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First published online March 27, 2009
Journal of Experimental Biology 212, 1163-1169 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.027938
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Mechanics of generating friction during locomotion on rough and smooth arboreal trackways
Department of Health Sciences, Cleveland State University, 2121 Euclid Ave, Cleveland, OH 44115, USA
e-mail: a.lammers13{at}csuohio.edu
Accepted 5 February 2009
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Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: arboreal locomotion, gray short-tailed opossum, Monodelphis domestica, normal force, shear force, substrate reaction force
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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). Such
substrates are commonly encountered by any animal that lives where vegetation
grows. The texture of such arboreal substrates varies considerably. Some have
rough bark, and animals moving on them can easily generate enough friction
between the substrate and their hand or foot. The animal can also (or instead)
use claws to generate or take advantage of surfaces that are relatively
perpendicular to the direction of locomotion
(Cartmill, 1985). On smooth
arboreal surfaces, creating and maintaining a stable contact with the branch
is probably more challenging. There may be fewer places for claws to engage
with the surface, and generating adequate friction force may be difficult
because the coefficient of static friction (µs, which is a
dimensionless number expressing shear force divided by normal force) is
lower.
When generating friction force (µs multiplied by normal
force) is the method (or an important method) of maintaining contact with a
substrate, there are three ways for the animal to generate enough friction
force. First, it can increase the normal force, which is directed
perpendicular to the substrate. On an arboreal substrate, which is roughly
cylindrical, a normal force runs from the center of pressure of the hand or
foot toward the centerline of the long axis of the branch
(Fig. 1). Normal force can be
increased by muscular effort; for example, contralateral limbs can adduct,
squeezing the branch between them and generating greater normal force. If the
contact is near the top of the branch (that is, near the dorsal-most part of a
long, narrow, horizontal cylinder), then considerable normal force will be
generated from vertical force. The vertical component of SRF is typically the
largest component, and when the limbs contact the top of the branch, most or
all of the vertical force is normal to the branch surface. The second way to
generate adequate friction force is to increase µs. It might be
possible for an animal to increase the effective µs by changing
the shape or moisture content of its hand or foot
(Haffner, 1998). Finally, the
animal can decrease the need to generate friction force by decreasing the
shear forces. Vertical and mediolateral components of the substrate reaction
force (SRF) typically have a shear component whose magnitude corresponds with
the location of the center of pressure on the branch cylinder
(Fig. 1). In addition, the
entire craniocaudal (fore–aft or anteroposterior) force component is a
shear force. Finally, the torque around the long axis of the branch, which is
generated separately from SRFs (abbreviated as 
CC,musc,
which stands for craniocaudal torque generated by muscular effort)
(Lammers and Gauntner, 2008),
also generates shear force (applied around a moment arm). Shear force can be
decreased by moving more slowly (which should decrease braking and propulsive
craniocaudal forces), by placing the limb on the top of the branch (which
decreases the shear component of the vertical force) or by decreasing
CC,musc. It is possible that an animal might use all
three methods (increasing normal force, increasing µs and
decreasing shear force) to ensure adequate friction force with a particular
substrate.
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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)] were used for
these experiments. All animal care and procedures conform to the Cleveland
State University Institutional Animal Care and Usage Committee guidelines and
NIH guidelines. The opossums were encouraged to run across two cylindrical trackways constructed of wooden dowel rods, 2 cm in diameter and about 2 m long. The first (rough) trackway was covered with 60-grit sandpaper, which provided a large µs between the trackway and the hand or foot. The second (smooth) trackway was covered with thick paper (actually, sandpaper with the grit side facing inward). Thus, the trackways were identical except for the surface texture. It is unlikely that the animals could sink their claws into the substrates because the glue used to attach paper to the cylinders was very hard. The animals ran into an enclosure placed at the end of the trackway.
A 3.8 cm-long region of each trackway was instrumented to measure the
vertical, craniocaudal (fore–aft or anteroposterior) and mediolateral
components of the SRF (FV, FCC and
FML, respectively). The force pole design is described more
fully by Lammers and Gauntner (Lammers and
Gauntner, 2008). Force data (in the form of voltage changes) were
collected at 2000 Hz with a National Instruments signal conditioning block
(SC-2345 with SCC-SG04 and SCC-DO01 modules) and a LabView 7.1 virtual
instrument (National Instruments, Austin, TX, USA). Each force trace consisted
of a right forelimb contact followed by a right hindlimb contact; typically,
there was little or no overlap between fore- and hindlimb. Voltages were then
filtered using a moving average filter (average of points 1-33, then points
2-34, etc.) in Microsoft Excel (Redmont, WA, USA). This filter removed 60 Hz
noise, but it had a negligible effect on the timing and magnitude of peaks and
valleys in the voltage record. A second LabView virtual instrument was used to
convert voltages into force [measured in Newtons (N)]. For the final analysis,
the body weights of individual opossums were taken into account by converting
Newtons into body weight units (BW units).
It was necessary to estimate the center of pressure in the hand and foot in
order to calculate shear and normal forces. Thus, the opossums were filmed
with three 60 Hz video cameras (JVC-DF550, JVC, Wayne, NJ, USA) focused on the
force pole and the limb contacts. Videos were uploaded to a computer using
U-Lead Videostudio 9.0 (Ulead Systems, Inc., Taipei, Taiwan), and the videos
were synchronized by kinematic event (usually forelimb touchdown time) using
the Trimmer module of APAS motion analysis system (Ariel Dynamics, San Diego,
CA, USA). Using the Digitize module of APAS, the distal tip of all digits on
the hand and foot were digitized, along with the lateral aspects of the wrist
joint and fifth metatarsophalangeal joint of the right limbs. The coordinates
from the three views were then combined into a single, three-dimensional set
of coordinates using the Transform module of APAS. Preliminary data from a
flat trackway indicate that the center of pressure is roughly in the middle of
the hand and foot. Although the center of pressure moves anteriorly throughout
the step, this was irrelevant for this study because I needed only the center
of pressure around the circumference of the cylindrical trackways. The average
of digits 1–5 was calculated for the hand and foot, and this value was
used to calculate 
, the center of pressure measured in polar
coordinates. The angle was then used to calculate the shear and normal
force components (Fshear and Fnormal,
respectively) of each SRF component (Eqns
1 and
2 and
Fig. 1). The torque around the
long axis of the branch that did not result from shear components of
FV or FML (CC,musc)
(Lammers and Gauntner, 2008)
was included in the vector sum to calculate Fshear. [If the
animal were moving on a branch that was free-floating in space instead of
being attached to a planet, then the CC,musc would
produce a rotation around the long axis of the branch; no linear translation
would take place. SRFs applied to the free-floating branch produce both
translation and rotation. The shear, or tangential, components of
SRFs produce only rotation of the free-floating branch, and normal components
cause linear translation. Because the branch is anchored (somewhat indirectly)
to the Earth, each SRF and torque results in linear translation and/or
rotation of the opossum's center of mass].
 | (1) |
 | (2) |
Because CC,musc has a distance factor in addition to
force, Fshear is also a torque around the long axis of the
branch. The distance from the manus/pes center of pressure to the long axis of
the branch was 1 cm, and torque was measured in BW units
cm–1. Thus, the numbers are not affected by the distance
component of torque, and I treated Fshear the same as
Fnormal. Slipping from the substrate is most likely to occur
during the peak Fshear; therefore, peak
Fshear (and Fnormal) were calculated. The
µreq, which is the ratio of Fshear to
Fnormal, was calculated as a measure of how likely the
animal was to slip from the substrate. A higher value of µreq
implies a higher Fshear and/or a lower
Fnormal. The animal is most likely to slip when
µreq is at its peak; therefore, I calculated the peak
µreq. Finally, to gain an overall measure of shear and normal
forces and µreq during each step, I calculated the median
Fshear, Fnormal and
µreq.
I measured speed with a high-speed video camera (120 Hz, JVC DVL 9800). I digitized the tip of the nose each time a forelimb (right or left) touched down and then calculated the craniocaudal displacement that occurred during each step. Craniocaudal displacement was divided by time to acquire step speed, and step speeds were averaged to calculate the speed for the individual trial. If step speeds were always within 15% of trial speed, then I accepted the trial as steady speed. This process eliminated many trials, resulting in small sample sizes for some individuals (Table 1).
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Systat version 11 (Richmond, CA, USA) was used for all analyses. Speed and
limb phase were compared between substrates using a two-sample
t-test. To determine if speed was a significant predictor of shear
and normal forces and the µreq, I calculated Pearson correlation
coefficients for each limb on each substrate. Because speed was generally
poorly correlated with peak and median forces and µreq, speed
was ignored in subsequent analyses. To determine the effects of substrate
texture and limb pair (hand versus foot) on how friction force is
generated, I used three analyses to compare the peak and median
Fshear and Fnormal, peak and median
µreq, and between limbs and between substrate textures.
Duty factor was also compared between limbs and between substrates in the same
way. First, for each measurement (e.g. peak shear force), the measurements
were averaged within individual opossum. Thus, each individual was weighted
equally, and a fixed-factor two-way analysis of variance (ANOVA) was used to
determine significant differences between substrates and between limb pairs.
(Because samples were very small for some individuals, a repeated-measures
analysis could not be performed; Table
1.) In the second analysis, I calculated the percentage
contribution of fore- and hindlimbs to each force and µreq
measurement [forelimb/(forelimb+hindlimb)x 100%]. These percentages were
compared between substrate textures using a two-sample t-test. In the
third analysis, I used two-way analysis of covariance (ANCOVA), with the polar
coordinate of the manus and pes contact locations in the transverse axis of
the branch trackways () as the covariate, to determine how forces and
µreq were affected by limb contact position among the substrate
and limb groups. When slopes were homogeneous between groups, the
least-squares means were compared. When slopes were not homogeneous, the
slopes were calculated using least-squares regression.
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Typical SRFs, µreq, Fshear and
Fnormal are shown in Fig.
3. ANOVA revealed no significant differences in
Fshear between limbs or between substrates
(P
0.0910) (Table
1; Fig. 4). Peak
and median Fnormal was significantly higher in forelimbs
compared with hindlimbs (P
0.0001). Peak and median
Fnormal were not significantly different between trackway
surface textures (P0.2769). Peak µreq was higher in
hindlimbs, but there were no significant differences in µreq
between rough and smooth arboreal trackways (P0.3162). Mean
was significantly higher in forelimbs than hindlimbs
(P=0.0393), but there was no significant difference in
between substrates (P=0.5879). There were no significant differences
between substrate textures with respect to the percentage contribution of the
forelimb to the total fore- and hindlimb contribution of force or
µreq (P0.1589)
(Table 3).
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Two-way ANCOVA was used to determine if peak and median
Fshear and Fnormal, and peak and median
µreq, changed with limb contact position () and if this
variation differed between substrates and/or between fore- and hindlimbs
(Table 4;
Fig. 5). The first part of this
test determined if the slopes (e.g. peak Fshear
versus ) were homogeneous among groups. In the case of peak
and median Fnormal, the slopes were significantly different
between limb pairs (peak Fnormal slopes were 0.0071 for
forelimbs and 0.0034 for hindlimbs; median Fnormal slopes
were 0.0060 for forelimbs and 0.0025 for hindlimbs; P0.0024). The
second part of the ANCOVA determined if slopes were significantly different
from zero and if least-squares means were significantly different. Median
Fshear was not correlated with . When was
taken into account by ANCOVA, patterns were essentially identical to those
revealed by the two ANOVA comparisons. The only difference was that peak and
median Fnormal were not significantly different between
rough and smooth trackways (P0.0651).
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DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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;
Lee and Cockburn, 1985), and
they are not particularly proficient at traveling on arboreal substrates [as
measured by the significant decreases in speed, increases in duty factor, and
changes in footfall sequence when switching from terrestrial to arboreal
substrates (Lammers and Biknevicius,
2004)]. Nevertheless, it seems that they have features that enable
them to negotiate arboreal substrates of various textures
(Cartmill, 1974;
Hamrick, 2001). Thus, Jenkins'
supposition that most small mammals must be at least somewhat well-adapted to
traveling on arboreal substrates (Jenkins,
1974) is supported.
Comparative data describing the effects of substrate texture on locomotion
are few, and the kinetic adjustments that cows, dogs, geckos, humans and
opossums use to remain stable on relatively slippery surfaces are probably
rather different because of body size, bipedalism versus
quadrupedalism, and having very different autopodial surfaces. A study by
Phillips and Morris (Phillips and Morris,
2001) found that dairy cows walking on surfaces with low
µs (0.33) walked slowly and with relatively upright limbs
(higher stride frequency, but short step length). On medium µs
floors (µs=0.42 and 0.49), they walked fastest and with the
greatest step length. On high µs floors (0.74), they slowed down
again, presumably to limit the amount of wear on their hooves. The relatively
upright posture of the limbs should increase normal force and decrease shear
force because body mass is being accelerated in a horizontal direction (or
more force is redirected through the limbs in a horizontal direction). Thus,
this posture (and decrease in speed) should also decrease shear force
when the cows move on relatively slippery surfaces. By contrast, Kapatkin et
al. found no differences in peak forces or impulses (vertical and craniocaudal
components of the SRF) generated by dogs trotting on linoleum versus
carpet-surfaced trackways (Kapatkin et al.,
2007). Therefore, dogs make no change in shear force, at
least when running on carpet versus linoleum. Finally, Tokay geckos
may increase shear force (up to twice the adhesive force, depending
on the direction of shear force relative to the setae) within arrays of
thousands of setae to cause powerful friction and adhesion forces that can
prevent a gecko from slipping from smooth, dry glass
(Autumn et al., 2006). My
comparison among these three groups is simplistic, mainly because the data
collected and the taxa are so varied. Nevertheless, it demonstrates
astonishing diversity among tetrapods in how they cope with traveling on
relatively smooth surfaces.
When the µreq that I calculated is compared with values of
µreq and µs from the literature, my values of
µreq appear surprisingly high. Cartmill reported a
µs of 
0.3–0.4 for leather on clean wood
(Cartmill, 1974). Redfern et
al. reported µreq data for humans walking down ramps; even at
the steepest ramp angle (20 deg.), µreq was less than 0.6
(Redfern et al., 2001). The
µreq represents
Fshear/Fnormal; Fshear
was rather high in my experiments because the vertical force had a
considerable shear component when the hands and feet contacted the sides of
the branch. The values of might have also been underestimated (that
is, they show center of pressure of the hand and foot as closer to the sides
of the branch than they actually are); this underestimation would occur if the
center of pressure was closer to the medial side of the hand and foot as
opposed to the center. Furthermore, the CC,musc
contributed substantially to the Fshear. Finally, it seems
likely that not all Fnormal could be measured. When the
opossums gripped the branch, the hand and foot most likely generate some
internal squeezing force, some or all of which is normal to the cylindrical
surface. My equipment could not measure this source of
Fnormal. It is possible that µreq is higher in
the hindlimbs because the opposable hallux of the foot allowed greater
Fnormal to be generated (but not measured). It seems that
designing a force pole that can measure center of pressure in the transverse
plane and the squeezing forces will be quite valuable.
Peak and median Fnormal were higher in forelimbs compared
with hindlimbs. This result is most likely caused by two important factors.
First, vertical force is greater in the forelimbs than in the hindlimbs
(measured by calculating peak vertical force and the vertical impulse)
(Lammers and Biknevicius,
2004). This pattern is the result of the location of the body
center of mass, which is closer to the forelimbs than to the hindlimbs
(Lammers et al., 2006).
Friction force is the result of Fnormal x
µs; thus, the opossum's weight is acting to increase the
friction force generated by both limbs, but more so in the forelimbs. The
second factor is where the fore- and hindlimbs contact the cylindrical
trackway around its circumference. Regardless of substrate texture, forelimbs
typically contacted the branch trackways at about 63 deg., whereas hindlimbs
contacted at about 42 deg. Because forelimbs contacted the branch at a point
closer to the top of the branch, the very large vertical forces should
contribute more to Fnormal in the forelimbs than in the
hindlimbs.
Peak and median Fshear were not significantly different
between limb pairs. At least three important factors contributed to this
pattern (Fig. 6). The first
major factor is the interaction between vertical force and the contact
location. Because the hindlimb contacts the branch more laterally, a greater
proportion of the vertical force generated by the animal's body weight is
tangential to the branch surface (that is, shear force). But the forelimbs
support more body weight (Lammers et al.,
2006), and so vertical force is greater. Thus, the hindlimbs have
a smaller vertical force contributing proportionally more to shear force,
whereas the forelimbs have a larger vertical force contributing proportionally
less to shear. The second major factor contributing to the lack of differences
between fore- and hindlimbs with respect to shear force is the interaction
between the shear component of mediolateral force and the
CC,musc. Lammers and Biknevicius found that fore- and
hindlimbs exerted net mediolateral impulse in a medial direction
(Lammers and Biknevicius,
2004). Thus, contralateral limbs squeeze the branch between them.
At the same time, the CC,musc was found to be in the
same direction in ipsilateral fore- and hindlimbs, but it was much smaller in
magnitude in hindlimbs (Lammers and
Gauntner, 2008). Therefore, in forelimbs, the shear component of
mediolateral force contributes more to shear force than in the
hindlimbs because of limb contact location
(Fig. 6). The
CC,musc contributes only to shear force, and it is
greater in the forelimbs. It appears that for the most part, the
CC,musc and shear component of mediolateral force
within each limb pair cancel each other out. Third, the craniocaudal force,
all of which contributes to shear force, apparently makes a minor contribution
to the total shear force. Craniocaudal shear force differs from the
other components of shear force because it presumably does not contribute to
making the animal slip from the sides of the branch. Lammers and Biknevicius
found that on a similar 2 cm arboreal trackway, M. domestica exerted
significantly greater braking and propulsive impulses than the hindlimbs
(Lammers and Biknevicius,
2004); recently collected (A.R.L., unpublished) data confirm that
pattern. It seems likely that craniocaudal force is not large enough to
influence shear force so much that significant differences between fore- and
hindlimbs are observed. Finally, it is also possible that there is some
interaction between grip location and claw use or in the positioning of the
digits. The opossums have claws on all digits except for the hallux, and the
foot may more effectively grip the substrate and reduce shear force with claws
or the somewhat opposable hallux.
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The opossums did not change grip location on the 2 cm-diameter arboreal
trackways to cope with the relatively smooth surface. Not only did not
differ significantly between substrates, but Fshear was also
not correlated with , or was very weakly correlated. [It is worth
pointing out that CC,musc contributes considerably to
Fshear, and CC,musc apparently has no
relationship with (Lammers and
Gauntner, 2008).] Correlations between peak and median
Fnormal and within each group (e.g. forelimb on the
rough trackway) were usually weak or non-existent
(r20.32). Thus, it appears at first that grip location
has little influence on how the opossums generate normal and shear forces.
However, it is also possible that the within-group variation in is not
great enough to produce strong correlations with normal and shear forces. The
opossums may be biomechanically constrained to grip the 2 cm-diameter branch
trackway such that the forelimb grips closer to the top of the branch and the
hindlimb grips approximately midway between the top and the sides of the
branch. If, on the smooth trackway, they place their hands or feet closer to
the top of the branch, then normal force will greatly increase because a much
greater proportion of the animal's weight is applied normal to the branch
surface. But gripping the top of the branch provides very little bracing
against mediolateral undulation or (in a natural environment) wind and branch
movement because the opossum's hand has no opposable digits, and it seems
likely that neither hand nor foot has a large enough span on the 2 cm branch
to grip strongly. If the opossums grip the sides of the branch, then with
sufficient mediolateral forces they could create a very stable grip with
opposable limbs. But gripping the sides of the branch will increase the shear
force because most of the vertical force will be tangential to the surface of
the branch. Thus, it appears that the size of the branch and the sizes and
morphologies of the hand and foot limit the ways that these opossums can
adjust to a more slippery substrate.
The gray short-tailed opossums, with their morphology being relatively
unspecialized for arboreal locomotion, seem constrained to grip the 2 cm
branch in one particular way. When they attempt to move on a trackway with the
same diameter but a smoother surface texture, the only way they can adapt is
to move more slowly and increase the total substrate–limb contact time
with as many limbs as possible. Many arboreal specialists have morphological
differences that almost certainly allow greater flexibility in how they can
move on rough or smooth branches. For example, many arboreal marsupials have
significantly longer digits than closely related terrestrial marsupials
(Lemelin, 1999). These longer
digits probably allow the animals to grip branches more strongly than they can
if their digits were shorter. Some arboreal rodents have pads with glands that
secrete fluid so as to increase the friction between autopodia and substrate
(Haffner, 1998). I predict that
animals that are morphologically specialized to move in trees will have
greater flexibility in terms of where and how they grip branches. An animal
with long, opposable digits (or fluid-secreting glands, claws or microscopic
setae that interact with the substrate at a molecular level)
(Cartmill, 1985;
Haffner, 1998;
Autumn et al., 2006) should be
able to grip the top of a branch, which means that much more of its body
weight is applied normal to the branch. Thus, even when moving about on a
relatively smooth or slippery branch, such a specialized animal will be able
to avoid slowing its speed and adjusting its footfall patterns (as measured by
duty factor and limb phase) as much as M. domestica.
LIST OF ABBREVIATIONS
CC,musc
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Footnotes |
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References |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Autumn, K., Dittmore, A., Santos, D., Spenko, M. and Cutkosky,
M. (2006). Frictional adhesion: a new angle on gecko
attachment. J. Exp. Biol.
209,3569
-3579.
Cartmill, M. (1972). Arboreal adaptations and the origin of the order primates. In The Functional and Evolutionary Biology of Primates (ed. R. Tuttle), pp.97 -122. Chicago, IL: Aldine Atherton.
Cartmill, M. (1974). Pads and claws in arboreal locomotion. In Primate Locomotion (ed. F. A. Jenkins, Jr), pp. 45-83. New York: Academic Press.
Cartmill, M. (1985). Climbing. In Functional Vertebrate Morphology (ed. M. Hildebrand, D. M. Bramble, K. F. Liem and D. B. Wake), pp. 73-88. Cambridge, MA: Belknap Press of Harvard University Press.
Haffner, M. (1998). A comparison of the gross morphology and micro-anatomy of the foot pads in two fossorial and two climbing rodents (Mammalia). J. Zool. (Lond.) 244,287 -294.[CrossRef]
Hamrick, M. W. (2001). Morphological diversity in digital skin microstructure of didelphid marsupials. J. Anat. 198,683 -688.[CrossRef][Medline]
Hildebrand, M. (1976). Analysis of tetrapod gaits: general considerations and symmetrical gaits. In Neural Control of Locomotion (ed. R. M. Herman, S. Grillner, P. Stein and D. G. Stuart), pp. 203-236. New York: Plenum Press.
Jenkins, F. A., Jr (1974). Tree shrew locomotion and the origins of primate arborealism. In Primate Locomotion (ed. F. A. Jenkins, Jr), pp.85 -115. New York: Academic Press.
Kapatkin, A. S., Arbittier, G., Kass, P. H., Gilley, R. S. and Smith, G. K. (2007). Kinetic gait analysis of healthy dogs on two different surfaces. Vet. Surg. 36,605 -608.[CrossRef][Medline]
Lammers, A. R. and Biknevicius, A. R. (2004).
The biodynamics of arboreal locomotion: the effects of substrate diameter on
locomotor kinetics in the gray short-tailed opossum (Monodelphis
domestica). J. Exp. Biol.
207,4325
-4336.
Lammers, A. R. and Gauntner, T. (2008). Mechanics of torque generation during quadrupedal arboreal locomotion. J. Biomech. 41,2388 -2395.[CrossRef][Medline]
Lammers, A. R., Earls, K. D. and Biknevicius, A. R.
(2006). Locomotor kinetics and kinematics on inclines and
declines in the gray short-tailed opossum Monodelphis domestica. J.
Exp. Biol. 209,4154
-4166.
Lee, A. K. and Cockburn, A. (1985). Evolutionary Ecology of Marsupials. Cambridge, MA: Cambridge University Press.
Lemelin, P. (1999). Morphological correlates of substrate use in didelphid marsupials: implications for primate origins. J. Zool. 247,165 -175.[CrossRef]
Phillips, C. J. C. and Morris, I. D. (2001). The locomotion of dairy cows on floor surfaces with different frictional properties. J. Dairy Sci. 84,623 -628.[Abstract]
Redfern, M. S., Cham, R., Gielo-Perczak, K., Grönqvist, R., Hirvonen, M., Lanshammar, H., Marpet, M., Pai, C. Y. C. and Powers, C. (2001). Biomechanics of slips. Ergonomics 44,1138 -1166.[Medline]
Wagner, J. A. (1842). Diagnosen neuer Arten brasilischer Säugetheire. Arch. Naturgesch. 8, 356-362.
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