The effect of directional inertias added to pelvis and ankle on gait
Journal of NeuroEngineering and Rehabilitation
The effect of directional inertias added to pelvis and ankle on gait
Jos H Meuleman 0 1
Edwin HF van Asseldonk 0
Herman van der Kooij 0 2
0 Department of Biomechanical Engineering, University of Twente , Enschede , The Netherlands
1 Moog Robotics , Nieuw-Vennep , The Netherlands
2 Biomechanical Engineering, Delft University of Technology , Delft , The Netherlands
Background: Gait training robots should display a minimum added inertia in order to allow normal walking. The effect of inertias in specific directions is yet unknown. We set up two experiments to assess the effect of inertia in anteroposterior (AP) direction to the ankle and AP and mediolateral (ML) direction to the pelvis. Methods: We developed an experimental setup to apply inertia in forward backward and or sideways directions. In two experiments nine healthy subjects walked on a treadmill at 1.5 km/h and 4.5 km/h with no load and with AP loads of 0.3, 1.55 and 3.5 kg to the left ankle in the first experiment and combinations of AP and ML loads on the pelvis (AP loads 0.7, 4.3 and 10.2 kg; ML loads 0.6, 2.3 and 5.3 kg). We recorded metabolic rate, EMG of major leg muscles, gait parameters and kinematics. Results & discussion: Adding 1.55 kg or more inertia to the ankle in AP direction increases the pelvis acceleration and decreases the foot acceleration in AP direction both at speeds of 4.5 km/h. Adding 3.5 kg of inertia to the ankle also increases the swing time as well as AP motions of the pelvis and head-arms-trunk (HAT) segment. Muscle activity remains largely unchanged. Adding 10.2 kg of inertia to the pelvis in AP direction causes a significant decrease of the pelvis and HAT segment motions, particularly at high speeds. Also the sagittal back flexion increases. Lower values of AP inertia and ML inertias up to 5.3 kg had negligible effect. In general the found effects are larger at high speeds. Conclusions: We found that inertia up to 2 kg at the ankle or 6 kg added to the pelvis induced significant changes, but since these changes were all within the normal inter subject variability we considered these changes as negligible for application as rehabilitation robotics and assistive devices.
Inertia; Kinematics; Pelvis; Metabolic rate; Locomotion; Leg loading; Emg; Robotic gait trainers
In Robot aided gait training the trend is moving from
position controlled robots as the early Lokomat  towards
force controlled robots . Where position controlled
robots impose a gait pattern on a patient, force controlled
robots offer the possibility to provide corrective- or
guiding forces when needed. These Assist As Needed control
algorithms [3-5] facilitate active participation, which have
a positive effect on the rehabilitation process . A
prerequisite for assist as needed is that the robot does not
affect gait when no assistance is needed, i.e., the robot must
be able to minimize the interaction forces. This is known as
zero impedance control  or transparent mode.
The target of transparent mode is to minimize interaction
force between robot and subject; however zero interaction
is impossible if the interaction force itself is the input for
the control. The remaining impedance can be expressed in
mechanical impedances such as inertia, damping, friction,
stiffness, and combinations. Performance of gait training
robots and other devices for force interactions with humans
is often expressed in these mechanical impedances. Most
impedances can be compensated for completely with
control algorithms, such as admittance control . Inertia,
however usually cannot be compensated for completely,
especially when passivity has to be guaranteed . In robotic
gait rehabilitation, this means that the inertia of the robot is
perceived by the patient. Therefore it is important to know
the effect of added inertia on gait, more specific, the effect
of added inertia on legs and trunk.
Several studies have investigated the effect of mass
added to body parts. These studies can be divided in two
groups. The first group applied weights to body parts.
These weights introduced inertia and a downward force
due to gravity. In these studies it cannot be distinguished
if the found effects are elicited by pure inertia or weight.
The second group did compensate for the weight e.g.
by means of body weight support, thus these studies
assessed the effect of pure inertia. Adding inertia of
2550% to the trunk of body mass resulted in an increase of
energetics  and muscle activity . Gait parameters
remained unchanged  or change hardly (<3% ).
The effect of inertia only on gait kinematics has not
been assessed, however the effect of added weight has.
The gravity component of the added weight has a
significant effect on gait , therefore the found effects
caused by added weight are likely to differ from effects
caused by pure inertia. Table 1 summarizes the found
effects of added inertia in previous studies.
No literature was found on the effect of inertia added
to the legs, only the effects of adding weight to legs have
been assessed. Browning et al. showed that 4 kg attached
to the ankle caused an increase of metabolic rate (36%)
which is close to the effect of adding 16 kg added on the
waist (32%) . Royer and Martin  added weight in
several distributions: the total weight remained constant
(5.64 kg), while the moment of inertia with respect to
the hip joint) varied. The largest increase was found in
metabolic rate (+8.2%) when 2.82 kg was added to the
proximal shank; other effects remained small. Though
the weights added to the feet and legs are considerably
less than the weights added to the pelvis by Grabowski
, the effect of gravity on these added weights is
expected to be considerable
To design robots for gait training, it is important to
assess the effect of added inertia on gait, and ideally the
Table 1 Effect of added inertia during walking
+21% Soleus 
~0  3% 
+8.2% @2.8 kg at
proximal shank 
+2% swing time
+1% Stride time
inertia that the robot displays to the subject is so low that
the effect on gait is negligible. Our objective is to establish
this threshold for added inertia. The above-mentioned
studies give an indication of this threshold, but there are
some limitations. First, in all studies on ankle and leg
loading, weight is added instead of inertia. Second, all
studies that assessed the effect of added inertia on the
trunk/pelvis did so by adding weights to a subject and
compensating for the gravity of the weight by a body
weight support system. A body weight support suspended
on a fixed point has an equivalent of a stabilizing effect as
a spring in a horizontal plane. Furthermore Aaslund and
colleagues  have shown that the harness itself, without
applying body weight support, has an effect on gait
kinematics. Third, no study assessed the effect of inertia on gait
kinematics. Fourth, in the different studies relatively large
added inertias (~20 kg) were added on the trunk, whereas
interaction control algorithms are expected to be able to
reduce the displayed inertia to values below 10 kg [15,16].
The fifth limitation is that all studies applied equal inertia
in all three translational degrees of freedom dimensions,
while each controlled degree of freedom can be tuned
independently, resulting in different inertias in different
degrees of freedom. The last limitation is that the existing
studies did not establish a threshold below which added
inertia leaves gait unaffected, and thus below which a
robot is transparent, and above which gait is affected.
The aim of this paper is to assess the effect of inertia
added to the pelvis and the ankle. The first experiment
adds inertia on the pelvis in anterior posterior (AP) and
mediolateral (ML) direction; the second experiment adds
inertia in AP direction on the ankle. We quantified the
effect of inertia on gait parameters, gait kinematics,
energetics, and muscle activity. These parameters are commonly
used in gait analysis [9-11], and therefore are selected in
our study, assuming that this set of parameters suffice in
quantifying changes of gait. Moreover, a threshold is
estimated for the allowable inertia of the gait training robot,
below which walking in the gait training robot resembles
normal walking. This serves as a recommendation for the
design of transparent gait training robots.
We hypothesize that adding inertia elicits an increase of
energetics or a decrease in gait motions (joint rotations,
segment motions) or both. We base this on Newtons
When inertia increases the first possible effect is that
the subject exerts more force (muscle activity and
energetics) to maintain the motion (acceleration). For extra
inertia on the ankle, we expect an increase of muscle
activity for push -off and stance preparation, since the
acceleration and deceleration are highest in these phases.
The second possible effect is that acceleration will
decrease when a mass increases, while the subject
maintains his effort (no change in energetics and muscle
activity. For loads on the pelvis this implies smaller
motions of the pelvis and trunk. For the ankle this would
imply shorter stride length, but this inadvertently leads
to an increase in cycle time (if speed is kept constant).
Finally we hypothesize that the effect of inertia is
larger at high speeds, since in general accelerations of
the segments are higher at high speeds, thus the absolute
effect of a change in inertia is likely to elicit a larger
absolute change in energetics.
Both experiments were executed with nine healthy
subjects. All subjects signed an informed consent before the
experiment. See Table 2 for subject data.
To add pure inertia, we designed a mechanism that
connects the subject to two modules with adjustable
inertias through a light-weight pelvis strap or ankle strap.
The pelvis strap contains a light-weight bar, a rigid belt,
and a trapezium construction, that allows pelvis rotation
in the coronal plane.
A single module of adjustable inertia consists of a
horizontal bar connected with spherical joints to a stand
at one end and to the pelvis strap at the other end.
Dumbbell weights are mounted on the bar. A steel wire
is connected to the stand and the joint with the strap to
assure vertical fixation of the bar, allowing only rotation
of the bar and module around the vertical axis of the
stand. The location of the dumbbell weight on the bar
determines the added inertia to the segment, according
Mdseigremcteinotn denotes the added inertia on the segment in a
specific direction; Mdumbbell is the mass of the dumbbell
weights; Mdaiprpecatriaotnus is the inertia of the construction
without the dumbbell weights at the segment (ankle 0.3 kg;
pelvis anterior-posterior 0.58 kg; pelvis mediolateral
0.41 kg). Parameter is the effective inertia gearing of the
Table 2 Subjects data
7 men; 2 women
25.1 5.2 years
7men; 2 women
30.9 10.3 years
dumbbell weights, determined by the location of the
dumbbell weight on its bar (see Table 3).
For the pelvis experiment we used two modules to apply
AP load and ML load independently (see Figure 1 and
Additional file 1); for the ankle experiment a single
module was used to apply inertia in AP direction only (see
Figure 2). In both studies, the inertia in other translations
and rotations added by the apparatus is negligible.
We used loads that are similar to the loads used in the
study of Browning and colleagues  (2 4 kg on the
foot; 4 16 kg on the waist).
The effects of added inertia were assessed by quantifying
kinematics, muscle activity and energetics.
Kinematics and gait parameters
Motions were measured using an optical tracking system
(Vicon Oxford Metrics, Oxford, UK). Twenty one
reflective markers were attached to the human body; these
markers were attached on both sides of the subject. Four
markers were placed on the upper extremity (shoulders,
front trunk and back trunk), five markers were placed
on the pelvis (sacrum, left and right anterior superior
iliac spine, left and right posterior superior iliac spine),
on each leg seven markers were placed (femur, knee,
tibia, malleolus, heel, fifth metatarsal joint). In both
experiments two extra markers were placed on the
apparatus, one on the stand and one on the strap near the
ankle or pelvis. All markers were recorded at a sampling
rate of 120 Hz by means of optical tracking.
The muscle activity was measured by recording the
electromyography (EMG) from eight different muscles of
the right leg: (1) the gluteus maximus, (2) gluteus medius,
(3) rectus femoris, (4) vastus lateralis, (5) biceps femoris
(6) gastrocnemicus medialis (7) soleus, and (8) tibialis
anterior. The analogue signals were sampled at 1024 Hz and
recorded with a Bagnoli system (Delsys, Boston, USA).
Amplified EMG data was synchronized with the VICON
System. Electrodes were placed over the muscle bellies
according to the Seniam guidelines .
Table 3 Parameter values for pelvis AP and ML loading
and ankle AP loading
2. Bar 1
3. Bar 2
4. Beam 3
5. Beam 4
6. Steel wires
Figure 1 Apparatus for applying inertia to the pelvis in AP and ML direction independently.
The energy expenditure was measured by the Oxycon
Pro system (Jaeger, Hoechberg, Germany). Subjects were
connected to the Oxycon with a flexible tube making an
airtight seal to a facemask, measuring oxygen
consumption (VO2) and volume expiration (VE). The heart rate
of the subjects was measure at the index finger by a
pulseoximeter. Every five seconds (0.2 Hz) all parameters were
measure and stored on the personal computer that was
connected to the Oxycon.
Figure 2 Apparatus attached to the ankle.
Both experiments started with two conditions in which
subjects were walking on a treadmill at 1.5 km/h and
4.5 km/h without being attached to the system, called no
load conditions (NL). These trials were followed by a
randomized sequence of the added inertia- and speed
conditions. In the pelvis experiment subjects walking with
every combination of three loading conditions in AP and
ML direction (see Table 3). In the ankle experiment, three
loadings were applied in AP direction (see Table 3).
Combining the loading conditions with speeds, resulted in 18
different loaded conditions for the pelvis-experiment and
six loading conditions for the ankle-experiment. All trials
consist of 3 minute walking.
The last 12 VO2 samples (1 minute) were converted to
VO2 rate per subject weight.
All kinematics and EMG data were split into
individual stride cycles, determined by movement of the left
heel marker . Only the last 30 seconds of each trial
was analyzed to eliminate the transition effects.
Marker data was converted to joint- and segment
kinematics using custom written software, resulting in
flexion and abduction of the left hip, left knee flexion,
left plantar flexion, and back sagittal- and frontal
rotation. For the pelvis and trunk the AP and ML motions
and for the left foot the AP motion are analyzed in terms
of position and acceleration. For the joint angles and
segment motions, the range of motion (RoM) was
calculated as the difference between the maximum and
minimum value within a stride cycle.
We calculated the following gait parameters: cycle time
[s], double stance time [s], swing time left [s], stance time
left [s], step width [m] and stride length [m].
The raw EMG data was band passed filtered at 10
25 Hz with a second order (zero-lag) Butterworth filter.
The filtered EMG data per subject per muscle was
normalized to its maximal activity over the last 30 seconds.
Mean muscle activity was calculated over seven intervals
per step as described by Van Asseldonk . The mean
activity per interval was averaged per subject per trial.
The double stance starting at left heel strike ending with
toe off right defines initial loading; the stance phase is
divided in two periods of equal length: mid stance,
terminal stance, The double stance from heel strike right
to toe off left defines the pre swing; the swing phase is
divided in three periods of equal length: initial swing,
mid swing and terminal stance. The intervals are
described in Figure 3.
The results of our research will be used as requirements
gait training robots that are transparent. This implies
walking in the gait training robot should resemble free
walking. To quantify this resemblance we first checked
the statistical significance first. However, this method
does not take into account the variance within a subject
(i.e. variance between steps). Even if differences are
consistent, as they are significant, they may be small relative
to the normal variance within a subject. Since our focus
is to state requirements for gait training robots that
allow normal walking and thus also the variability of
normal walking, any effect that is smaller than the
variability of walking is deemed negligible.
First we tested whether the NL conditions differed
significantly from the BLSN condition to assess whether
merely attaching the mechanical setup already affected the
walking pattern. Subsequently we assessed the effects of
the different loads.
To assess whether inertia had a significant effect on gait,
we performed a two-way (velocity, AP load) repeated
Figure 3 Phases of gait.
measures (ANOVA) in the ankle experiment; we used a
three-way (velocity, AP load, ML load) in the pelvis
experiment. We examined the main effects of load and the
interaction effects between load and speed. Pair wise
comparisons were performed on main- and interaction effects
that are significant.
The intra subject variability (ISV) is calculated as twice
the standard deviation in the baseline condition for a
single subject. For data that is cut into steps (all except
energetics) the standard deviation is taken over the number of
steps. For the energetics the standard deviation is taken
over the number of samples. If a parameter change due to
added inertia does not exceed the averaged intra-subject
variability the effect is judged as negligible.
In total we observed 31 parameters: energetics (1
parameter), gait parameters (6 parameters), joint angles (6
parameters), segment translation (5 parameters) and accelerations
(5 parameters), and EMG activity (8 parameters). In both
experiments 261 tests are performed: 31 parameters are
observed + 56 muscle-phase combinations, resulting in 87
main effects, 174 interaction effects with speed (high and
Effect of apparatus on the ankle
When the apparatus was attached to the subjects ankle
with the inertia of the apparatus only (minimal added
inertia), no significant increase is found in energetics and
gait parameters relative to the free walking on the
treadmill. Hip flexion range of motion however increased
significantly (p = 0.009). The motions of the pelvis
segment increased significantly in AP direction in position
range of motion (RoM) (p = 0.008) and acceleration RoM
(p = 0.006). The head-arm-trunk (HAT) position RoM
increased significantly (p = 0.028). There is also a significant
interaction effect with speed on the range of motion of the
pelvis (p = 0.025) and HAT (p = 0.028). The post hoc tests
showed the increase at low speed (see Table 4).
The soleus shows a significant (p = 0.005) increase of
mean activity due to the apparatus and moreover, the
apparatus has a significant (p = 0.011) interaction effect
with phases, and pair wise comparisons show significant
increase in pre swing, initial swing and mid swing. The
gluteus maximus and the gastrocnemicus medialis show a
significant interaction effect (p = 0.041 and p = 0.037
respectively) on phase speed load. Pair wise comparison
shows only a significant decrease (p = 0.028) of gluteus
maximus in mid stance at slow speed.
None of the changes exceeded the intra subject variability.
Table 4 List of significant effects of baseline validation
LHip flexion RoM [deg]
Pos pelvis AP RoM [mm]
Pos HAT AP RoM [mm]
Acc pelvis AP RoM [m/s2]
Soleus - pre swing
Soleus - inital swing
Soleus - mid swing
Gluteus maximus - mid stance
* Significantly different from NL (p < 0.05).
Minimum added inertia is compared with no load; The table lists significant main effects (independent of speed) and significant interaction effects with speed,
but only at speeds that were significant in pair wise comparisons.
Effect of apparatus on the pelvis
When the apparatus was attached to the subjects pelvis
with the inertia of the apparatus only (minimal added
inertia), no significant increase is found in energetics
relative to the free walking on the treadmill. Of the gait
parameters, only the stride length showed a significant
increase of load (p = 0.024) and load speed (p = 0.030)
(see Table 5). The pair wise comparison showed a
significant increase at slow speed.
Of the joint angles, plantar flexion range of motion
increased significantly (p = 0.010). The hip flexion range
of motion has a significant interaction effect with speed
(p = 0.028), but no significance was found in the pair
There was a significant interaction effect of load and
speed on the pelvis AP position RoM (p = 0.002) and the
head-arm-trunk (HAT) segment (p = 0.029). In both
cases pair wise comparison showed an increase at slow
speed. The pelvis acceleration range of motion increased
significantly (p = 0.048) with 0.13 m/s2.
The EMG showed a significant (p = 0.047) effect on
the soleus (from 0.087 to 0.091) and a significant (p =
0.042) interaction effect of phase, load and speed at the
biceps femoris. The pair wise comparison showed a
significant decrease of the biceps femoris in mid stance
during fast walking.
Of all significant changes, only the stride length and
foot RoM at low speed exceeded the averaged intra
Effect of inertia on the ankle in AP direction
Adding inertia in AP direction on the ankle causes a
significant increase in metabolic rate (p = 0.001), and in
interaction with speed (p = 0.006). The pair wise
comparison revealed a significant increase at high speed only
(see Table 6).
In the muscle activity there is an interaction effect of
AP inertia with phase on the gluteus medius (p = 0.045),
the vastus lateralis (p < 0.001), the soleus (p = 0.020) and
the tibialis anterior (p < 0.001), but pair wise
comparisons revealed significant decrease only of soleus in
terminal stance and the tibialis anterior in initial swing and
The double stance time decreased significantly (p =
0.008), whereas the swing time increased (p < 0.001), and
has an interaction effect with speed (p = 0.028). The
stride length decreased significantly (p = 0.009), but pair
wise comparison showed not significant changes.
Of the joint angles, we found significant decreases in
the knee flexion (p = 0.001) and the plantar flexion (p =
0.010). Also significant interaction effects with speed
appeared at both trunk frontal (p = 0.025) and sagittal
rotation (p = 0.011), but the pair wise comparisons
revealed no significant differences, also no clear trends
The pelvis and HAT segment motions AP increased
significantly in position (pelvis p < 0.001; HAT p = 0.009)
and acceleration (pelvis p < 0.001; HAT p = 0.001); for
both segments the acceleration also has a significant
interaction effect with speed (pelvis p = 0.001; HAT p =
0.042), which is significant only at high speed according
to pair wise comparison.
The HAT segment position RoM in ML direction
changed significantly (p = 0.035) due to load, but no
consistent increase or decrease. Also pair wise comparison
did not reveal significant differences.
Table 5 List of significant and appreciable effects of baseline validation
Stride length [m]
Left plantar flexion RoM [deg]
LHip flexion RoM [deg]
Pos pelvis AP RoM [mm]
Acc pelvis ML RoM [m/s2]
Pos HAT AP RoM [mm]
Pos Left foot RoM [mm]
Biceps femoris mid stance
* Significantly different from NL (p < 0.05).
Bold: change larger than the average intra subject variability given in brackets.
Minimum added inertia is compared with no load; the table lists significant main effects (independent of speed) and significant interaction effects with speed, but
only at speeds that were significant in pair wise comparisons.
Finally the left foot RoM decreased significantly in
position RoM (p = 0.015) and acceleration RoM (p < 0.001).
The acceleration has a significant interaction effect with
speed (p < 0.001), at both speeds as revealed by pair wise
comparison, but the decrease is considerably larger at high
speeds (see Table 6).
Of the significant changes due to adding 1.55 kg to the
ankle, only two exceed the average intra-subject variability:
at high speed the acceleration range of motion in AP
direction of the pelvis and the left ankle. Adding 3.5 kg
caused more changes that exceeded the ISV: the increase
in swing time, the increase of pelvis- and HAT
acceleration in AP direction, the decrease of the foot acceleration
and the decrease of the tibialis anterior in initial swing. All
these effects except for EMG are plotted in Figure 4.
Effect of inertia on the Pelvis in AP direction
Adding inertia in AP direction on the pelvis during
walking on a treadmill has no effect on energetics.
Of all the gait parameters only the stance time shows a
significant (p = 0.050) interaction effect with speed, though
a clear trend is not visible and also not revealed by pair
wise comparisons (see Table 7).
The hip abduction, -flexion and knee flexion decrease at
significantly (p = 0.002, p = 0.014 and p = 0.03) due to a
load at the pelvis in AP direction. The trunk sagittal
rotation increases significantly (p = 0.002). This has a
significant interaction effect with speed as well (p = 0.003). Pair
wise comparisons show that the increase is larger at high
The pelvis and HAT motions in AP direction both
decrease significantly in position RoM (pelvis p < 0.001;
HAT: p = 0.003) and acceleration RoM (both p < 0.001).
For both segments the acceleration RoM also has an
interaction effect with speed (both p = 0.003). Pair wise
comparison reveals that for the pelvis this occurs at high
speed and high load only and for the HAT segment this
occurs at both speeds, high load only, but the decrease
is larger at high speeds (see Table 7).
The vastus lateralis has a significant interaction effect
with speed and phase (p = 0.050). Pair wise comparison
reveals a decrease during mid stance at slow speed, though
this is not a clear consistent decrease (see Table 7). During
terminal swing a decrease of activity is found at high
speed. Both gastrocnemicus medialis and soleus show a
significant interaction effect with phase (p = 0.018 and
p = 0.022 respectively); both muscles showed an increase
during mid stance.
In short, although adding 4.3 kg to the pelvis in AP
direction caused significant effects, none of these effects
exceeded the averaged ISV. Adding 10.2 kg however did
cause changes larger than the ISV: the increase of the
trunk sagittal rotation, the acceleration in AP direction
of pelvis and HAT segments (see Figure 5).
Effect of inertia on the pelvis in ML direction
Adding inertia to the pelvis in ML direction during
walking has no effect on energetics, gait parameters and
joint angles. Of the segment motions only the
acceleration range of motion of the pelvis and HAT segment
in ML direction decreased significantly (p = 0.037 and
p = 0.007), though pair wise comparisons revealed no
The overall activity of the tibialis anterior has a
significant change (p = 0.013), though a clear trend is not visible
(see Table 8). And the vastus lateralis has a significant
interaction effect with phase and speed (p = 0.004), but
pair wise comparisons did not reveal significant changes.
None of the significant changes exceeded the average
A Acceleration Left Foot AP [m/s2] 4.5km/h
TOR HSR TOL
B Acceleration pelvis AP [m/s2] 4.5km/h
TOR HSR TOL 50 0 50
C Acceleration HAT AP [m/s2] 4.5km/h
TOR HSR TOL
Figure 4 Effect of inertia in AP direction on the ankle.
Acceleration profiles of the foot (A), pelvis (B) and trunk (C) as a
function of the foot, pelvis and trunk as a function of the % gait
cycle. Profiles are averaged across subjects and the shaded areas
show the average intra subject variability. The cycle starts at 0% at
heel strike left, followed by toe off right (TOR), heel strike right (HSR),
toe off left (TOL) and ends with a heel strike left at 100%.
We assessed the effect of adding inertia during walking on
a treadmill in order to assess the effect of a gait training
robot on gait. This study is novel in that we decoupled
the inertia from gravitational effect and that we decoupled
the inertia in different directions. We conducted two
experiments, one with adding inertia to the ankle in
anterior-posterior direction and one with adding inertia to
the pelvis in AP and ML direction.
Effect of the apparatus
In both experiments we first assessed the effect of the
apparatus with minimum added inertia with free walking.
The overall effect of the apparatus is negligible in both
experiments. There were some significant changes, but
these were very relatively small (few percent) and few in
number: 11 for the ankle experiment and 10 for the pelvis
Most of these significant changes involve slow walking.
All the loaded conditions, including the baseline
conditions were randomized, but the free walking conditions
were not randomized. Every subject started with slow
walking. It is likely that the subjects were not completely
familiarized with walking on the treadmill during the
first trial i.e. free walking at slow speed. This could
account for the significant interaction effects (load
speed) that were found in the baseline validation.
Effect of AP load on ankle
Adding inertia to the ankle during walking on a treadmill
caused several significant changes. We hypothesized an
increase in effort by the subject in order to maintain gait
patterns. We did see a significant increase in energetics;
this was not accompanied by an increase in muscle
activity of the left (loaded) leg. This can be explained by the
fact that muscle activity of the right leg increased, however
this was not investigated. An argument in favor of this
explanation could lie in the fact that the pelvis and hat
segment show increased acceleration mainly during the
terminal swing phase of the left leg. Since the left leg is
swinging, effort for increased acceleration is likely to be
caused by the right leg.
Adding 1.55 kg inertia to the ankle caused an increased
in metabolic rate of 5.7%, which is a little less than the
7.6% that Royer and Martin found when applying a weight
of 1.2 kg to the ankle and 0.8 kg to the knee . They
also found a significant increase of the soleus activity,
where we found a small decrease. In our study the added
load did not require vertical acceleration during push-off,
whereas the extra weight in their study did require extra
effort in vertical acceleration.
The muscle activity of the loaded leg remained
unchanged largely, except for a few decreases: The first is
that of the soleus in terminal stance, which indicates a
reduced effort in push off, which is also visible in the
reduced plantar flexion range of motion. Consequently
the foot acceleration decreases and the stride length
decreases. Contrary to our hypothesis the subject reduces
the effort to accelerate the foot and its extra inertia, and
accepts changed gait patterns. The second reduction of
muscle activity is the tibialis anterior in swing phase,
indicating a reduced effort to lift the toe, which is
explained by a reduced push off: if the plantar flexion is
reduced, less effort is needed to lift the toes for sufficient
ground clearance. Another consequence of the decreased
acceleration is the significant increase in the swing time
for the left leg: it takes longer before the foot touches the
ground. Also this change is larger than the ISV, and
therefore stated as appreciable.
Adding 1.55 kg caused only an appreciable change in
acceleration range of motion of the pelvis and left foot
at high speeds only; the other 29 parameters remained
unaffected. In both cases the changes just exceed the
average intra subject variability. Therefore we conclude
that walking with 1.55 kg added to the ankle in AP
direction resembles normal walking.
Adding 3.5 kg also caused appreciable changes at low
speeds and especially the changes of the pelvis and foot
acceleration RoM at high speeds are much larger than
the average intra subject variability. Therefore we
conclude that walking with 3.5 kg added to the ankle in AP
direction does not resemble normal walking.
Table 7 Significant main effects and speed interaction effects of inertia added to the pelvis in AP direction
Joint- & Segment angles
Stance time left [s]
Hip abduction RoM [deg]
Hip flexion RoM [deg]
Knee flexion RoM [deg]
Back sagittal flexion RoM [deg]
Pos pelvis AP RoM [mm]
Acc pelvis AP RoM [m/s2]
Pos HAT AP RoM [mm]
Acc HAT AP RoM [m/s2]
Vastus lateralis - mid stance
Vastus lateralis - terminal swing
Gastrocnemius medialis - mid stance
Soleus - mid stance
* Significantly different from 0.3 kg (p < 0.05).
+ Significantly different from 1.55 kg (p < 0.05).
Bold: change larger than the average intra subject variability indicated between brackets at baseline.
Loaded conditions are compared to baseline condition. The table lists significant main effects (independent of speed) and significant interaction effects with
speed, but only at speeds that are significant in pair wise comparisons.
Effect of AP load on pelvis
We assessed the effect of adding inertia to the pelvis in AP
direction during walking on a treadmill. We hypothesized
that the effort remains unchanged and this is confirmed
by the fact that energetics remain unchanged. The EMG
activity does show significant changes, but, though
significant, the changes are very small, and do not exceed the
average intra subject variability.
As hypothesized the pelvis motions decrease due to
added inertia in AP direction. Though the decreases are
less than the average intra subject variability, the pelvis
position- and acceleration RoM decrease significantly.
As the trunk is connected to pelvis also the trunk motions
decrease significantly. However the sagittal rotation
between the trunk and the pelvis, the back sagittal flexion
increases. A possible explanation is that the pelvis shows
more sagittal rotation, this however was not investigated
in the study. The inertial forces due to the added inertia
may elicit a moment in the sagittal plane, causing the
Of all significant changes only the AP acceleration of
the pelvis and hat segment and the sagittal rotation of
the back exceed the average intra subject variability, only
when 10.2 kg was attached. Therefore we consider
walking with 4.3 kg to be similar to normal walking, whereas
10.2 kg does not resemble normal walking.
Effect of ML load on pelvis
We assessed the effect of adding inertia to the pelvis in
mediolateral direction during walking on a treadmill. We
hypothesized that the ML motions of the pelvis would
decrease, and correspondingly adding inertia did decrease
the range of motion of the pelvis and HAT segment in ML
direction significantly. These changes however are small
and did not prove to be significant in pair wise
Trunk tilt RoM [deg] @4.5km/h
Acc pelvis AP RoM [m/s2] @4.5km/h
TOR HSR TOL
Acc HAT AP RoM [m/s2] @4.5km/h
TOR HSR TOL 0.73 kg 4.33 kg 10.18 kg
Figure 5 Effect of inertia in AP direction on the pelvis. Trunk tilt
(A), pelvis mediolateral acceleration (B) and trunk mediolateral
acceleration (C) as a function of the% gait cycle. Profiles are
averaged across subjects and the shaded areas show the average
intra subject variability. The cycle starts at 0% at heel strike left,
followed by toe off right (TOR), heel strike right (HSR), toe off left
(TOL) and ends with a heel strike left at 100%.
comparisons. Therefore we conclude that 5.3 kg can be
added on the pelvis in ML direction without affecting the
During the experiments subjects claimed that they did
perceive the inertia, in several condition of low and high
inertia. This can be explained by the Weber fraction .
The smallest noticeable difference in weight (the least
difference that the test person can still perceive as a
difference), is proportional to the starting value of the weight
Based on this, one could estimate what would be the just
noticeable difference (JND) of added inertia, simply by
taking the Weber fraction of the mass of the leg. For mass
the Weber fraction is 1/10 [19,20] Applying this to the
mass distribution of the human body gives a JND of
3.2 kg for the trunk and 0.15 kg for the foot (see Table 9).
In our study the applied inertia was more than the JND
except for the baseline and the pelvis ML 2.3 kg condition.
Table 8 Significant main effects and speed interaction
effects of inertia added to the pelvis in ML direction
Acc pelvis ML RoM [m/s2]
Acc HAT ML RoM [m/s2]
* Significantly different from 0.3 kg (p < 0.05).
This can explain why subject did perceive the difference
even if physical measurement did not.
Comparisons between experiments
In our experiments we found that adding inertia to the
ankle causes more effect that adding the same inertia to
the pelvis. Browning found similar results , with added
weights, meaning that the found effects cannot be
ascribed to the gravitational component only. An
explanation is given by the fact that the acceleration of the foot
is ten times larger than the acceleration of the pelvis in
AP direction. Similarly, the acceleration of the pelvis in
forward direction is three times higher than the
acceleration of the pelvis in ML direction.
As hypothesized the effects are larger at high speeds.
In the ankle experiment four appreciable effects at high
speeds are found, only one for low speed. In the pelvis
experiment for AP loading, three appreciable effects at
high speeds are found, none for low speed.
Comparison with other studies
In the pelvis experiment we applied AP inertia up to
10.2 kg and ML inertia of 5.3 kg which is approximately
13% and 7% of the body mass. Grabowski applied inertia
of 25% of body weight in all directions and found an
increase in metabolic rate (+25%). In our study the
metabolic rate remains unchanged when applying inertias to
the pelvis in the horizontal plane only. McGowan and
colleagues applied inertias equal to 25% and 50% of the
body mass and found an increase of soleus activity at
the late stance of 17% and 43%. They found that the
soleus is the primary contributor to forward trunk
propulsion  and that the soleus and gastrocnemicus
both contribute in both support. In our study we
reported no change of muscle activity in terminal stance,
when adding 10.2 kg in AP direction or 5.2 kg in ML
direction. However we did see a significant increase of
both soleus and gastrocnemicus in mid stance. McGowan
applied inertia in all directions including vertical hence
affecting the AP component of propulsion and the vertical
component of propulsion, whereas we applied inertia only
in one direction, only affecting the horizontal component
of propulsion. Comparing our results with found results
from Grabowski and McGowan suggests that vertical
Table 9 Just noticeable difference for body segments
according to the Weber fraction
Weight Weight [kg] JND [kg] according to
percentage (75 kg bodyweight) Weber fraction (1/10)
Upper leg 12%
Lower leg 5%
motion of the pelvis may be the degree of freedom that is
most sensitive to added inertia.
To find requirements for gait training robots, we started
with applying inertia on one segment in one or two
directions. Since nearly all robotic gait trainers have an
interface to the lower shank and the pelvis, we applied inertia
to the ankle and the pelvis. To obtain a complete set of
requirements for gait training robots, the effect of inertia
added to the knee should be investigated, as well as the effect
of combined inertias added to the ankle, knee and pelvis.
In order to allow normal walking in a gait training robot,
the robot should be transparent. In our study we
quantified the requirements for transparent walking. We assume
that when energetics, kinematics and gait parameters are
unaffected, transparency in gait training is guaranteed. We
found that inertia up to 2 kg to the ankle or 6 kg added to the
pelvis have negligible effect on energetics, kinematics and gait
parameters. Therefore, for gait training robots to be
transparent, they should display inertias less than the found thresholds.
Additional file 1: Movie of adding inertia to the pelvis in
anteriorposterior and lateral direction independently.
Jos Meuleman works at Moog, working on the design of a gait training robot.
JM conducted the research, data analysis and writing. EA and HK contributed in the
design of the study and writing. All authors read and approved the final manuscript.
Authors would like to thank Wybren Terpstra and Thijs Lohuis for their
contribution in the execution of the experiment and their preliminary
analysis of the data. This study was supported by a grant from Dutch
Ministry of Economic affairs and Province of Overijssel, the Netherlands
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