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First published online January 8, 2007
Journal of Experimental Biology 210, 208-216 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02645
Ground forces applied by galloping dogs
Biology Department, University of Utah, Salt Lake, UT 84112, USA
* Author for correspondence (e-mail: walter{at}biology.utah.edu)
Accepted 9 November 2006
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Summary |
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Key words: locomotion, gallop, ground force, gait, biomechanics, dog
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). Whereas the bound, half-bound and gallop all
take advantage of sagittal bending, the gallop is the high-speed gait of the
fastest mammalian runners (Gambaryan,
1974; Hildebrand,
1977). There is no clear consensus in the literature, however, as
to what advantages the gallop holds over the bound or half-bound.
These gaits that employ sagittal bending are called asymmetrical gaits
because the ground contacts of the two limbs of each pair (fore- or hindlimbs)
are not evenly or symmetrically spaced in time
(Hildebrand, 1977). The gallop
differs from the bound and half-bound in that contralateral limbs of both
pairs contact the ground at different times
(Fig. 1). In the rotary gallop,
which is used by dogs at high speed, the trailing forelimb contacts the ground
first, followed by the lead forelimb (the lead forelimb `leads' in that it
lands in front of the trailing forelimb). Thereafter, liftoff of the trailing
forelimb occurs, followed by that of the lead forelimb. An airborne phase with
the limbs gathered beneath the body then precedes hindlimb contact. The
hindlimbs then follow the same pattern of trailing and leading contact and
takeoff, using the opposite limbs as the lead and trail. Finally an airborne
phase with the limbs extended precedes the forelimb contact of the next stride
(Fig. 1). The transverse
gallop, which is used by dogs at lower speeds and by horses at all galloping
speeds, is similar to the rotary gallop. However, in the transverse gallop the
right and left hindlimbs land in the same order as the forelimbs rather than
the reverse (Hildebrand,
1977).
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Howell noted that it would be disadvantageous for the two forelimbs of
large animals to land simultaneously, as occurs in the bounding gait of small
mammals, because it would be difficult to overcome the decelerating impulse
(Howell, 1944). He does not
explain, however, why the forelimbs would create a greater decelerating
impulse if they landed together rather separately. Ruina and colleagues
proposed that a four-beat gait, in which each of the limbs impacts the ground
independently, should be the most energy-efficient gait as it would minimize
the energy lost at ground impact (Ruina et
al., 2005). They envision this running gait as a rimless wheel,
where maximizing the number of spokes would lead to greatest efficiency.
Similarly, according to their model, spacing out the ground contact periods of
the four limbs decreases the supporting impulse each limb applies while it is
angled in opposition to the direction of travel and thereby decreases the
decelerating impulse (Ruina et al.,
2005).
Due to the unique timing of their ground contacts in a gallop,
contralateral limbs need not be functionally equivalent, as they are in a
bound or trot. In fact, due to differences in velocity and center of mass
height at the time of ground contact, it is not possible for them to be
identical in all locomotor parameters. Cantering horses apply greater
decelerating impulses with their lead limbs and greater accelerating impulses
with their trailing limbs (Merkens et al.,
1993). A previous study on galloping dogs found the same pattern
in the forelimbs whereas differences between hindlimbs were not significant
(Bryant et al., 1987). Inherent
differences in the positions and ground forces between lead and trailing limbs
could affect agility by favoring turning in one direction rather than the
other. In turns, galloping mammals prefer to use the inside forelimb as the
lead limb (Hildebrand, 1977).
Differences in bone and muscle strain between lead and trailing limbs could be
of clinical importance as they might make galloping mammals more prone to
injury on a particular side. Both racing dogs and horses develop more injuries
in the right forelimb than in the left, although these differences, as well as
any asymmetries in the limb bones due to remodeling or breeding for track
racing, may be attributed to the turn direction of racetracks
(Boudrieau et al., 1984;
Rooney, 1977;
Palmer, 1986). Subtle
differences in ground forces between leading and trailing limbs might also
lead to the evolution of unique anatomical specializations in the preferred
leading and trailing limbs. Asymmetries in limb bone lengths and diameters
have been reported in horses, although these may be adaptations to the turn
direction of racetracks (Pearce et al.,
2005; Watson et al.,
2003; Hanson and Markel,
1994). Due to these factors, a greater understanding of the
interlimb differences in ground forces during the high-speed gallop is of
interest.
The present study extends the research of Bryant and colleagues by further investigating the extent to which the four limbs of a galloping dog differ in their contribution to a running stride. Here, a wider range of force parameters is investigated in dogs galloping at higher speeds. This allows for a comparison between the rotary gallop used by dogs at high speeds and the transverse gallop used by horses and provides maximum force data during the gallop for comparison with forces applied during other activities.
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Procedure
Dogs were encouraged to gallop along the runway as close as possible to
maximum speed by having them chase either a tennis ball or an experimenter
running with a hotdog. Dogs that did not appear to gallop with maximum effort
after several practice trials were not used for this study. On each day in
which trials were recorded, dogs performed trials until their velocity
decreased due to fatigue or boredom. After the completion of each recording
session, the dog was weighed on the force plate. Recording sessions were
repeated on separate days for each dog until a sufficient number of acceptable
`maximal effort' trials were recorded for each limb.
Analysis
Trials were acceptable for analysis if they met the following criteria: (1)
velocity was within 15% of the maximum measured for that dog, (2) the limb on
which forces were analyzed landed fully on the force plate and no other feet
contacted the plate during its stance period and (3) velocity measurements
taken over the 2.5 m before and after the center of the force plate differed
by less than 10%. Of the trials meeting these criteria, five trials for each
limb (lead and trailing fore- and hindlimbs) were selected for analysis. These
trials were chosen so as to minimize the variation in velocity among the
trials analyzed for each dog. Care was taken to ensure that velocity did not
differ significantly between paired limbs in the trials analyzed for any dog.
For one of the six dogs (dog C), only four trials for each limb were
acceptable for analysis. The following parameters were measured for each trial
analyzed: velocity, contact time, mean and maximum vertical, fore-aft and
mediolateral forces and force impulses. Contact time was taken as the period
over which dogs applied forces greater than or equal to 4% body weight to the
plate.
Statistics
For each of the measured parameters, means for each limb of each dog were
calculated. These means were then used in paired, two-tailed Student's
t-tests in Microsoft Excel software to compare lead and trailing
limbs of fore- and hindlimb pairs and both fore-versus both
hindlimbs.
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Results |
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Lead vs trailing forelimb
The lead forelimb had a 5% longer stance period than the trailing forelimb
(P=0.03). The average mean and maximum vertical forces for the
trailing forelimb were 5% greater than those of the lead forelimb, but the
difference was not significant (P=0.08 and P=0.10,
respectively) (Table 2; Figs
2,
3). Because the lead forelimb
had a greater contact time but a lower vertical force, both forelimbs had
equal vertical impulses (Fig.
4). In the fore-aft direction, the trailing forelimb had a 12%
greater peak accelerating force and a 14% greater accelerating force impulse,
whereas the lead forelimb had an 11% greater decelerating force impulse
(Table 2).
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20-25% into the contact phase. Then, at 30% of ground contact,
forces returned to the lateral direction until at least midstance. From
midstance to takeoff, mediolateral force patterns differed greatly between
dogs, however each individual dog applied similar forces in all trials. Peak
medial and lateral forces were similar in magnitude and were 7% and 34% as
large as peak vertical and accelerating forces, respectively
(Table 2;
Fig. 3).
Lead vs trailing hindlimb
The trailing hindlimb tended to have a 4% longer stance period than the
lead (P=0.06), while the lead hindlimb exerted 10% greater peak
vertical forces and 5% greater mean vertical forces than those of the trailing
hindlimb (P=0.03 for both) (Table
2; Figs 2,
3). Both the peak accelerating
force and the net accelerating force impulse were roughly 18% greater in the
lead hindlimb (Fig. 4).
Mediolateral force curves for the leading and trailing hindlimbs were similar
in appearance and showed the same general pattern for five of the six dogs
(Fig. 2). For these dogs,
mediolateral forces hovered around zero during the first third of stance and
then medial forces were applied for the remainder of stance. Mediolateral
forces in the sixth dog were equally small but were laterally directed over
the entire stance. Net mediolateral forces were not significantly different
from zero for either of the hindlimbs, and the two hindlimbs did not differ
for one another in any of the measured mediolateral force parameters
(Table 2).
Forelimbs vs hindlimbs
The total vertical impulse for both forelimbs was 32% greater than that for
both hindlimbs. The decelerating impulse was 92% greater in the forelimbs than
in the hindlimbs, while the total accelerating impulses for the fore- and
hindlimbs were similar. The net fore-aft impulse was accelerating in the
hindlimbs and did not differ significantly from zero in the forelimbs
(Table 2).
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).
Differences in ground forces between the leading and trailing forelimbs of
cantering and galloping horses show the same trends as in dogs but are of
greater magnitudes. During cantering at slow speeds (4.4-5.6 m
s-1), peak vertical forces are 25% greater in the trailing forelimb
of horses, whereas at higher galloping speeds (12 m s-1) peak
vertical forces are predicted to be only 19% greater for the trailing forelimb
based on the maximum metacarpophalangeal joint angles
(Merkens et al., 1993;
McGuigan and Wilson, 2003).
Horses galloping at high speed also have a longer stance period on the lead
forelimb (Deuel and Lawrence,
1986). During slow cantering, horses apply four times greater peak
accelerating forces with their trailing forelimbs than with their leading
forelimbs (Merkens et al.,
1993), which is also much greater than the 12% difference observed
in dogs. Differences between dogs galloping at high speed and cantering horses
could be due to interspecific differences in body morphology, or they could
represent inherent differences between the two gaits. The canter is used by
horses at moderate speeds and differs from the high-speed gallop in that the
contact phases of the lead forelimb and trailing hindlimb overlap entirely
(Merkens et al., 1993;
Hildebrand, 1977). Even at
high speeds, the transverse gallop of horses differs from the rotary gallop of
dogs in that right and left hindlimb ground contacts occur in the same order
as forelimb contact. Further, horses galloping at high speeds do not exhibit a
flight phase between the stance phases of the lead hindlimb and trailing
forelimb. Unfortunately, the ground forces for the transverse gallop of horses
or for other animals galloping at high speeds have not been reported.
Whereas one might expect the two forelimbs to act together, first
decelerating and then accelerating the body, in both dogs and horses the
trailing forelimb applies a greater accelerating impulse while the lead
forelimb applies a greater braking impulse
(Bryant et al., 1987;
Merkens et al., 1993). This
difference in fore-aft impulses may be explained by the vertical position of
the center of mass during each limb's stance. The center of mass is relatively
high when the trailing forelimb lands, low when the trailing forelimb pushes
off and the lead forelimb lands, and high again when the lead forelimb pushes
off (D. Bramble, personal communication)
(Cavagna et al., 1977). Thus,
the lead forelimb must touchdown either at a more protracted angle than the
trailing (i.e. further in front of the shoulder) or with a more crouched limb
posture whereas the trailing forelimb must be more retracted (i.e. further
behind the shoulder) or extended at takeoff. In fact, results from dalmatians
show that the trailing forearm was significantly more retracted at takeoff
whereas the lead forearm tended to be more protracted on landing, although
this trend was not significant (Alexander
et al., 1980). Thus, the vertical oscillations of the center of
mass during the gallop likely constrain the trailing forelimb to spend a
greater proportion of stance with the ground contact caudal to the limb's
fulcrum, whereas the lead forelimb must spend a greater portion of stance with
its ground contact cranial to the limb's fulcrum. Because the primary
retractor muscles of a dog's forelimb show little or no activity associated
with stance phase during a steady-state gallop (D.R.C., unpublished data), the
forelimbs appear to act as elastic struts rather than as levers actively
propelling the dog. As such, the angles of the limbs are a main determinant of
the polarity of their fore-aft forces, such that retracted forelimbs tend to
apply propulsive forces while protracted forelimbs apply braking forces. Thus,
the trailing forelimb, which lands in a more retracted position and spends a
greater portion of its stance time with the ground contact point caudal to the
limb's fulcrum, exerts a lower braking impulse and a greater accelerating
impulse than the lead forelimb.
Lead vs trailing hindlimb
Both galloping horses (Deuel and
Lawrence, 1986) and dogs tended to have a slightly longer stance
period on the trailing hindlimb, although in dogs this difference was not
significant. Forces in the hindlimbs were opposite to those in the forelimbs,
with the lead hindlimb exerting greater vertical and 18% greater accelerating
forces. A similar trend toward greater accelerating forces in the lead
hindlimb of galloping dogs was found by Bryant and colleagues
(Bryant et al., 1987).
Cantering horses also apply greater vertical forces with the lead hindlimb,
however their hindlimb fore-aft forces are opposite to those of dogs, with the
trailing hindlimb applying a much greater accelerating impulse
(Merkens et al., 1993).
Because the center of mass is higher at touchdown and lower at takeoff
(Cavagna et al., 1977;
Minetti et al., 1999), an
elastic strut model in which the limbs are not actively retracted or extended
during stance (as described above for the forelimbs) predicts that both dogs
and horses should apply greater accelerating forces with the trailing
hindlimb. This suggests that the hindlimbs of cantering horses act in a more
strutlike fashion whereas galloping dogs may use more muscular power in
retracting or extending their hindlimbs. Hindlimb ground forces are also
likely to differ between dogs and horses because sagittal bending tends to
decrease with increasing body size and is generally greater in carnivores than
ungulates (Gambaryan, 1974).
Much of the back extension that occurs was observed during hindlimb stance.
This back extension simultaneously increases center of mass height and applies
strong propulsive forces, which is inconsistent with a simple strut model. In
fact, mechanical energy traces for galloping dogs show large increases in both
kinetic and potential energy during the ground contact period of the lead
hindlimb (Cavagna et al.,
1977), demonstrating that the hindlimbs of galloping dogs cannot
be acting as elastic struts as do the forelimbs.
Whereas active extension and retraction can explain why the net fore-aft impulse of the lead hindlimb is so strongly propulsive, it does not explain why the accelerating impulse of the trailing hindlimb is so small. In fact, the accelerating impulse of the trailing hindlimb is smaller than that of either forelimb. There is likely a limitation in how effective propulsive forces from the trailing hindlimb can be during the period that the lead hindfoot is in front of the hip joint. Because the lead hindlimb may be limited in its ability to apply propulsive forces during this period, greater accelerating forces from the trailing hindlimb might simply lead to greater braking forces in the lead hindlimb.
Mediolateral forces
Initially upon ground contact, both forelimbs applied laterally directed
ground forces followed by a relatively large medially directed ground force
peak and then further lateral forces until midstance. After midstance,
mediolateral forces varied in their polarity among dogs but were consistent
through the five trials for each dog. In five of the dogs, mediolateral forces
in both hindlimbs fluctuated about zero during the first third of stance and
then medial forces were applied for the remainder of stance. Because of these
changes in polarity, net mediolateral impulses were not significantly
different from zero for any of the limbs
(Fig. 2;
Table 2). Laterally directed
forces could result from feet placed lateral to the midline applying a net
force vector directly through the center of mass. Alternatively, if the feet
were placed on or near the midline, abductor muscles in the shoulders or hips
could exert lateral forces to prevent the limb from collapsing. Feet
positioned near the midline could also apply medial forces if the net force
vector passed through the shoulder girdle or hip joint. Because the
mediolateral positions of the feet during force application were not recorded,
the yaw and roll moments produced by the mediolateral forces cannot be
determined from these data. Mediolateral forces were quite small, with peaks
only 7% and 34% as large as peak vertical and accelerating forces,
respectively. The mediolateral forces recorded from cantering horses were
highly variable and were less than 5% and 20% as large as fore-aft forces and
vertical forces, respectively (Merkens et
al., 1993; Biewener,
1998).
Implications of force differences between lead and trailing limbs
Although ground forces differed between lead and trailing limbs, and four
of the six dogs had preferred lead limbs (P<0.01), it seems
unlikely that natural selection would favor significant musculoskeletal
asymmetries in the limbs of mammals. Galloping in the natural environment
requires mammals to turn and to adapt their gait to varying terrain, which
would severely limit the usefulness of favoring one limb over another. The
skeletal asymmetries observed in horses are more likely due to selection and
remodeling for the turn direction of racetracks
(Pearce et al., 2005;
Watson et al., 2003;
Hanson and Markel, 1994).
Switching leads could help gallopers delay muscle fatigue by alternating the
forces each limb must produce. Force differences between lead and trailing
limbs also seem to play a role in turning. In turns, gallopers prefer to use
the inside forelimb as the lead limb
(Hildebrand, 1977). This is
advantageous because in a rotary gallop the trailing forelimb and lead
hindlimb, both of which apply greater accelerating forces than their
contralateral limbs, are placed on the outside of the turn.
Forelimbs vs hindlimbs
Although the net duty factor for the forelimbs was the same as that for the
hindlimbs, the forelimbs supported 57% of body weight whereas the hindlimbs
supported only 43%. This vertical force distribution between the fore- and
hindlimbs is similar to that found in dogs trotting at constant speed, where
the forelimbs supported 64% and 56% of body weight in labradors and
greyhounds, respectively (Lee et al.,
1999), and to that found in dogs galloping at 7.5 m s-1
while accelerating slightly, where the forelimbs supported 56-59% of body
weight (Bryant et al., 1987).
Cantering horses similarly support 56% of the body weight with the forelimbs
despite an equal duty factor in the fore- and hindlimbs
(Merkens et al., 1993).
The accelerating impulse did not differ between both fore- and both
hindlimbs whereas the decelerating impulse was much greater for the forelimbs.
Thus, the hindlimbs of galloping dogs did show net fore-aft impulses that were
more accelerating than those of the forelimbs, as expected based on their
location relative to the center of mass. However, this difference was not
achieved by the hindlimbs applying greater accelerating impulses but by their
applying smaller decelerating impulses. Whereas the net fore-aft forces of the
forelimbs were not significantly different from zero, this result is most
likely due to the slight net acceleration that occurred in the trials. Without
this net acceleration, the net fore-aft impulse of the forelimbs would likely
have been negative while that of the hindlimbs would have been less
accelerating. Bryant and colleagues (Bryant
et al., 1987) similarly found that galloping dogs applied only
slightly greater accelerating impulses with the hindlimbs than with the
forelimbs but much greater decelerating impulses with the forelimbs.
Why gallop?
Both the lead forelimb and the trailing hindlimb exerted lower peak forces
than their contralateral limbs. They also had longer ground contact periods,
which suggests that unless these limbs rotate over a greater angle, or their
joints extend through greater angles, their muscles are contracting at a lower
velocity. This combination of lower ground forces and lower contraction
velocity in the lead forelimb and trailing hindlimb would suggest that the
muscles of these limbs produce less power than those of their contralateral
limbs. Intuition might suggest that if maximum running speed were limited by
the force or power produced by limb muscles, dogs and horses might achieve
higher speeds using a bounding gait that would allow all limbs to produce
maximum power. Alternatively, the increased power that an animal produced by
bounding might be offset by a decrease in efficiency.
The collisional loss model proposed by Ruina and colleagues
(Ruina et al., 2005) contends
that the main energetic cost of locomotion is overcoming the kinetic energy
lost upon foot impact with the ground. Comparing the limbs of a runner to the
spokes on a rimless wheel, it suggests that more spokes would make for a
rounder, more efficient wheel, as less energy would be lost in the collision
of the spokes with the ground. Thus, the gallop, where each limb acts as an
independent spoke, would be more efficient than the bound, where paired limbs
combine to form a single spoke, or the half-bound
(Ruina et al., 2005).
The gallop may also increase efficiency because less vertical motion of the
center of mass is required to achieve the same stride length. In a gallop, the
distance traveled during the support phases is based on the summed angular
excursions of all four limbs (minus half the angular excursion that occurs
during the phases of forelimb and hindlimb double contact). In a bound,
because the contact period of contralateral limbs overlaps completely, the
distance covered during the support phases is based only on the angular
excursion of one fore- and one hindlimb,and is less than in a gallop. To
achieve the same stride length, a bounding animal must spend a greater portion
of the stride in suspension phases, which requires a greater vertical
displacement of the center of mass. For example, when hybrid deer bound, the
pitch angle of their back undergoes a greater excursion than when they gallop,
suggesting a more vertically oriented flight phase trajectory and a greater
vertical displacement of the center of mass (Lingle, 1992). Because kinetic
and potential energy fluctuations are in phase during a bounding gait, this
greater fluctuation in center of mass height equates to a greater fluctuation
in the mechanical energy over the stride
(Heglund et al., 1982). This
means that more mechanical work is required for each stride of a bound. If all
of the energy required to elevate the center of mass could be stored
elastically and released during each stride, then this increase in mechanical
work might be irrelevant. However, previous studies on running, galloping and
hopping mammals have shown energetic recoveries of only 20-40% through elastic
storage (Biewener, 1998). Thus,
more muscular work is likely required to lift the center of mass in a bounding
stride than in a galloping stride of equal length. In fact, it is likely that
a combination of greater collisional energy losses and greater fluctuation in
center of mass height makes the bound less efficient than the gallop.
Large mammals can probably achieve higher velocities by galloping than by
bounding because galloping is more energetically efficient, even though one
limb of each pair is unable to operate at full power as it could in a bound.
Based on this, mammals could be expected to switch to a half-bound or bound
during sharp turns and rapid accelerations and decelerations when power
production is more important than efficiency. If increased efficiency is the
primary advantage of the gallop over other gaits involving sagittal bending of
the trunk, there are several possible explanations for why many small mammals
use the bound or half-bound. First, their locomotor behaviors often include
more accelerations and sharp turns than larger mammals. This could increase
the importance of power production relative to efficiency. Second, because
their limb muscles are more powerful relative to their body mass
(Alexander et al., 1981), their
speed could be reduced more by limiting the force and power production of the
lead forelimb and trailing hindlimb. Third, the crouched posture and muscle
tendon properties of smaller animals may decrease their ability to save energy
through either kinetic/potential energy transfer between fore- and hindlimbs
or elastic storage within the trunk and limbs, as large mammals are able to
achieve in the gallop. This could decrease the difference in energetic
efficiency between galloping and bounding. Thus, the use of the bound or
half-bound by small mammals and by large mammals during accelerations and
decelerations is consistent with the hypothesis that the gallop is preferred
due to increased efficiency.
Conclusion
Galloping dogs apply greater accelerating forces with their trailing
forelimbs and greater decelerating forces with their lead forelimbs. As the
trailing forelimb spends a greater portion of the stance phase in a retracted
position and the lead forelimb spends a greater portion protracted
(Alexander et al., 1980), this
force difference would be expected if the forelimbs were to behave as elastic
struts rather than being actively extended or retracted during stance. The two
forelimbs exert equal vertical impulses over the stride, however the trailing
forelimb tends to exert higher mean and peak vertical forces whereas the lead
forelimb exerts forces over a longer time interval. Forces in the hindlimbs
are the opposite, with the lead hindlimb applying greater vertical and
accelerating forces than the trailing hindlimb. The trailing hindlimb may be
unable to apply greater accelerating forces without incurring greater
decelerating forces from the lead hindlimb. Furthermore, back extension likely
contributes more to the accelerating forces during lead hindlimb contact.
Although the accelerating impulse is not significantly different between the
fore- and hindlimbs, the forelimbs do net deceleration overall because they
apply a greater decelerating impulse whereas the hindlimbs do net
acceleration.
In the gallop, the lead forelimb and trailing hindlimb are constrained in their ground force production. The gallop is likely preferred over the bound and half-bound, which may allow more of the limb muscles to operate at full power, because it is a more efficient gait. For mammals rapidly accelerating or decelerating and for small mammals running at constant speed, the importance of power relative to efficiency may be greater, making the bound or half-bound more advantageous. During turns, quadrupeds make use of the force differences between lead and trailing limbs by positioning the trailing forelimb and the lead hindlimb, both of which apply greater accelerating forces than their paired limb, on the outside of the turn.
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Acknowledgments |
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