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1992; 72:45-53.PHYS THER.
David A WinterMultifactorial Motor Control TaskFoot Trajectory in Human Gait: A Precise and
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Research Report
Foot Trajectory in Human Gait:
A
Precise and
Multifactorial
Motor
Control Task
The trajecto
y
of the heel and toe during the swing phase of human gait were an-
alyzed on young adults. The magnitude and variability of minimum toe clear-
ance and heel-contact velocity were documented on
10 repeat walking trials on
11 subjects. The energetics that controlled step length resulted from a separate
study of walking trials conducted on subjects walking at slow, natural, and
fast cadeitces.
A
sensitivity analysis of the toe clearance and heel-contact velocity
measures revealed the individual changes at each joint in the link-segment chain
that could be responsible for changes in those measures. Toe clearance was very
small (1.29 cm) and had low variability (about 4 mm). Heel-contact velocity was
negligible vertically and small (0.87 mls) horizontally. Six joints in the link-
segment chain could, with vey small changes (+0.86 -k3.3 ) independently ac-
count for toe clearance variability. Only one muscle group in the chain (swing-
phase hamstring muscles) could be responsible for altering the heel-contact
velocity prior to heel contact. Four mechanical power phases in gait (ankle push-
8hip ptrll-08 knee extensor eccentric power at push-08 and knee flexor eccen-
tric power prior to heel contact) could alter step length and cadence. These anuly-
ses demonstrate that the safe trajectoy of the foot during swing is a precise end-
point control task that is under the multisegment motor control of both the stance
and swiqg limbs. /Winter
DA.
Foot trajectoy in human gait: a precise and multi-
factorial motor control task. Pbys Ther. 1992;72:45-561
Key
Words Kinesiologylbiomechaniu;
gait analysis; Lower-limb trajectoy,
measurements; Slipping; Tripping.
Walking is primarily a lower-extremity
control a'ctivity, and researchers have
recognized this by focusing their re-
search on the kinematics and kinetics
of the lower limb. The upper body
(head, arms, and trunk [HAT]) has
received limited attention, and that
has dealt mainly with kinematic de-
scriptions.1 Some recent focus has
been placed on the HAT'S large iner-
tial load, as it affects balance,2 and on
the HAT'S large gravitational load, as it
affects collapse.3 The role of the lower
extremity in controlling both balance
and collapse was identified as unique
stance-phase tasks. The detailed role
of the lower extremity in achieving
forward progression has been limited,
however, to kinematic descriptions
and a number of kinetic analyses. For-
ward progression is essentially a
lower-extremity task and begins late
in stance during push-ofF and contin-
ues throughout swing. The detailed
DA Winter PhD PEng is Professor De partm ent of Kinesiology University of Waterloo Waterlo o
Ontario Canada N2L 3G1.
his research was funded in part by Grant MT4343 from the Medical Research Council of Canada.
hb article w s submitted November 26 1990, and w s accepted uly 24 1991.
energetics that decide the magnitu
of step length and the precise traje
tory of the foot during swing have
been analyzed and were the subjec
of this research.
Review of Literature
To date, there has been considerab
effort focused on the kinematics
of
the lower limb during normal walk
ing. Joint angle data have most com
monly been reported.5-12 Absolute
segment kinematics (linear and ang
lar displacements, velocities, and ac
celerations) are not commonly rep
ed.12 Other than the occasional sti
diagram plot and a few individual
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trajectory plots,l3 there has not been a
comprehensive study that has exam-
ined [he trajectory of the foot (heel
and toe), especially critical variables
such as toe clearance and heel-contact
velocity.
Several energy-related motor patterns
have been identified as influencing
the magnitude of step length.14
Be
cause the swing limb constitutes the
major energy demand in walking,l5J6
we must look at the mechanical
energy-generating and energy-
absorbing phases that accelerate and
decelerate the lower limb immedi-
ately prior to and during swing. En-
ergy generation during push-off by
the plantar flexors is the largest single
work phase in the gait cycle4 and is
responsible for the upward and for-
ward acceleration of the lower limb.
Simultaneous with this plantar-flexor
contraction (during 40%-60% of the
walking stride), the knee is flexing
under the control of the eccentrically
acting quadriceps femoris muscle.
During late stance (50% of stride), the
hip flexors commence a concentric
contraction, initiating a pull-off'
power phase that continues past toe-
off (TO) into mid-swing (80% of
stride). Finally, the major deceleration
of the leg and foot is achieved by the
hamstring muscles, which contract
eccentrically to reduce the foot veloc-
ity to near-zero prior to heel contact
(HC). What is not known is how these
energy-generating and energy-
absorbing phases vary as stride length
(and cadence) varies in normal level
gait.
Methodology
Biomechanical Model
The precision of any task must be
considered relative to the number of
segments involved, their size and
mass, and the number of degrees of
freedom. The link chain for the con-
trol of the foot during swing begins
with the stance foot and proceeds up
to the hip, across the pelvis, and
down to the distal end of the swing
foot/phalangeal segment. This chain
can be considered to consist of seven
segments (or nine if a phalangeal seg-
Figure 1
Stick diagram of link-
chain system of seven segments of the
support limb pelvis and swing limb in-
volved in the control of the toe and heel
trajectories. The 12 major degrees off iee-
dom at the six joints that injluence those
trajectories are indicated.
rnent is considered), with 12 major
angular degrees of freedom at the
ankle, knee, and hip that can influ-
ence the displacement of the heel or
toe during the swing phase of gait.
Figure represents this anatomical
model with those important degrees
of freedom indicated. For a typical
adult male subject (mass=70 kg,
height= 1.8 m), the length of this
chain exceeds 2 m. If we consider the
large number of muscles crossing
those joints, the end-point control of
the heel and toe trajectories is a chal-
lenging task.
Procedure and Subjects
The experimental evidence presented
in this report was taken from gait lab-
oratory data collected from young
adults. Some analyses were based o n
individual walking trials, and other
analyses were based on repeat trials
conducted over a period of hour.
Details of the kinematic and kinetic
systems have been reported previous-
lpJ2J4J6 and have recently been sum-
marized in a recent report on walking
pattern changes in the elderly.17 For
the foot-trajectory component of this
study, a group of young adults (six
men, five women), who ranged in age
from 21 to 28 years (X=24.9), were
analyzed. Their average height was
1.73 m, and their average weight was
69.2 kg. Each subject walked at his or
her natural cadence on a level walk-
way a minimum of 10 times; repeat
trials were conducted over a period
of hour (one trial every 5 or 6 min-
utes). For the analysis of the energetic
factors that affect step length, data
were taken from analyses performed
over the past 10 years using 55 young
subjects averaging 22.6 years of age.
Their average height was 1.75 m, and
their average weight was 71.2 kg. The
data-collection protocol of this analy-
sis was identical to that of the foot-
trajectory analysis, except each subjec
underwent only one walking trial at
his or her natural cadence, at a fast
cadence (defined as the subject's nat-
ural cadence+20 steps/min), or at a
slow cadence (defined as the subject'
natural cadence-20 stepdmin). to-
tal of 19 subjects were analyzed at
slow and natural cadences, and 17
subjects were analyzed at fast ca-
dences. Each subject provided in-
formed consent before participation
in the study.
Data nalysis
The trajectories of the heel and toe
markers were plotted over the stride
period, which was normalized to
loo%, with HC at 0% and 100%.
These heel and toe profiles were then
averaged over the 10 repeat walking
trials to assess intrasubject variability.
Each intrasubject average was then
ensemble-averaged to produce an
intersubject average. Based on the
variability measurements recorded at
minimum toe clearance, each critical
degree of freedom in the link chain
was varied independently to demon-
strate the sensitivity of the toe trajec-
tory to small angular variations at
each joint in the chain. In this way,
the fine control necessary at each of
the joints was documented. In a simi-
lar manner, the velocities of the heel
in the vertical and horizontal direc-
tions were calculated in order
to as-
sess the rapid reduction in velocity of
the heel during the latter half of
swing and after HC. similar sensitiv
ity analysis on the angular velocities
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STRI E
Oh )
Figure 2
Ensemble-averaged displacement and velocities of the toe over one stride
of subjects walking at their natural cadence. Heel contact was at 0° and 100 of
stride, and toe-off (TO) was at 60 of stride. Minimum toe vertical displacement for
each subject was set at zero at the minimum reached as the toe pressed downu~ard nto
the Joor immediately before TO. (CV=coeficient of variation.)
of all segments in the link chain were
examined at HC to determine their
individual contributions to the slow-
ing down of the heel at this poten-
tially dangerous impact time. Finally,
the joint mechanical power patterns
immediately prior to and during
swing were assessed* to determine
how they changed as cadence and
step length increased.
Resutts
Figure ; plots the average vertical
trajectory and both horizontal and
vertical velocities of the toe for 11
subjects over the stride period. The
toe trajectory showed the toe to reach
its lowest point at about 56 of stride
as the toe pushed downward during
the final phase of push-off. This mini-
mum on each trial was considered to
be zero toe clearance for the purpose
of plotting this displacement profile.
Me r TO, the toe reached a height of
a few centimeters. During mid-swing,
the toe dropped t its minimum
clearance; for these subjects, this
mean clearance averaged 1.29 cm.
During the latter half of swing, the toe
Figure
3
Position of body at th
instant of minimum toe clearance fo
one representative walking trial show
the high forward toe velocity (4. 6m
and center of gravity of the head, ar
and trunk located ahead of the stan
foot.
R
represents the ground-reacti
force vector, and mg represents the b
center-ofgravity vector.)
rose to its maximum of about 15
just prior to HC. The mean intra-
subject variability for this minimu
toe clearance was 0.45 cm. Figure
shows that this minimum clearan
was achieved when the forward v
ity of the toe was at its maximum
about 4.6 m/s). Figure 3 demonst
the position of the stance and sw
limbs and the upper body at this
tentially dangerous tripping time
ing one representative walking tri
The forward velocity of the body
1.4 m/s at this time, and the cente
gravity of the HAT was just folwar
the stance foot. The combination
this center-of-gravity location and
body s forward momentum mean
that, if a trip occurs, there is no p
bility that the support limb can re
cover to return the body s center
gravity within the safe borders of
foot. The only possible safe recov
is by a safe placement of the swin
limb itself. It is noted that the coe
cients of variation
(CVs) of these
tersubject ensemble averages (Fig
are quite low and indicate consid
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Table
1.
Joint Angle Changes Potentially Responsible for Toe Clearance Variability
JointlSegment Controlling Joint 0 B ~
Swing ankle
Swing knee
Swing hip
Pelvis
Stance knee
Stance ankle
Ankle dorsiflexors/plantar flexors
Knee flexors
Hip flexors
Stance hip abductors/adductors
Knee flexors
Ankle dorsiflexorslplantar flexors
3.2 plantar flexion
49 flexion
23
flexion
Horizontal
9.4 flexion
4.6 dorsiflexion
aO=joint angle at minimum toe clearance
bAO=joint angle change
able consistency in this small grou p
of young adults.
The
sensitivity analysis of the kinemat-
ics from on e of the subjects examined
all joints in the link segment that had
a potential for influencing the toe tra-
jectoly at the time of minim um toe
clearance: swing ankle, swing knee,
swing hip, stance hip abductor (pelvic
list), stance knee, and stance ankle.
The sensitivity analysis calculated the
angular chan ges that, at each joint by
itself, would cause the '0.45-cm toe
clearance variability. These results are
reported in Table 1 , and on e typical
calculation is presented in Figure 4.
According to this interpretation of the
results, if all the remaining joints r e-
mained unchanged, a chan ge of
k0. 86 degree at this time in stance
hip abduction alone could be respon-
sible fo r all of th e variability se en in
toe clearance.
Figure 5 plots the av erage vertical
trajectory and both horizontal and
vertical velocities of th e he el for th ese
sam e subjects over the stride period .
The heel began rising in mid-stance at
heel-off and reached a maximum of
abou t 25 cm just after TO, then d e-
creased rapidly, reaching about
1
cm
above the grou nd at 90 of the stride
period. During the last 10 of the
stride prior to HC, the trajectoly was
almost horizontal; the horizontal ve-
locity also decrea sed drastically from
4 m/s, reaching abo ut 0.87 m/s at HC.
This forward velocity decreased to
zero at about
4
of th e strid e, indicat-
ing a small skidding of the heel of the HAT, durin g on e representative walk-
sh oe imm ediately after HC. Figure 6 ing trial.
demonstrates the position of the body
at HC, especially the heel velocity vec- A h r t h e r sensitivity analysis of the
tors relative to the fo rward velocity of
kinematics of the link chain at this
time of HC was completed to assess
What angular change at the knee alone would
result In a k0.4 5-c m vertical change at the toe?
With the foot position unchanged, there would be
a k0.45cm vertlcal change at the ankle.
The leg would have to change * A 8 o achieve
Vertical distance from knee to ankle =.425 sin 64
=0.382 m
: .425
sln (64
+do) =
.382
0045
sin (64 *A0) .9094
:
A0 1.4'
sln
(64 +.dB)
.I3882 :
A0 1.4
: a I .4 change in kne e angle by itself would cause
the k0.45cm change in toe clearance.
k0.45
cm
f
Figure
4 ample of sensitivity calculation to determine the angular change
kAO
necessary at the knee alone to cause the k0.45-cm displacement variability seen
at th toe at the instant of minimum toe clearance.
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I
. . . . . . I
20
4
6 80 100
STRIDE
( )
Figure
6
Position of body at he
contact for one representative walkin
trial showing the low heel velocities r
tive to the forward velocity of the bod
center of mas R represents the grou
reaction-force vector, and mg represe
the body's center-ofgravity vector.)
length of 1.51 m (walking veloci-
ty= 1.33 m/s). The 19 slow walker
had a cadence of 86.8 steps/min a
step length of 1.38 m (walking vel
ty=1.00 m/s), and the 17 fast walk
had a cadence of 123.1
steps/min
a step length of 1.64 m (walking v
locity= 1.68 m/s)
Figure5
Ensemble-averaged displacement and velocities of the heel of the same
I
subjects as represented in Fig.
2
over one stride, from heel contact (HC) to HC. Hori-
zontal heel velocity reached a peak in mid-swing and decreased to virtually zero in the
vertical direction and to a low value horizontally at HC. (CV=coeficient of variation;
TO
=toe-( )
the angu~lar elocity changes that, by
themselves, would be necessary to
reduce the forward heel velocity by
0.87 m/s, thus reducing it to exactly
zero at HC. The potential angular ve-
locities to which heel velocity is sensi-
tive are swing foot, swing leg, swing
thigh, pelvic horizontal velocity (con-
trolled bly hip rotators), stance thigh,
stance leg, and stance foot. The neces-
sary angular velocity changes are sum-
marized in Table 2 with an indication
of what :muscle group would be re-
sponsible in each case (remembering
that during stance the muscles at ei-
ther the proximal or distal end of
each segment can control). One typi-
cal calculation of the velocity sensitiv-
ity is presented in Figure 7.
The variability of the heel trajectories,
as demonstrated by the CVs in the
ensemble averages presented in
Figure 5, is quite low. Again, this low
variability is indicative of consistency
in this small group of young adults.
Figures 8 through 10 present mechan-
ical power profiles drawn from the
database from subjects walking at
three different cadences and at differ-
ent step lengths. The 19 natural-
cadence walkers had a mean cadence
of 105.3 steps/min and a mean step
Toe clearance has been considere
be a major responsibility of the sw
leg dorsiflexors, and, as expected,
is quite sensitive to small angular
changes (22.07 )f the swing ank
The sensitivity analysis results
(Tab. I), however, show that the e
point toe trajectory is also very se
tive to small angular changes at fiv
other joints in the total link-segme
chain. Toe clearance is sensitive to
even smaller angular changes at th
knee (2 1.35-d during stance h
abduction and adduction (20.869
Clinically, it is important to observ
each walking patient and note any
clearance problems and at which j
compensations are taking place. T
it is not surprising that certain pa-
tients, such as those with below-k
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STRI E
Oh )
lgure8. Mechanical power generation and absorption proJles at the ankle for
three walking-speed cadences: natural, slow, and fast. The push-offpower
(A2
burst) by
the plantar flexors drastically increased )om slow to fast walking cadences and repre-
sents over
75%
of all energy generated in the stride period. The
A
power phase was the
absorption of e n e w as the plantar flexors lengthen as the leg rotates forward over the
foot.
O
=:toe-off)
which means that the biarticulate
hamstring muscles would be pre-
dicted to decelerate both the swing
thigh and leg and therefore are the
major decelerators of the foot. Elec-
tromyographic profiles show the ham-
string muscles to be active in late
swing.19J Mechanical power analyses
have also shown this to be true in
both walking4 and running,21during
which the eccentric work done at the
knee during the latter half of swing
was dominant. In running,21a small,
short-duration burst of positive power
immediately followed this K4 negative
work and was due to a concentric
contraction as these same hamstrin
muscles momentarily accelerated t
leg backward. This finding does no
mean that the foot was traveling ba
ward at this time. Rather, the body
had a forward velocity of about 3 m
and, to reduce the foot velocity to
near-zero, the foot would need a m
mentary backward velocity of abou
m/s relative to the center of mass
the body. The central nervous syst
obviously recognizes the energetic
this fine control. The third possible
muscle group noted in Table 2 tha
could control the swing limb's for-
ward velocity are the stance hip ex
nal rotators. Because the angular ro
tion and velocity of the pelvis in th
transverse plane were quite small,
these rotators would have only min
mal potential for control.
The clinical significance of this HC
velocity analysis relates
to
the pote
tial for a patient to slip at this critic
phase of the gait cycle. Heel contac
usually involves weight bearing on
small surface area of the heel, and,
the ground contact area is wet or s
pery, there is an increased probabi
of slipping. In a study on fit and no
disabled elderly subjects, we have
documented that their HC velocity
was 1.15 m/s, which is significantly
higher (P<.01) than for the young
adults in this study. Thus, these el-
derly individuals are at a greater ri
for slipping, even though their wal
ing velocity was significantly lower
than that of the younger adults in t
study (1.29 versus 1.43 m/s, respec-
tively). To date, we have not docu-
mented the HC velocity for patient
who are prone
to
fall; such studies
are currently ongoing.
Four of the power bursts (ie, A2, K
K4, and H3) shown in Figures 8
through 10 demonstrated drastic
changes during push-off and swing
that could influence step length. Th
ankle push-off burst (A2 in Fig.
8)
showed a dramatic increase as the
subjects accelerated their lower lim
prior to TO to achieve a longer ste
length. Almost simultaneous to this
push-off impulse was an increasing
absorption of energy at the knee
(K3 in Fig. 9) by the eccentrically ac
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I . l . . ~ . . . t . . . . . . . . . . l . . . . . . . , . ~
2 4 6 8 1
STRI E
( )
Figure
9
Mechanical power absorption and generation at the knee for the same
three cadence groups as represented in Fig 8 The U burst was the power associated
with the eccentrically contracting quadriceps femoris muscle necessary to control knee
jlexion caused by the 'piston-like push-off
y
the ankle in late stance. The K burst was
due to the eccentrically contracting hamtn'ng muscles decelerating the swinging leg
prior to heel contact. Both and K increased
as
cadence and stride length increased.
The KI bum was the absorption by the knee extensors as they lengthen when the knee
jlexes. The
k
burst was the generation
y
the same knee extensors as the knee extends
during mid-stance. (TO=toe-off)
ing quadriceps femoris muscle. This the hip flexors contracted concentri-
absorption represents a necessary loss cally to commence a pull-off of the
of energy to prevent t o o rapid a knee
lower limb H3 in Fig. lo), which con-
flexion prior to TO (60% of stride)
tinued past TO until midswing. This
resulting from the forceful upward
impulse of pull-off energy also in-
acceleration of the leg caused by A2. At
creased dramatically with increased
mid-double support (50% of stride), cadence and step length. In mid-swing,
the swinging lower limb (mainly leg
and foot) reached its maximum en-
ergy, which must be removed prior
to
HC The K burst (Fig. 9) showed the
knee flexors (hamstring muscles) to
be eccentrically acting, mainly to re-
move the kinetic energy from the
swinging leg and foot. Thus, increased
step length (and cadence) is normally
achieved with an increase in both pos
tive work by the ankle plantar flexors
and hip flexors and a matched in-
crease in the negative work by the
knee extensors during late stance and
the knee flexors during late swing.
The influence of these energy bursts
on the gait patterns of fit and nondis-
abled elderly subjects has also been
demonstrated recently.17 These elderly
subjects were seen
to
have the same
natural cadence as the younger adults
in this study, but a significantly
(Pc.01) shorter stride length. Two
motor pattern changes responsible for
this reduction were a significantly re-
duced push-off power (A2 burst) and
significant increase in quadriceps fem
oris muscle absorption (K3 burst).
Conclusions
The trajectory of the f oo t during gait
is a precise end-point control task. It
is under the multisegment motor con
trol of both stance and swing limbs.
Toe clearance of slightly more than
1 cm was found
to
be sensitive
to
fin
control by at least six muscle groups
in the link-segment chain. Heel-
contact velocity was virtually zero in
the vertical direction, with a low hori
zontal velocity. The dominant muscle
group responsible for reducing that
velocity was the hamstrings. The mag
nitude of step length was found
to
be
under the control of four concentric
and eccentric motor patterns during
late stance and swing. Step length and
walking velocity were increased by
increased plantar-flexor power during
push-off and by increased hip-flexor
power during pull-off. Step length
can be reduced by increased eccen-
tric quadriceps femoris muscle activit
during late stance and by increased
eccentric hamstring muscle activity
during late swing. In spite of the con-
sistency in the foot trajectory profiles
for this small group of young adults,
62 / 52
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References
STRI E
( )
Figure 10 Mechanical power generation and absorption at the hip for the same
three caa'ence groups as represented in Fig. 8. The H burst represents the 'pull-of'
power generation by the hipJexors. This positive work began in late stance (50 ), con-
tinued into mid-swing (go ), and increased drastically
as
cadence increased. TheH I
power ph'ase resulted )om the hip extensors shortening immediately after heel contact.
The
H 2
power burst resulted from the hipJexors; lengthening during mid-stance to de-
celerate rhe backward-rotating thigh. (TO=toe-of)
mo re research may be necessary to
Acknowledgment
quantify any differences in larger
groups of young adults and in other
acknowledge the technical assistance
age groups.
of Mr Paul Guy.
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walking. Acta Physiol Scand. 1984;1215-
2 Patla
AE
Frank
JS
Winter DA. Assessm
balance control in the elderly: some issu
Physiotherapy Can ada. 1990;42:89-98.
3 Winter DA. Overall principle of lower
suppo rt during stance phase of gait.J Bi
mech. 1980;13:923-927
4 Winter D k Energy generation and abso
at the ankle and knee du ring fast natural
slow cadences. Clin Orthop. 1983;197:147
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David A WinterMultifactorial Motor Control TaskFoot Trajectory in Human Gait: A Precise and
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