Advanced Robotics, 2015
http://dx.doi.org/10.1080/01691864.2015.1055799

FULL PAPER
Interaction forces beneath cuffs of physical assistant robots and their motion-based estimation
Yasuhiro Akiyama∗ , Yoji Yamada and Shogo Okamoto
Department of Mechanical Science and Engineering, Nagoya University, Nagoya, Aichi, Japan

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(Received 20 October 2014; revised 21 February 2015; accepted 8 May 2015)
Most lower-limb physical assistant robots are fixed to wearers using cuffs. Hence, skin injuries beneath the cuffs are oneof the major concerns of the users. A model that describes the relationship between the body posture and the interaction
forces at the cuff was developed for use in assessing the risk of injury and improving user comfort. We measured the
motion and interaction force beneath cuffs during the sitting and standing motions of subjects and a physical assistantrobot which has been hardly reported thus far. Because of slippage and biomechanical motion, a traditional spring-damper
model was found to be insufficient to describe the interaction forces associated with the measured motion of the cuffs.
A parameter representing the motion or the knee joint angle was added to take into account these factors. Our modelfor estimation of the interaction forces using a spring, a damper, and the attitude of the lower leg fits the measured data
especially well for the thigh cuff and is better than the traditional model. The applicability of this model was verified
for several assist modes and wearers. The model was found to describe approximately 90% of the burden on the wearer,which reached a peak of approximately 60 N, the most hazardous condition. Having been validated for a commercial
assistant robot, the model can be used to estimate the skin burdens beneath the cuffs without any force-sensitive elements.
Keywords: physical assistant robot; safety; sit–to–stand; human–robot interaction

1. Introduction
Physical assistant robots have been used mainly to assist in
the rehabilitation of patients such as stroke survivors, under the supervision of physical therapists,[1–3] and trained
workers and soldiers in special environments.[4] However,
the range of applicability of physical assistant robots has
been expanding in recent years. For example, improving the
locomotion of elderly persons has become a new target application of lower-limb physical assistant robots.[5] Whensuch assistant robots are used in daily living, a problem
arises that had been considered somewhat minor, comparedwith high-risk problems such as falling. This problem isthe occurrence of skin injuries caused by the skin being
repeatedly stretched or scratched by the cuffs used to fix therobot to human limbs. Such injuries easily occur in people
who have weak skin, such as patients with cirrhosis.
Assistant robots apply interaction or supportive forces tothe wearer through cuffs. When the ergonomic mismatchand imperfect adjustment between a human body and aphysical assistant robot are not negligible, the interaction
forces that can lead to skin injury increase.[6] The risk
of skin injury increases with the magnitudes of these interaction forces and the frequencies with which they areapplied.[7] Therefore, it is necessary to validate the contact
safety of physical assistant robots through testing. Suchsafety measures have to be considered in accordance with
ISO 13482,[8] which is a safety standard for personal carerobots, including physical assistant robots.
Skin stretching caused by interaction forces between theskin and cuffs is largely unavoidable because the motionof a robotic single-degree-of-freedom (1-DOF) pin joint
and the ergonomic rotation and translation of a human joint[9,10] are fundamentally different, although some researchers have studied an advanced mechanism to mitigate thishuman–robot kinematic mismatch.[11] The assessment andprevention of large interaction forces and discomfort that
could lead to skin injury are important to the safe use ofphysical assistant robots. However, with commercial robots,
it is not easy to measure such forces or skin deformations
beneath the cuffs. Direct measurement of skin deformation
or interaction forces is needed for this purpose. Esmaeili etal., for example, suggested a relationship between the deformation energy of the skin and discomfort.[12] Other studies
have used force sensors to measure interaction forces between the skin and fixed parts of a robot, such as cuffs, during motion.[13,14] However, commercial robots are rarely
equipped with sensors for measurement of interaction forces
or skin deformations under the cuffs. Such measurements
are typically only possible in a laboratory setting. Therefore,
while it is necessary to avoid large interaction forces beneath∗ Corresponding author. Email: akiyama-yasuhiro@mech.nagoya-u.ac.jp© 2015 Taylor & Francis and The Robotics Society of Japan

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the cuffs, most commercial robots lack sensors in their cuffs
and are thus unable to measure the forces or deformations
that occur.
One possible solution to this problem is to estimate theinteraction forces between the cuffs and the skin using kinematic information about the robot, which is usually accurately measured. However, the interactions between the
fixed parts of a robot and a user’s skin, such as viscoelastic
deformation and slippage, remain incompletely understoodand modeled. Hence, it is necessary to tune the parameters of
the force estimation model for each user, using a customized
robot equipped with force sensors. Once such parameters
are tuned, the model can be used to estimate interaction
forces without force sensors. In this study, we adopted anexperimental approach to estimate interaction forces beneath the skin. We first attempted to estimate the forces on
the basis of the relative displacement between the cuff andskin, using a spring–damper model. However, because ofslippage between the skin and cuff, the hysteresis of humanmotions, and the changes in the physical parameters withhuman motion, this model was found to be insufficient. To
compensate for the effect of slippage, we introduced a body
posture term that is related to the fixation condition of thecuff with changes in posture. Furthermore, to counteract
the hysteresis effect, models to estimate interaction forceswere built for two phases of human motion: the standing
and sitting phases. Models such as these for estimating
the interaction forces between robot cuffs and human skin,based on kinematic information that is generally available
for commercial robots, will contribute to improving thesafety of use of physical assistant robots.

2. Method
This experiment was conducted with the permission of theInstitutional Review Board (IRB) of Nagoya University.

2.1. Apparatus
The motions of a physical assistant robot and wearers were
measured at 100 Hz using a three-dimensional (3D) motion
capture system (MAC 3D system, Motion Analysis Corporation, US). Markers for the motion capture system wereplaced on the left sides of the bodies of the robot and thewearers. Cluster markers were used at positions coveredby the robot. A commercially available physical assistantrobot1 was used for the tests. All links were connected by
1-DOF joints, and the hip and knee joints were actuated.
Figure 1 shows an overview of how the robot was fixed
to a wearer using belted cuffs. The robot could support
itself because the frame of the robot reached the groundwhen standing straight. The lengths of the thigh link andshank link could be changed in 15-mm increments andwere adjusted for each subject. The positions of the rotation
centers of the hip and knee joints were aligned manually.

Figure 1. Overview of physical assistant robot.

The rotation center of the human was defined as the positionof the great trochanter and lateral epicondyle.
The cuffs of the left leg were modified to measure theinteraction forces, as shown in Figure 2. Two three-axis
force sensors (US06-H5, Tech Gihan Co., Ltd., Japan), theoutputs from which were sampled at 50 Hz, were attachedto the base of cuff. The surface plate of each of the cuffs wasthen attached to the force sensors. The contact surface of the
instrumented cuff, 65 × 90 mm in size, was covered withurethane. An artificial leather belt 50 mm wide was used toattach the cuff to the subject, and the belt was connectedto the cuff. Thus, the measured interaction force included
the force transferred through the belt. The instrumented cuff
and belt were attached to the skin of the subject directory
without any clothes.
In this experiment, three assist modes which include a
non-assisted mode in which the robot was not actuatedand the other two assist modes were used: a resistancecompensation mode and a standing–sitting support mode.
The resistance compensation mode cancels the resistancetorque of the friction caused by the actuators and gears. The
standing–sitting assist mode assists the sitting and standing
motions by applying torque when the robot detects motions
by installed encoders at the joints.

2.2. Protocol
This experiment was conducted with 10 healthy male volunteers who were between 22 and 24 years old (average age
23.1 years) and between 169 and 180 cm tall (average height174.2 cm). The participants were not familiar with any typesof physical assistant robots. The cuffs were fixed securely
without causing discomfort to the subject. The tightening
force (tension) of the belt was about 30–50 N. After the
robot and markers were attached, three assist modes which
include non-actuation case were tested for adaptation: nonassisted, resistance compensation, and standing–sitting support. The adaptation continued until the subject became

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Figure 2. Structure of instrumented cuff (left: bird’s eye view, right: sectional view).

Figure 3. Conditions of sitting–standing motion.

comfortable. Then, the subject repeated sitting and standing
10 times for each assist mode. During the trial, the subject
was ordered to grab the same position of the handrail. The
sit–to–stand motion was selected because it is one of thefundamental motions of daily activities and because there
is information about it in previous studies [15,16] that canbe used for reference. Although the subject was informed
about the assist mode of the next trial, the order of the assist
modes was randomized to prevent order effect.
A chair and hand rails, which were fixed in position, wereused to help with the motion. The chair was 52 cm tall, andthe hand rails were set to a height of 124 cm, as shownin Figure 3. The horizontal spacing of the hand rails was
84 cm. The subjects were instructed to not move their feetand to minimize the variation in standing–sitting motions
performed during the experiments.
2.3. Data processing
The motion capture markers were set so that the positionsof more than two points of each link (pelvis, thigh, andlower thigh) were traced in the sagittal plane, with markers
at each joint center and at the pelvis. The position of the
hip joint of the wearer was calculated from markers on
sacral and anterior superior iliac points on the spine.[17]External malleolus, lateral epicondyle, sacral vertebra, andFigure 4. Geometry of attitude and position calculation.

anterior superior iliac spine locations were determined on
the basis of palpation as the positions of markers on thesubject. Markers were also placed at the centers of the ankle,
knee, and hip joints on the robot. In addition, two markers
were placed on the median line of the pelvis.
The angle of each link was defined using two markers
for each link, and the angle of each joint was defined as theangle between neighboring links. The relative displacementof the cuff, which was defined as the distance between the
cuff of the robot and its initial position of the subject, wascalculated as follows. The initial cuff position was first fixed
to the coordinates of each link. The cuff position was thentraced by monitoring the position of each link.
Figure 4 shows the geometry of the angle and cuff
distances. The coordinate system of the interaction forces
matched that of the robotic links because force sensors were
fixed to each robot’s link. The origin of each coordination
system is located at the center of each cuff, i.e. the centerof two force sensors. The coordinate directions of each cuff
were Xt , Yt , Xs , and Ys . In this figure,  p , t , and s
represent the angles of the human links (pelvis, thigh, andshank, respectively); h and k represent the angles of thehuman joints (hip and knee, respectively); θ p , θt , θs , θh , andθk represent the respective angles of the robot; Dt and Ds
represent the distances between the human knee joint andthigh or shank cuff, respectively; and dt and ds represent the
distances between the robotic joint and cuffs, respectively.

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Data on the link attitude and position, joint angle, relative
displacement of the cuff, and interaction force were filteredwith a linear-phase finite-impulse response (FIR) low-passfilter with a cutoff frequency of 2 Hz and a filter order of
30. The whole motion was separated into the sitting andstanding phases. When the phases were separated, the edgeof each phase was trimmed to ignore the effect of the static
phase, i.e. still standing and sitting postures. One percent of
the motion range for the robotic knee joint was used to trim
the edge of each motion.
3. Results
This section summarizes the results obtained for the nonassisted mode, analyzed for the purpose of building kinematic models to estimate the interaction forces at the cuffs.
The effect of each mode is discussed in Section 5.
3.1. Motion of subjects
Table 1 presents the results of a comparison of the paceof motion of each subject, conducted to verify the stabilityof the motion. The pace of motion was highly individual,
but stable for almost all subjects. Figures 5–7 compare thechanges in the angles of the links for each subject. The
temporal sequence data were normalized by the length ofthe motions of the sitting and standing phases. All links
became 90◦ when the subject stood erect, and forward tilting
increased the link angle.
During the motion of sitting phase, the angle of the thighlink decreased with the flexion of the knee joint. At the sametime, for many subjects, the lower thigh angle remained
more than 90◦ , which means that the link was slightly bent
forward. On the other hand, the pelvises of all subjects werebent backward at the end of sitting.
The trends for the motion of the standing phase were
almost the opposite of those for the motion of the sitting
phase, except for the early standing phase. Typically, whena subject stood up from the chair, the lower thigh and pelvis
first bent forward to move the center of gravity forward.
These sitting–standing motion patterns of the subjects corresponded to a general motion pattern that has been describedin previous studies.[18,19]
3.2. Relative displacement between human limbs androbotic cuffs at cuff position
Because of the mismatch between the subject and the robot,
which is the result of both the adjustment problem and theergonomic motion, the position of the rotation center differs
between the subject and the robot. Thus, a mismatch of the
trajectory of the initial cuff position between the subject andthe robot occurs, depending on the flexion of the knee joint.
Figure 8 shows the initial, middle, and final postures of thesubject and the robot. This figure clearly shows the relative
motion, as described below.

Table 1. Average duration of motion of each subject.
Subject no. Sitting pace [s] ± SD Standing pace [s] ± SD
1
2
3
4
5
6
7
8
9
10

2.7
2.0
4.2
1.5
1.8
2.2
2.6
1.4
1.9
1.8

0.2
0.1
0.1
0.1
0.1
0.2
0.4
0.1
0.1
0.2

2.6
2.1
3.5
1.4
1.5
2.3
2.5
1.7
2.0
1.7

0.2
0.1
0.2
0.1
0.1
0.1
0.3
0.1
0.2
0.2

Figure 5. Change in θ p of each subject during phases (top: sitting,bottom: standing).

3.2.1. Variance of the cuff position between subjects
Because of the limited accuracy of the manual alignment
process and the difference of physical frame among individuals, the relative position of the cuff differs initiallyfrom one subject to another. This difference remains evenafter the motion becomes stable. Figures 9 and 10 illustrate
the differences in the cuff positions of different subjects.
In these graphs, the coordinates are fixed to the robotic
thigh and shank link. The direction of the vertical axis
matches the longitudinal axis of each link. The origin of
this coordination system is the center of the robotic knee
joint. The symbols indicate the trace of the position of thecuff at the initial setting along the center axis of humanlimb. The symbols for the standing posture are filled, andthose for the sitting posture are not. The circles represent
the motion of the sitting phase, and the squares represent
the motion of the standing phase. The symbols of different
colors represent the different subjects.

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Figure 6. Change in θt of each subject during phases (top: sitting,bottom: standing).

Figure 7. Change in θs of each subject during phases (top: sitting,bottom: standing).

Initially, because of the differences in the thigh lengthsof the subjects, the nominal alignment point for the thighcuff was (0, 200) for most of the subjects and (0, 230)
for two of the subjects (represented by yellow and black
symbols). In the sitting posture, the cuff position moved
leftward and upward for many of the subjects, meaningthat the subjects’ limbs moved forward and upward fromthe robotic cuffs. However, the amounts of relative motion,
indicated by the distances between the filled symbols andthe blank symbols, differed among the subjects, and therelationship between initial misalignment and relative motion is not clear. Although initial misalignment might affectthe relative motion between a subject’s limb and a robotic
cuff, there are many other factors, such as the shape of thesubject’s limb, muscle tension, and kinematic parametersof the skin and tissue, that influence the relative motion.
The complex interaction between these factors should beanalyzed and modeled carefully in another study to identify
the effect of each factor.

Figure 8. Postures of human and robot (left: sitting, right: standing).

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Figure 9. The positions of thigh cuffs from the center of therobotic knee joint. (The origin of the coordinate system is therobotic knee joint. Negative direction represents forward direction.
Filled symbols represent the standing posture, and others represent
the sitting posture. Each color represents a different subject.)Figure 10. The positions of shank cuffs from the center of therobotic knee joint. (The origin of the coordinate system is therobotic knee joint. Negative direction represents forward direction.
Filled symbols represent the standing posture, and others represent
the sitting posture. Each color represents a different subject.)

3.2.2. Relative displacement between the human thigh andthigh cuff over time
The relative displacements between the subjects’ thighs andthe robotic thigh cuff were compared. Figure 11 shows theaverage relative displacements and their standard deviations(SD) for all subjects. The SD, which represents individual
differences, increased during sitting motions and decreased

Figure 11. Relative displacement between human and robot at theposition of the thigh cuff (top: sitting, bottom: standing).

during standing motions, which means that the individualityof the subjects was more pronounced in the sitting posture.
The thigh link of the robot moved backward (Xt < 0) andin the distal direction Yt > 0) with respect to the thighof the subject during the sitting motion. These motions
indicate that the robotic thigh link moved downward fromthe subject’s thigh. When standing straight, the robot supported itself through its frame. However, the weight of eachrobotic link was applied to the subject through cuffs, withthe posture becoming a half-crouching position. Thus, therobotic thigh link might have hung down from the thigh of
the subject because of its weight.
The trend for the motion of the standing phase was not
the reverse of that for the motion of the sitting phase. The
relative displacement decreased gradually during motion of
the standing phase. In addition, the cuff might have slipped,because the range of the relative displacement was too large
to be the result of skin deformation.

3.2.3. Relative displacement between the human shankand shank cuff over time
Figure 12 shows the relative displacement between the subjects’ shanks and the robotic shank cuff. As with the thighcuff, the differences from one subject to another were more
pronounced in the sitting posture. The robotic shank link
moved forward (Xs > 0) and in the proximal (Ys < 0)direction with respect to that of the subject when sitting.
The motion of the shank link should be related to that of
the thigh link because the two links are connected at theknee joint. Therefore, the thigh link may push the shanklink forward, leading to motion in the Xs > 0 direction, inDownloaded by [Robotics Society of Japan] at 13:52 29 July 2015

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Figure 12. Relative displacement between human and robot at theposition of the shank cuff (top: sitting, bottom: standing).

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Figure 13. Interaction force between human and robot at shankcuff (top: sitting, bottom: standing).

the middle and later parts of the motion of the sitting phase.
In addition, the change in the relative angle of the shank
between the human and the robot influences the downward
motion of the human shank, i.e. the motion in the Ys < 0direction.
As this figure shows, the relative displacement of theshank cuff in the anteroposterior direction (Xs ) decreasedin the early part of the motion of the standing phase because
the lower thigh of the subject bent forward when the subject
began to stand. This trend differed from that of the motionof the sitting phase. In addition, the range of the relative
displacement was so large that it could not be describedwithout the slippage of the cuff being the same as that of
the thigh cuff.

3.3. Interaction force at cuffs
The relative motion at the cuff position produces an interaction force. Figures 13 and 14 show the average interaction forces at each cuff and their SD. These forces are thesummation of both force sensors at a cuff. The interaction
forces along Yt increased with the sitting motion, whichmeans that the robot hung down. This corresponded to therelative displacement of the cuff. In addition, the interaction
forces at the shank cuff largely corresponded to the relative
motion of the shank cuff. However, the interaction force of
Xs became large late in the motion of the standing phase,
which means that the shank of the subject was pushed frombehind. When the subject pulled up the thigh of the robot,
the shank link of the robot was pushed through the knee
joint.

Figure 14. Interaction force between human and robot at thighcuff (top: sitting, bottom: standing).

4. Fitting of physical model
4.1. Spring–damper model
Estimating and validating the interaction forces of a dynamic motion are difficult because of the unidentified biomechanical interactions between the skin and the cuff. In thisstudy, a spring–damper model was used to describe thephysical contact between the wearer and the robot. Viscoelastic deformation of the tissue [20,21] and fixed parts
are collectively included in the parameters for the motionof the sitting and standing phases.

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22

Table 2. R of spring–damper models.

Xs
Ys
Xt
Yt

Table 3. R of spring–damper and attitude models.

Sitting phase

Standing phase

0.15
0.50
0.80
0.37

0.16
0.07
0.58
0.22

Xs
Ys
Xt
Yt

Sitting phase

Standing phase

0.44
0.50
0.90
0.81

0.89
0.09
0.80
0.78

A spring–damper model described by the following
formula was employed. A linear approximation was usedbecause the displacements were assumed to be small. To
determine the values of the parameters of this model, fitting
was conducted using the least-squares regression method.

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F(t) = kd(t) + cv(t)(1)

The values of k and c, which represent the spring constantand viscosity, respectively, were determined after the valuesof F, d, and v, which represent the interaction force, thedisplacement between the cuff and the link, and its timederivative value, respectively, were standardized for each2
subject. Table 2 lists the value of R , which is the adjusted
coefficient of determination, for each phase and part of the
non-assisted mode. The results suggest that an inadequate
2
R was obtained for almost all conditions, especially the
motion of the standing phase. The spring–damper modelcannot describe the actual interaction forces of the sitting
and standing motions.

4.2. Spring–damper and attitude model
4.2.1. Introduction of body attitude into the estimation
model
A more advanced model was needed because the spring–
damper model was found to be insufficient to describe theinteraction forces associated with the motion observed. In
general, the spring constant of skin tissue increases withdisplacement because the stretching range of skin tissue
is limited.[22,23] However, a precipitous increase in theinteraction forces against motion did not occur, except for
Xs in the motion of the standing phase. Other factors thatmight affect the interaction forces are the slippage of the cuff
and the shapes and diameters of the human thigh and shank.
However, direct observation of the events that occur beneaththe cuffs is difficult because this position is covered by the
cuff. On the other hand, during the motion of the sitting
and standing phases, the slippage direction of the cuff isprobably consistent because the directions of human motion
and gravity, which cause slippage, are fairly constant. In
addition, the direction and magnitude of motion and gravity
change with the attitude. Other parameters, such as thestiffness and shape of the subject’s thigh and shank, alsochange with motion. Therefore, the angle of the robotic
knee joint, which changes with the motion of the sitting and

Figure 15. Comparison of actual interaction force (Act) andforces estimated from the models (S_D: spring–damper model,
S_D_A: spring–damper and attitude model) at the shank cuff (top:sitting, bottom: standing).

standing phases, was added as new parameter. This model
is described by the following formula, using the knee angle
θk and its coefficient a:
F(t) = kd(t) + cv(t) + aθk (t).

(2)

Fitting of this model was performed in the same manner2
as for the spring–damper model. Table 3 lists the R value
for each phase and part for the non-assisted mode. Except
2
for Ys , the R values were substantially greater than those2
for the previous model. The R value for Ys was apparently small because the average interaction forces along Ys
were small, nearly zero, across the entire body motions,whereas their variations were somewhat large. Under such2
conditions, R necessarily becomes small. In practice, we
may not need to be concerned about the forces along Ys
because the risks of skin injuries caused by them are considered minuscule. The improvement in the estimation of
the interaction forces is illustrated in Figures 15 and 16.
According to these figures, the forces predicted by the
spring–damper and attitude model fit the measured forcesmore accurately than those predicted by the spring–damper
model. The improvement in the prediction of Xs is obvious.
To confirm the stability of the model, leave-one-out crossvalidation was performed. As shown in Figure 17, theAdvanced Robotics

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Table 4. Regression coefficients of spring–damper and attitude
models.
R
Sitting phase

Standing phase

2

k

Xs
Ys
Xt
Yt

0.44
0.50
0.90
0.81

0.64
0.75
0.46
0.29

Xs
Ys
Xt
Yt

0.89
0.09
0.80
0.78

0.26
0.35

c

a

0.28
0.19

−0.65
0.12
−0.57
0.76

0.17

−0.87
−0.32
−0.82
0.75

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Note: Statistically insignificant coefficients are not shown.

Figure 16. Comparison of actual interaction force (Act) andforces estimated from the models (S_D: spring–damper model,
S_D_A: spring–damper and attitude model) at the thigh cuff (top:sitting, bottom: standing).

2

Figure 17. R of cross validation using spring–damper andattitude model for all subjects.
2interaction forces at the thigh cuff have high R values,
as does Xs in the motion of the standing phase. This trend2
corresponds to the R values listed in Table 3. However,certain outliers were observed. These are indicated by open
circles in Figure 17.

4.2.2. Regression coefﬁcients of the model
The physical model helps us to understand the phenomenathat occur under the cuff and to specify each parameter ofthe model. To determine the contribution of each term of
the model, the standard partial regression coefficients werecompared as shown in Table 4. The value of k was larger

than that of c for almost all force components. In addition,|a| was the largest parameter among the three coefficients.
This suggests that the effect of the change in posture wasgreater than that of the relative displacement between thehuman limb and the robotic cuff and its velocity.
The interaction force generated by the relative displacement most likely results from the elasticity of human bodytissues and cuff fixation parts. On the other hand, the force
that results from the change in posture is the result of theslippage, muscle stiffness, and shape of the subject’s thighand shank.
A comparison of the coefficient values obtained from2
the regression showed that cases with high R values hadcoefficient values of the same order of magnitude. On the2other hand, the coefficient values for cases with low R
values, such as Ys for both phases and Xs for the motionof the sitting phase, differed drastically from this trend.
Therefore, we only discuss the coefficient values of the cases2with high R values here. The coefficient values differedamong the force components because of the differences in
the fixation conditions, such as the tightening force, thethickness of the tissue, and the anisotropy of the fixation
strength. The coefficient values of Xt changed between
phases, in contrast to those of Yt . In particular, the valueof k was not significant during the motion of the standing
phase but was during the motion of the sitting phase. Thesechanges in the coefficient values suggest that the fixation
conditions changed between phases. In addition, for Xs ,2both the coefficient values and the R value changed withthe phase.
4.2.3. Physical parameters of the estimated model
The coefficients k, c, and a are dimensionless because they
are based on normalized forces and postures. We translated
these coefficients into the physical parameters, k  , c , anda  , which represent the coefficients of the elasticity, the viscosity, and the attitude elements, respectively. The physical2parameters for cases with sufficiently high R values arelisted in Table 5.

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Table 5. Physical parameters of spring–damper and attitude
models.
k  [N/mm]
Sitting phasec [Ns/m]a  [N/deg]

Xt 0.20 to 0.98
−0.24 to −0.07
0.16 to 0.37
Yt 0.19 to 0.72 0.63 to 1.84

−1.58 to −0.46
Standing phase Xs 0.70 to 2.73
−0.31 to −0.04
Xt
0.12 to 0.27
Yt 0.28 to 0.76 0.05 to 0.21

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Note: Statistically insignificant coefficients are not shown.

Although it is difficult to separate the coefficients by theskin, belt, and other components, some suggestions are provided in the literature. Clark measured the elastic coefficientof the antebrachial region of healthy humans.[24] The value
obtained, 0.75 N/mm, is close to the value obtained in our
calculations. Lundström measured the elastic and viscouscoefficients of human fingers.[25] Their measurements indicated that k  was in the range of 1.5–5.6 N/mm and thatc was in the range of 1.0–2.8 Ns/m. Aso et al. measured
the longitudinal elastic modulus of human thighs [26] andobtained values in the range of 0.7–2.8 N/mm. The k  andc values obtained are close to those reported in previous
studies, even though the region of the skin differs. This similarity in the results obtained suggests that the mechanicalcharacteristics of the fixed parts of the physical assistancerobot are primarily affected by the characteristics of skintissue.
In practice, clothes must be worn underneath some robots.
In these cases, interaction forces are affected by both thecharacteristics of the wearers and the characteristics of theirclothes. Clothes are expected to reduce friction between acuff and human skin, and the effect of slip increases. Therefore, the contributions of the spring and damper elements
will change when clothes are worn.

5. Generality of the spring–damper and attitude model
5.1. Effect of individuality
5.1.1. Individual ﬁtting improves the estimation
The differences in fixation conditions included differencesin the area of contact, tightening force, thickness of tissue,
friction coefficient, and shape of the fixation area. These2
parameters differed among individuals. If the low R of thespring–damper and attitude model is attributable to individuality, this model should more accurately fit each subject.
Therefore, the model was separately fitted to the data foreach subject. The results are summarized in Figure 18.
2
Although these results show an improvement in R , there
is still room for improvement in some force components.
The results suggest that other factors, such as unevennessof the contact force, nonlinearity of the human tissue, and2

Figure 18. R of the spring–damper and attitude model tuned foreach individual.

shape factors, may affect the contact between human skinand a cuff.
5.1.2. Individual difference in interaction force comes fromthe cuff position
We tested the individual differences in the maximum interaction forces applied to the cuffs because the residual
individual differences might suggest the necessity of additional parameters that affect the interaction force. Figures 19
and 20 show the minimum and maximum interaction forcesof each subject. Each subject is represented by a different
color. The colors correspond with those used in other figuresin this paper. The initial setting of the position of the cuff
may be the main concern with respect to the residual parameters because it potentially affects the relative motion.
However, as discussed previously, the cuff position in thestanding or sitting postures did not appear to affect therelative motion of the cuff. Thus, the effect of differencesin the cuff position can be reflected in the interaction force
at the cuff.
The Tukey-Kramer method was used to determine
whether the differences in the interaction forces of thesesubjects were significant. The maximum absolute values of
the interaction force were compared because the interaction
force affects discomfort and skin injury. As a result, it was
hard to associate the pairs of the subjects whose interaction
force differed significantly with the position of the thighcuff, which was shown in Figure 9, in the Xt direction.
In contrast, in the Yt direction, the forces for the subjects
represented by the black and yellow symbols, which weredifferent in the direction of the longitudinal axis, were significantly greater than those of the other subjects. This difference most likely arose from the shape of the human thighAdvanced Robotics

11

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Figure 19. Range of interaction force at the thigh cuff.

Figure 20. Range of interaction force at the shank cuff.

under the cuff. The diameter of the lower part of the thighincreases with the height, and the gradient becomes milder
because of the shape of muscle. In this experiment, the thighcuff was located 230 mm from the center of the knee joint on
the subjects represented by the black and yellow symbols,
which was 30 mm farther away than for the other subjects
because of the different thigh lengths of the subjects. Thus,
for those two subjects, the cuff might have been strongly
fixed in the direction of the lower side because the shape ofthe human thigh became more cylindrical with increasing
length. Although there were some pairs of subjects whose
interaction forces differed significantly at the shank cuff,
which was shown in Figure 10, it was difficult to associatethese differences with the position of the cuff.

5.2. Effect of assist mode
The assist torque should change the sitting and standing
motions and the interaction forces. We checked to ensurethat our model was valid for the different assist modes.

Figure 21. Motion time of each mode.

Figure 21 compares the lengths of the phases of eachmode. The motion decreases with assistance. This suggeststhat the resistance torque prevents motion of the subject in
the non-assisted mode. However, there was no difference
between the two assist modes.

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12

Y. Akiyama et al.

Figure 22. Interaction force of shank cuff in anteroposterior
direction (Xs ) (top: sitting, bottom: standing).

Figure 24. Interaction force of thigh cuff in anteroposterior
direction (Xt ) (top: sitting, bottom: standing).

Figure 23. Interaction force of shank cuff in anteroposterior
direction (Ys ) (top: sitting, bottom: standing).

Figure 25. Interaction force of thigh cuff in anteroposterior
direction (Yt ) (top: sitting, bottom: standing).

Figures 22–25 compare the interaction forces at the cuffs.
According to these figures, the interaction forces differed
between the non-assisted and other modes, and the difference between two assist modes was small. These changes
reflect the change in motion caused by the assist torque.
For example, Xs in the motion of the standing phase differs
drastically by mode, and the fact that the peak value of Xs
decreases because of the change suggests that assist torquecompensates for the mass and resistance that push the shankforward in the non-assisted mode.
To evaluate the changes in the fitting parameters, the R 2
and coefficient values for each mode were compared, as
shown in Tables 6 and 7. According to these tables andTable 4, there is a large difference between the non-assistedmode and the other modes. In particular, Ys in the motionof the standing phase is completely different, although Ys
is considered insignificant, as described before. Therefore,
this model should be tuned for each assist mode to obtainan adequate R 2 . In addition, a negative value of k was obtained for Ys , which is unrealistic and suggests the necessityof explicit consideration of assist torque when estimating
kinematic parameters.
It seems strange that the two assist modes had no differences. However, this can be explained by the assumed
motion speed of the assistance. The robot was designed toassist in rehabilitation, and the speed of its motion is suitableAdvanced Robotics

Table 6. Coefficient values of spring–damper and attitude models
in resistance compensation mode.
R
Sitting phase

Standing phase

2

k

c

a

0.19
0.36

−0.69
−0.47
−0.77
0.79

Xs
Ys
Xt
Yt

0.62
0.38
0.91
0.76

0.66
0.08
0.20
0.33

Xs
Ys
Xt
Yt

0.65
0.52
0.86
0.84

0.52

0.19

−0.85
−0.76
−0.90
0.84

0.21

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Note: Statistically insignificant coefficients are not shown.

13

5.3. Estimation error and safety margin
The magnitude of the shear force applied to the skin is
an indicator of the potential for skin injury.[7] Thus, an
important requirement of the model was to be able to accurately estimate the amplitude of the interaction force.
Figure 26 shows the ratio of the average peak force ofeach subject between the estimated interaction force andmeasured one. For the thigh cuff, for which the most critical
shear forces were measured, the estimated force exerted
at the thigh cuff, whose R 2 was comparatively high, waswithin approximately 50–120% of the actual values. These
differences should be taken into consideration by applying
a safety margin to the prediction of the risk of skin injury
by the robot.

Table 7. Coefficient values of spring–damper and attitude models
in sitting-standing support mode.
R
Sitting phase

Standing phase

2

k

c

a

0.18
0.32

−0.72
−0.68
−0.82
0.79

Xs
Ys
Xt
Yt

0.64
0.44
0.92
0.77

0.71
−0.10
0.16
0.31

Xs
Ys
Xt
Yt

0.71
0.61
0.85
0.85

0.49
−0.33

0.18

0.23

−0.87
−1.08
−0.86
0.82

Note: Statistically insignificant coefficients are not shown.

Figure 26. Ratio of the average peak force between the estimatedand measured force.

6. Conclusions
The interaction forces at the cuffs of a physical assistantrobot should not be substantially larger than the magnitudes
required to facilitate motion while ensuring the safety andcomfort of the user. However, it is difficult to estimate
the interaction forces during actual motions because thefrictional behaviors and human limb shapes at the cuff are
not easily modeled. In this study, a spring–damper and attitude model was developed to describe the interaction forces
during sitting and standing motions. The effects of factorsthat depend on the posture, such as slippage between the cuff
and human skin, were successfully represented in this modelby the addition of an attitude parameter that represents therelationship between motion and slippage. The goodness of
fit of the model was evaluated using the adjusted coefficientof determination. The values of the spring constant k  andviscosity c were found to be within their valid ranges,
given the mechanical characteristics of the skin. The spring–
damper and attitude model can, to a certain degree, estimate
the interaction forces that occur during sitting and standing
motions, despite differences from person to person.
The results suggest that the interaction force along Xs
exceeds 60 N for the most hazardous conditions that can
produce skin injury. Our model was able to describe approximately 90% of this maximum burden. It is important
to note that the conditions under which this model can beapplied should be carefully identified. However, the interaction forces can be estimated for an individual wearer fromhis or her motions, once the parameters are adjusted. Ourmodel can be used to estimate signs of potential wounds ofthe skin even for commercial robots that do not have force
sensing elements installed in the cuffs.
Funding

for a stroke patient. The subjects in this study moved too
quickly for assistance to work properly.

This study was conducted as a part of the ‘Practical Applicationsof Service Robot Project,’ which is directed by the New Energy

14

Y. Akiyama et al.

and Industrial Technology Development Organization (NEDO);
JSPS KAKENHI [grant number 26750121].

Disclosure statement
No potential conflict of interest was reported by the authors.

Note
1. Because of contractual obligations, the name, manufacturer,
and details of the assist algorithm cannot be mentioned, toavoid the evaluation of this particular robot.

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Notes on contributors
Yasuhiro Akiyama received the BE degree
in engineering from Tokyo Institute ofTechnology, Tokyo, Japan, in 2006, and the
MS and the PhD degree in engineering fromthe University of Tokyo, Tokyo, Japan, in 2008
and 2011, respectively. Since then, he has been
a postdoctoral researcher at Nagoya University,
Nagoya, Japan. His main areas of researchinterests are mechanical safety, human–robot
interaction, and manned space mission.
Yoji Yamada received a doctor degreefrom Tokyo Institute of Technology in 1990.
He had been with Toyota Technological
Institute, Nagoya, Japan, since 1983 andbecame an associate professor in the Graduate
School of the Institute. In 2004, he joinedIntelligent Systems Research Institute of
National Institute of Advanced Industrial andScience Technology (AIST). In 2009, he moved
to the Department of Mechanical Science and Engineering,
Graduate School of Engineering, Nagoya University as aprofessor. Dr Yamada is a member of Robotics Society of Japan,
and his current research interests include safety and intelligence
technology in human/ machine systems, their robotic sensing andcontrol.
Shogo Okamoto received MS and PhD
degrees in information sciences in 2007 and2010, respectively, from the Graduate Schoolof Information Sciences, Tohoku University.
Since 2010, he has been an assistant professor
at the Graduate School of Engineering, Nagoya
University. His research interests include
haptics and human-assistive technology.

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