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Cite this article: Loscher DM, Meyer F, Kracht
K, Nyakatura JA. 2016 Timing of head
movements is consistent with energy
minimization in walking ungulates.
Proc. R. Soc. B 283: 20161908.
http://dx.doi.org/10.1098/rspb.2016.1908
Received: 31 August 2016
Accepted: 3 November 2016
Subject Areas:
biomechanics, physiology
Keywords:
kinematics, walk, quadruped,
collision mechanics, head, mammal
Author for correspondence:
John A. Nyakatura
e-mail: john.nyakatura@hu-berlin.de
†
These authors contributed equally to this
study.
Electronic supplementary material is available
online at https://dx.doi.org/10.6084/m9.fig-
share.c.3579821.
Timing of head movements is consistent
with energy minimization in walking
ungulates
David M. Loscher1,†, Fiete Meyer2,†, Kerstin Kracht3and John A. Nyakatura4
1
AG Humanbiologie, Department of Biology, Freie Universita
¨t Berlin, Albrecht-Thaer-Weg 6, 14195 Berlin,
Germany
2
FG Mechatronische Maschinendynamik, Department of Mechanics, Einsteinufer 5, Technische Universita
¨t Berlin,
10587 Berlin, Germany
3
PAConsult GmbH, Environmental and Structural Dynamics Test Lab, Birkenau 3, 22087 Hamburg, Germany
4
AG Morphologie und Formengeschichte, Image Knowledge Gestaltung: an interdisciplinary laboratory,
Institute of Biology, Humboldt University, Philippstraße 13, 10115 Berlin, Germany
JAN, 0000-0001-8088-8684
Many ungulates show a conspicuous nodding motion of the head when walk-
ing. Until now, the functional significance of this behaviour remained unclear.
Combining in vivo kinematics of quadrupedal mammals with a computer
model, we show that the timing of vertical displacements of the head and
neck is consistent with minimizing energy expenditure for carrying these
body parts in an inverted pendulum walking gait. Varying the timing of
head movements in the model resulted in increased metabolic cost estimate
for carrying the head and neck of up to 63%. Oscillations of the head– neck
unit result in weight force oscillations transmitted to the forelimbs. Advan-
tageous timing increases the load in single support phases, in which
redirecting the trajectory of the centre of mass (COM) is thought to be energe-
tically inexpensive. During double support, in which—according to collision
mechanics—directional changes of the impulse of the COM are expensive,
the observed timing decreases the load. Because the head and neck comprise
approximately 10% of body mass, the effect shown here should also affect the
animals’ overall energy expenditure. This mechanism, working analogously
in high-tech backpacks for energy-saving load carriage, is widespread in
ungulates, and provides insight into how animals economize locomotion.
1. Background
The majority of larger mammals use the quadruped walking gait as the main
form of locomotion for travelling large distances [1–5]. Running gaits are
used in bursts and for high-speed locomotion, e.g. for hunting and escaping,
so an animal’s life depends largely on the effective outputs of this behaviour.
Nevertheless, it is the walking gait in which on average the most energy in
absolute terms is consumed over an entire day [4,6,7]. As locomotion is an
important energy-consuming factor for most mammals [4,6– 8], the main selec-
tive pressure shaping the walking gait used in slow locomotion should be
energy efficiency rather than high performance.
Many large mammals, such as horses, exhibit a conspicuous nodding of
the head when walking. The head and neck of mammals form a highly mobile
cantilever on the trunk that constitutes a substantial part of the animal’s whole
body mass. To date, biomechanical studies on the locomotion of quadrupedal
mammals have focused almost exclusively on movements of the limbs and the
trunk. The potentially energy-consuming effects of head movements relative to
the trunk remain for the most part unexplored in large mammals, but have
been shown to be significant in birds [9]. The few existing studies on head
movements that accompany the quadrupedal mammalian walking gait
[10– 14], confirm that the head’s kinematics are decoupled from the movements
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of the trunk. It was therefore proposed that the head move-
ments compensated for fluctuations of the trunk in height
and velocity, and stabilized optical and vestibular perception
[12– 14]. However, available data for head-nodding behaviour
in horses suggest that it exceeds the vertical motion of the with-
ers [11,14,15]. Thus,the motion of the head relative to the trunk
might increase the overall amplitude of cranial oscillation
and appears to contradict the hypothesis that this specific
movement has a sensory compensatory function. Moreover,
when affected by unilateral forelimb lameness, horses show a
reduction in the amplitude of vertical head movement during
the stance phase of the lame leg and an increase during
the stance phase of the sound leg [16]. This implies that head
movement influences forelimb loading, but does not explain
the functional significance of head nodding for the sound
animal. As the head– neck unit makes up around 10% of a
horse’s body mass [17,18], and can be expected to constitute
a similar proportion in other hoofed mammals, it is clear that
the movements of this cantilever have a relevant mechanical
influence on walking mechanics and energetics.
Over the last decade, collision mechanics have success-
fully been used to explain experimental observations on the
basic mechanics and energetics of walking gaits [19– 25].
Although studies have mainly focused on human bipedal
walking, collision mechanics have also been applied to the
quadrupedal walking gait of larger mammals [26– 28]. For
the walking gait, it has been demonstrated that during the
single support phases the trajectory of the body’s centre of
mass (COM) closely resembles that of an inverse pendulum.
This passively conserves mechanical energy and only very
little active mechanical work is necessary [21]. By contrast,
according to collision mechanics, the step-to-step transitions
during the double support phases require that the impulse
of the body’s COM is actively redirected. This inevitably
involves positive work from the muscles of the trailing limb
accelerating the body in a forward–upward direction and
negative work from the muscles of the leading limb deceler-
ating the body in a backward– upward direction [21]. During
walking, single support phases therefore are considered to be
energetically inexpensive and double support phases are con-
sidered to be energetically expensive. Considering the
possible mechanical effects of head movements on the
trunk and legs, it is intriguing that specialized, high-tech
backpacks have managed to significantly reduce the energetic
costs of transport in humans by decoupling the movement of
the load from that of the carrier’s body [29,30]. The carried
mass is supported in suspension, thus enabling it to swing
vertically out of phase to the vertical oscillations of the car-
rier’s body mass. As a result, the fluctuations of the weight
force exerted from the load to the carrier’s body are phase
shifted, so that the carrier’s legs are relieved during the
expensive double support phases and loaded during the
inexpensive single support phases. The collisional energy
losses and therefore the overall costs of locomotion are
reduced.
We hypothesized that the movements of the head –neck
unit of larger mammals fulfil a similar function. To test
this, we began with a video analysis of the movements of
eight horses during walking. The data were then used as
input parameters for a simple computer model of a horse’s
fore-quarters and head– neck unit. With the model, we
assessed mechanical work and estimated energetic effects of
the vertically directed forces acting on the shoulder resulting
from the observed motions of the head– neck unit relative to
the trunk. We subsequently investigated the influence of the
timing of these relative vertical movements on the metabolic
costs for carrying the head using our model. Finally, in order
to facilitate the discussion of the findings in a wider zoolo-
gical context, the phase relationship of head– neck and
thorax movements of 18 additional species of cursorial mam-
mals (ungulates, carnivores and semi-terrestrial primates)
were also studied (table 1).
2. Results
In the walking gait of a horse, the head and withers showed two
complete oscillatorycycles of sinusoidal vertical movements per
stride within the sagittal plane. The range of absolute vertical
motion was higher for the head than for the withers in all
individuals. The mean range of vertical cranial oscillation
(mean +1 s.d.: 9.1 +3.4 cm) exceeded thoracic oscillation
(3.2 +1.0 cm). Thus, vertical displacement and peak accele-
rations of the eyes and the vestibular system exceeded that of
the thorax by 2.9 and 2.5 times, respectively (figure 1).
The head and withers oscillated vertically with a distinct
phase shift of 25.0+2.5% (mean +1 s.d.) of the stride cycle
duration, leading to an out-of-phase vertical movement of
these body parts. In a symmetrical gait, like the walk, the
body axis undergoes two vertical oscillations (one per step)
150
160
170
180
0 25 50 75 100
displacement (cm)
stride duration (%)
–6
–3
0
3
6
acceleration (m s–2)
(a)
(b)
Figure 1. Mean (+1 s.d.) vertical accelerations (a) and displacements (b)of
head (red) and withers (blue) of eight warmblood horses during one stride at
normal walk. Mean displacements (p¼0.0001) and accelerations (p¼
0.0004) differed significantly at the p¼0.001 level. For better comparison,
the mean vertical anatomical positions of different sized horses were fitted.
Horizontal bars indicate substrate contact of the right (grey) and left (black)
forelimb; vertical lines indicate changes from phases of double forelimb
support to single forelimb support. Note that the stride consists of two
steps and thus vertical movements of the body axis are bi-phasic.
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during each stride. Therefore, a phase shift between the head
and the withers of 0 and 50% of stride duration equals a vertical
in-phase movement, whereas a phase shift of 25 and 75% indi-
cates a vertical out-of-phase movement (figure 1). Carried by
the inverse pendulum movements of the forelegs during walk-
ing, the equine thorax reached its lowest position along with
the strongest upwards directed acceleration during the single
support phase of the forelegs (figure 1a,b). By contrast, being
out-of-phase with the thorax, the head reached its highest
position along with the maximum downward directed
acceleration during the double support phase. So, as the head
and neck were accelerated downward with a certain pro-
portion of gravitational acceleration during the double
support phase, the forelegs only had to provide the support
necessary to resist the remaining proportion of the gravita-
tional acceleration. Swinging the head with 4.2 m s
22
(43% of
gravitational acceleration) downwards during the double sup-
port phase lowered the weight force of the head during this
fraction of time by 43% compared to the force on the head in
a static position. As the COM of the combined head –neck
unit is closer to the pivot of the oscillating cantilever than the
head marker, its vertical range of motion (as well as the accel-
eration) was determined to be just 79% of that of the head
marker, but this does not affect the phase shift relative to the
thorax and still lowered the weight force of the complete
head– neck unit during double support up to 34%.
Accordingly, our simple model of a horse’s fore-quarters
showed a distinct correlation between energy expenditure and
the phase relation of vertical motion between the head and
the point in which the trunk is connected to the forelimbs,
i.e. the attachment area of the serratus ventralis muscle at the
scapula (trunk–forelimb suspension point (SP) hereafter).
Moving the head– neck unit with a considerable phase shift
relative to the thorax reduced the energetic effort of the whole
model in comparison to in-phase movements (figure 2). In the
model, the optimum energetic phase relation was reached at a
shift of 25.25%, which agrees with the observed phase shift in
horses within the experimental error. Deviating from this
optimal phase shift resulted in an increase of the energy expen-
diture share for bearing the load of the unit of head and neck
by up to 63.15%.
Comparing the timing of head nodding relative to thorax
movements in an additional 18 species, we discovered that
the timing observed in horses is not uncommon among
larger quadruped mammals (figure 3). Taking into account
the relative neck lengths of all 19 mammalian species studied,
a relationship between these kinematic and anatomical features
can be asserted. Species with a neck– trunk ratio below 0.3
did not regularly exhibit appreciable phase shifts of head
and thorax motion. Those mammals examined with ratios
between 0.3 and 0.4 (dogs and maned wolves) showed a
speed-dependent change in head movement. During slower
walking cycles, using step frequencies of less than 1.3 Hz,
both species moved the head in phase with the trunk. When
exhibiting step frequencies more than 1.3 Hz, the rhythm of
the vertical head movements shifted to about 20– 25% in
phase. Without exception, quadrupeds with intermediate
neck lengths (ratio between 0.4 and 0.53) moved the head
with similar phase shifts to the horse. However, only one of
the four species with even longer necks (ratio between 0.55
and 1.35) exhibited phase shifts comparable to that of the horse.
3. Discussion
We examined the head movement relative to the trunk in 19
species of cursorial quadruped mammals in order to evaluate
Table 1. Species sample for kinematic analysis of head and shoulder motion.
species trivial name classification individuals
Bos taurus indicus zebu Artiodactyla, Bovidae 3
Connochaetes taurinus blue wildebeest Artiodactyla, Bovidae 5
Eudorcas thomsoni Thomson’s gazelle Artiodactyla, Bovidae 4
Oryx leucoryx Arabian oryx Artiodactyla, Bovidae 5
Tragelaphus strepsiceros greater kudu Artiodactyla, Bovidae 3
Camelus bactrianus Bactrian camel Artiodactyla, Camelidae 4
Giraffa camelopardalis giraffe Artiodactyla, Giraffidae 4
Canis lupus familiaris domestic dog Carnivora, Canidae 6
Chrysocyon brachyurus maned wolf Carnivora, Canidae 4
Acinonyx jubatus cheetah Carnivora, Felidae 3
Felis silvestris catus domestic cat Carnivora, Felidae 5
Panthera leo lion Carnivora, Felidae 4
Crocuta crocuta spotted hyena Carnivora, Hyaenidae 4
Equus africanus African wild ass Perissodactyla, Equidae 4
Equus ferus caballus domestic horse Perissodactyla, Equidae 8
Equus quagga plains zebra Perissodactyla, Equidae 6
Erythrocebus patas patas monkey Primates, Cercopithecidae 3
Macaca nemestrina southern pig-tailed macaque Primates, Cercopithecidae 4
Semnopithecus entellus grey langur Primates, Cercopithecidae 3
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the energetic effects of the timing of conspicuous head-nodding
behaviour during walking. There are few comparable studies
on head kinematics of the quadruped mammalian walking
gait, but our findings are consistent with existing data for the
head and thorax movement of horses [2,5,6,10]. In horses,
the basic kinematic pattern of the head and withers moving ver-
tically out-of-phase appears to be typical in a majority of hoofed
mammals, and is even shared by some Carnivora. It was
previously hypothesized that these movements stabilized
axial elements in horses, thus enabling the nervous system to
maintain spatial orientation [5]. However, we found that the
observed movement patterns increased the vertical displace-
ments and accelerations of the head, and hence the optical
and vestibular organs in comparison to a hypothetical motion
of the head rigidly fixed to the trunk, by far. This calls into ques-
tion the suggestion that the stabilization of a spatial reference
frame is a primary function of this kinematic feature.
As an alternative explanation for this conspicuous behav-
iour, we demonstrate how the specific timing of head
movement relative to the thorax is consistent with a way of
minimizing energy expenditure. In horses, characteristic verti-
cal motions of head and neck result in a reduced weight force of
these body parts transmitted to the forelegs during the double
support phases. The weight force is equivalently increased
during the single support phases of the forelegs. A similar
phase shift in weight fluctuation constitutes the core premise
of the energy-saving weight bearing in high-tech backpacks
[29,30]. As our model used the dimensions, inertial properties
and kinematics of a horse’s fore-quarters as input parameters,
it directly assesses the mechanical effect of head movements
only in horses. However, the highly reductionist model more
generally allows qualitative predictions on the basic energetic
effect of head movements for relatively large mammalian
quadrupeds with similar relative head– neck masses and kin-
ematics. For species exhibiting a comparable timing between
head-nodding and thorax movements, we hypothesize a
similar mechanical effect.
Comparing the kinematics of the collision-reducing back-
pack and the observed head movements of quadruped
mammals, as exemplified by the horse, the most important
difference can be found in the amplitude of displacement of
the mass that is moving out of phase with the proximal
joints of the supporting limbs. In the backpack, the oscillating
load moves vertically with a relative amplitude to the car-
rier’s back that is similar to the absolute amplitude of the
walking human’s trunk [29]. Therefore, the phase shift of
the load’s vertical motion results in a strong reduction in
the oscillatory amplitude of the load. By contrast, the head
movements of the walking horses showed an absolute verti-
cal amplitude that far exceeded that of the withers. It has
been shown that head– neck movement, unlike that of the
swinging load within the backpack, is not performed exclu-
sively passively, but rather involves muscular activity [11].
With varying phase shift between the vertical oscillations of
head– neck unit and thorax, we expect both for the work to
be performed by the limbs, and also for the energetic cost of
sustaining the head–neck unit’s relative movements to
change. Generally, to achieve a net energy-saving effect, the
changes in energy expenditure for sustaining deviating
head– neck movement relative to the trunk must not overcom-
pensate for the energetic disadvantagesof bearing the loadat a
different phase shift. Thus, the observed timing likely reflects
an optimization of the combination of both factors.
In this regard, the anatomical and biomechanical studies of
Gellman and colleagues on the cervical spines of horses are of
particular interest [10,11,31]. The authors showed that the elas-
tic nuchal ligament stores and recovers up to 59% of the energy
needed to sustain head movement during walking (i.e. at least
41% need to be actively performed) [11]. Therefore, this elastin-
rich structure that dorsally spans from the occiput to the
thoracic spinous processes could play a vital role in sustaining
the collision-reducing motion of the head and neck at low cost,
optimizing or even enabling the net energy-saving effect.
Could the presence (or the absence) of a nuchal ligament be a
potential explanation for the occurrence of out-of-phase or in-
phase movements of the head and trunk in different species?
The fact that this ligament is inherent to ungulate and canid
species in general [32–34], but is absent in felid species and
non-human primates, is in line with our results and seems to
support this notion. Hyaenas, however (like other feloid carni-
vores), do not have nuchal ligaments [35,36] but still exhibit
pronounced head movements—albeit with a lower mean
phase shift relative to the trunk than ungulates and fast walk-
ing canids (figure 3). We can postulate, therefore, that while
this ligament probably helps to make the collision-reducing
head movements more efficient, it does not seem to be crucial
to this kinematic feature.
In vivo electromyography of the cervical musculature of
walking horses showed that the splenius muscle exhibits
bilateral activity during the single support stance of each fore-
limb [37–39], that is when head and neck reach the lowest
position. It would seem that the activity pattern of this
main dorsal muscle of the cervical spine is enough to
induce the observed vertical motion of the head– neck unit.
To decelerate and reaccelerate the falling cantilever, it was
proposed that isometric contractions could be used, thus
avoiding any need to shorten muscle fibres [31]. This
means that the vertical oscillations of the head and neck
can be maintained with highly economic muscle activity—a
strategy that is complemented by, but not entirely dependent
on, the presence of a nuchal ligament.
Another anatomical feature that must be taken into account
is the length of the head– neck cantilever that actsas an oscillat-
ing pendulum. To sustain an oscillatory motion with loweffort,
the oscillating frequency has to be kept close to the natural fre-
quency of the swinging system. As the natural frequency of an
ideal pendulum (with frictionless pivot and massless rod) is
inversely proportional to the square root of the length of the
DEm
DEm,min
1.6
1.0
1.1
1.2
1.3
1.4
1.5
phase shift (%)
01020304050
Figure 2. Relative metabolic energy (DE
m
) costs of locomotion depending
on the phase shift between the vertical oscillations of the head– neck unit
and the trunk–forelimb SP calculated by the simple horse model. (Online
version in colour.)
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pendulum, a longer neck should determine a lower natural fre-
quency of the vertical movements of head and neck—and vice
versa for a shorter neck. Figure 3 shows that in our sample the
length of the cervical spine is related to the timing of head
movement. The majority of quadrupedal mammals with rela-
tively long necks, like most ungulates and the spotted
hyaena, use out-of-phase movements of the head-and-neck
cantilever, which appear to reduce collisional energy loss.
The natural frequency of an oscillation is also influenced by
material properties, and various studies have shown that the
adjustable stiffness of muscle– tendon complexes may modulate
the natural frequency of body parts that exhibit spring-like
mechanics [40– 43]. Therefore, the optimal stiffness to maximize
elastic energy storage can be tuned to match a range of step
frequencies. Whilewe here focus on neck length, other morpho-
logical properties like neck stiffness and neck– head unit inertial
properties might furtherinfluence the oscillating pendulum and
should be addressed in future studies.
In our study, the quadrupeds with relatively short necks,
like felids and monkeys, show no phase-shifted movements
of the head– neck unit during walking, but keep the cervico-
thoracic joint straight and move the head in phase with the
thorax. One possiblereason for this result is that the natural fre-
quency of the oscillations of a short head– neck unit is too high
to be tuned to match the step frequency, and the motion would
be too costly to sustain. Given that the modulation of the natu-
ral frequency works by muscle contractions stiffening the
spring, the adjustable range of modulation mainly extends
towards increasing this frequency, not reducing it. One obser-
vation that supports this notion is the step frequency-related
change in head movements within the two species of canids
examined (dogs and maned wolves). In our sample, only
these two species displayed a speed-dependent phase shift.
As both these species have intermediate neck lengths, the
step frequency during a slower walking gait might be too
low to meet the natural frequency of the head–neck cantilever,
just as in the short-necked species. When walking speed
increases, so does the step frequency: this increased frequency
may be closer to the natural oscillatory frequency of the canti-
lever and, thus, relative vertical head movements could be
accomplished with much less effort.
For the relatively long-necked ungulates and the hyaena,
the length of the neck allows them to adjust the natural fre-
quency to cover the range of usual walking step frequencies
at relatively low cost, and thus out-of-phase head motions
are a habitual kinematic feature. So, why then do three species
of relatively long-necked ungulates (giraffe, Thomson’s gazelle
and Bactrian camel) show head movements with very little
phase shift relative to the vertical movements of the thorax?
Firstly, as short necks can determine natural frequencies that
are too high, long necks might have low oscillatory frequen-
cies—possibly too low to fall into the range of adequate step
frequencies of walking. This seems a particularly plausible
explanation, as all three species of ungulates that do not exhibit
the timing characteristic for horses fall within the range of the
longest necks measured.
Secondly, it must be considered that the cantilever of the
head and neck moves like a pendulum around a pivot located
at the intersection between the cervical and thoracic spine.
Even when the neck is in a perfectly horizontal orientation,
the movement of the cantileveralways exhibits a slight longitu-
dinal component. The closer the orientation of the neck gets to
the vertical axis, the larger the longitudinal component of the
motion becomes, and—accordingly—the smaller the vertical
component. In fact, the three hoofed species that exhibit the
smallest vertical amplitudes of head movements in this study
carry the cervical spine relatively straight upwards. A pendu-
lum motion of the neck around the cervico-thoracic joint
would therefore lead to a relatively small vertical displacement
of the head, but to a large longitudinal motion. Within the
0
0.5
1.0
1.5
2.0
0
10
20
30
neck–trunk ratio
phase shift (%)
phase shift neck–trunk ratio
0.25 0.40 0.55
pig-tailed macaque
Hanuman langur
patas monkey
cheetah
domestic cat
lion
maned wolf (fast)
maned wolf (slow)
domestic dog (fast)
zebu
blue wildebeest
spotted hyena
Arabian oryx
African wild ass
domestic horse
plains zebra
greater kudu
Thomson’s gazelle
Bactrian camel
giraffe
domestic dog (slow)
Figure 3. Phase shift of the vertical oscillations of head and withers (black squares; mean+1 s.d.) and the corresponding length ratio of the neck and trunk
(white bars; mean +1 s.d.) of 19 species of quadrupedal mammals. The horizontal red line indicates the energetically optimum phase shift calculated by the horse
model. For two species (maned wolf and domestic dog) data were separated between slower and faster walking trials, because of a speed-dependent change of the
phase shift in these species. All other sampled species did not show a speed-dependent phase shift. The vertical lines separate groups of species with mainly
observed phase shifts (see text). (Online version in colour.)
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three species of ungulates that showed a low phase shift of the
vertical oscillations of head and withers, large longitudinal
out-of-phase movements of these body parts were qualitatively
observed. By exerting forward- and backward-directed accel-
erations onto the trunk, these movements of the head–neck
cantilever—when correctly timed—could attenuate the fluctu-
ations of kinetic energyof the trunk during walk and therefore,
again, reduce collisional energy loss at forefoot step-to-step
transition. However, the possible collision-reducing effect of
longitudinal out-of-phase movements of body compartments
has not yet been evaluated in vivo or by computer modelling.
We do not, therefore, discuss this potential kinematic adjust-
ment to economize collisional energy loss here, but it could
be addressed in future studies along with other adjustments
of the phase relationships between different body parts. Never-
theless, we can state that an orientation of the cervical spine
that favours longitudinal movements of the head– neck cantile-
ver over vertical movements is a plausible explanation for the
observed difference in kinematics of the three ungulate species
with diverging patterns of head– neck movement.
The study presented here uses a simple model to demon-
strate that the timing of head– neck unit movements relative
to the trunk is a mechanism with the potential to consider-
ably reduce the metabolic energy costs of locomotion by
reducing collisional energy losses. The predicted optimum
phase shift of the head–neck unit relative to the trunk is
closely matched by many mammalian species, especially
ungulates. In walking horses, the observed head movements
relative to the trunk cannot be sustained completely passively
and are thus connected to costs [11]. We expect that as a result
of the observed timing of vertical head– neck movement, the
involved costs for actively sustaining these head movements
and the costs for bearing the unit’s load are optimized simul-
taneously to minimize overall costs. The presence or the
absence of a highly elastic nuchal ligament, the relative
length of the neck determining the natural frequency of the
oscillating cantilever, and the orientation of the neck appear
to influence the effectiveness of this kinematic adjustment
to minimize collisional energy losses. This study indicates—
for the first time—that this energy-saving mechanism,
already implemented in engineered mechanical carrying
aids, also evolved in animals. The fact that the energy-
saving effect of this motion could be confirmed for two mech-
anical structures as different as the mass in a backpack and
the head–neck cantilever of a horse and other larger
mammals, suggests this mechanism is an expedient way of
bearing a load while walking.
In summary, by demonstrating that this mechanism is pre-
sent in animals, we provide new evidence for the kinematic
optimization of natural locomotion. It is possible that vertical
head movements are not the only way by which animals
use the timing of moving body parts to minimize energy
expenditure related to collision effects. The mechanism also
has the potential to be used in the field of bio-informed robotics
to design more effective walking machines as well as in the
field of paleobiology to infer locomotor characteristics
in extinct mammalian species, e.g. from the presence of
osteological correlates of a nuchal ligament.
4. Methods
Additional information on the methods is provided in the elec-
tronic supplementary material and all custom code for data
processing and modelling is made available. For the kinematic
analysis (figure 4), white markers were placed on the occiput,
between the forehead and muzzle, the scapula and withers of
eight adult warmblood horses (six geldings and two mares; age:
5– 16 years, mean 10.4 +3.7 years; height at withers: 150 – 169 cm,
mean: 161.4 +6.0 cm). During trials, the horses were led by a
loosely held cord through a calibrated space to cover a range of
walking speeds. None of the other animals were marked. They
were filmed either following their owners (dogs) or walking
freely (cats), or in zoological gardens (Zoologischer Garten Berlin
head marker model SP
(Dxsp(t)/ysp(t))
withers marker
model head–neck mass
(xhn(t)/yhn(t))
Y
X
w
ithers mark
er
Mz
Fx
Fy
scapula marker
COM
head–neck unit
(a)(b)
rostral marker
Figure 4. Modelling the energetic effect of conspicuous nodding of the head – neck unit relative to the thorax in a horse. (a) Position of the withers, head, rostral
and scapula markers for the kinematic analysis of amplitude and phase relationship of the modelled trunk– forelimb SP (see text) and COM of the head–neck unit.
(b) Illustration of the reductionist model during the double support phase. The model is driven by kinematic data of a reference individual and, in the case of the
vertically directed movement ( y
hn
(t)) of the head–neck unit, also by imposing phase-shifted kinematics. The latter is used to calculate the vertically directed force
at the SP. We here considered the opposing force of equal magnitude to maintain equilibrium at the SP (F
y
). This force, in combination with the vertically as well as
horizontally directed movement of the SP (Dx
sp
(t), y
sp
(t)), is subsequently used to estimate the energetic effects of the timing of the head– neck unit’s vertically
directed movement relative to the trunk (see text). We modelled progression as if on a treadmill, i.e. averaged over an entire stride the position of the SP remains
stationary. Horizontally directed movement of the head– neck unit (x
hn
(t)) and corresponding horizontally directed force (F
x
) and moment at the SP (M
z
) are not
considered in the model.
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and Tiergarten Friedrichsfelde, both Germany; all other species)
while walking at their preferred speed on flat ground.
The animals were filmed using a Sharp ViewCam Z VL-Z3 at
a frequency of 50 fps perpendicular to the animals’ line of move-
ment. For each individual, 10 full and steady-state movement
cycles, covering a range of walking speeds, were selected for
data analysis. With the APAS software (v. 9.3, 2003, Ariel
Performance Analysis System, Ariel Dynamics, San Diego, CA,
USA) the motion of the head and withers of the horses within
the sagittal plane was measured by identifying the x- and y-pos-
itions of the markers. From these data, the linear vertical
displacement and acceleration of the markers were calculated.
For the animals without markers, the positions of the occiput
and the dorsal spinal processes of the thoracic vertebrae were
digitized by hand frame by frame. Spatial calibration was under-
taken only for the horses. For all other animals, we calculated
the phase relation of the vertical displacements of the head and
withers. All motion data were filtered using the integrated
second-order, low-pass Butterworth filter of the APAS Software
with a cut-off frequency of 5 Hz. To statistically test for differ-
ences between observed timing in head and thorax vertical
movements we first confirmed the Gaussian distribution using
the Shapiro–Wilks test. This allowed us to use Student’s t-test
for parametric data of paired samples. The significance level
was set at p¼0.001.
To determine the ratio of cervical spine length to trunk length
of the 18 additionally analysed species, still images were taken
from the films of each animal at touchdown of a forefoot. The
length between the occiput and the cervico-thoracic joint, as
well as between the cervico-thoracic joint and the head of the
femur, was measured directly (to determine the ratio no cali-
bration of the lengths was necessary) using the software IMAGEJ
[44]. The positions of the joints were estimated using anatomical
drawings of corresponding or closely related species.
Based on the anatomical characteristics of a warmblood horse,
in particular with regard to the masses and COM positions
of the head and neck, the position of the trunk– forelimb SP and
the kinematic restrictions to be imposed upon the forelimbs
and the head–neck cantilever, a simple model was built. This
was done with the aim of estimating the energetic consequences
of the vertically directed forces in the shoulder that result from ver-
tical movements of the head–neck unit relative to the thorax
(figure 4). To achieve this, we first recorded the actual kinematics
of the head–neck unit and the thorax of a reference individual
(warmblood gelding Leroy). In addition, we systematically
varied the phase shift between the vertical motions of the shoulder
and the head– neck unit in the model. Subsequently, based on the
inertial properties of the combined unit of the head and neck and
the observed and modelled kinematics, we determined the verti-
cally directed force resulting in the shoulder through an inverse
dynamics approach. Hereafter, distribution of the opposing force
upon the supporting limbs was identified according to instan-
taneous orientations of the respective extremities. Next, we
calculated the contribution of these forces to the necessary mechan-
ical work to be done by the forelimbs. Finally, in order to estimate
the influence of the timing of head movements relative to the trunk
on the energy expenditure of carrying the head–neck unit, we
used the published empiric relationship between mechanical
work and metabolic energy cost [45] to quantify the effect (refer
to the electronic supplementary material for a detailed characteriz-
ation of the model).
In this first approach to study the energetic effects of relative
movements of body parts some limitations were accepted. The
model does not consider horizontally directed oscillations of
the head–neck unit, which were found to be minimal (less
than 0.3 cm), nor the corresponding forces in the trunk– forelimb
SP. Also, the moment that is necessary to sustain the movement
of the head–neck unit relative to the thorax is not considered in
the model. It has previously been shown that much, but not all,
of this movement can be sustained passively [11].
The head and neck mass of a horse were scaled to the refer-
ence individual in accordance with the linear regression
formulae available in the literature [18], and then used to deter-
mine the corresponding parameters in the model. Motion
capture data of the same individual during unrestrained walking
were used to drive the model. Combining these methods, inertial
and kinematic parameters of the model were identified (table 2).
An inverse dynamics approach was used to derive the mech-
anical work (W) necessary to bear the load of the head– neck unit
with respect to the observed head-nodding behaviour. We discri-
minated between positive and negative mechanical work (W
þ
and W
2
, respectively). As both forms of mechanical work
independently result in the consumption of metabolic energy,
they would partially cancel each other out over the course of
a full stride cycle if they were not treated separately [22].
The two contributing types of work were thus defined as:
Wþ¼ððFvÞdtif Fv0
and W¼ððFvÞdtif Fv,0:
Here, Fand vare the vectors of force and velocity, respectively.
Fcan be determined from inverse dynamics and wasapproximated
based on the kinematic analysis of the reference individual as
described in the electronic supplementary material. The measure-
ment of oxygen consumption of uphill and downhill walking
individuals had previously been used to establish a relationship
between metabolic energy costs and mechanical work [45]. Based
on this, we estimated the energetic costs (E
m
)ofbearingtheload
of the head– neck unit using the following equation:
Em¼4X
i
Wþ
iþ5
6X
j
jW
jj:
The head– neck unit is modelled as a point mass (m
hn
) fixed to
a massless bar, which adequately represents the unit’s total weight
and its location of the COM. In mammals, the vertically directed
forces induced by the head– neck movement relative to the limbs
are transmitted to the limbs via the serratus ventralis muscle
that connects the trunk with the medial fossae and borders of
the scapulae of both forelimbs [46]. We modelled this point
of trunk–forelimb suspension (SP) as a frictionless hinge joint
and used motion capture data of the scapula marker. Finally,
both forelimbs were modelled as actuating struts of variable
length transmitting the forces induced at the SP to the points of
ground contact. Flexion or extension of these elements at any
given moment was determined by the instantaneous positions of
the SP and ground contact of the respective limb.
Data accessibility. The datasets supporting this article as well as the
source code for custom MATLAB and Maple analyses have been
uploaded as part of the supplementary material and to the Dryad
archive under http://dx.doi.org/10.5061/dryad.rf5bj [47].
Table 2. Parameters of the simple model.
length of stride
a
l
S
1.813 m
duration of stride Dt
S
1.328 s
mean velocity v
m
1.365 m s
21
mass of body m
b
620 kg
mass of head–neck unit m
hn
57.7 kg
a
A stride is defined to last from touchdown of a limb to the subsequent
touchdown of the same limb.
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Authors’ contributions. D.M.L. conceived the study, carried out the kin-
ematic analysis and drafted the manuscript; F.M. carried out the
modelling and participated in drafting the manuscript; K.K. initially
helped with conceiving the study and details of the model. J.A.N.
also contributed to the design of the study and drafted the manu-
script. All authors interpreted the results, and participated in the
in-depth revisions of previous versions of the paper, and gave final
approval for publication.
Competing interests. We have no competing interests.
Funding. The study was carried out using budgetary funds of the
respective institutions and received funding from the German
Research Council (DFG-EXC 1027 Image Knowledge Gestaltung. An
interdisciplinary laboratory).
Acknowledgements. We thank Utz von Wagner for helpful discussions
and Emanuel Andrada, the anonymous reviewers and the managing
editor for insightful criticism on previous versions of this manuscript.
We thank Helen Johnson (www.brownfoxlazydog.co.uk) for pro-
fessional language polishing.
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