Gait & Posture 27 (2008) 316–322
www.elsevier.com/locate/gaitpost
Roll-over shapes of the able-bodied knee–ankle–foot system during
gait initiation, steady-state walking, and gait termination
Steve C. Miff a,b, Andrew H. Hansen b,c,d,*, Dudley S. Childress b,c,
Steven A. Gard b,c,d, Margrit R. Meier c,e
a
Sg2, Skokie, IL, United States
Department of Biomedical Engineering, McCormick School of Engineering and Applied Science,
Northwestern University, Evanston, IL, United States
c
Northwestern University Prosthetics Research Laboratory and Rehabilitation Engineering Research Program,
Department of Physical Medicine and Rehabilitation, Feinberg School of Medicine, Northwestern University, Chicago, IL, United States
d
Jesse Brown VA Medical Center, Department of Veterans Affairs, Chicago, IL, United States
e
National Centre of Training and Education in Prosthetics and Orthotics, University of Strathclyde, Glasgow, Scotland, UK
b
Received 24 August 2006; received in revised form 5 April 2007; accepted 18 April 2007
Abstract
A few investigators have described the movement of the center of pressure (COP) of the ground reaction force and the activation patterns of
the lower limb muscles during gait initiation and termination. This study examines the effective rocker (roll-over shape) behavior of the knee–
ankle–foot (KAF) system during gait initiation, steady-state walking (i.e. constant speed gait), and gait termination. The KAF roll-over shapes
were characterized by transforming COP data of 10 able-bodied subjects from a laboratory-based coordinate system into a leg-based
coordinate system. The resulting roll-over shapes (effective rockers) were characterized using a circular arc model. The KAF roll-over shapes
exhibit an overall ‘‘flexed’’ orientation during the first step of gait initiation and an ‘‘extended’’ orientation during the last step of gait
termination. Understanding the behavior of the anatomical KAF system during gait initiation and termination may aid in the design of
prosthetic components, i.e. mechanical devices that replace complete anatomical structures. Prostheses that intend to mimic the overall
behavior of physiological KAF systems (biomimetic designs) could be manufactured using approaches that are much simpler than attempting
to reconstruct the complexity of the lower limb.
# 2007 Elsevier B.V. All rights reserved.
Keywords: Rocker; Roll-over shape; Center of pressure; Prosthetics
1. Introduction
Human walking is an amalgamation of well-planned and
well-timed events that usually start and end with an upright
standing position. Characteristics of steady-state walking
have been described in detail by a number of authors who
have conducted kinematic and kinetic analyses [1–6],
studies of electromyography [7–10] and energetic behaviors
* Corresponding author at: Northwestern University Prosthetics Research
Laboratory and Rehabilitation Engineering Research Program, 345 E.
Superior Street, Room 1441, Chicago, IL 60611, United States
Tel.: +1 312 238 6500; fax: +1 312 238 6510.
E-mail address: a-hansen@northwestern.edu (A.H. Hansen).
0966-6362/$ – see front matter # 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.gaitpost.2007.04.011
[11–13], and more recently investigations of roll-over
shapes [14]. Gait initiation studies [1,15–18] and gait
termination research [19–21] have focused mainly on
kinematic, kinetic, and/or EMG analyses. A few authors
have also described the trajectory of the center of pressure
(COP) and the activation patterns of the lower limb muscles
during gait initiation and termination [18,22,23]. Michel and
Do [24] examined whether stance ankle plantar flexor
muscles create the forward propulsive force generated
during gait initiation. Their results show that use of a passive
mechanical system (the above-knee prosthesis) leads to
similar results in gait initiation as the complex physiologic
lower-limb system. This finding suggests that a passive
rocker model could be used to explain gait initiation. Jian
S.C. Miff et al. / Gait & Posture 27 (2008) 316–322
et al. [22] examined the interaction between the center of
mass (COM) of the body and COP during gait initiation and
termination. They concluded that this interaction ‘‘is tightly
regulated to control the trajectory of the COM and thereby
control total body balance.’’ Jian et al. used the mechanical
properties of a simple inverted pendulum model to predict
relationships between the COP/COM vector and the forward
acceleration of the COM. While a good model, the COP
clearly moves anteriorly/posteriorly during gait initiation,
steady-state walking, and gait termination—a characteristic
that cannot be captured with the simple inverted pendulum
model without ‘‘sliding’’ the contact point forward. For this
reason, we chose to model gait initiation, steady-state
walking, and gait termination as a rocker-based inverted
pendulum. The rocker-based inverted pendulum has been
used previously to describe steady-state walking [25]. The
effective rockers created by the lower limb have been
measured for steady-state walking [14], but there are no
studies examining the model parameters during gait
initiation and/or termination.
The foot and ankle have been modeled as rockers by
several investigators. Perry [26] has described the function
of the foot and ankle using heel, ankle, and forefoot rockers.
Hansen et al. measured the knee–ankle–foot (KAF) roll-over
shapes for able-bodied humans walking over a range of
speeds [14], while carrying various amounts of added weight
to the torso [27], and when using shoes of different heel
heights [28]. The KAF roll-over shapes represent the
effective rockers created by the KAF system during the
‘‘roll-over’’ phase of gait (from heel contact (HC) to
opposite heel contact (OHC)) and can be measured by
transforming the COP of the ground reaction force (under
one foot) into a leg-based reference frame. In these previous
studies, the KAF roll-over shape radius was found to be
generally invariant to the amplitude of speed, the amount of
weight carried, and the shoes used.
The purpose of this study is to utilize roll-over shape to
gain a better understanding of the functional behavior of the
KAF system during gait initiation and termination, and to
compare with roll-over shapes obtained during steady-state
walking. We believe the measurement of these roll-over
shapes provides additional insight into these important
activities of daily living and may suggest treatments for
persons with disabilities affecting their ability to initiate or
terminate gait. We also believe that the effective rockers
measured in this paper could be useful toward the design of
lower limb prostheses (i.e. mechanical devices designed to
mimic the functions of amputated legs) that can adapt for the
intended task of the user. A ‘‘black-box’’ approach, such as
the one used in this paper, may allow future prosthesis
designs to be biomimetic (i.e., mimicking biology) without
reconstructing all of the complexity of the lower limb.
It was hypothesized that the roll-over shape of the ablebodied KAF system would (1) take a ‘‘flexed’’ orientation
during the first step of initiation, (2) be maintained in a
neutral position during steady-state walking, and (3) take an
317
Fig. 1. Illustration describing the hypothesized effective rocker shapes
(roll-over shapes) created by the KAF system during the 1st step of
initiation, steady state walking, and the last step of gait termination. The
effective rocker created by the lower limb system takes a ‘‘flexed’’
appearance during gait initiation, is maintained in a neutral position during
steady state walking, and is ‘‘extended’’ during gait termination. Xnadir is the
anterior position of the point having the lowest elevation on the best-fit
circle of the roll-over shape.
‘‘extended’’ orientation during the last step of rapid gait
termination (Fig. 1). This hypothesis was explored using
circular arc fittings to the roll-over shapes (i.e. the measured
effective rockers). Best-fit circular arcs with effective rocker
centers posterior to the leg-based coordinate system were
considered ‘‘flexed’’ while those with rocker centers anterior
to the leg-based coordinate system were considered
‘‘extended’’ (Fig. 1).
2. Methods
Roll-over shapes presented in this paper are defined as the
effective rockers that the corresponding lower limb systems conform to during the ‘‘roll-over’’ phase of gait, i.e. between HC and
OHC [14]. The KAF roll-over shapes were calculated using sagittal
plane marker data and COP measurements. For these calculations,
ankle and virtual hip markers were used. Specifically, markers used
included the lateral malleolus (ANKLE), left and right anterior
superior iliac spines (LASIS and RASIS), and a sacral marker
(SACRAL). These markers are a subset of the Helen Hayes marker
set [29], which is commonly used in clinical gait analysis. The hip
joint center position was estimated using LASIS, RASIS, and
SACRAL marker positions [30].
For each frame of data captured, the leg-based coordinate
system was created as shown in Fig. 2(A). The Z-component of
this coordinate system was constructed by normalizing a vector
from the ankle marker to the virtual hip marker. The X-component
of this coordinate system was found from the cross product of an
out-of-plane unit vector (in the Y-direction) and the unit vector in
the Z-direction. For the right leg, the Y-vector pointed medially.
For the left leg, the Y-vector pointed laterally. For each frame of
data, the COP was transformed from the laboratory coordinate
system to the leg-based coordinate system (Fig. 2(B)). The rollover shape is the sequence of COP locations in the leg’s coordinate
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S.C. Miff et al. / Gait & Posture 27 (2008) 316–322
Fig. 2. (A) Schematic representation of the leg-based coordinate systems. The position of the virtual HIP marker, used to create the leg-based coordinate system,
was estimated as described by Vaughan et al. [30]. The Z-coordinate for the leg-based coordinate system is determined using a vector starting at the ANKLE
marker and passing through the virtual HIP marker. The X-coordinate of the leg-based coordinate system is found as the perpendicular vector to the Z-axis that
lies in the sagittal plane and points ‘‘forward’’. (B) The KAF roll-over shape is found by transforming the COP data from a laboratory-based coordinate system
to a leg-based coordinate system.
system throughout the activity, thus approximating an effective
rocker shape that the leg used during that portion of stance phase.
2.1. Experimental protocol
The COP position and the trajectories of individual body
markers were measured during gait initiation, steady-state walking,
and during gait termination in 10 healthy able-bodied subjects
between the ages of 18 and 70 years old (nine males, one female;
average age 28 4 years; average mass 79.8 10.7 kg; average
height 175.9 7 cm). Each participant signed a consent form
approved by the Northwestern University Institutional Review
Board. Data were acquired at the VA Chicago Motion Analysis
Research Laboratory, which is equipped with eight motion analysis
cameras (Motion Analysis Corporation, Santa Rosa, CA, USA).
COP data were simultaneously collected using six force platforms
(Advanced Mechanical Technology, Inc., Watertown, MA, USA).
For gait initiation, all subjects were instructed to stand quietly
and to begin walking at a normal, slow, or fast pace at any time after
an auditory signal was given. Normal speed trials were collected
first, followed by slow and then fast trials. Prior to gait initiation,
the subjects were asked to stand on two side-by-side force plates.
Having each foot on a separate force platform allowed the COP
data to be measured independently for the initial stance leg and for
the initial swing leg during the first step of gait initiation. For the
gait termination trials the subjects were asked to begin walking at a
slow, normal, or fast walking speed and to come to a comfortable
and complete stop with feet side-by-side as soon as possible after
hearing an auditory signal. The stopping signal was given during
randomly selected trials at approximately OHC, timed such that the
subject would stop on one of the force platforms. The stop signal
was not given during every walking trial in order to prevent the
subjects from prematurely slowing down in anticipation of a stop
signal. Steady-state walking data were collected by asking the
subjects to walk across the laboratory floor at either slow, normal,
or fast walking speeds. Trials were repeated at a given walking
speed until three ‘‘clean’’ force platform hits had been captured for
each foot. ‘‘Clean’’ force plate hits were ones in which only one
foot contacted a force platform, without stepping over the edges of
the platform.
Speeds for all three data collection schemes (initiation, steadystate, and termination) were self-selected by the study participants.
The goal of this study was not to test specific target speeds but to
gather data over a broad range of speeds, mimicking everyday
walking conditions.
2.2. Data processing
The initiation roll-over shapes were calculated during the first
step of initiation, i.e. on the first leg that experienced a single-limb
support phase, from the beginning of forward acceleration of the
body’s center of mass to the time of OHC [31]. The termination
roll-over shapes were calculated during the last step of termination,
i.e. on the last foot that experienced a single-limb support phase,
from HC to OHC. For steady-state walking, the roll-over shapes
were computed from HC to OHC. All shapes were normalized by
the subject’s height and by the time required to create them [14].
For each group, the time-normalized shapes were then set into
equal length arrays of 101 data points using a cubic spline routine to
allow averaging of shapes for similar conditions (i.e., same walking
condition—first step initiation, steady-state, termination, and for
each walking speed). The standard deviations of the X (fore-aft) and
Z (vertical) components of the splined roll-over shapes were
calculated at every 10th point (i.e. in 10% intervals) and were
represented by lines extending from the mean of the shape at that
point. Means and standard deviations were calculated on all trials
from all subjects within a speed and walking condition (i.e. 30 trials
– 3 trials from each of 10 subjects – were used in the analysis).
2.3. Roll-over shape characterization
Circular arcs were fitted to the KAF roll-over shapes using a
non-linear least squares algorithm (steepest descent). The initial
parameters for the algorithm were calculated as the solution of the
second-order linear Taylor series expansion of the equation of the
lower half of a circle [14]. This approach allowed for examination
S.C. Miff et al. / Gait & Posture 27 (2008) 316–322
319
of the fore-aft position of the nadir (i.e., Xnadir) of the best-fit circle
defining the effective rocker’s arc (Fig. 1).
2.4. Statistical analysis
The dependence of the Xnadir positions on walking speed was
characterized using linear regression analysis. This statistical test
was performed using a commercially available software package
(SPSS, Chicago, IL).
3. Results
Means and standard deviations of the walking speeds
attained in the constant speed section of all three tasks (i.e.
gait initiation, steady-state walking, and gait termination)
are shown in Table 1. For initiation, the speed reported is that
which occurred after the body had finished accelerating. For
termination, the speed reported is that which occurred just
prior to deceleration of the body. The mean KAF roll-over
shapes for the first step of gait initiation (for slow, normal,
and fast speeds) are shown in Fig. 3. Similar plots for the
roll-over shapes used in steady-state walking and in gait
termination are shown in Figs. 4 and 5, respectively. The
gray circles in the figures indicate the origins of the legbased coordinate systems for each of the three speeds. The
thinner lines in the plots indicate standard deviations of the X
(horizontal) and Z (vertical) components of the roll-over
shapes at every 10% of the time period of the measurement.
The roll-over shapes in these plots appear to change very
little if at all as walking speed is increased; however, there
appear to be large changes between the shapes for the
different tasks (i.e. between the three figures).
The mean KAF roll-over shapes for the first step of gait
initiation, during steady-state walking, and for the first step of
gait termination at slow, normal, and fast speeds are overlaid
in Fig. 6. The orientation (planar rotation) of the shape appears
unchanged during steady state walking. During gait initiation,
the KAF roll-over shapes were rotated into an increasingly
‘‘flexed’’ orientation as walking speed was increased. For gait
termination, the KAF roll-over shapes were oriented with
greater ‘‘extension’’ when compared with steady-state rollover shapes. The Xnadir positions of the best fit circles to the
KAF roll-over shapes are compared for the first step of
initiation, steady-state walking, and gait termination in Fig. 7.
The Xnadir position for gait initiation decreases linearly with
walking speed: (Xnadir/height = 0.034 speed + 0.003,
R2 = 0.54). Regression analysis indicates that the intercept
is not statistically different from zero ( p = 0.096), but the
Table 1
Mean speeds (in m/s) attained in gait initiation, steady-state walking, and
gait termination: mean [standard deviation]
Slow
Normal
Fast
Gait initiation
Steady-state walking
Gait termination
0.91 [0.21]
1.29 [0.12]
1.60 [0.14]
0.94 [0.19]
1.28 [0.13]
1.81 [0.21]
1.03 [0.17]
1.40 [0.13]
1.82 [0.19]
Fig. 3. Roll-over shapes for the first step of gait initiation (first limb that
experiences a single-limb support phase) for slow, normal, and fast speeds.
The average roll-over shape is shown with a thick black line. Thinner lines
are used to indicate the inter-subject variability of the roll-over shape at 10%
time intervals of the period between the start of body COM acceleration to
OHC. Cross-sectional outlines of feet are shown for context only and are not
necessarily to scale.
Fig. 4. Roll-over shapes for steady-state self-selected slow, normal, and fast
speeds. The average roll-over shape is shown with a thick black line.
Thinner lines are used to indicate the inter-subject variability of the roll-over
shape at 10% time intervals of the period between HC to OHC. Crosssectional outlines of feet are shown for context only and are not necessarily
to scale.
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S.C. Miff et al. / Gait & Posture 27 (2008) 316–322
Fig. 5. Roll-over shapes for the last step of gait termination (last limb that
experiences a single-limb support phase) for slow, normal, and fast speeds.
The average roll-over shape is shown with a thick black line. Thinner lines
are used to indicate the inter-subject variability of the roll-over shape at 10%
time intervals of the period between HC to OHC. Cross-sectional outlines of
feet are shown for context only and are not necessarily to scale.
slope is statistically different from zero ( p < 0.0001). The
negative values for the Xnadir variable indicate rockers with
their centers posterior to the leg, i.e. ‘‘flexed’’ roll-over shapes,
assuming minimal changes in the shape geometry. The Xnadir
for steady-state walking does not appear to change with
walking speed, having a best-fit line slope that is not
significantly different than zero, p = 0.47. The averaged
steady-state Xnadir/height is 0.012 0.008, slightly anterior to
the leg-based coordinate system. These results are in close
agreement with earlier measured values for steady-state
walking [14]. The Xnadir position for gait termination increases
with walking speed. Regression analysis indicates a slope
significantly different than zero of 0.017 ( p = 0.011) and a yintercept not significantly different than zero of 0.013
( p = 0.094).
Fig. 6. Averaged roll-over shapes for the first step of gait initiation (light
gray), steady-state walking (black), and gait termination (darker gray) at
slow, normal, and fast walking speeds. The figure shows that the gait
initiation shapes are ‘‘flexed’’ while the gait termination shapes are
‘‘extended’’ compared with steady-state shapes. Cross-sectional outlines
of feet are shown for context only and are not necessarily to scale.
activations in the tibialis-anterior and gastrocnemius have
been noted as a possible explanation for the COP shift, but
the effective rocker shapes used by the lower limb have not
been examined.
4. Discussion
Although steady-state walking has been analyzed broadly
by a number of investigators, gait initiation and termination
have not been examined extensively. As a result, many
characteristics of gait initiation and termination are not well
understood. One such aspect is the initial momentum
generation at the start of forward initiation and the final
momentum reduction during stopping. A number of authors
have observed a backward shift in the trajectory of the center
of pressure (COP) after the decision to start walking is made,
but before the first step is conducted [22,23]. Muscle
Fig. 7. Roll-over shape Xnadir positions (normalized by height) for the first
step of gait initiation (diamonds), steady state walking (triangles), and
termination (circles) vs. walking speeds. The Xnadir position decreases as
initiation speed increases, it remains relatively constant for steady-state
walking, and increases with increasing speed for gait termination.
S.C. Miff et al. / Gait & Posture 27 (2008) 316–322
In this study it was hypothesized that the transition from
standing to steady-state walking and from steady-state
walking to stopping is achieved through ‘‘re-alignments’’ of
the effective rocker of the KAF system (i.e. re-alignment of
the KAF roll-over shapes). Specifically, the results show that
the KAF roll-over shape has a ‘‘flexed’’ orientation during
the first step of gait initiation, it is maintained in a relatively
neutral position during steady-state gait, and has an
‘‘extended’’ orientation during gait termination, supporting
our hypothesis (see Figs. 1 and 6).
During gait initiation, the roll-over shape rocker center is
shifted backwards (Figs. 3, 6 and 7). The amount of the shift,
measured by the position of the rocker center, Xnadir, appears
to be linearly related to the steady-state walking speed
(Fig. 7). This ‘‘re-alignment’’ of the KAF rocker seems to
occur at the moment when the decision to initiate gait is
made, and thus when forward acceleration begins. When the
decision to initiate gait is made, the ankle is dorsiflexed
[17,31]. The dorsiflexion at the ankle moves the COP
backwards, creating an anteriorly directed COP–COM
vector that initiates the forward fall. The posterior shift of
the COP sets the initial conditions and creates a tendency of
the body to roll forward.
During gait termination, the opposite effect was
observed. The KAF system developed a roll-over shape
with an ‘‘extended’’ appearance (Figs. 5–7). The amount of
‘‘extension’’ increased with walking speed. This change is
indicated by an increase in forward shift in the KAF Xnadir
position with increasing speed. This change in Xnadir position
is analogous to a forward COP shift relative to the
progression of the stance leg in the lab coordinates. The
‘‘extension’’ used to terminate gait is exaggerated during
situations when an individual needs to stop suddenly and
cannot take another step. In this extreme case, the rocker realignment achieved through rapid ankle plantarflexion
moves the COP further in front of the ankle and causes
the individual to rise up onto their toes, thus positioning the
COP in front of the COM and creating a posteriorly directed
braking force that serves to rapidly decelerate the body.
Additionally, this extreme rocker re-alignment achieved
when one rises up on his/her toes serves to elevate the
position of the BCOM, thus transforming some of the body’s
kinetic energy into gravitational potential energy.
4.1. Limitations of the study
One of the limitations of this study includes the use of twodimensional sagittal plane data as opposed to threedimensional marker trajectories. Although it is possible to
measure three-dimensional roll-over shapes by constructing
the leg-based coordinate system using three markers and
transforming the three-dimensional coordinates of the COP,
our unpublished work in this area has shown little or no
difference between two-dimensional roll-over shapes and the
sagittal plane projection of the three-dimensional roll-over
shapes. The majority of our studies of roll-over shape have
321
focused on gaits where primary movements occur in the
sagittal plane, namely able-bodied gait and gait of lower-limb
prosthesis users. For studies of pathologic gaits utilizing
extensive coronal plane movements, a three-dimensional
approach is necessary and has been used by our group [32].
The standard deviations of the roll-over shapes are
dependent on the geometries of the shapes, but also the
timing associated with their formation. The portions of the
variability that arise from the shape and the timing are not
distinguishable from one another as presented in this paper.
Future work could establish methods for independent
investigation of each of these sources of variability.
In our study, we have chosen to model the roll-over shapes
as a circle. The circle has been shown to be a good fit for
steady-state roll-over shapes [33], but may not necessarily be
the best fit for gait initiation and gait termination roll-over
shapes. However, use of circles simplifies the analysis and
provides a general behavior of the KAF system for these tasks.
More advanced modeling of the roll-over shapes may lend
additional insight in future analyses.
The roll-over shape shows only the COP in the leg-based
coordinate system but does not show the direction of the
ground reaction forces in this reference frame. This type of
analysis is possible, as illustrated by Knox’s ‘‘rockerfly’’
diagrams [34]. In our study, the COP is used because it
indicates an important interaction point between the body
and the ground and can help to estimate effective rockers of
the KAF system. Our analysis suggests that the body may
aim to create effective rockers that encourage a forward fall
of the body to initiate gait and that slow the body to a halt to
terminate gait.
4.2. Future applications of KAF roll-over shapes
The findings in this study may be used in the future in the
development of adaptive lower-limb prostheses. For
example, a person may indicate their intent to start walking,
possibly using EMG or a simple mechanical signal, and the
prosthesis could generate or allow an increased amount of
dorsiflexion at the ankle. This change would lead to a
‘‘flexed’’ roll-over shape compared with the one used in
steady-state walking. Similarly, during gait termination, an
advanced prosthesis could sense the user’s intent to stop
walking and create plantarflexion at the ankle and/or slight
controlled flexion of the knee (either of which would
contribute to an ‘‘extended’’ KAF roll-over shape). This
information could be similarly relevant to the development
of advanced lower limb orthoses to assist persons who have
particular trouble initiating and/or terminating gait.
5. Conclusions
The results suggest that gait initiation begins with a realignment of the effective rocker created by the KAF system
(i.e. a planar rotation of the KAF roll-over shape). This
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S.C. Miff et al. / Gait & Posture 27 (2008) 316–322
‘‘flexed’’ re-alignment moves the COP backwards, encouraging the body to roll forward. During rapid termination, the
KAF system creates an ‘‘extended’’ effective rocker. This
rocker re-alignment moves the COP further in front of the
ankle, encouraging the body to stop moving forward.
Acknowledgements
The authors would like to acknowledge the use of the VA
Chicago Motion Analysis Research Laboratory of the Jesse
Brown VA Medical Center, Department of Veterans Affairs,
Chicago, Illinois.
The work described in the paper was supported by the
National Institute on Disability and Rehabilitation Research
(NIDRR) of the U.S. Department of Education under grants
no. H133E980023 and H133E030030. The opinions contained in this publication are those of the grantee and do not
necessarily reflect those of the Department of Education.
Conflict of interest
The authors have no conflicts of interest in this work.
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