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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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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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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

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( )

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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AE

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JS

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4 Winter D k Energy generation and abso

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AB

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