Gard Comparison of kinematic and kinetic methodsfor computing the vertical motion of thebody center of mass during walking 2003

Human Movement Science 22 (2004) 597–610
www.elsevier.com/locate/humov
Comparison of kinematic and kinetic methods
for computing the vertical motion of the
body center of mass during walking
Steven A. Gard
a,b,c,*
, Steve C. Miff
a,b
, Arthur D. Kuo
d
a
Northwestern University Prosthetics Research Laboratory and Rehabilitation Engineering
Research Program, Department of Physical Medicine and Rehabilitation, Northwestern University Medical
School, 345 East Superior Street, RIC 1441, Chicago, IL 60611, USA
b
Department of Biomedical Engineering, Northwestern University, Evanston, IL 60208, USA
c
VA Chicago Health Care System, Lakeside Division, Department of Veterans Affairs, Chicago,
IL 60611, USA
d
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA
Accepted 14 November 2003
Abstract
The vertical excursion of the body center of mass (BCOM) was calculated using three different techniques commonly used by motion analysis laboratories. The sacral marker method
involved estimating vertical BCOM motion by tracking the position of a reflective marker that
was placed on the sacrum of subjects as they walked. The body segmental analysis technique
determined the vertical motion of the BCOM from a weighted average of the vertical positions
of the centers of mass of individual body segments for each frame of kinematic data acquired
during the data trial. Anthropomorphic data from standard tables were used to determine the
mass fractions and the locations of the centers of mass of each body segment. The third technique involved calculating BCOM vertical motion through double integration of force platform data. Data was acquired from 10 able-bodied, adult research subjects – 5 males and 5
females – walking at speeds of 0.8, 1.2, 1.6, and 2.0 m/s. A repeated measures ANOVA indicated that at the slowest walking speed the vertical excursions calculated by all three techniques were similar, but at faster speeds the sacral marker significantly (p < 0:001)
overestimated the vertical excursion of the BCOM compared with the other two methods.
*
Corresponding author. Address: Northwestern University Prosthetics Research Laboratory and
Rehabilitation Engineering Research Program, 345 East Superior Street, RIC 1441, Chicago, IL 60611,
USA. Tel.: +1-312-238-6500; fax: +1-312-238-6510.
E-mail address: [email protected] (S.A. Gard).
0167-9457/$ - see front matter 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.humov.2003.11.002
598
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
The body segmental analysis and force platform techniques were in agreement at all walking
speeds. Discrepancies between the sacral marker method and the other two techniques were
explained using a simple model; the reciprocal configuration of the legs during double support
phase significantly raises the position of the BCOM within the trunk at longer step lengths,
corresponding to faster walking speeds. The sacral marker method may provide a reasonable
approximation of vertical BCOM motion at slow and freely selected speeds of able-bodied
walking. However, the body segmental analysis or force platform techniques will probably
yield better estimates at faster walking speeds or in persons with gait pathologies.
2003 Elsevier B.V. All rights reserved.
PsycINFO classification: 2260
Keywords: Human movement; Gait analysis; Center of mass
1. Introduction
Translation of the body center of mass (BCOM) from one place to another is a
fundamental objective of walking. Normal human walking is characterized by a periodic vertical displacement of the BCOM that moves through a complete cycle of vertical motion with each step, or two cycles during each stride. The peak-to-peak
amplitude of the vertical BCOM displacement, referred to as the vertical excursion,
is generally regarded to be about 4–5 cm for adult ambulators at their freely selected
walking speed (Murray, Drought, & Kory, 1964; Inman, Ralston, & Todd, 1994;
Saunders, Inman, & Eberhart, 1953). Investigators have used vertical BCOM motion
during walking to estimate mechanical energy changes (Cavagna, 1975; Iida &
Yamamuro, 1987; Tesio, Civaschi, & Tessari, 1985; Tesio, Lanzi, & Detrembleur,
1998a, 1998b), to gauge efficiency (Cavagna, Tesio, Fuchimoto, & Heglund, 1983;
Saunders et al., 1953), to estimate work (Cavagna, Saibene, & Margaria, 1963; Cavagna & Margaria, 1966; Donelan, Kram, & Kuo, 2002), to describe symmetry (Cavagna et al., 1983; Crowe, Schiereck, & Keessen, 1992; Gard, Knox, & Childress,
1996), and as an indicator of the overall quality of gait (Bowker & Hall, 1975; Saunders et al., 1953). All of these applications rely on accurate determination of vertical
BCOM motion.
Investigators have developed a number of basic methodologies for calculating
BCOM motion during walking. Some of the methods utilize kinematic data acquired
from markers that are placed on the body, and others utilize kinetic data acquired
from force platforms. One of the simplest kinematic methods, the sacral marker
method, uses a single marker placed on the sacrum to approximate BCOM motion.
A more sophisticated approach, the segmental analysis method, uses multiple markers to measure body segment positions, and incorporates an anthropometric model
to calculate segmental center of mass positions. These segmental center of mass positions are then used to calculate the BCOM. In contrast, the force platform method
uses measured ground reaction forces to calculate BCOM motion based upon Newton’s Second Law, which states that the net external force acting upon a body is
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
599
equal to its mass multiplied by its acceleration. The displacement of the BCOM can
be calculated through double integration of the acceleration term with proper consideration for the integration constants. Comparisons of BCOM motion between
the kinematic and kinetic methods, utilizing data that have been simultaneously acquired from walking individuals, have been shown to yield results with significantly
different excursion magnitudes, especially in the vertical direction (Saini, Kerrigan,
Thirunarayan, & Duff-Raffaele, 1998; Thirunarayan, Kerrigan, Rabuffetti, Croce,
& Saini, 1996; Whittle, 1997). Investigators using the force platform method have
generally reported much smaller BCOM excursions than those who have used the
sacral marker method (Gard & Childress, 1997; Lee & Farley, 1998; Tesio et al.,
1998a). In theory, the BCOM motion calculated from kinematic and kinetic data
should match, but the reason for this inconsistency has not yet been adequately
explained.
The discrepancies reported in the literature may be due to the assumptions associated with each method. The sacral marker method assumes that the BCOM can be
closely approximated by the motion of a single marker. The segmental analysis
method assumes that segmental masses and center of mass locations can be determined accurately. The force platform method makes none of these assumptions
(Elftman, 1939), and does not rely on accurate placement of markers on the body
as required for a kinematic analysis. Instead, it assumes that integration constants
can be determined accurately. In principle, the segmental analysis and force platform
methods should agree well, and a likely explanation for the difference with the sacral
marker method is the motion of the limbs (Whittle, 1997). The configuration of the
limbs varies between double support and mid-stance, so that the BCOM’s location
may vary relative to any single point on the pelvis.
The purpose of the current investigation was to account for differences in vertical
BCOM excursion calculated from kinematic data and kinetic data. The vertical
BCOM excursions were measured during walking in able-bodied adults using the sacral marker, segmental analysis, and force platform methods. We propose a simple
kinematic model that explains the differences observed between the measurement
techniques. Comparisons are made between the excursions predicted by the model
and those calculated from empirical data.
2. Theoretical model
A simple, three-link model (Fig. 1) illustrates why motion of the limbs may affect
estimates of BCOM excursion. Analysis of the model is used to show how deviation
between BCOM calculations and the sacral marker method may occur as walking
speed varies. The three rigid links of the model represent the trunk and two rigid legs
having rocker feet. Motion of two legs is sufficient to cause the BCOM position to
change relative to a sacral marker, because each leg has its own COM that moves
with the leg, and both leg COMs contribute to the overall BCOM position.
The rocker feet are added because an inverted pendulum model having legs without
rocker feet, referred to as a Ôcompass gait’ model (Saunders et al., 1953), is known to
600
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
Fig. 1. A simple model can be used to explain the differences observed when calculating the vertical excursion of the BCOM using the sacral marker method, the segmental analysis method, and the force platform
method. In the model, the trunk COM and the BCOM are at their highest elevations in midstance when
the legs are vertical (figure at left), and they are at their lowest elevations in the middle of double support
(figure at right). As step length increases, the trunk COM and BCOM both undergo greater vertical excursions during the step. However, reciprocal action of the legs effectively raises the BCOM position within
the trunk, thereby causing the vertical excursion of the BCOM over the gait cycle to be less than that of the
trunk.
produce excessive vertical excursion. Rocker feet effectively lengthen the leg and
result in a flattened trajectory that more closely matches human walking (Gard &
Childress, 2001).
We used this model to predict differences between the BCOM calculation methods. The model’s trunk mass was set to the combined masses of the head, arms,
and thorax, totaling approximately 64% of body mass (Table 1). Each leg comprised
approximately 18% of body mass. Body segment dimensions were scaled according
to an assumed individual’s height of 178 cm. Leg length was assumed to be 96 cm
(54% of height), and the foot rockers were defined as circular arcs with radii equal
to 35 cm. The vertical positions of the trunk COM and the BCOM were calculated
for two geometric configurations of the model corresponding to the times during the
gait cycle when the body is at its highest and lowest elevations. The body reaches its
highest elevation at midstance when the legs are vertical, and it reaches its lowest elevation during double support when the legs are outstretched. For the calculations,
the trunk is assumed to remain vertical in both configurations. The highest elevations
of the trunk COM and BCOM are independent of step length, but their lowest elevations decrease with longer step lengths. The lowest elevations of the trunk COM
and BCOM were calculated for step lengths ranging from 50 to 90 cm, corresponding to the range of step lengths observed in our research subjects’ data at speeds from
0.8 to 2.0 m/s. The vertical excursions of the trunk COM and the BCOM were calculated as the difference between their respective maximum and minimum elevations
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
601
Table 1
Definitions, lengths, and center of mass locations for body segments (Drillis, Contini, & Bluestein, 1964)
Segment
Definition (proximal/distal)
% Body weight
Segment COM
location from
proximal endpoint
Foot
Shank
Thigh
Forearm, hand
Upper arm
Head, neck, trunk
Heel marker/virtual toe marker
Knee center/ankle center
Hip center/knee center
Elbow marker/wrist marker
Shoulder marker/elbow marker
Shoulder markers midpoint/hip joints
midpoint
1.8
4.4
11.2
2.6
3.3
53.4
0.506
0.433
0.433
0.682
0.430
0.540
8.0
Vertical Excursion (cm)
7.0
6.0
Trunk
5.0
4.0
BCOM
3.0
2.0
1.0
0.0
50
60
70
80
90
Step Length (cm)
Fig. 2. The vertical excursions of the trunk and BCOM, from the simple model depicted in Fig. 1, plotted
as functions of step length. As step length increases, the reciprocal action of the legs raise the position of
the BCOM relative to the trunk, causing its vertical excursion to be less.
at these two body configurations. The difference between these two excursions is
small for very short step lengths, but increases substantially for longer step lengths
(Fig. 2). This analysis therefore predicts that the sacral marker method, which tracks
trunk motion, will tend to over-estimate vertical trunk excursion compared to the
segmental analysis and force platform methods.
3. Methods
Kinematic and force plate data were recorded from 10 subjects – 5 males and 5
females – using non-invasive procedures routinely employed in clinical gait analysis
facilities. All subjects were considered to be non-pathologic ambulators in good
health. The subjects were presented with a simple description of the experimental
protocol and were asked to sign consent forms approved by Northwestern University’s Institutional Review Board.
602
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
Fig. 3. The measurement volume of the kinematic measurement system occupies an area on the walkway
of 4.9 m · 1.2 m, with a height of approximately 1.8 m. The six platforms, numbered 1–6, are arranged
along the walkway such that the array measures 2.5 m end-to-end, which enables a minimum of three foot
strikes (one stride) to be captured at the fastest walking speeds of able-bodied subjects. The total length
of the walkway is approximately 11 m.
Data collection was conducted at the VA Chicago Motion Analysis Research
Laboratory (VACMARL) of the VA Chicago Health Care System. The laboratory
is equipped with an eight-camera Eagle Digital Real-Time motion measurement system from Motion Analysis Corporation. 1 Kinematic data for this study were acquired at 120 Hz. Bilateral gait analysis was performed on all subjects using a
modified Helen Hayes marker set. A total of 21 markers were placed on feet, legs,
pelvis, and upper extremities. Locations of the markers were on the dorsum of the
feet at the MTP joints, the heels of the feet, the lateral malleolli, the lateral femoral
epicondyles, on wands extending laterally from the shank and thigh segments, the
anterior superior iliac spines (ASIS), the sacrum at the midpoint between the posterior superior iliac spinae (PSIS), the tips of the acromion process, the lateral epicondyles of each humerus, and at the midpoint of the wrists between the styloid
processes. This marker set allowed the creation of a 12-segment rigid-link model
of the body, consisting of a seven-segment model of the locomotor system and
a five-segment model of the trunk and arms.
VACMARL has six AMTI 2 force platforms embedded in the walkway for measuring ground reaction forces as subjects walked across them. Simultaneous with the
acquisition of the marker position data, ground reaction forces were acquired at 960
Hz as the subjects walked along the walkway and stepped on the force platforms
embedded in the floor. The measurement volume and the number and layout of force
platforms (shown in Fig. 3) are designed so that subjects can walk with a wide range
of step lengths without needing to pay attention to stepping cleanly from one force
platform to another, even for an able-bodied subject who is walking at his or her
fastest comfortable speed. The cross-over of a foot strike from one plate to another
1
Motion Analysis Corporation 3617 Westwind Boulevard Santa Rosa, CA 95403-1067, Tel: +707-5796500.
2
AMTI, 176 Waltham Street Watertown, MA 02172, Tel.: +617-926-6700.
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
603
during a trial was not a problem since the summed vertical ground reaction forces
between all plates were utilized for the experiment. However, only those foot strikes
that occurred within the perimeter of the force platform array were analyzed.
Subjects were instructed to walk at four pre-determined speeds between 0.8 and
2.0 m/s. The walkway for the experiment was marked with two lines 3.66 m apart.
The time needed to traverse the distance between the lines at a given steady-state
velocity was monitored by the investigator with a stop watch. The subjects were instructed to walk faster or slower from trial-to-trial in order to achieve the desired
walking speed. Three good trials were recorded at each walking speed; a trial was
considered acceptable if the subject’s speed was within 5% of the target speed.
Data processing was initially performed using Motion AnalysisTM Software (EvA
and Orthotrak). Raw marker position data were filtered using a fourth order bidirectional low pass filter with an effective cutoff frequency of 6 Hz. The force platform data were unfiltered. The kinematic and kinetic data were further processed
and analyzed using custom macros and templates for Matlab 5.3 and Microsoft
Excel 2000.
Vertical BCOM excursion was calculated using three different methods: (1) the sacral marker method, (2) the segmental analysis method, and (3) the force platform
method. Vertical excursion data derived from these methods were analyzed using intra-class correlation and a repeated measures ANOVA at each of the four speeds to
determine if there were significant differences between the three techniques. Post hoc
analyses were performed using paired t-tests with Bonferroni corrections when significant differences were observed in the ANOVA.
The sacral marker method simply involved tracking the vertical position of the
marker that was placed between the PSIS as the subject walked through the measurement volume (Miff, Childress, & Gard, 2001). For an able-bodied adult in quiet
standing, the BCOM has been reported to lie in the midline of the body at a distance
from the ground corresponding to about 55% of the person’s height, at a position
just anterior to the second sacral vertebra (Saunders et al., 1953). The sacral marker
technique is probably accurate if one assumes that (1) pelvic tilt is negligible, as is
the case in able-bodied walking (Murray et al., 1964), and (2) the BCOM does not
move significantly relative to the pelvis.
For the segmental analysis method, the locations of the segmental centers of mass
were determined from the positions of markers that were placed on the body and the
calculated joint centers. Body mass segment fractions were based upon data from
Harless (Drillis et al., 1964), and the segmental lengths were from data by Dempster
(Drillis et al., 1964). Body segment definitions, mass fractions, and center of mass
locations are provided in Table 1. For each subjects’ data, the BCOM vertical position was determined for each frame of kinematic data by calculating the vertical
positions of the centers of mass of each body segment, and then using a weighted
average based upon the segment mass fractions to calculate overall BCOM position
(Winter, 1990). The peak-to-peak amplitudes of the resulting vertical displacement
waveforms were averaged for each trial in order to calculate the vertical excursion.
For the force platform method, BCOM kinematics were estimated from ground
reaction force data. A step was defined as the interval from initial contact of one foot
604
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
to the initial contact of the opposite foot. The BCOM velocity and position were
determined through integration over a complete step of the vector sum of vertical
ground reaction forces acting under both limbs (Cavagna, 1975).
The vertical acceleration of the BCOM, az ðtÞ, was calculated from the summed
vertical ground reaction forces, Fz ðtÞ, less the body weight, m g, and divided by
body mass, m:
az ðtÞ ¼
Fz ðtÞ m g
:
m
The vertical velocity of the BCOM was calculated by integrating the BCOM acceleration over a single step:
Z
Z t
1 t
vz ðtÞ ¼ v0 þ
az ðsÞ ds ¼ v0 þ
ðFz ðsÞ m gÞ ds;
m 0
0
where v0 is the integration constant representing the vertical velocity of the BCOM
at the beginning of the step cycle. The integration constant was determined by
requiring the average vertical BCOM velocity to be zero (Donelan et al., 2002).
The vertical position, zBCOM ðtÞ, was found by integrating the vertical velocity
over a single step:
Z t
vz ðsÞ ds;
zBCOM ðtÞ ¼ z0 þ
0
where z0 is the integration constant representing the vertical position of the BCOM
at the beginning of the step cycle. The integration constant z0 was set to zero since
only the vertical displacement, rather than absolute position, of the BCOM was
desired. The vertical excursion of BCOM was calculated as the peak-to-peak
amplitude of the vertical displacement waveform.
4. Results
The vertical displacement waveforms that were generated from the empirical data
using the three techniques that were investigated were fundamentally similar in
appearance at all walking speeds (Fig. 4). Vertical excursion of the BCOM was
found to increase with walking speed in all three methods (Fig. 5), with the vertical
excursions calculated at 2.0 m/s being about two to three times those at 0.8 m/s. The
intraclass correlation between all three methods was 0.78. Among methods, the two
kinematic methods appeared to be in relatively good agreement with the force platform technique at speeds less than about 1.4 m/s. However, at faster speeds, the sacral marker method produced estimates of BCOM excursion that were considerably
greater than those of the other two methods. The force platform and the body segmental analysis methods showed good agreement in the vertical excursion calculations at all speeds (Table 2). Statistical analyses revealed no significant differences
between the three methods at the walking speed of 0.8 m/s. The differences between
the calculated BCOM vertical excursions using the sacral marker method and the
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
605
Fig. 4. The vertical displacement of the BCOM was calculated at each of four walking speeds with the
segmental analysis, force platform, and sacral marker methods. The displacement trajectories are similar
in appearance between the three methods, but their amplitudes begin to differ at higher speeds. The data
shown here are the average BCOM trajectories from the trials of one representative subject. The shaded
region indicates the entire range of trials from the same subject, computed with the segmental analysis
method. Because the force platform and sacral marker methods do not compute absolute position, their
trajectories were aligned with the highest elevation of the segmental analysis method. According to the
model, the segmental analysis and sacral marker methods correspond at that point.
other two methods were found to be statistically significant (p < 0:001) at walking
speeds of 1.2, 1.6 and 2.0 m/s.
The discrepancies between the techniques increased with walking speed in the
empirical data in a manner comparable to the predictions from the simple walking
model (Fig. 2). Generally, in able-bodied walking step length increases with walking
speed. In the model, vertical excursions of the trunk and BCOM are small at the
shorter step lengths, differing by only about 5 mm. This difference increases with step
length, reaching approximately 18 mm at the longest step length, which corresponds
with the fastest walking speed. The observed differences between the techniques in
empirical data were lower than that predicted by the model at the slower walking
speeds (0.8 and 1.2 m/s), but at higher speeds the vertical excursions were nearly
identical to those predicted by the model.
606
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
8.0
Sacral marker
Vertical Excursion (cm)
7.0
Segmental analysis
6.0
Force platform
5.0
4.0
3.0
2.0
1.0
0.0
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Walking speed (m/sec)
Fig. 5. The vertical excursion of the BCOM for the sacral marker method, the segmental analysis method,
and the force platform method, plotted as a function of walking speed. All three methods yield comparable
results at the slowest walking speed of 0.8 m/s, but the sacral marker method appears to overestimate the
BCOM vertical excursion at faster speeds. The vertical bars represent one standard deviation from the
mean; the thicker, gray error bars correspond with the segmental analysis data.
Table 2
Mean and standard deviations for walking speed and the vertical excursions calculated from the three
methods
Walking speed (m/s)
0.83
1.22
1.62
2.02
(±0.04)
(±0.05)
(±0.08)
(±0.08)
Vertical excursion (cm)
Sacral marker method
Body segment analysis
method
Force platform method
2.7
4.0
5.8
6.7
2.7
3.5
4.7
4.9
2.4
3.4
4.6
4.8
(±0.4)
(±0.8)a
(±0.8)a
(±1.1)a
(±0.4)
(±0.7)b
(±0.8)b
(±0.9)b
(±0.4)
(±0.6)c
(±0.8)c
(±1.0)c
Paired t-test comparisons were made between methods within each velocity.
a
Statistically significant differences at p < 0:001.
b
Differences between sacral marker and segment analysis methods.
c
Differences between sacral marker and force platform methods.
5. Discussion
Previous investigations that have analyzed vertical motion of the BCOM during
walking have shown imperfect agreement between kinematic methods based upon
body segment markers and kinetic methods that utilize force platform data. Our
empirical data show that the segmental analysis and force platform methods for calculating BCOM vertical excursion during walking yield similar results (Fig. 5). This
agreement between these two techniques is believed to be associated with the
assumption that we utilized for calculating the integration constant, v0 , generated
with the force platform method. The sacral marker method differed from the other
two methods by an amount that increased with walking speed, leading us to believe
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
607
that segmental analysis and force platform methods are more accurate for estimating
vertical BCOM motion than the sacral marker method. Statistically significant differences at p < 0:001 were found between the sacral marker method and the other
two techniques at speeds of 1.2, 1.6 and 2.0 m/s. No statistically significant differences were found between the vertical BCOM excursions calculated with the force
platform and the body segmental methods at any of the walking speeds, suggesting
that both are reasonably consistent measures of BCOM vertical motion during ablebodied walking.
The discrepancies observed in the vertical excursion calculations using the sacral
marker method and the other two techniques can be explained with a simple, threelink model (Fig. 1). As step length increases, the trunk COM and BCOM both undergo greater vertical excursions during each step. The reciprocal configuration of
the legs during the double support phase of walking effectively raises the BCOM position within the trunk, thereby causing the vertical excursion of the BCOM to be less
than that of the trunk COM. While the vertical excursions of the trunk COM and the
BCOM are of comparable magnitude at slower walking speeds when step lengths are
relatively short, the differences become appreciable at the longer step lengths that
occur with faster walking speeds (Figs. 2 and 5). We believe that this simple model
accounts for the differences observed between the sacral marker estimation and the
other two BCOM calculation techniques, especially at the higher walking speeds. A
more complex model may have matched our empirical data better, had we included
knee joints to account for the actual configuration of the legs during mid-stance, or
had we added reciprocal action of the arms during gait. We could have also developed a custom model for each research subject and based its dimensions on the actual heights of our research subjects. However, we felt that this added complexity
was not necessary, and would possibly even detract from the primary reason for
the observed difference in the vertical excursion measures: the reciprocal configuration of the legs during the double support phase of gait. The simple model remains
useful as a means to clearly illustrate the reason why the sacral marker method will
differ from the other methods.
Another reason why other investigators may not have shown good agreement between the body segmental analysis and the force platform technique could be differences in the configuration of laboratory force platforms. Many gait analysis
laboratories have two force platforms that are mounted rigidly in the floor and cannot easily be moved to accommodate different step lengths of individuals. Even if
force platform separation is satisfactory for a particular subject walking at their slow
or freely selected speeds, as they walk faster and their step length increases they will
have difficulty striking both platforms unless they alter their gait and target the
plates. Step length ultimately affects vertical BCOM motion (Miff et al., 2001); the
vertical excursion of the BCOM during the gait cycle increases directly with step
length. In this situation where the two force platforms are immovable, kinematic
data may in fact be collected over multiple gait cycles, while force platform data is
only collected over one step (from initial contact of one leg through toe-off of the
opposite leg). If the subject alters their step length to strike both plates, then their
vertical BCOM motion will be changed for that one step. In contrast, the vertical
608
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
BCOM excursions from the kinematic data may be averaged across several steps, so
that the altered vertical excursion of a single step has a relatively smaller effect on the
final kinematic result. Having a constrained step length on the force platforms may
also explain why some of the previous studies show much less variability between
subjects in the vertical BCOM excursions calculated from force platform data than
in the kinematic data. If the step lengths of the research subjects were dictated by the
force platform separation, then the subjects’ vertical excursions would probably be
approximately the same.
Different methods for performing the force platform method could be another
reason why previous studies have shown poor agreement between kinetic and kinematic techniques. Integration tends to filter out noise, but it is particularly sensitive
to drift and to the choice of integration constants. The integration constant not only
determines the initial value of a quantity, but also can contribute to drift if that
quantity is then integrated, as is the case with the BCOM velocity at the beginning
of a step. Working with steady-state walking data actually simplifies the removal of
these errors, since no net change in the vertical velocity or displacement of the
BCOM can occur over a gait cycle during level walking of able-bodied subjects
(Donelan et al., 2002). Under these conditions, any linear trends in the integrals
can be removed, and the force plate method agrees well with the segmental analysis
method. However, poor selection of integration constants, or a lack of symmetry
or periodicity in gait, can lead to significant errors.
Our results suggest that the sacral marker method for estimating vertical BCOM
motion should generally be avoided at faster walking speeds of able-bodied ambulators, but it may provide a reasonably good estimate of vertical BCOM motion at relatively short step lengths that occur at or below the freely selected walking speed of
about 1.4 m/s. As walking speed increases above the freely selected speed, the reciprocal action of the legs extending forwards and backwards raises the BCOM position relative to the trunk and pelvis, so that the sacral marker overestimates vertical
excursion of the BCOM. In addition, the sacral marker may potentially yield poor
estimates of vertical BCOM motion in some pathological gaits because of significantly increased pelvic rotations, most notably pelvic tilt. Large pelvic tilt rotations
can appreciably change the magnitude of the vertical motion of a body surface marker on the sacrum with respect to the actual BCOM position due to apparent translation that occurs with out-of-plane rotations (Gard et al., 1996).
Comparing all three methods, each has complementary advantages and disadvantages. The sacral marker method, despite its inaccuracies at large step lengths,
remains attractive because of its simplicity. The segmental marker method is potentially more accurate, but it is also dependent on marker measurements that can be
noisy due to relative motion between marker and bone. It also assumes that the body
segments behave as rigid bodies, and are well characterized by anthropometric
parameters that can be estimated with limited accuracy. The force platform method
makes no such assumptions, but requires accurate measurements of ground reaction
forces and of the BCOM position and velocity at the beginning of a step. A combination of kinematic and kinetic methods could potentially yield even better estimates
of BCOM excursion.
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
609
Acknowledgements
This work was supported by the National Institute on Disability and Rehabilitation Research (NIDRR) of the US Department of Education under grant
H133E980023. The opinions in this publication are those of the grantee and do
not necessarily reflect those of the Department of Education. Data for this project
were acquired in the VA Chicago Motion Analysis Research Laboratory of the
VA Chicago Health Care System, Lakeside Division.
References
Bowker, J. H., & Hall, C. B. (1975). Normal human gait. In The American Academy of Orthopaedic
Surgeon’s Atlas of Orthotics: Biomechanical Principles and Application (pp. 133–143). St. Louis, MO:
C.V. Mosby Company.
Cavagna, G. A. (1975). Force platforms as ergometers. Journal of Applied Physiology, 39, 174–179.
Cavagna, G. A., & Margaria, R. (1966). Mechanics of walking. Journal of Applied Physiology, 21, 271–
278.
Cavagna, G. A., Saibene, F. P., & Margaria, R. (1963). External work in walking. Journal of Applied
Physiology, 18(1), 1–9.
Cavagna, G. A., Tesio, L., Fuchimoto, T., & Heglund, N. C. (1983). Ergometric evaluation of
pathological gait. Journal of Applied Physiology, 55, 607–613.
Crowe, A., Schiereck, P. & Keessen, W. (1992). Only three parameters suffice to adequately describe the
symmetric aspects of gait. In Proceedings of NACOB II, the second North American Congress on
biomechanics, Chicago, 24–28 August (pp. 373–374).
Donelan, J. M., Kram, R., & Kuo, A. D. (2002). Simultaneous positive and negative external mechanical
work in human walking. Journal of Biomechanics, 35, 117–124.
Drillis, R., Contini, R., & Bluestein, M. (1964). Body segment parameters: A survey of measurement
techniques. In Selected articles from artificial limbs (pp. 329–351). Huntington, NY: Robert E. Krieger
Publishing Co. Inc.
Elftman, H. (1939). The force exerted by the ground in walking. Arbeitsphysiologie, 10, 485–491.
Gard, S. A., & Childress, D. S. (1997). The effect of pelvic list on the vertical displacement of the trunk
during normal walking. Gait and Posture, 5, 233–238.
Gard, S. A., & Childress, D. S. (2001). What determines the vertical displacement of the body during
normal walking? JPO: Journal of Prosthetics and Orthotics, 13(3), 64–67.
Gard, S. A., Knox, E. H., & Childress, D. S. (1996). Two-dimensional representation of three-dimensional
pelvic motion during human walking: An example of how projections can be misleading. Journal of
Biomechanics, 29(10), 1387–1391.
Iida, H., & Yamamuro, T. (1987). Kinetic analysis of the center of gravity of the human body in normal
and pathological gaits. Journal of Biomechanics, 20(10), 987–995.
Inman, V. T., Ralston, H. J., & Todd, F. (1994). Human locomotion. In J. Rose & J. G. Gamble (Eds.),
Human walking (2nd ed., pp. 1–22). Baltimore, MD: Williams and Wilkins (Chapter 1).
Lee, C. R., & Farley, C. T. (1998). Determinants of the center of mass trajectory in human walking and
running. The Journal of Experimental Biology, 201, 2935–2944.
Miff, S. C., Childress, D. S., & Gard, S. A. (2001). Vertical excursion of the trunk during gait is determined
by step length. In 6th annual meeting of the Gait and Clinical Movement Analysis Society (GCMAS),
Sacramento, CA, 25–28 April.
Murray, M. P., Drought, A. B., & Kory, R. C. (1964). Walking patterns of normal men. Journal of Bone
and Joint Surgery, 46A, 335–360.
Saini, M., Kerrigan, D. C., Thirunarayan, M. A., & Duff-Raffaele, M. (1998). The vertical displacement of
the center of mass during walking: A comparison of four measurement methods. Journal of
Biomechanical Engineering (Transactions of the ASME), 120(2), 133–139.
610
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610
Saunders, J. B., Inman, V. T., & Eberhart, H. D. (1953). The major determinants in normal and
pathological gait. The Journal of Bone and Joint Surgery, 35-A(3), 543–558.
Tesio, L., Civaschi, P., & Tessari, L. (1985). Motion of the center of gravity of the body in clinical
evaluation of gait. American Journal of Physical Medicine, 64(2), 57–70.
Tesio, L., Lanzi, D., & Detrembleur, C. (1998a). The 3-D motion of the centre of gravity of the human
body during level walking: I. Normal subjects at low and intermediate walking speeds. Clinical
Biomechanics, 13(2), 77–82.
Tesio, L., Lanzi, D., & Detrembleur, C. (1998b). The 3-D motion of the centre of gravity of the human
body during level walking: II. Lower limb amputees. Clinical Biomechanics, 13(2), 83–90.
Thirunarayan, M. A., Kerrigan, D. C., Rabuffetti, M., Croce, U. D., & Saini, M. (1996). Comparison of
three methods for estimating vertical displacement of center of mass during level walking in patients.
Gait and Posture, 4(4), 306–314.
Whittle, M. W. (1997). Three-dimensional motion of the center of gravity of the body during walking.
Human Movement Science, 16, 347–355.
Winter, D. A. (1990). Biomechanics and motor control of human movement (2nd ed.). New York: John
Wiley and Sons, Inc.