SICE Journal of Control, Measurement, and System Integration, Vol. 11, No. 2, pp. 128–135, March 2018

A Three-Dimensional Skin-Shape Reproduction Mechanism for Evaluating
the Risk of Wounds When Using a Wearable Robot
Yuma SAKAI ∗ , Yasuhiro AKIYAMA ∗ , Yoji YAMADA ∗ , and Shogo OKAMOTO ∗Abstract : When using a wearable robot, the interaction force applied at the point of contact may cause skin injuries.
Therefore, validating the safety of wearable robots becomes important for their practical application. One method forevaluating contact safety at the fixation area of a wearable robot is to reproduce the relative motion and interaction force
that occur at the area on a dummy. However, humans have various shapes, and evaluation of various human skin shapes isrequired. This study aims to develop a three-dimensional skin-shape reproduction mechanism with which to validate thesafety of wearable robots. To that end, we have developed a simulation consisting of a cable-reinforced membrane that
estimates surface deformation to examine diﬀerent dummy shapes. Comparisons between device and simulation shapes
validated the process of reproducing human skin and the range of deformation and elasticity of the dummy.
Key Words : wearable robot, contact safety, skin shape.

Nomenclature
γ xy

Shearing strain of a membrane(ε x )k εyStrain of k-th cables in the x direction

εx

Strain of a membrane in the x direction

εyStrain of a membrane in the y direction

A

Sectional area of cables

Ai jIn-plane stiﬀness of a membrane

E

Young’s modulus of cables

H

Mean curvature

K

Number of cables in the x direction

L

Number of cables in the y directionp

Inner pressure

T kx

Tension of k-th cables in the x direction

T ly

Tension of l-th cables in the y directionuk

Displacement in the x direction of k-th cables in the x
direction

Vc

Strain energy of cables

vl

Displacement in the y direction of l-th cables in the y
directionl∗External workw

Displacement in the z direction

wkx

Displacement in the z direction of k-th cables in the x
direction

wly

Displacement in the z direction of l-th cables in the y
direction

Strain of l-th cables in the y direction

1. Introduction

Strain energy of a membrane

Vm

W

Department of Mechanical Science and Engineering, Nagoya
University, Furo-cho, Nagoya, Aichi 464-8603, Japan
E-mail: sakai.yuma@c.mbox.nagoya-u.ac.jp(Received June 22, 2017)(Revised October 3, 2017)

The importance of wearable robots is increasing in aging societies, as such robots are expected to improve workforce productivity and quality of life for people with disabilities [1]–[3].
Thus, the use of these robots has begun to spread from hospitals
and the rehabilitation field to society at-large. Whether for daily
life or industry, the use of wearable robots is likely to expand.
Wearable robots are attached closely to the human body andexert assistive torque and force through the area at which fixation occurs [4]–[6]; hence, the safety of wearable robots should
be considered carefully. For example, some studies have assessed conduction risks from wearable robots [7],[8] and examined human-robot interaction at the fixation area [9]–[11]. Further, the international standard ISO-13482:2014 [12] requiresconsidering the contact safety of wearable robots.
Previously, our group developed a method with which toevaluate the contact safety of a wearable robot by estimating therisk of skin injury. For obvious ethical reasons, safety tests cannot endanger humans; therefore, we adopted a dummy to evaluate the risk of skin injury. For our dummy, we utilized porcine
skin, which is a common substitute for human skin [13],[14] because of its proven durability against repetitive shear force [15]and similarity to human skin [16],[17]. To identify whether
skin injury occurs when using a wearable robot, we observed
the relative motion and interaction force applied by a robotic
cuﬀ during use [18],[19] and reproduced them using manipulator on the dummy skin [20],[21]. An overview of this safety
evaluation test is shown in Fig. 1.

c 2017 SICEJCMSI 0002/18/1102–0128 

SICE JCMSI, Vol. 11, No. 2, March 2018

Fig. 1

The wounds risk evaluation process.

Fig. 2

An example human shape (pelvis).

129

Fig. 4 A 3D skin-shape reproduction mechanism.

of this device and the corresponding processes to reproduce adesired shape.

2. Development of a Three-Dimensional (3D) SkinShape Reproduction Mechanism
2.1
Fig. 3 Safety test with variable-shape dummy.

It would be reasonable to determine the representative human shape and evaluate the wounds risk of that shape. However, stress concentration, which aﬀects wound risk, is probably
caused by the unevenness of human shape as shown in Fig. 2
and their relationship has not been quantified. Thus, it is difficult to determine a typical human form to represent the riskof wounds to the user of a wearable device. In addition, actual
wounds risk likely varies considerably because of individual
diﬀerences in people’s shapes [22]. Therefore, a transformabledevice that can mimic the variable features of human shape isrequired to evaluate the wound risk of wearable devices andanalyze the stress concentration caused by surface unevenness.
Several methods for reproducing a 3D shape have previously
been reported [23],[24]. A general method uses many pins
equipped under each surface element; the surface shape is controlled by changing the height of each pin, arranged in a grid.
However, this method requires that an actuator be equipped under each deformation area. The performance required of thedevice in this study is the control of shape and elasticity to emulate subsurface tissue. Hence, we employ a method that uses
cables and air pressure, which can easily control shape and elasticity with only a few control parameters (the tension of eachcable and air pressure).
Figure 3 depicts a safety validation test using a new device,in which a largely deformable membrane is manipulated using
numerical pressure. In this study, we demonstrate the capacity

Surface Deformation Mechanism

The 3D shape-reproduction mechanism consists of DC motors (RE30, Maxon Motor, Switzerland), cables, and a siliconrubber sheet, as shown in Fig. 4 (a). The tension in each cable iscontrolled individually by a corresponding motor. The rubber
sheet is inflated using air pressure injected from the bottom of
the deformation area. Shape reproduction with the developed
mechanism proceeds as follows: First, the deformable rubber
sheet is pressurized and inflated. Then, the rubber sheet is restricted by adding tension to each cable. Because the tensionof each cable can be set to a diﬀerent value, a variety of deformation patterns, including diﬀerent curvatures and local andasymmetric deformation, can be achieved.
2.2

Deformation Controller

A wiring diagram of the developed device is shown in
Fig. 4 (b). The desired tension of each cable is input into motor
drivers (ESCON 50/5, Maxon Motor, Switzerland) as the target
torque of each motor. The drivers control corresponding motors
using a PID algorithm. The actual motor torque is sent back to
a computer monitoring actual condition. The air pressure of therubber sheet is controlled by a regulator (ITV-1010312S, SMC
Corporation, Japan) in the same manner as the motor torque.
2.3

Deformation Ability of the Developed Device

2.3.1 Basic conditions
The developed mechanism was used to reproduce shapes.
The physical parameters, geometry, and experimental conditions of the device are shown in Fig. 5 and Table 1 with air pressure p and cable tensions T kx and T ly as input parameters. The

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SICE JCMSI, Vol. 11, No. 2, March 2018

Fig. 5 Cable-restricted membrane [25].
Table 1

Conditions of shape reproduction.

Air pressure p
Young’s modulus (Rubber sheet)
Young’s modulus (Cable) E
Poisson’s ratio (Rubber sheet)
Thickness of rubber sheet
Deformation area (x-direction)
Deformation area (y-direction)
Number of cables (x-direction) K
Number of cables (y-direction) L
Initial tension of cables T kx , T ly

Fig. 7 Reproduction of a shape with a large local deformation.

0.02 MPa
8.9 MPa
70.5 GPa
0.5
2.0 mm
90 mm
90 mm
9
9
1.0 N

Fig. 6 The result of shape reproduction.

other conditions reflect the mechanical parameters of the developed mechanism. The deformed shape is shown in Fig. 6. Owing to the restriction of the deformation applied by the cables,
the inflation of the center of the rubber sheet is especially restricted. Additionally, the developed mechanism must support
the dummy skin during wound risk evaluation. Therefore, thedeformable rubber sheet was more rigid than muscle [26]–[28].
2.3.2 Shape with large local deformation
Because of the unevenness of actual human skin, which includes local convexities, large deformations should be considered. Thus, to reproduce large local deformations, cable tensions were adjusted separately. Air pressure was set to 0.1 MPaand the cable tensions were 0 N in the deformed area (k = 4,
5, 6, l = 4, 5, 6) and 10 N elsewhere. The shape reproduced
using the new conditions is shown in Fig. 7, in which it can beobserved that only the central area of the rubber is significantly
deformed.
We then compared the displacements and mean curvature of
the rubber sheet in cross-section in the two conditions, calculating the displacement and curvature at every center point of
the wire grid in the x-direction. We employed a 3D scanner(Artec Space Spider, Artec 3D, Luxembourg) to measure theshape of the deformed surface. The mean curvature is the arithmetic mean of the principal curvatures at points in the region.
Curvature can be calculated as follows:

Fig. 8 Numerical analysis of a reproduced shape with a large local deformation.

H =

1



2  32
2 1 + (∂ x w)2 + ∂y w





2 
∂ xx w 1 + ∂y w
−2∂ x w∂y w∂ xy w + ∂yy w 1 + (∂ x w)2 .

(1)This study emphasized the reproduction of curvatures, because the risk of wounds is probably related to curvature. The
shear stress that occurs between a robotic cuﬀ and human skinincreases in areas of high curvature because of its concentration. Thus, wound risk possibly increases in such areas.
The comparison between displacement and curvature isshown in Fig. 8. In this figure, the curvature is negative when
the displacement is convex. From these results, we can confirm
our mechanism’s ability to reproduce large local deformations.
2.3.3 Asymmetric shape
Similarly, we conducted an experiment to confirm the reproducibility of asymmetric shapes. For asymmetric deformation,
the air pressure was set to 0.05 MPa and the cable tensions were
10 N in the strongly restricted area (k = 1, 2, 3) and 0 N else-

SICE JCMSI, Vol. 11, No. 2, March 2018131

Fig. 11 Device for the elasticity measurement.
Fig. 9Reproduction of an asymmetric shape.

in Fig. 11. The pressure was set to 0.1 MPa and the maximum
stroke of the contactor was 5 mm. The stress per displacement
was thus measured as 102 kPa/mm. The pressure applied tothe cuﬀ can be calculated experimentally by recording the interaction force applied when using a wearable robot [15]. Because the pressure (9.38 kPa) corresponded to a displacement of
0.09 mm considering the elasticity of the deformed surface, thedeformation of the rubber sheet can be ignored when the reproduced motion and force are applied to the device in safety tests.
Thus, we confirm that the device is suﬃciently rigid to model
human musculoskeletal tissue. On the other hand, the rigidityof relaxed muscle with a large deformation can be calculated as
approximately 5.5 kPa/mm from the strain-stress diagram [29].
Although the rigidity observed in the device was too high, theelasticity of the deformed area can be modified by changing thepressure or adding a softer surface sheet.

3. Deformation Estimation of Cable-Restricted Membrane
When conducting shape reproduction, the cable tension andair pressure, which reproduce the objective shape, should be
related to the surface shape to control the surface shape freely.
Therefore, deformation simulation is required to determine thevalue of such input parameters.
3.1

Fig. 10 The result of an asymmetric shape reproduction.

where. The asymmetric conditions, in which only the rightside of the rubber area is deformed, are shown in Fig. 9. We
found the displacements and mean curvatures to be similar to
those of the shape with a large local deformation, as shown in
Fig. 10. Given these results, we could confirm the reproducibility of asymmetric shapes.
2.4 Mechanical Properties of Reproducing Shapes
The deformed surface is comprised of a rigid base and elastic tissue that mimic the musculoskeletal system, as well as acovering surface that mimics skin or soft tissue. That is, thedeformed shape must reproduce the mechanical properties ofhuman bone, muscle, and fat. Therefore, in this study, we measured the elasticity of the deformed surface using a device consisting of a linear slider, contactor, and load cell. The linear
slider was fixed vertically from the fixed flame. Then, the loadcell and contactor were also fixed on the slider. The compression force applied to the contactor was measured by the loadcell. The device used for the elasticity measurement is shown

Fundamental Equations of the Deformation Analysis

In this simulation, we assumed that the cables touched themembrane constantly. In addition, for simplicity, the initial deflection, bending stiﬀness, friction coeﬃcient, and volume of
the cable were ignored. Strain-displacement relations of thecable-restricted membrane are shown in the following equations [30].
 2
⎧
⎪
⎪
∂u + 1 ∂w ,
⎪
⎪
=
ε
x
⎪
⎪
∂x 2 ∂x
⎪
⎪
⎪
⎪
⎪
 2
⎪
⎪
⎨
∂v 1 ∂w
(2)
⎪
+
=
,
ε
⎪
y
⎪
⎪
∂y 2 ∂y⎪⎪⎪⎪⎪⎪∂u ∂v ∂w ∂w
⎪
⎪
⎪
+
+
.
⎩ γ xy =∂y ∂x ∂x ∂yFurther, the strain-displacement relations of the cables in the xand y-axes are2⎧⎪∂uk 1 ∂wkx⎪⎪⎪
(ε x )k =
+
,
⎪
⎪
⎪
∂x
2 ∂x
⎨
(3)
⎪

2
⎪
⎪
 
⎪
∂vl 1 ∂wly⎪⎪
⎪ εy =+.
⎩l∂y 2 ∂yMoreover, the potential energy Π of the cable-restricted membrane is shown in the following equation [25],[30]:132

SICE JCMSI, Vol. 11, No. 2, March 2018

Π = Vm + Vc − W,(4)where Vm , and Vc are as follows: 
1
A11 ε x 2 + A22 εy 2 + A66 γ xy 2 + 2A12 ε x εyVm =2+2A16 ε x γ xy + 2A26 εy γ xy dxdy,
1
Vc =
2 k=1
K

(5)


2 ⎤
 ⎡⎢
∂wkx ⎥⎥⎥⎥
⎢⎢⎢
2
⎥ dx,
⎢⎣EA {(ε x )k } + T kx
∂x ⎦

⎡

 ⎤
L  ⎢

∂wly 2 ⎥⎥⎥⎢⎢⎢   2⎥⎥ dy,+⎢⎣EA εy l + T ly
∂y ⎦
l=1


W =p

wdxdy.

(7)

Next, the boundary conditions of the rectangle membrane towhich the edge of the membrane is fixed are⎧⎪⎪⎨ x = ±a : u = v = w = 0,(8)⎪⎪
⎩ y = ±b : u = v = w = 0,
and the displacement functions of the membrane, which fulfill
the boundary conditions, are assumed to be as follows [25]:
⎧
N
M 
⎪

⎪
nπ
mπ
⎪
⎪
⎪
(x + a) sin(y + b) ,(x,
Umn sin
u
y)
=
⎪
⎪
⎪
2a
2b
⎪
⎪
m=1 n=1
⎪
⎪
⎪
⎪
N
M 
⎪

⎪
nπ
mπ
⎨
(x + a) sin(y + b) ,v (x, y) =Vmn sin
⎪
⎪
⎪
2a
2b
⎪
⎪
m=1 n=1
⎪
⎪
⎪
⎪
N
M 
⎪

⎪
nπ
mπ
⎪
⎪
⎪
(x,
(x + a) sin(y + b) .
w
y)=
Wmn sin⎪⎪⎩2a2bm=1 n=1(9)
Similarly, the displacement functions of the cable that fulfill theboundary conditions are assumed as follows [25]:
⎧
N
M 
⎪

⎪
nπk
mπ
⎪
⎪
⎪
(x + a) sin(x),
Umn sin
=
u
⎪
k
⎪
⎪
2a
K
+1
⎪
⎨
m=1 n=1
(10)
⎪
⎪
N
M 
⎪

⎪
mπ
nπk
⎪
⎪
⎪
(x + a) sin
Wmn sin,⎪⎪ wkx (x) =⎩2aK+1
m=1 n=1

⎧
N
M 
⎪

⎪
nπ
mπl
⎪
⎪
⎪
(y)
(y + b) ,sin
Vmn sin
=
v
⎪
l
⎪
⎪
L+1
2b
⎪
⎨
m=1 n=1
⎪
⎪
N
M 
⎪

⎪
nπ
mπl
⎪
⎪
⎪
(y + b) .
(y)sin
Wmn sin
=
w
⎪
ly
⎪
⎩
L
+
1
2b
m=1 n=1(11)

By substituting strain-displacement relations (Eqs. (2) and (3))
and displacement functions (Eqs. (9), (10), and (11)) into
Eq. (4), we can express the potential energy using the unknown
constants Umn , Vmn , and Wmn . We can obtain the unknown constants by minimizing potential energy [25]. In this study, thedeformation of the cable-restricted membrane is obtained bydetermining the unknown coeﬃcients that minimize the potential energy at the specified air pressure. Therefore, the optimization problem is defined as follows:
min J = ΠFig. 12 Deformation analysis of the cable-restricted membrane.

(6)

(12)

where J is the objective function having Umn , Vmn , and Wmn
as decision variables. The Broyden-Fletcher-Goldfarb-Shanno(BFGS) algorithm, which is a quasi-Newtonian method, wasused for optimization [25].
3.2

Deformation Analysis of the Cable-Restricted Membrane
The result of the deformation simulation is shown in Fig. 12.
In this simulation, the condition was the same as in Table 1,
except for a Young’s modulus of 1.5 GPa. The diﬀerence occurred because a nylon cable, which was originally used in thedevice, was assumed in this simulation. As the boundary condition, displacement at the edge of the deformable area was set
to 0.

4. Validity Evaluation of the Deformation Analysis
The deformed shape was compared between the simulationand device to evaluate the performance and feasibility of using
simulation to obtain the input value of the device from surface
shape. The same input parameters (cable tension and air pressure) were used for each method.
4.1 Appearance Comparison
The shape reproduced with the 3D deformation device isshown in Fig. 13. As mentioned above, a nylon cable was usedin this experiment as same as the simulation. The eﬀect of thecable restriction was observed only around the center of the rubber sheet, as shown in Figs. 12 and 13. This result corroborates
the validity of the developed mechanism.
4.2 Displacement Comparison
For more detailed evaluation, we compared the displacementof cross-sections of both methods. The displacement in the zaxis of both methods was compared as in previous sections, theresult of which is shown in Fig. 14 (a). This comparison suggests that, despite the small diﬀerence between the two methods(especially around the area slightly separated from the center of
deformation), the diﬀerence is at most 0.7 mm, which is negligible when reproducing contact conditions between a wearable
robot and its human wearer. Therefore, we can conclude thatthe shapes of the deformation simulation and the reproduced
device shape matched at a level that would produce no practical problems.
4.3 Curvature Comparison
We similarly compared the mean curvatures of the two
shapes at the center of the wire grid along the x-direction, which

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SICE JCMSI, Vol. 11, No. 2, March 2018

Fig. 13 Reproducing shape with the developed mechanism.

Fig. 15 The shape reproduction process.

Fig. 16

Fig. 14

Displacement and curvature comparison between actual reproduced shape and result of deformation analysis.

is shown in Fig. 14 (b). In this result, the curvatures of the two
shapes nearly match, suggesting at the validity of the simulation
for the deformation of the cable-restricted membrane.

5. Discussion
The developed surface deformation mechanism and simulation are integrated into a 3D skin-shape reproduction system toimprove the method by which we evaluate the contact safetyof a wearable robot. In this system, shape reproduction is conducted as shown in Fig. 15. In this process, the optimizationof the design parameters (air pressure and cable tensions) is included.
First, as shown in Fig. 2, the shape of the skin at the test area
is measured or modeled. Then, using a deformation analysis
that calculates the surface shape from the pressure and tensionof each cable of the surface deformation mechanism, we cancalculate the input parameters of the surface deformation device
with an optimization process using sequential quadratic programming. Thus, an objective shape is reproduced by inputting
the optimized parameters into the developed mechanism. Then,

Cross-section of the reproduced shape.

the dummy skin is put on the reproduced shape and wound risk
evaluation can be conducted.
A cross-section of the reproduced shape during this process
is shown in Fig. 16. The dummy skin, which covers the deformed surface, is used not only to diminish the unevenness ofthe surface, which comes from the inflation of the rubber sheet
between cable restrictions, but also to modify the physical parameters of the skin surface. Although the device is capable ofmimicking the rigidity of the musculoskeletal system, surface
friction should be adjusted by using artificial skin. In addition,
the unevenness in the rigidity of actual humans, which comesfrom diﬀerences in tissue thickness, should be adjusted.
As mentioned above, the proposed device has suﬃcient deformation ability to reproduce the shape of uneven skin of thehuman. In addition, the deformation, which reproduced a basic shape, of the device and simulation matched. Although thesimulation should be improved to reproduce larger deformationand the shape reproduction system should be installed, the feasibility of the skin-shape reproduction process is demonstrated
in this paper.
In this study, we only focused on the eﬀect of parts where thewounds risk becomes particularly large, which is reflected inour reproductions. However, if required for evaluating woundrisks, we can adopt a wider reproduction area that consists ofcomponents with diﬀerent physical coeﬃcients by combining
smaller sections.

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6. Conclusion
In this study, we developed a 3D skin-shape reproduction
mechanism for use in evaluating the risk of skin injury aroundthe fixation point of a wearable robot. We confirmed the ability of this mechanism to reproduce the convexity and curvature of human skin. In addition, we have made suggestions forthe possibility of adjusting the rigidity of the surface to that ofvarious human tissue. Then, to control the surface shape, wedeveloped a simulator that estimates the surface shape from the
input parameters of the device (the pressure and tension of eachcable). The similarity in surface shape between the simulationand device suggest the simulation’s validity. Furthermore, we
introduced and optimized a flow with which to reproduce a desired shape and physical parameters corresponding to humancharacteristics. Thus, in this study, we have proposed a methodthat can consider human individuality in determining the risk ofskin injury and evaluated its validity. By using this method, theevaluation of the wound risk can be conducted in made to order.
This method helps not only to evaluate the risk of skin injury
of individuals but also to analyze the relationships between therisk of skin injury and cuﬀ motion, skin shape, and physical parameters, which are important for improving the contact safetyof wearable robots.

Acknowledgments
This study is based on the results of research and development of Japan Agency for Medical Research and Development (Project to Promote the Development and Introduction of
Robotic Devices for Nursing Care).
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Yuma SAKAIHe received the B.E. degree in engineering from
Nagoya University, Nagoya, Japan, in 2016. He is currently a master’s course student at Nagoya University.
His research interests are human-robot interaction, wearable robotics, and mechanical safety.

Yasuhiro AKIYAMAHe received the B.E. degree in engineering from Tokyo
Institute of Technology, Tokyo, Japan, in 2006, and the
M.S. and the Ph.D. degrees in engineering from the University of Tokyo, Tokyo, Japan, in 2008 and 2011, respectively. Since 2016, he has been an assistant professor
at the Graduate School of Engineering, Nagoya University. His main areas of research interests are mechanicalsafety, human-robot interaction, and manned space mission.

Yoji YAMADA (Member)He received a doctor degree from Tokyo Institute ofTechnology in 1990. He had been with Toyota Technological Institute since 1983 and became an associate professor in the Graduate School of the Institute. In 2004, hejoined Intelligent Systems Research Institute of National
Institute of Advanced Industrial and Science Technology(AIST). In 2009, he moved to the Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya
University as a professor. His current research interests include safety andintelligence technology in human/machine systems, their robotic sensing
and control.

Shogo OKAMOTO
He received M.S. and Ph.D. degrees in information sciences in 2007 and 2010, respectively, from the Graduate School of Information Sciences, Tohoku University.
Since 2016, he has been a senior lecturer at the Graduate
School of Engineering, Nagoya University. His researchinterests include haptics and human-assistive technology.

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