1 Dan 2 Gaya Inti Dan Transformasi Energi

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Energy transformation during erect and bent-hip, bent-kneewalking by humans with implications for the evolution of

bipedalism

W.J. Wang*, R.H. Crompton, Y. Li, M.M. Gunther

Department of Human Anatomy and Cell Biology, The University of Liverpool, PO Box 147, Liverpool L69 3BX, UK

Received 1 November 2002; accepted 3 March 2003

Abstract

We have previously reported that predictive dynamic modeling suggests that the bent-hip, bent-knee gait, which

some attribute to Australopithecus afarensis AL-288-1, would have been much more expensive in mechanical terms for

this hominid than an upright gait. Normal walking by modern adult humans owes much of its efficiency to conservation

of energy by transformation between its potential and kinetic states. These findings suggest the question if, and to what

extent, energy transformation exists in bent-hip, bent-knee gait.

This study calculates energy transformation in humans walking upright, at three different speeds, and walking

bent-hip, bent-knee. Kinematic data were gathered from video sequences and kinetic (ground reaction force) datafrom synchronous forceplate measurement. Applying Newtonian mechanics to our experimental data, the fluctuations

of kinetic and potential energy in the body centre of mass were obtained and the effects of energy transformation

evaluated and compared. In erect walking the fluctuations of two forms of energy are indeed largely out-of-phase, so

that energy transformation occurs and total energy is conserved. In bent-hip, bent-knee walking, however, the

fluctuations of the kinetic and potential energy are much more in-phase, so that energy transformation occurs to a much

lesser extent. Among all modes of walking the highest energy recovery is obtained in subjectively comfortable walking,

the next highest in subjectively fast or slow walking, and the least lowest in bent-hip, bent-knee walking. The results

imply that if bent-hip, bent-knee gait was indeed habitually practiced by early bipedal hominids, a very substantial

(and in our view as yet unidentified) selective advantage would have had to accrue, to offset the selective disadvantages

of bent-hip, bent-knee gait in terms of energy transformation.

2003 Elsevier Science Ltd. All rights reserved.

Keywords: Energy exchange; Phase-shift; Bent-hip, bent-knee; Erect walking; Evolution of bipedalism

Introduction

It has been proposed (Cavagna et al., 1975), and

experimental studies confirm (Cavagna et al., 1976,

1977, 1983, 2000), that the energy conservation

characteristic of human walking is the result of

* Corresponding author. Tel.: +44-151-794-6867;

fax: +44-151-794-5517

E-mail addresses: [email protected] (W.J. Wang),

[email protected] (R.H. Crompton), [email protected]

(Y. Li), [email protected] (M.M. Gunther).

Journal of Human Evolution 44 (2003) 563579

0047-2484/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0047-2484(03)00045-9


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out-of-phase fluctuations in kinetic and potential

energy of the body centre of mass (CM). In

general, as the forward velocity of the CM

decreasesfrom heel-strike to mid-stancetheheight of the CM increases, as the body passes

over the stance leg: the potential energy of the CM,

therefore, increases over the time when the kinetic

energy is decreasing. Contrarily, the kinetic energy

of the CM will increase from mid-stance to toe-off,

as the forward velocity of the CM increases, while

the potential energy decreases, as the height of the

CM falls. It was further proposed (Alexander and

Jayes, 1980; Alexander, 1992) that energy transfor-

mation in humans is dependent on a so-called

stiff gait (i.e. one where the hip and knee joint

tend to be kept in relatively extended postures).

The gait is associated with a characteristically

double-humped curve for vertical ground reac-

tion forces (GRFs). According to this hypothesis,

if the knee is allowed to remain in substantially

flexed postures, the vertical ground reaction force

curves will show a single hump, and energy trans-

formation should be reduced or absent. A bio-

mechanical link between the form of vertical

ground reaction force curves and the kinematics of

the hip and knee joint has subsequently been

experimentally confirmed (Li et al., 1996). Energytransformation has been investigated in chimpan-

zees trained to walk bipedally, in an upright pos-

ture (Kimura, 1996). However, a link between

bent-hip, bent-knee (BHBK, or compliant) gait

and low rates of energy transformation in the CM

has not yet been demonstrated. While human

running is characterized by higher muscle forces

and GRFs than human walking (Winter, 1990),

normal human running may be expected to benefit

from compliance (cycle time being short enough to

permit return of energy by elastic recoil), andmoderately flexed knee postures should therefore

be tolerable. The mechanisms of bipedal walking

and running are, thus, very different.

The evolution of bipedal walking is generally

regarded as the Rubicon of hominization. While

our closest relatives, the African apes, do exhibit

voluntary bipedalism, it is a relatively rare event,

and typically characterized by flexed postures of

the hip and knee joints (Jenkins, 1972). The earliest

relatively complete skeletal evidence for the acqui-

sition of bipedalityand hence that for which we

can reasonably expect to be able to determine its

mode (Wade, 2002)remains the 3.18 million

year old skeleton of Australopithecus afarensisAL-288-1 Lucy (Johanson et al., 1982; Kimbel

et al., 1994; Leakey et al., 1995; Sarmientos [e.g.

1998] suggestion that this hominid was a quadru-

ped is almost universally rejected.) The nature

or mode of bipedalism in A. afarensis, however,

remains disputed, since individual features of the

skeleton suggest adaptations for both bipedality

and for arboreal climbing (see, e.g. Susman et al.,

1984) It has been proposed (e.g. Stern and

Susman, 1983; Hunt, 1994), therefore, that

bipedalism in A. afarensis may have been faculta-

tive rather than habitual, and their gait more like

the occasional bent-hip, bent-knee (BHBK) or

compliant bipedalism characteristic of other

(untrained) living African apes than the erect walk-

ing of modern humans. However, some are uncon-

vinced by the evidence for arboreality, and regard

A. afarensis as a committed upright biped (see, e.g.

Latimer et al., 1987, and also Ward, 2002). The

assessment that Lucys bipedalism was compliant

is problematic, since it suggests that, (to the extent

which early human ancestors walked rather than

ran, see above) their bipedalism would have beenof a form that might be expected to be mechani-

cally (and presumably physiologically) inefficient,

lacking the kinematic requirements for energy

transformation. (We shall report an experimental

physiological evaluation of BHBK gait in humans

elsewhere).

Since it is extremely difficult to measure the

metabolic costs of different gaits for untrained

non-human primates, no unequivocal evidence

exists that erect bipedalism offers direct advan-

tages over BHBK gait, despite an extensive litera-ture (see, e.g., Taylor and Rowntree, 1973;

Rodman and McHenry, 1980; Carrier, 1984;

Leonard and Robertson, 1995; Steudel, 1996).

Inverse dynamic modelling studies, based on limb

proportions, suggest that A. afarensis could have

been a mechanically effective upright biped

(Kramer, 1999), but would have incurred greatly

increased mechanical costs in BHBK walking

(Crompton et al., 1998). Others have suggested

that as a compliant gait reduces peak vertical

W.J. Wang et al. / Journal of Human Evolution 44 (2003) 563579564


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GRFs during walking, the (peak) loads imposed

on the sacroiliac and other joints by bipedalism

would have been reduced, favouring compliant/

BHBK walking as a transitional gait during theacquisition of bipedality (Schmitt et al., 1996). It

has also been suggested that flexed joint postures

may be beneficial to changes of direction and

acceleration (Preuschoft and Witte, 1991).

Sellers and collaborators (2003) have recently

demonstrated that forwards dynamic modelling

(where motion is driven by tension generators,

representing muscles, and taking into account

some of their physiological properties, rather than

by sets of kinematics) can predict experimentally

derived metabolic costs of human upright walking

within 15%. This modelling approach is currently

being applied to BHBK gaits, where costs may

be validated by comparison to the experimental

assessments of metabolic costs of Carey (1998).

In this paper, we address only the effects

of BHBK gaits on transformation of mechanical

energies. Using particle mechanics, we set out to

determine: 1) whether and to what extent BHBK

bipedal walking in humans can benefit from energy

transformation, comparing the rates of transfor-

mation with those in erect walking by humans in

self-assessed slow, comfortable and fast speeds;and 2) whether the characteristic changes in the

pattern of GRFs in upright and BHBK walking

are accompanied respectively by relatively out-of-

phase and relatively in-phase fluctuations in the

kinetic and potential energy of the body centre of

mass.

Materials and methods

Subjects

The subjects were 8 adult men and women, aged

between 20 and 40 years and 1.61.85 m in height.

Each subject walked along a 25 m plywood walk-

way in four (subjectively determined) modes:

slow, comfortable and fast erect walking, and

BHBK (compliant) walking. 10 trials were

recorded for each subject for each mode. A Kistler

9281B force platform (surface dimensions:

0.40.6 m) was set into the walkway, level with its

surface, and was used to record ground reaction

forces (GRFs) to computer disk via an AD con-

verter, using DIA/DAGO software (GfS, Aachen).

To obtain general 3D kinematic data, as well asparticular information on the double support

phase and the velocity of the CM, two genlocked

standard CCD PAL video cameras, giving a 50 Hz

sampling rate, were set parallel and at 90( respec-

tively to the long axis of the walkway. Recordings

were made split screen via a special effects genera-

tor, and were synchronised with the force records

using LEDs in the field of one camera, triggered by

any of the four force transducers. All subjects

walked barefoot and wore a tight-fitting swimsuit.

Kinematics were analyzed using our own, specially

written software (Wang, 1999). The subjects

started walking well before, and finished walking

well after, the force platform, so that the forward

velocity of the body centre of mass (CM) was kept

as constant as possible, while permitting as natural

a gait as possible. A total of 80 trials for each mode

of walking were retained for analysis. After delet-

ing some recording failures (such as where only

half of the foot landed on the force platform, or

where step length was determined to have been

adjusted by the subject to permit foot contact with

the force platform) 70 trials for each gait remainedavailable for the calculation of energies.

Calculation of energy

There are various ways of calculating fluctua-

tions in the energies of the body centre of mass

(see, e.g. Zarrugh, 1981; Williams and Cavanagh,

1983; Winter, 1983 and 1990; Williams et al.,

1995). Using Newtonian mechanics and employing

a force platform, Cavagna and colleagues inte-

grated GRFs to calculate the kinetic and potentialenergy in the CM, and then estimated the recovery

of work done (Cavagna, 1975; Cavagna et al.,

1976). This method is less than ideal. Firstly, it

may give slightly low estimates of the total work

done (Donelan et al., 2002). Secondly, as indicated

by authors including Winter (1979) and Williams

et al. (1995), the energy changes of the CM do not

fully represent the energy changes of the whole

body: symmetrical, reciprocal movements of the

limbs, which are typical for walking (erect or

W.J. Wang et al. / Journal of Human Evolution 44 (2003) 563579 565


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compliant) do not result in changes in the position

of the CM. The differences in energy changes of

the CM between different gaits, therefore, reflect

only part of the energetics of walking. Never-theless, the method remains a simple and straight-

forward approach.

As this study does not concern itself with a

complete estimate of segment energies, we employ

a similar technique to that of Cavagna and col-

leagues (1975 and 1976). However, our approach is

a slightly modified version. Unlike Cavagna and

colleagues, who calculated energy exchange from

absolute values of work done, we utilize the value

of fluctuation in energy, which should enable us to

take the effects of both energy output and absorp-

tion into consideration. In this study, therefore,

work done is estimated by calculating the fluctua-

tions in potential and kinetic energies and the sum

of both. The fluctuations of kinetic and potential

energies are defined as the work done in maintain-

ing motion of the body CM, and the fluctuation of

the sum of the kinetic and potential energy as the

work produced by the body. To permit use of a

single forceplate, avoiding the problems of ensur-

ing contact with two plates, and thus permitting a

more natural gait, we assumed that the subjects

walked symmetrically. GRFs for one side weremirrored to the other side and offset by 50% of a

stride cycle. By integrating force platform data,

we readily obtain curves of kinetic energy and

potential energy, and can, then, investigate their

dynamic trends during walking. The method is

described in detail below.

The energies of the CM can be obtained by

calculation from GRFs. If the whole body is

considered as a particle, Newtons Second Law can

be written as:

Fx,ymax,y (1)

Fzmgmaz (2)

where F is the GRF acting on a subject, measured

by a force platform; m the body mass; a the

acceleration of the subjects CM; and x, y and z

respectively represent the transverse axis, the

anterior-posterior axis, and the vertical axis. F in

this case is total ground force, i.e., the sum of the

reaction forces for both feet, taking the double

support phase into consideration. Thus, the accel-

eration of the CM, a, can be obtained. By integrat-

ing a once, we obtain velocity (Eq. 34) and twice,displacement (Eq. 5):

vx,y(t)vx,y(t0)1

m

t0

t

Fx,y(t)dt (3)

vz(t)vz(t0)1

m

t0

t

(Fz(t)mg)dt (4)

sx,y,z(t)sx,y,z(t0)t0

t

vx,y,z(t)dt (5)

where v is velocity and s displacement.

From the definition of mechanical energy, the

translational kinetic energy and the gravitational

potential energy of the CM of a subject are:

KE1

2mvc

2 (6)

PEmgzc (7)

where PE is the potential energy; KE the kinetic

energy; vc the velocity of the CM in horizontal and

vertical directions; and zc the displacement of the

CM in the vertical direction.

Fluctuation of energies

To analyse the work done by the whole system

(the body) to maintain motion, the fluctuation ofthe energies, E, over the total stride (i.e. stance

and swing phases together) is computed as follows:

Emax(E)min(E) (8)

E represents the work done by the body to

maintain whole body movement, and can be deter-

mined for kinetic energy, potential energy or their

sum. The larger E, the more work done. KE

and PE indicate the energy for maintaining



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motion and (KE + PE) signifies the energy out-

put of the body, or in other words, the work done

by the body tissues (see Appendix A).

Energy-transfer value

To compare the effect of energy transformation

in different modes of walking, we have defined a

coefficient, , the energy-transfer value, as:

KE1PE

(PE1KE)(9)

This dimensionless coefficient reflects the ratio of

energy transformation and is thus independent of

the mode of walking. The larger , the more theenergy exchanged.

Energy-velocity value

To compare the effect of per unit energy on

the velocity of the CM, another coefficient, , is

created. This may be termed the energy-velocity

value, and is defined as below:

VCM

E(10)

where VCM is the average velocity of the CM and

E is the range of fluctuation of the energy of the

whole body. In this case, VCM is defined as the

distance covered in a complete stride divided by

the strides duration, and is calculated using the

recorded kinematic data, and E is the fluctuation

of the sum of kinetic and potential energies,

(KE + PE). therefore expresses the per unit

effect of energy use on the velocity of the CM. The

larger , the higher the velocity achieved for a

given expenditure of energy.

Recovery of energy

In order to evaluate the effectiveness of energy

transformation, we have defined a new coefficient

of energy recovery:

Recoveryn(PE1KE)K(PE1KE)

(PE1KE)(11)

where PE is the maximum change in the potential

energy; KE the maximum change in the kinetic

energy; and (PE + KE) the maximum change in

the sum of the two energies. Although the Eq. (11)has a different form from that of Cavagna et al.,

(1976), it demonstrably reflects the effectiveness of

energy transformation between the two forms of

energies (see Appendix B).

In order to test whether or not there are signifi-

cant differences between the experimental gaits

and the calculated parameters, a statistical analy-

sis was carried out using ANOVA (Bowker and

Lieberman 1959).

Results

Range of joint angles

The recorded kinematic data show that during

BHBK walking, the range of hip angles (angle

between the long axes of the thigh and trunk) of

the subjects averagely ranged from a mean 23 to a

mean 69(, the knee angle (defined as the angle

between the long axes of the thigh and the lower

leg) from 35 to 92(

and the ankle angle (defined asthe angle between the foot and lower leg) from

2.86 to 34(. In upright walking, in comparison,

hip angles ranged from 12 to 34(, knee angles

from 0 to 60( and ankle angles from 12 to 20((Fig. 1.ac). In the literature (Winter, 1991, pp.29),

the joint angles in erect walking are about 10 to

20( for the ankle, 0 to 60( for the knee and18 to

23( for the hip. The slight differences between the

literature and our data may result from two causes:

1) the marker positions defined on subjects for

kinematic measurement may be diff

erent; and/or 2)the velocities of the subjects may be slightly differ-

ent: those for fast, normal, and slow walking in

Winter (1991, pp. 12) are about 1.6824, 1.325, and

0.998 (m/s), while the velocities for our subjects are

1.93, 1.47, and 1.04 (m/s) respectively (see Table 1).

Since the four gaits in our study were determined

by the subjects themselves and are internally con-

sistent, the slight differences in joint angles

between Winters (1991) and our data may safely

be ignored (see Fig. 1.ac).



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Energy fluctuation

From the computed results, it was found that in

erect walking, the fluctuations of the two energies

are largely out-of-phase or nearly so (i.e. one

increases while the other decreases). However, in

BHBK walking, the fluctuations are reasonably

in-phase or nearly so (i.e. both increase or decrease

roughly at the same time) (see, especially, Figs. 25).

The averages of the computed energies (KE, PE and

KE + PE) in different modes of walking, and their

standard deviations, are also given in Figs. 25.

In Figs. 2.b5.b, the curves for kinetic energy

(KE) and potential energy (PE) have been moved

Fig. 1. Two gaits: erect walking and bent-hip, bent-knee walking. a) Digitised stick-figure illustration of typical kinematics of

comfortable erect walking in the sagittal view. b) Digitised stick-figure illustration of typical kinematics of bent-hip, bent-kneewalking in the sagittal view. c) Averaged ranges of joint angle for the subjects in different modes of walking. Right: erect walking. Left:BHBK walking.



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to the coordinate system of the sum of the kinetic

and potential energies (KE + PE) in order to facili-

tate comparison of energy changes. The curves

start at left heel strike (LHS), then right toe off

(RTO), right heel strike (RHS), left toe off (LTO)

and finish at the next left heel strike (LHS).

Because the period of double support differs

between the modes of walking, the timing of these

parameters differs. RHS however is always at 50%

of the cycle, as the right and left side of the bodywere assumed to move symmetrically. In comfort-

able walking, RTO occurs at a mean of 7.5% and

LTO at a mean of 57.5% (S.D. 0.027) of a gait

cycle. In fast walking, RTO occurs at a mean of

5% and LTO at a mean of 55% (S.D. 0.038) of the

cycle. In slow walking RTO occurs at a mean of

10% and LTO at a mean 60% (S.D. 0.033) of the

cycle, and in BHBK walking RTO occurs at a

mean of 11% and LTO at a mean 61% (S.D. 0.031)

of the cycle (see Figs 2.b5.b, and see also the

swing factor in Table 1). It may readily be seenfrom Figs 2.b, 3.b and 4.b that in upright walking

the kinetic and potential energies fluctuate alter-

nately: KE increases as PE decreases and vice-

versa. This permits energy transformation or

energy exchange. In erect walking, the sum of

kinetic and potential energy (PE + KE) oscillates

within a relatively smaller range than does KE and

PE. In BHBK walking (Fig. 5.b), however, the

range of (KE + PE) is not obviously smaller than

that of KE or of PE.

As expected, kinetic energy increases with in-

crease of the velocity of CM (see Fig. 7), while

potential energy does not change with increasing

velocity (see Fig.6). Calculated results of energies

for all trials in the different modes of walking are

shown in Figs. 68, and the averages listed in

Table 1.

Direct comparisons of KE and PE in the

different modes of walking should not be taken too

far, since the KE and PE of any subject areproportional to the velocity of the CM (VCM).

Thus, as VCM in BHBK walking is relatively

small, so too are KE and PE (see Figs 6 and 7).

However, we may note that the fluctuation of

the sum of the two energies (i.e. (KE + PE)) is

relatively larger-compared to KE and PE

in BHBK walking than it is in other modes

(Fig. 68). Further, though the VCM in BHBK

walking is lower than that in comfortable walk-

ing, the fluctuation of (KE + PE) is at least as

large (see also Table 1). Finally, we can also see(Table 1) that because energy exchange is so small,

BHBK walking is higher in (KE + PE) for a

lower velocity.

The mean of for comfortable walking is the

greatest, at 2.479; while the values for fast and

slow walking are almost exactly the same: 2.2014

and 2.2002, but the for BHBK walking is the

smallest, at 1.5241 (see Fig. 9 and Table 2), mean-

ing that comfortable walking achieves the largest

energy transformation and BHBK walking the

Table 1

Comparison of energy fluctuations in different modes of walking

SF

Mean

VCM(m/s)

Mean STD

KE(J/kg)

Mean STD

PE(J/kg)

Mean STD

(KE + PE)(J/kg)

Mean STDBW 0.3900 1.22610.23 0.28010.10 0.25480.12 0.38830.16

FW 0.4500 1.93290.14 0.64750.15 0.41750.13 0.52040.13

SW 0.3950 1.03880.11 0.31300.05 0.26500.09 0.29440.10

CW 0.4250 1.47030.13 0.48500.08 0.30750.10 0.35290.09

1. BW, bent-hip, bent-knee walking; FW, fast erect walking; SW, slow erect walking; CW, comfortable erect walking (n = 70

trials each mode).

2. SF, swing factor, the proportion of the swing time to the cycle duration.

3. VCM, velocity of the body centre of mass.

4. KE, range of change of kinetic energy; PE, range of change in potential energy; (KE + PE), range of change in the sum of

kinetic and potential energies.



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least. All trials are displayed in Fig. 9, and the

average values for different modes of walking are

listed in Table 2.

The highest energy-velocity value () is

obtained, once again, from comfortable walking

(mean 4.5449) and the lowest from BHBK walking

(mean 3.7638) (see Table 2). Values of for alltrials are displayed in Fig. 10, and the average

values of for different modes of walking are listed

in Table 2.

The values of energy recovery show a similar

trend to other parameters: the values decrease in

turn from comfortable walking (55%) to fast walk-

ing (51%), to slow walking (49%), and finally to

BHBK walking (27%) (see Table 2).

The results of the ANOVA for influences of

gaits on calculated parameters are given in Table 3.

Fig. 2. Energy fluctuation in comfortable walking. a) Top:mean range of fluctuation in PE (potential energy, solid line)and its standard deviations (dashed lines) in J/kg. Middle: meanrange of fluctuation in KE (kinetic energy, solid line) and itsstandard deviations (dashed lines) in J/kg. Bottom: mean rangeof fluctuation in KE + PE (sum of kinetic and potential ener-gies, solid line) and its standard deviations (dashed lines).Trails = 70. b) Mean fluctuation of the centre of mass inKE + PE (the sum of kinetic and potential energies, * line) inKE ( lines) and in PE (B line) in J/kg, trails = 70. LHS: leftheel strike, RTO: right toe off, RHS: right heel strike, and LTO:left toe off. Comfortable walking obtains the highest values inthe effectiveness of energy transformation among all modes ofwalking.

Fig. 3. Energy fluctuation in fast walking. a) All symbols are thesame as those in Fig. 2a, b) All symbols are the same as thosein Fig. 2b. Fast walking obtains higher values in the effective-ness of energy transformation than that in BHBK walking.



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In brief, almost all variables show significant

differences between the groups (see Table 3).

Discussion

Possible reasons

Two influences on energy transformation in

walking may readily be identified. The first derives

from the shape of the fore-aft and vertical ground

reaction force curves from which our figures for

transformation are derived. The averages of theseGRFs are given in Fig. 11. In comfortable and

fast walking, the valley in the vertical (Z) force

curves is well marked. This indicates that vertical

acceleration decreases as the displacement (height)

of the CM increases, which will have the effect

of converting kinetic energy into gravitational

energy. The valley is smaller in slow walking and

nearly absent in BHBK walking, so that less

transformation can occur. However, this factor

cannot explain why, while the valley is deepest in

Fig. 4. Energy fluctuation in slow walking. a) All symbols arethe same as those in Fig. 2a, b) All symbols are the same asthose in Fig. 2b. Slow walking obtains higher values in theeffectiveness of energy transformation than that in BHBKwalking.

Fig. 5. Energy fluctuation in bent-hip, bent-knee walking. a)All symbols are the same as those in Fig. 2a, b) All symbols arethe same as those in Fig. 2b. Bent-hip, bent-knee walkingobtains the lowest values in the effectiveness in energy transfor-mation among all modes of walking.



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fast walking, energy transformation in this gait is

less than that in comfortable walking, and in fact

similar to that in slow walking.The second, and in view of the above, probably

more important factor is the phase relationship

between the fluctuations in the kinetic and poten-

tial energies. In Fig. 11, we can see that in normal

walking, the fore-aft (Y) force changes sign, from

negative to positive, at about mid-stance. This

implies that the velocity of the CM, and, hence, the

KE will be lowest at mid-stance. On the other

hand, the simultaneous valley in the vertical force

(Z) indicates that the vertical displacement (height)

of the CM, and, hence, the PE is greatest at midstance. In particular, Fig. 2.b shows that in com-

fortable walking, KE reaches its minimum and PE

its maximum at about 30% and again at about 80%

of the gait cycle. In BHBK walking, as in erect

walking (see Fig. 5.b), the fore-aft force (Y)

changes sign at about mid-stance, so that the

velocity of CM, and thus the KE, is the lowest at

the mid-stance, but the minimum vertical (Z)

force, and, hence, maximum PE, occurs after mid-

stance. The shift of phase, bringing KE and PE

into phase or nearly so, prevents substantial energy

transformation (see Figs 11 and 5.b). Figs. 3.b and

4.b show that in fast and slow walking, the fluc-tuations, and, hence, the energy transformation,

are intermediate between these extremes, although

considerably closer to the pattern in comfortable

walking than to that in BHBK walking.

Comparison with other studies

The above suggests that the mode of gait may

indeed be a major factor in determining energy

recovery. From the calculated results, comfortable

walking obtains the highest recovery, 55%, fastand slow walking about 50%, and BHBK walking

the lowest, at 27%. Even though recovery in this

study has a somewhat different meaning from that

in Cavagna et al. (1976, 1977) and some other

studies, the values fall within the range given by

Cavagna and colleagues for humans. However, a

smaller difference was found between comfortable

and fast walking than the nearly-twofold difference

suggested by Cavagna and colleagues. In his study

of chimpanzees trained in upright bipedalism,

Fig. 6. The ranges of fluctuation in PE in different modes of walking for all trials. PE: fluctuations in potential energy.B = bent-hip, bent-knee walking, = slow walking, + = fast walking * = comfortable walking.



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Kimura (1996) found that energy recovery falls off

much more sharply with increasing speed: it is

highest, 40%, at 0.5 m/s, but zero by around1.6 m/s. From our results, recovery in human

BHBK walking is nearly half that in human erect,

comfortable, and slow walking, although BHBK

walking achieved similar speeds.

McMahon and colleagues (1985, 1987) com-

pared Groucho running (in essence, BHBK run-

ning) to normal running, and found that in this

gait, both stiffness of the legs and GRFs were

reduced, but the rates of O2 consumption

increased by as much as 50%. The results suggest

that even in running compliance may not alwaysresult in return of elastic energy. Carey (1998)

measured the metabolic costs of BHBK walking

for adults at different speeds, and found that costs

are much greater in BHBK walking than in erect

walking (Carey and Crompton, 1997). Finally,

Schmitt et al. (1996) tested compliant and normal

gaits using a force platform and found that peak

(but not mean) vertical force is reduced by 1025%

of body weight during compliant gait, a conclusion

with which our results agree. Thus, kinetic and

physiological experiments, both on BHBK walking

and on running suggest that although peak GRFs

may well be reduced, metabolic costs are greatlyincreased in gaits where hip and knee flexion is

substantially larger than the values seen in erect

walking. We do not here address the mechanism

whereby higher mechanical costs and low rates of

transformation in BHBK gaits may be related to

higher metabolic costs: but these parameters are

more than likely to be functionally related.

Implications for the evolution of bipedalism

What does this study imply for the evolution ofbipedalism? Biomechanical factors (Rose, 1991)

may, all other things being equal, be expected to

select for changes in morphology that will reduce

energetic costs or increase performance in any

species most ecologically or reproductively crucial

locomotor behaviour. While natural selection

sometimes appears to produce solutions other

than the most energetically optimal one (e.g., the

probably inefficient knuckle-walking gait of

African apes [Richmond and Strait 2000]), it

Fig. 7. The ranges of fluctuation in KE in different modes of walking for all trials. KE: fluctuations in kinetic energy.B = bent-hip,bent-knee walking, = slow walking, + = fast walking and * = comfortable walking.



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should equally be borne in mind that such solu-

tions may be functional consequences of strong

selection in favour of other (more expensive,

more stress-inducing or more ecologically crucial)behaviours, an issue we shall address elsewhere.

Maintenance of extended hip and knee joint

posture is demonstrably possible in trained African

apes and in untrained orang-utans, despite a non-

human-like joint conformation, and a non-human-

like lumbar spine. Recalling the prediction that

BHBK walking in Australopithecus afarensis

would have high mechanical joint power require-

ments (Crompton, et al., 1998), our present finding

that energy transformation is much lower in bent-

knee, bent-hip walking than in erect walking,suggests that for BHBK gait to have practiced by

early bipeds, very large offsetting selective advan-

tages would have had to accrue to BHBK (but not

erect bipedalism), for the former to be adopted as

habitual gait. In our view, neither (putatively)

reduced peak loads on the sacroiliac joint (Schmitt

et al., 1996) nor advantages for change in direction

or speed (Preuschoft and Witte, 1991) are entirely

convincing as such offsetting selective advantages.

Such selective advantages remain to be identified.

As Rose (1991) pointed out, many ecological,

social and morphological factors will have influ-

enced the evolution of bipedalism. Therefore,

biomechanical factors would be expected tooperate to find a best-compromise solution for

performance/efficiency in several different aspects

of locomotor adaptation (sensu lato) (and see also

Alexander, 1996 and 1991; Wang et al., 2003), but

energetic effectiveness in walking would certainly

be expected to be among the most important

factors in determining the compromise.

Summary

This study has investigated whether there aredifferences in energy transformation between the

erect and bent-knee-bent-hip walking. A group of

human adults were required to walk using various

modes of walking. Force platform and kinematic

data were collected, and energy fluctuations in the

body centre of mass calculated. The results show

that in erect walking, the energy fluctuations are

substantially out-of-phase, so that the kinetic and

potential energies can frequently be exchanged

with each other; however, in bent-knee, bent-hip

Fig. 8. The ranges of fluctuation in the sum of (KE + PE) in different modes of walking. (KE + PE): fluctuations in the sum of twoenergies.B = bent-hip, bent-knee walking, = slow walking, + = fast walking and * = comfortable walking.



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walking, the energy fluctuations are relatively

in-phase or nearly so, so that little or no energy

transformation between kinetic and potential

energies would be possible. Regarding energy

recovery, among the four modes of walking

investigated, the highest energy recovery occurs in

comfortable walking, the next highest in fast or

slow walking, and the lowest in bent-knee, bent-

hip walking. The results imply that if bent-knee,

bent-hip gait was indeed habitually practiced byearly hominids, an as yet unidentified selective

advantage of BHBK over erect bipedalism would

have had to exist, sufficient to offset its demon-

strably large energetic disadvantage.

Acknowledgements

We are grateful to Profs. R. McN. Alexander,H. Preuschoft and M. D. Rose for their helpful

comments. We would like to thank the associate

editor and three referees for the constructive com-

ments during peer-review of the manuscript. The

authors thank Drs. A. Conant and R. Payne for

the assistance with early draughts. This research is

funded by grants from the Biotechnology and

Biological Sciences Research Council, the

Natural Environment Research Council, and The

Leverhulme Trust, UK.

Fig. 9. Values of energy-transfer coefficient, . The average for comfortable walking is the highest and that for bent-hip, bent-hipwalking the lowest. B = bent-hip, bent-knee walking, = slow walking, + = fast walking, and * = comfortable walking.

Table 2

Comparison of the effects of energy transformation in

different modes of walking (n = 70 trials each mode)

VCM Recoveryn %

BW 1.22610.23 3.76381.70 1.52410.58 27

FW 1.93290.14 4.00751.23 2.20140.80 51

SW 1.03880.11 3.90411.24 2.20020.87 49

CW 1.47000.13 4.54491.49 2.47900.99 55

Note: 1. BW, FW, SW and CW: see Table 1.

2. VCM, velocity of the centre of mass.

3. , energy-velocity coefficient, see Eq. (10) in the Methods.

4. , energy-transfer value, see Eq. (9) in the Methods.

5. Recoveryn, energy recovery value, see Eq. (11) in the

Methods.



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theoretically, be zero because the velocities in three

directions and the displacement in the direction z

will repeat the values occurring in the previous

cycle. Thus, we may consider the maximum change

in energy fluctuations to represent the work done

in walking (see Eq. 8).

Appendix B

Cavagna et al. (1975, 1976, 1983 and 2000) have

expressed energy recovery in terms of work:

RecoveryWfWvWext

WfWv(1)

where Wf is the positive work in the forward

direction; Wv the positive work in the verti-

cal direction; and Wext the positive work in the

vertical and forward directions.

As we express the work done by the change in

energies (see Appendix A), the energy recovery can

be calculated using Eq. (11):

Recoveryn(PE1KE)K(PE1KE)

(PE1KE)(11)

Equation (11) has a clear physical meaning: it

estimates the effectiveness of energy transforma-

tion between the kinetic and potential energies.

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