
==='''Extreme types of gallop'''===
The canter is a term applied to horses only. It is a slow form of gallop, which in its pure form is a three beat gait because the non–leading forefoot makes a simultaneous hoof beat with the contralateral striking hindfoot (Figs. 10.11 a, 10.13). Because three legs are in a support phase twice in the cycle, it is a very stable gait, with the limbs "collected" beneath the trunk. To produce this effect, the head is carried high on a curved neck.
The bound is a two beat asymmetrical gait because the pairs of forelimbs and hindlimbs strike simultaneously. Small animals, or large ones if travelling in deep mud or snow may make it.
The half bound occurs when a spring is made using both hindlimbs together, but the animal lands on one forefoot before the other, as seen in rabbits and hares.
The running jump occurs in with a springing gallop during the stage of extended suspension (Fig. 10.11 d: 4th stage). In the horse, the jump is not part of a normal gallop.
:::::'''Fig 10.14 The running jump of a horse'''
:::::The action of the hindlimbs involves extension of the joints to only a minor extent. Instead, the horse appears to use the elasticity of its limbs in a similar way to a pole-vaulter using a pole.
The kinetic energy of the horse has been partly stored as elastic energy in the hindlimbs; this energy can subsequently be released to oppose gravity. The necessity for a concept of elasticity in quadrupedal mechanics cannot be overstated.
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[[Category:Musculoskeletal System - Anatomy & Physiology]]
[[Category:Musculoskeletal System - Anatomy & Physiology]]