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

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 dif-
ferent 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 tech-
nique involved calculating BCOM vertical motion through double integration of force plat-
form 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 indi-
cated that at the slowest walking speed the vertical excursions calculated by all three tech-
niques 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.: [phone]; fax: [phone].
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
Human Movement Science 22 (2004) 597–610
www.elsevier.com/locate/humov

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 peri-
odic vertical displacement of the BCOM that moves through a complete cycle of ver-
tical 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; Cav-
agna & Margaria, 1966; Donelan, Kram, & Kuo, 2002), to describe symmetry (Cav-
agna et al., 1983; Crowe, Schiereck, & Keessen, 1992; Gard, Knox, & Childress,
1996), and as an indicator of the overall quality of gait (Bowker & Hall, 1975; Saun-
ders 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 mark-
ers to measure body segment positions, and incorporates an anthropometric model
to calculate segmental center of mass positions. These segmental center of mass posi-
tions are then used to calculate the BCOM. In contrast, the force platform method
uses measured ground reaction forces to calculate BCOM motion based upon New-
ton’s Second Law, which states that the net external force acting upon a body is
598 S.A. Gard et al. / Human Movement Science 22 (2004) 597–610

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 con-
sideration for the integration constants. Comparisons of BCOM motion between
the kinematic and kinetic methods, utilizing data that have been simultaneously ac-
quired 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 asso-
ciated 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 deter-
mined 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 sa-
cral 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
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610 599

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 meth-
ods. 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 ele-
vation 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 ele-
vations 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, correspond-
ing 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 cal-
culated as the difference between their respective maximum and minimum elevations
Fig. 1. A simple model can be used to explain the differences observed when calculating the vertical excur-
sion 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 excur-
sions 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.
600 S.A. Gard et al. / Human Movement Science 22 (2004) 597–610

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 Univer-
sity’s Institutional Review Board.
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 Heel marker/virtual toe marker 1.8 0.506
Shank Knee center/ankle center 4.4 0.433
Thigh Hip center/knee center 11.2 0.433
Forearm, hand Elbow marker/wrist marker 2.6 0.682
Upper arm Shoulder marker/elbow marker 3.3 0.430
Head, neck, trunk Shoulder markers midpoint/hip joints
midpoint
53.4 0.540
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
50 60 70 80 90
Step Length (cm)
Vertical Excursion (cm)
Trunk
BCOM
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.
S.A. Gard et al. / Human Movement Science 22 (2004) 597–610 601