Understanding brachiation: insight from a collisional perspective
Food, Nutrition and Exercise Sciences, Sandels Building, Florida State University, Tallahassee, Florida 32306, USA
* Author for correspondence (e-mail: jbertram{at}garnet.acns.fsu.edu)
Accepted 21 February 2003
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Summary |
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We suggest two reasons for overshooting smooth transition trajectories: in the case of continuous contact brachiation, excess mechanical energy can be maintained with a high amplitude swing, and an overshoot during ricochetal brachiation produces a safety margin.
The degree of energy loss with the transition to the swing phase is dependent both on the alignment of the pre- and post-transition paths, and on the kinetic energy at that instant. Active mechanisms reduce the effects of overshoots in both brachiation gaits. During continuous-contact brachiation, the path of the centre of mass can be controlled actively by flexion both of the trailing arm and the legs. During ricochetal brachiation, the length between the hand and the centre of mass (determining the subsequent swing path) can be controlled throughout the flight phase with leg flexion/extension. In addition, the elongated arms characteristic of gibbons improves the geometry of a collision for a given overshoot, and so may be viewed as a morphological adaptation reducing the energetic losses caused by overshooting for safety.
Key words: Gibbon, locomotion, collision, energy, pendulum, Hylobates lar
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Introduction |
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Previous work on brachiation has largely focussed on the mechanics of the
swing (Fleagle, 1974;
Preuschoft and Demes, 1984
;
Swartz, 1989
;
Turnquist et al., 1999
;
Chang et al., 2000
;
Usherwood et al., 2003
),
occasionally including an intervening ballistic flight
(Bertram et al., 1999
). While
the mechanics and equations governing pendulum-like swinging and ballistic
flight are familiar, neither suggests significant sources of energetic
loss.
This study highlights the mechanics and implications associated with
connecting two swing phases (continuous contact) or a flight and a swing phase
(ricochetal), focussing on the consequences of inelastic collision at contact
with new handholds. Expressions are developed for energetic losses due to
inelastic collision in brachiation for both point-mass and distributed-mass
cases. Two point-mass models are presented that highlight the effects of
missing `ideal' contact conditions. Model 1 uses starting conditions derived
from observed kinematics of gibbons brachiating under a range of controlled
conditions described in previous studies
(Chang et al., 1997;
Bertram et al., 1999
;
Chang et al., 2000
;
Usherwood et al., 2003
).
Active trailing-arm flexion and leg-lifting (deviations from passive
brachiation) are discussed as potential strategies for collision energy-loss
reduction during brachiation. Model 2 presents a simple point-mass model for
the energetic consequences of collision given a range of `overshoot'
distances, and mass to handhold length. It is used as a novel account for the
pressure towards arm elongation in specialist brachiators: we suggest that the
long arms characteristic of gibbons act to reduce collision losses associated
with `safe' brachiation. The principles of the jointed-body form of Model 2
provide a qualitative description of the benefits of the `double pendulum'
kinematics typical of fast ricochetal brachiation as a behaviour to reduce
collisional energy loss resulting from an overshoot of the handhold.
Gibbons as pendulums
Previous analyses of brachiation have generally focussed on the
pendulum-like behaviour of the gibbon body swinging beneath a handhold while
supported by a passive, stiff, arm
(Fleagle, 1974;
Preuschoft and Demes, 1984
;
Swartz, 1989
;
Turnquist et al., 1999
). Such
studies show that the swing-phase of both continuous-contact and slow
ricochetal brachiation acts mechanically as a simple pendulum. At higher
velocities, with fast ricochetal brachiation, the arm and body acts more as a
double or more complex pendulum (Bertram
and Chang, 2001
); during the swing phase, the arm and shoulder
rotate about the handhold, while the hips and body rotate about the shoulder.
Deviations from simple, or complex, passive pendulum behaviour can be
informative about energy input to a `brachiating system'
(Usherwood et al., 2003
). The
energy losses from a pendulum-like gibbon cited by Jungers and Stern
(1984
) of aerodynamics or
internal friction are slight (a gently swinging pendulum of 1 m length and 10
kg mass loses energy slowly, at less than 1% per swing cycle; our empirical
observation), and the particulars of the pendulum (arm length, mass
distribution etc.) are unlikely to increase such energy losses beyond the
negligible. Mechanisms by which mechanical energy can be gained or lost are
discussed in Usherwood et al.
(2003
). In addition, in
brachiation, velocity is not constrained to zero at the beginning or
end of the contact (swinging) phase. So, unlike clock-like pendulum behaviour,
pendulum mechanics provides no limitations on locomotion speed.
Brachiation by analogy with terrestrial gaits
Continuous-contact brachiation can be considered mechanically as analogous
to bipedal walking, where pendular exchange between potential and kinetic
energies dominate (e.g. Cavagna and Keneko,
1977). Unlike bipedal running, however, high speed ricochetal
brachiation does not appear to be dominated by spring-based mechanics.
Instead, ricochetal brachiation typically involves complex motions, including
rotation of the body about the shoulder joint. In such cases, the gibbon
becomes a jointed pendulum, suspended from the handhold by an outstretched
pectoral limb (Bertram and Chang,
2001
). In this motion there is no indication of extensive elastic
energy storage, although some use of the elastic characteristics of the
branches used as a superstrate should not be completely discounted.
Based on our previous work (Chang et
al., 2000; Bertram et al.,
1999
) and the absence of obvious elastic structures, ricochetal
brachiation is not viewed here as the analogue of the bouncing gait of
terrestrial running. Instead, brachiation is considered mechanically more
analogous to the skipping of a stone across water, where the path of the stone
is altered by interaction with the surface in a manner that resembles
bouncing, but does not involve spring-like energy storage and recovery.
Re-orientation of the velocity of the centre of mass (CoM) is achieved by
inelastic collisions with non-deflecting handholds in much the same way as
interaction with the water surface reorientates the travel of the skipping
stone without removing all of its velocity.
Collision in brachiation
The role of inelastic collision in terrestrial walking is becoming
increasingly recognised, both in terms of energy loss, and in loss reduction
(McGeer, 1990;
Garcia et al., 1998
;
Kuo, 2001
;
Donelan et al., 2002
). The
physics of inelastic collision also appear applicable to both
continuous-contact brachiation and ricochetal brachiation, as neither gait
involves extensive elastic energy storage. Dissipation of mechanical energy
must be associated with a deflection in the same direction as an applied force
(`negative work'), both of which can be directly observable (an approach
adopted by Usherwood et al., in press). An inelastic collision would result in
such a force and deflection (whether in the handhold, or somewhere in the
gibbon body, is not predicted), and this negative work may be spread over a
finite time (see Donelan et al.,
2002
); energy loss due to collision, and the initiation of the
swing phase, need not be instantaneous. Given that inelastic collision may not
be the sole cause of mechanical energy dissipation energy may be lost
from a smoothly swinging pendulum if it is allowed to extend, or if a moment
is applied opposing the direction of rotation a direct assessment of
energy losses due to collision is impossible, even from accurate force
measurements at the handhold. However, the geometry and energetic consequences
of collision, which we assume to be largely inelastic, can be inferred from
the path of the gibbon mass at the initiation of a swing phase. We believe
that the management of collisional energy loss during brachiation influences
the mechanics of this animal, and must be considered in order to truly
understand both the constraints of brachiation, and the opportunities that
this hylobatid's unique morphology and behaviour exploit. Below we describe
simple expressions for point-mass energetic losses due to inelastic collision
appropriate for brachiation.
Point mass description of collision losses in brachiation
The velocity (V') of a point centre of mass an instant after
colliding with a rigid superstrate using an inextensible, inelastic arm,
depends on the velocity the moment before (V), and the angle ß
subtended between the ballistic path and the support at that instant
(Fig. 1):
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This agrees with the point-mass model presented by Bertram et al.
(1999), which describes ideal
paths that avoid all losses due to collision: contact can be made with a new
handhold without collision losses only if kinetic energy is zero, or
if the paths are perfectly matched, and so ß equals
/2. This
description of inelastic tension-collision also accounts for the sudden jolt
familiar to over-eager children playing on swings. If a child swings too high,
allowing the swing rope to become loose, then the jerk as the rope becomes
taught again is related to the changes in velocity described in Equation 1,
and can cause some discomfort associated with the inevitable, and potentially
substantial, dissipation of kinetic energy.
The energetics of inelastic collision beyond the point-mass view
The above concept can be extended more generally, beyond a point-mass view
of inelastic collision in ricochetal brachiation. The principles of inelastic
collision result in conservation of momentum (both linear and angular, though
see below) while allowing energy to be dissipated. The point-mass model
supposes that the velocity vector of the point mass suddenly changes direction
on contact, losing the entire component of velocity orientated along the arm
(the velocity given to the Earth satisfies the conservation of linear
momentum, but can be ignored). If no torque is applied about the handhold
[supported by both gibbon anatomy
(Jenkins, 1981) and direct
measurements (Chang et al.,
2000
)], then the angular momentum of the gibbon about the handhold
is maintained throughout the instant of collision. Thus, a second way of
viewing the energetics of collision is in terms of angular and linear
momentum, and their associated energies. Immediately after collision, angular
momentum about the handhold is conserved (there being no torques about the
handhold) but translational momentum is not (using this frame of reference
the slight increase in velocity of the massive Earth is not
considered). Thus, ignoring (for the moment) gravity and any changes in gibbon
shape at the instant of collision, the rotational kinetic energy associated
with motion about (or past) the handhold is unaffected by collision. However,
the component of kinetic energy associated with translation towards or away
from the handhold prior to collision is lost. Thus, the energy loss due to
collision is the difference between the total kinetic energy prior to
collision, and the kinetic energy associated with motion about (past) the
handhold prior (=post) collision. This can be used in a general method of
stating the no-collision-loss conditions described by Bertram et al.
(1999
): no energy is lost if
collision occurs at the instant of zero kinetic energy; and no collision loss
occurs if the total kinetic energy equates to the rotational kinetic energy
associated with motion about (equivalent, at that instant, to motion past) the
new handhold (i.e. there is no motion towards, or away from, the handhold).
Hence this represents a form of the path-matching criterion that extends
beyond the point-mass view.
Error, safety and overshoot in ricochetal brachiation
Any movement towards a target is subject to a certain degree of error.
Ricochetal brachiation is unusual in locomotion in that the consequences of an
error in trajectory are highly dependent upon the direction of the error: a
small overshoot results in an imperfect contact, and some collisional energy
losses, whereas a small undershoot of the handhold results in a complete miss,
a subsequent fall, and high likelihood of injury or death. We develop a simple
point-mass model (Model 2) of energetic losses due to collision during
ricochetal brachiation that allows for a degree of `overshoot' e of
the ideal contact path. This model is then used to quantify the energetic
consequences of such an overshoot. The results suggest that this provides a
previously unrecognised pressure towards arm elongation as an adaptation for
collision reduction in ricochetal brachiation.
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Models and methods |
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Parameters for Model 1 were derived from video observation of brachiation from slow, continuous-contact, to fast, richochetal brachiation (Table 1). For each case, the range of possible paths given the observed `brachiation energy' state was calculated, where brachiation energy was defined as the mechanical energy available from the first of two brachiation `steps'. The energetic consequences of collision are presented for each potential path, and are related to release timing.
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Model 1
Point-mass ballistic paths and their collision consequences due to
release angle (timing): parameters derived from gibbon observation.
A captive, adult, female white-handed gibbon Hylobates lar L. was
filmed brachiating freely in the animal facility of the Department of Anatomy,
Stony Brook University, as reported in previous studies (Chang et al.,
1997,
2000
;
Bertram et al., 1999
;
Usherwood et al., 2003
). A
series of aligned handholds at constant height were placed to encourage
brachiation perpendicular to the plane of the video camera (Sony CCD/RGB).
Handhold spacing (D) was altered between trials in order to induce a range of
brachiation styles, from continuous-contact (D=1.2 m) to extreme ricochetal
(D=1.93 m, the maximum spacing in which two handholds could be viewed with the
camera). Video sequences were digitised of brachiation past two handholds.
Every fifth field was traced using Adobe software, providing a constant
interval between images of 0.083 s. Three example runs are presented here.
Centres of body mass CoM were estimated from the tracings. With the support
arm extended and the legs folded, the CoM was judged to lie just below the
pectoral girdle, following the morphological observations of Preuschoft and
Demes (1984
), and the kinetics
described by Chang and Bertram (Chang et
al., 1997
; Bertram and Chang,
2001
). With the legs extended, the centre of mass was assumed to
move distally, to halfway down the trunk (a reasonable approximation for use
in this model to demonstrate the potential effects of leg extension; however,
not a highly accurate quantitative assessment). The relevant length between
contact handhold and estimated centre of mass (L) was then calculated for the
bottom of the first swing (Fig.
2). In one instance (Example Run B) the distance between the
second handhold and the estimated position of the centre of mass at the bottom
of the second swing was also determined, providing a second value of L,
L', useful in demonstrating the effects of a `leg-lift'.
The total initial `brachiation energy' E was calculated from the sum of kinetic and potential energies measured at the end (top) of the first swing. The bottom point of the first swing was defined as zero potential energy, at which point all mechanical energy was assumed to be in the form of kinetic energy. This method of determining the energy state of the motion maximises accuracy, as the body moves slowest at the highest point in the cycle, thus centres of mass can be estimated most accurately. Relevant parameters for the three Example Runs are shown in Table 1.
Model 1 construction
For each of three Example Runs, the consequences of a range of potential
release angles (the angle between CoM, handhold, and vertical; see
Fig. 2C) were calculated. If
the swing phase was passive, then the empirically observed `brachiation
energy' for the highest position was also the kinetic energy at the bottom of
the first swing. The range of ballistic flight paths available for each
Example Run was calculated numerically (using G in LabVIEW 5.1,
National Instruments, Austin, TX, USA). Release at
=0, when the support
arm was vertical, resulted initially in a horizontal path of the point-CoM,
which dropped immediately in a parabolic path, under the influence of gravity.
The velocity V
at any angle
(up to the
`potential release angle'
) was calculated from the remaining kinetic
energy KE, as progressively more brachiation energy E became
converted to potential energy PE during the swing:
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The direction of the velocity vector at each potential release position lay parallel to the arc described by the CoM-hand length L about the first handhold. Simple ballistic paths were calculated (assuming gravity to be 9.81 m s1, and neglecting aerodynamic forces), and used to provide the kinematics at overlap with an arc described by the appropriate length about the second handhold (in most cases taken to be the same value of L, but see below). Those paths that would result in a tension-collision with the second arm, along with the geometry of the second arc at that point, were used to determine the collision characteristics of the point-mass model as in Equations 13. Any energy levels or release angles that resulted in a total miss of the second handhold were excluded from consideration.
Each release angle was also related to a release timing
trel, as measured from the moment at which the centre of
mass was directly beneath the first handhold:
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Model 2
Consequences of arm length on collision with overshoot
The energetic consequences of some overshoot distance e of the
`ideal', no-loss ballistic path described by Bertram et al.
(1999), whether attributed to
error due to unpredictable environmental or biological variability, or a
safety strategy, can be calculated for a point-mass brachiation collision. The
geometry of collision (Equation 1) depends on both the magnitude of
`overshoot' and hand to CoM length L
(Fig. 3):
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|
Focussing specifically on the collision interaction, and ignoring gravity,
Equations 2, 3 and 7 combine to give an expression for proportional energy
loss due to an overshoot:
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Results and Discussion |
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Excess energy in continuous-contact brachiation
In Example Runs A and B, displayed in Figs
4 and
5, the brachiation energy of
the first swing is considerably greater than the minimum required to allow
contact to be made with the second handhold. In both cases the first swing
continues well past the intersection of the two arcs defined by L
(see kinematics shown in Figs
2A and
4A); in both cases energy is
clearly not lost deliberately to allow a zero-collision contact due
to zero kinetic energy (Equation 3). This observation makes sense from the
perspective of the brachiating animal: maintaining a high energy level
resulting from previous actions, and suffering the consequences of higher
collision losses, preserves more energy than `dumping' the energy to achieve
zero kinetic energy at contact.
In Fig. 4D the energetic consequences of a range of release angles for a passive system with constant L and appropriate initial brachiation energy are modelled. At release angles below 20° the ballistic path of the CoM is such that contact with the second handhold cannot be made, and would result in a fall with whatever negative consequences that would ensue. Release angles of 2029° (an interval of approximately 40 ms), would allow completely passive brachiation with collision losses lower than those associated with any subsequent release. The fact that the time-window for this region is so small, and the cost of falling if release is too early is so large, may account for the usual decision (based on observations of the gibbons using the laboratory apparatus in this analysis) to extend the contact period, and overshoot the `ideal' contact conditions slightly. However, it should be noted that ricochetal brachiation between even close handholds can be observed, so it would be unwise to suggest undue limitations on gibbon performance. Also, the energetic losses due to collision with delayed release may be overestimated. The model only calculates the losses for a passively brachiating system: in reality gibbons are active systems, and collision losses may be considerably reduced by a variety of active mechanisms. Some of these are discussed below.
Trailing-arm-bend in continuous-contact brachiation
Level, continuous-contact brachiation typically involves an arm-bend of the
trailing arm while it remains in contact with the previous handhold, as shown
in Example Runs A and B (Figs
2B,
4A,C). This trailing-arm-bend
appears to be associated with active muscular forces
(Usherwood et al., 2003),
which act to pull the CoM backwards, towards the first handhold, and results
in a characteristic looping path of the CoM. The action may reduce the
energetic losses due to collision by two mechanisms. First, it may allow the
path of the CoM to be connected to the arc described by the second L
while the mass is moving slowly, with almost all energy converted to
potential. It may also allow the path of the CoM to be actively adjusted to
one with a more favourable angle when the tension connection is established
with the second swing path. Thus a small amount of active muscular effort may
help in the avoidance of large collision losses during continuous-contact
brachiation. Using this strategy, excess mechanical energy from one swing can
be carried to the next, and the deliberate loss of energy prior to a collision
is unnecessary.
Leg-lift
A leg-lift can also affect collision energy losses (Example Run B;
Fig. 5). While the
trailing-arm-bend beneficially alters the path of the CoM to match that of the
second arc, the leg-lift can also actively alter the relevant contact arc
about the second handhold. This can result in improvements both in collision
geometry, and a reduction in the amount of kinetic energy available to be
lost, as a greater component of the brachiation energy is in the form of
potential energy at the instant of collision. Together these account for the
lower energy loss shown in Fig.
5D compared with Fig.
5B, the difference resulting from the shift in the CoM caused by
the leg-bend, and the use of L' (0.79 m) instead of L
(0.93 m) for the second arc in the model. This leg-bend can be achieved when
the body approaches a horizontal orientation, and so energy is not
deliberately put in to the `brachiating system' per se, unlike the
alternative case described by Fleagle
(1974) for continuous-contact
brachiation, and Usherwood et al.
(2003
) for the ricochetal
gait. Instead, the leg-lift can simply provide a way of shortening the
distance between CoM and hand.
The control of hand to CoM length could also be achieved with a flexion of
the newly supporting arm. In a passive brachiating system, without mechanical
energy input or removal, the CoM cannot move towards (implying an energy
input) or away from (losing energy) the handhold while the arm is loaded
(Usherwood et al., 2003).
Passive brachiation while maintaining a knee-lift, or a flexed support arm,
posture throughout the swing would result in identical (zero) mechanical work.
However, the metabolic costs of, or the absolute capability to perform, the
two strategies may differ dramatically. The isometric forces associated with
opposing tension throughout the swing are dependent on gravity, the angular
velocity of the swing, and the mass distribution distal to the element under
consideration. The tension force Tr experienced by any
part of a swinging body of length R at a distance from the handhold
r' (while maintaining a constant shape) and an angular velocity
is given by:
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Model 1 with ricochetal brachiation
In ricochetal brachiation, handhold contact is interrupted by periods of
ballistic flight. The high velocities and requirement to change from parabolic
(ballistic) flight to suspended (swing) paths make the animal susceptible to
substantial collision loss. Fig.
6 shows the results for ricochetal brachiation. Two points are
notable: (1) there is a limited total time window (120 ms) with which a
release will result in a ballistic path that allows successful contact to be
made with the second handhold; and (2) the energy losses may be high (up to
46%) due to collision, even when the second handhold is successfully attained,
if the geometry of contact is not perfect. The exact paths of the CoM are
uncertain even when calculated using directly measured force data, as the
assumptions used for terrestrial force plate studies
(Cavagna, 1975) are less valid
for brachiation; an assumption that the CoM does not change in height over a
complete cycle is highly unreliable. Some degree of overshoot, however, is
readily apparent for fast ricochetal brachiation
(Fig. 6F): the left arm flexes
considerably after initial contact; and force records for typical
double-pendulum brachiation (Chang et al.,
2000
) show that there is a delay between initial contact and
loading of the handhold. During the interim between contact and full loading,
the arm becomes partially flexed. Thus, the CoM appears to pass within the arc
described by L, overshooting the path required for ß=
/2
matching (see Fig. 1) of the
parabolic flight and circular swing paths that determine a no-loss interaction
between the animal and its support.
Given the considerable energetic consequences of a slight mistiming due to collision losses, and the potentially fatal consequences of a complete miss, strategies to allow some degree of overshoot while minimising collision energy losses may be expected. The trailing-arm-bend strategy described above, which adjusts the swing path in continuous-contact brachiation, is unavailable during ricochetal brachiation, as the trailing arm loses contact with the superstrate before path adjustments can be useful. Using a leg-lifting action to control the distance between the catching hand and the centre of mass, however, can be advantageous in ricochetal brachiation. Such a behaviour may reduce collisional energy losses by both mechanisms: with a reduction in the proportion of mechanical energy as kinetic by control of the timing of collision, and by improvement in collision geometry, this time through alteration of the subsequent swing trajectory. Further, a slight undershoot of the ideal path may be compensated for with leg extension; movement of the leg mass distally lengthens the distance between the CoM and hand (while the CoM would continue on its ballistic path), thus permitting the avoidance of a catastrophic fall. Leg extension and retraction during flight is indeed frequently observed and, while unable to affect the ballistic path of the CoM, allows last-millisecond adjustment of the hand-CoM length, and thus the collision geometry.
Collision-reduction behaviours may save energy
While we suggest that both arm flexion and leg-lifting may be mechanisms to
limit energy losses due to collision, they do not relate directly to the
losses that would have been caused by inelastic collision without their
actions. It is conceivable that these behaviours achieve a controlled movement
of the centre of mass prior to collision, influence the timing (and so
proportion of energy present as KE), or determine the subsequent
swing trajectory, with relatively little energetic input. For the
trailing-arm-bend, while some energetic input is presumably required to move
the CoM, this is achieved when both support arms are relatively unloaded, at
the top of the swing (Usherwood et al.,
2003). In the case of the leg-lift during ricochetal brachiation,
there are no net mechanical energy changes as the path of the CoM remains
unaltered, though subsequent isometric muscle forces during the swing may
incur some metabolic costs. Whatever the energetic investments required for
these behaviours, they should not be considered as directly due to
collision.
Model 2 and further collision-minimisation strategies for ricochetal
brachiation
Arm elongation
Elongated arms may be viewed as beneficial to a brachiator for a variety of
reasons (Preuschoft and Demes,
1984): increased reach can allow weight to be distributed among
many branches, the chances of finding suitable support within grasping
distance are increased, the number of handhold changes can be reduced, and
feeding may be aided by increased reach. Previous attempts to relate the
distinctive limb elongation observed in all specialist brachiators directly to
advantages in the mechanics of brachiation have been unsatisfying. These
explanations are usually based on pendular models of motion (e.g.
Preuschoft and Demes, 1984
).
However, brachiation viewed as periods of pendular swinging interspersed with
periods of ballistic flight, achieving ideal no-loss contacts, provides no
pressures on arm length: energetic losses, even for relatively small
pendulums, are trivial, and mean velocity is totally unconstrained by pendulum
behaviour if the swing can begin and end at non-zero velocities.
The extension of the point-mass model into a method for calculating the
collisional energy costs for imperfect handhold contacts, combined with a
consideration of biological pressures in gibbon evolution, allows a novel
account to be made for the elongated arms of specialist brachiators. If (1)
release timing cannot be perfect, perhaps because of the brief availability of
perfect release conditions, and (2) the cost of falling, either due to injury
and subsequent repair (Schultz,
1944), or fatality, is high, then energetic losses due to
collision are likely to be selectively important in the evolution of
brachiators. Elongation of the arms not only results in a greater chance for
any contact to be made with a subsequent handhold (by allowing a
greater volume to be reachable for a given ballistic path), it also improves
the collision geometry, and so reduces the energetic loss associated with an
overshoot of the optimum contact path (see Equation 8).
While there need not be a constant relationship between mechanical energy cost and metabolic energy, it can be assumed that mechanical energy costs do translate to metabolic losses. Equation 8 can be used to estimate the metabolic consequences of collision due to overshooting the `ideal' path (Fig. 7). For a given absolute overshoot, long arms improve the collision geometry, and energetic savings may be considerable. Clearly, if overshoot is proportional to arm length, then arm length has no bearing on collision geometry. However, overshoot is more likely to be related to some degree of error, or safety factor, related to an absolute distance determined by the environmental conditions, such as the spacing of available handholds.
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Brachiation energetics are influenced by tension-collision losses that may be unfamiliar to most readers. More familiar might be the compression-collision analogue of the tension-collision situation described here. The advantage of long arms for collision made with a small overshoot is the same as the advantage of large wheel size for operation over rough surfaces. While wheel size has relatively little bearing on energy losses for rolling on horizontal, smooth surfaces, increased wheel size does allow smaller loss on rough surfaces. `Monster' trucks (e.g. Bigfoot) make use of large wheels to allow large obstacles (such as cars) to be driven over, while small-diameter rollerblade wheels fare poorly on a rough pavement. As an extreme case, a stiff, inelastic wheel colliding with an obstacle at the height of the axle loses all kinetic energy, just as a gibbon overshooting a handhold by length L suffers total kinetic energy loss.
The `double pendulum' and collisional energy loss reduction
The above account for the benefits of arm elongation as an adaptation for
limiting the energetic costs due to an overshoot may be extended beyond the
point-mass case. In rapid ricochetal brachiation between widely spaced
handholds, gibbons do not swing with their body in line with their supporting
arm (Bertram and Chang, 2001;
see Fig. 6D,F). While
distributed mass parameters are difficult to determine accurately and
dynamically, the principles of inelastic collision may be extended beyond the
point-mass model to provide a qualitative explanation for the body posture at
the moment of collision. Energy loss due to collision is given by the
difference between the total kinetic energy and the energy associated with
motion about (past) the handhold. This difference is minimised for a given
overshoot if the body is orientated to maximise the second moment of mass
(moment of inertia) about the handhold at collision. So, just as for the
point-mass model, an overshoot has a proportionally smaller effect on bodies
with a distal mass distribution than proximal. This is achieved if the body is
aligned perpendicular to the path of the CoM
(Fig. 8). Combined with a
slight overshoot, this results in a `double pendulum' phenomenon. Thus, the
double pendulum in itself may not be of direct importance in terms of control
(compare Bertram and Chang,
2001
); rather, it may be better viewed as an epiphenomenon,
properly understood as a strategy in the context of collision energy loss
minimisation.
|
Further biological implications of brachiation mechanics
The view of brachiation presented in this study, as locomotion utilising
pendular and ballistic mechanics, but also substantially influenced by
collision interactions with supporting structures, may have a bearing on many
aspects of gibbon biology. The benefits of accurate release timing on
minimisation of the costs of both collision and falling may have implications
on the evolution and development of visual and mental abilities; these may
limit the use of ricochetal brachiation to diurnal animals with well-developed
brains and vision. Also, loss of energy due to collision, while avoiding
tissue damage may affect both morphology and behaviour. For instance, the
double-pendulum mechanism not only minimises collision losses, but can also
allow large muscle groups (particularly the latissimus dorsi) to provide
torques about the shoulder in a sense opposite to that of the rotation of the
body. Thus the muscle can perform `negative' work, and safely dissipate the
`internal' kinetic energy resulting from collision. This would allow the
energy associated with collision, inevitable for each ricochetal `step' if a
margin for error is provided, to be lost without requiring a large jerk (rate
of change of acceleration). Thus, contact can be made smoothly (although not
avoiding the energetic consequences of collision), and damage to the arm or
shoulder, or failure of the supporting tree limb, can be reduced.
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References |
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