Received 14 September 2022, accepted 1 January 2023, date of publication 16 January 2023, date of current version 25 January 2023.
Digital Object Identifier 10.1109/ACCESS.2023.3237763

Development of Dummy Based on Impedance
Properties of Human Soft Tissue Using a
Nonlinear Viscoelastic Model
JIAN LIU 1 , YOJI YAMADA1,2 , (Member, IEEE), YASUHIRO AKIYAMASHOGO OKAMOTO 4 , (Member, IEEE), AND YUMENA IKI5

3 , (Member, IEEE),

1 Department of Mechanical Systems Engineering, Nagoya University, Nagoya 464-8603, Japan
2 Toyota College, National Institute of Technology, Toyota 471-0067, Japan
3 Faculty of Textile Science and Technology, Shinshu University, Ueda 386-8567, Japan
4 Department of Computer Science, Tokyo Metropolitan University, Hino 191-0065, Japan
5 Denso Corporation, Kariya 448-0029, Japan

Corresponding author: Jian Liu (liu.jian@k.mbox.nagoya-u.ac.jp)
This work was supported in part by the Ministry of Economy, Trade and Industry, Japan, under Grant SSU53-437-sen46, Project Name:‘‘International Standardization of Safety Test Methods for Minor Hand Injuries Based on Actual Use Cases of Human-Collaborating
Machines;’’ in part by the Aichi Science and Technology Foundation, Japan, Project Name: R7 of the ‘‘Knowledge Hub Aichi.’’This work involved human subjects or animals in its research. Approval of all ethical and experimental procedures and protocols was
granted by the Ethics Committee of the Department of Engineering of Nagoya University under Approval No. 18-14.

ABSTRACT Securing human safety in a physical human–robot interaction (pHRI) has been extensively
studied to allow for the expansion of robotic applications. Dummies with the same impedance properties
as those of human soft tissues are suitable substitutes for the validation of the safety assurance of the
pHRI experiment. This study demonstrated the development process of dummies with high biofidelity.
A psychophysiological experiment was designed to replicate the clamping scenario, and the center of thepalm, thenar eminence, and forefinger pad were selected as three soft tissues of the human hand to be
impacted to obtain the dynamic response of the contact force. A nonlinear five-element viscoelastic model
was developed to quantify the viscoelasticity of the three soft tissues through curve fitting of the contact
force. Subsequently, three dummies were fabricated using a polyurethane resin material. The biofidelity ofthe dummies was examined via a parametric comparison with the soft tissues and curve comparisons to
examine whether the steady-state force and the dynamic response of the contact force were located within
the corresponding ranges enclosed by the calibration curves of the soft tissues. All three dummies showed
high biofidelity in the case where the steady-state force exceeded approximately 5 N, even though they havedifferent nonlinearity of elasticity from that of soft tissues.
INDEX TERMS Physical human–robot interaction, impedance property, viscoelasticity, dummy development, nonlinear viscoelastic model, human soft tissue.

I. INTRODUCTION

As robots are being applied in various fields, removal of thebarriers between humans and robots is being increasingly
investigated [1]. Thus, humans and robots would share aphysical environment, thereby inevitably increasing the posThe associate editor coordinating the review of this manuscript andapproving it for publication was Jingang Jiang
7782.

sibility of the physical human–robot interaction (pHRI) [2],[3]. Ensuring human safety in a human–robot coexistenceenvironment is currently one of the most important fields inrobotics [4]. Certain studies regarding safe pHRIs were basedon validation experiments conducted directly on human bodyparts [5], [6], [7]. To a certain degree, the experiments onhuman subjects sufficiently validated the effectiveness of the
pHRI framework; however, their safety must be guaranteed,

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

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J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

and an injury validation experiment (e.g., slight injury) is
prohibited and unattainable.
In recent years, the injury criteria for different human bodyparts in pHRI have been stressed in the ISO documentation [8], [9]. Owing to ethical prohibition, injury criteria were
estimated through substitutes of the human soft tissue, suchas porcine skin [10], [11], [12]. Dummy skins have been
considered as suitable substitutes for human soft tissue andused in injury validation experiments. The transferability ofa Hybrid III dummy from the automotive industry for use
in robotics was demonstrated by Oberer and Schraft [13].
Haddadin et al. [14], [15] investigated the influence of robot
mass and velocity on the injury indices using a Hybrid III
dummy and developed a head–neck dummy consisting of acompliant covering and spring. These studies mainly focusedon the head injury criterion, and the dummy had low biofidelity owing to a higher stiffness of the head–neck structure
than that of humans [16].
Therefore, for the validation of safety assurance of the
pHRI experiment, dummies that represent the same mechanical properties as those of the human soft tissue are primarily
imperative as suitable substitutes. This also indicates the possibility for large quantity production, convenience for experiments, and high biofidelity, thereby guaranteeing efficiency.
In a more advanced version, pressure/stress distribution sensors can be inserted to measure the pressure of different soft
tissue layers for further study [17], [18].
The biofidelity of dummies should be embodied in the viscoelasticity because the human soft tissue intrinsically possesses creep, stress relaxation, and hysteresis behaviors [19].
Viscoelasticity is crucial for quantifying the severity of injury
caused by pHRI, such as the allowable transient force andpower [9], [20] and the total transferred energy [11], [12].
To model the viscoelasticity of soft tissue, precise viscoelastic finite element models were proposed in previous
studies [21], [22], [23]. Nevertheless, the application of thesemodels to dummy development is difficult, thereby necessitating a simplified mechanical model that has a brief representation of elasticity and viscosity and is suitable formaterial production. An alternative would be such models
to be combinations of the Maxwell and Voigt bodies, whichhave been applied in many research studies [24], [25], [26],[27]. However, in the aforementioned studies, the method formeasuring the viscoelastic properties of soft tissue was basedon the force–displacement (or stress–strain) relation, in otherwords, an admittance property from the viewpoint of pHRI
modeling [28]. The impedance and admittance properties
describe the input–output properties of a dynamic system
and are inverse to each other, but the inverse operation isdifficult to carry out if the system possesses nonlinearity.
Most industrial robots are operated under motion control.
When the human soft tissue is clamped by an industrial
robot, the contact force is generated by the compressive displacement. Regarding the soft tissue as a dynamic system,
the compressive displacement and response contact force
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are the input and output, respectively. The impedance property is exhibited in most cases of the pHRI. Therefore, theimpedance property of human soft tissue is more applicable indummy development. Aso et al. [29] measured the impedance
properties of the human thigh in the frequency domain, but
no specific viscoelastic model was proposed. A linear fourelement viscoelastic model was used by Nakazawa et al. [30]to describe the impedance property of the human fingertip.
Our previous study [31] proposed a nonlinear two-layer
viscoelastic model for analyzing the mechanical property of
the human soft tissue. However, the derivation of an analytic
expression for the model was difficult, and the redundancyof optimal solutions for curve fitting was disregarded. These
noticeable points are addressed in this study by proposing anonlinear five-element viscoelastic model.
This paper proposes a development process of highbiofidelity dummies as substitutes for the human soft tissue
for hazardous pHRI experiments. The rest of the paper isorganized as follows: First, the human hand was selected as
the object of study, given that it is one of the body parts thatare most likely to be impacted in a human–robot collaboration
operation. A psychophysiological experiment was conducted
to measure the dynamic response of the contact force ofhuman hands under the worst case of pHRI: the clamping
scenario. Second, a nonlinear viscoelastic model was developed to quantify the viscoelasticity of the soft tissues of thehuman hand based on five viscoelastic parameters. Third,
based on the analysis results, dummies were fabricated usinga polyurethane resin material. Finally, the biofidelity of thedummies was examined via the following two approaches:a comparison between the viscoelastic parameters of thedummies and those of the soft tissues, and curve comparisons
to determine whether the steady-state force and the dynamic
response of the contact force of the dummies are locatedwithin the corresponding ranges enclosed by the calibration
curves of the soft tissues.
II. PSYCHOPHYSIOLOGICAL EXPERIMENTThe clamping scenario is the worst case of the pHRI, andthe dynamic response of the contact force generated in the
dynamic impact is stressed in ISO 15066 [9] as a factor
affecting human safety. Therefore, the psychophysiological experiment designed in this study aimed to establish amethodology for replicating a dynamic clamping scenario,
where the human hand was clamped by a fixed obstacle andan approaching end effector of a robot [32]. The dynamic
response of the contact force obtained through the impact
experiment was analyzed using the proposed nonlinear viscoelastic model, and the viscoelasticity of the human handwas quantified using five viscoelastic parameters. The analysis results were used for the dummy development.
The associated safety standard [9] proposed several regionsof the hand for validation. However, considering that clamping the dorsal side of the hand is hazardous, the palmar side
was considered, and the center of the palm, forefinger pad,7783

J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

FIGURE 1. Three contact areas of the human hand, i.e., the center of apalm, thenar eminence, and forefinger pad, which are marked by red
squares coinciding with the square contact surface of the impactor.
FIGURE 3. Structure of the device that mechanically secures the safety ofhuman hands.

FIGURE 2. (a) Aerial view of the experimental setup for replicating theclamping scenario. The red dash-dotted line represents thecentrosymmetric line of the hand-clamp device, which is also the impact
direction. The hand-clamp device is shown in Fig. 3. (b) The block diagram
describes the dynamic system, including the impactor and human hand in
the replicated clamping scenario in (c).

As shown in Fig. 3, a device to mechanically secure thesafety of human hands in the impact experiment was developed. Under normal working conditions, two magnets (component 3) cling to the steel block (component 4) to achieve
an attractive force of 100 N, and thus, the removable body(components 4 and 10–13) is kept close to component 1. The
plate (component 13) supports the hand, as shown in Fig. 2.
If the impact applied to the hand is sufficiently intense tocause the contact force to exceed the threshold value of 100 N,
the removable body breaks away from the magnets and slides
to component 9. Therefore, this device helps the human handto slide away from the collision to limit the maximum amountof contact force within 100 N.
As an additional safety measure, software monitored thecontact force applied via two force sensors (9313AA1, The
Kistler Group, Japan) mounted on the impactor and developed device.
B. EXPERIMENT DESIGN

and thenar eminence were chosen as specific areas in theimpact experiment, as shown in Fig. 1.
The Ethics Committee of the Department of Engineeringat Nagoya University (approval No. 18-14) approved thispsychophysiological experimental method.
A. EXPERIMENT APPARATUS

A manipulator (VS-050, DENSO WAVE Incorporated,Japan) was used to provide precise compressive displacement
and contact velocity. A six-axis force sensor (LFS100-50010-U, Nippon Liniax Co. Ltd., Japan) attached on the end
effector was used to measure the contact force. A squareimpactor with a size of 14 × 14 mm2 was attached on the
six-axis force. The impact orientation was organized along
the centrosymmetric line of the developed device to allow for
the application of normal forces, as shown in Fig. 2. The sixaxis force sensor can measure the contact force and wrench
in Cartesian coordinates; therefore, by checking the contact
force in the three axes, the normal direction of the contact
force was confirmed.
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The procedure of the experiment is as follows:(a) The dorsal side of the hand is maintained in contact withthe circular plate (component 13 in Fig. 3) of the device,as shown in Fig. 2, and the hand is kept relaxed to avoid
the potential influences of muscle activations.
(b) The impactor is gradually moved to clamp the specific contact area, and the compressive displacement isadjusted to meet the desired steady-state force.
(c) The impactor is moved a specified distance from thespecific contact area, e.g., 300 mm.
(d) The impactor is moved with the desired contact velocity
to impact the specific contact area, then stopped for 10 sat the compressive displacement determined in step (b).
(e) Step (c) is repeated.
The steady-state force mentioned in step (b) indicates thesteady-state phase of the contact force corresponding to thestress relaxation behavior of human soft tissue, as determinedby the contact force after the impactor is stopped for 10 s.
Additionally, after observing the contact force profile shownin Fig. 5, the 10 s period was chosen.
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J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

Human subjects determined the maximum steady-state
force by marking their thresholds for discomfort or unbearable pain due to repeated impact. As a result, the steady-state
force was set at 5, 10, and 15 N. Because the human subjects
felt pain as the steady-state force reached 20 N, the maximum
steady-state force was set at 15 N, which is below 20 N. The
contact velocities were set at 10 and 250 mm/s for quasi-staticand dynamic contacts, respectively [33].
As mentioned above, the manipulator was employed torealize precise compressive displacement and contact velocity. The entire dynamic system, including the manipulator anda human hand, is explained using a block diagram, as shownin Fig. 2(b). The controller, C (s), generates a reference
torque, τref , to move the end effector and resist the reaction
torque, J T F, where J and F denote the Jacobean matrix
and contact force, respectively. The difference between thecommand velocity, ẋcmd , and response velocity, ẋ, that is, theerror, e, is reduced to approximately zero. The end effector
impacts the human hand under a compressive displacement,x, and receives a response contact force, F, owing to theimpedance, Z (s), of the human hand. This motion controller
is a closed-loop system provided by DENSO WAVE Incorporated, and the precision reaches ±0.02 mm in the operationalspace motion tracking. In this study, the dummy development
necessitates the analysis of the impedance of the soft tissues
on the human hand, which is regarded as the property ofa dynamic system where the compressive displacement, x,
is the input and the contact force, F, the output.
Five healthy male human subjects participated in the experiments. Each contact condition involved three trials.

FIGURE 4. (a) FFT result of the contact force signal. The red line denotes
the frequency of 35 Hz. (b) Comparison among the raw data and filteredcontact force with a cutoff frequency of 35, 25, 15, and 5 Hz. The rightgraph shows details around the peak value timing of the left graph.

experiments. A nonlinear viscoelastic model was developed
to quantitatively analyze the viscoelasticity of the soft tissues
as well as the developed dummies. By using the model,
calibration curves of both the steady-state force and dynamic
response of the contact force were provided to examine thebiofidelity of the dummies.

C. EXPERIMENT RESULTS

The profile of the contact force variation is shown in Fig. 4(b).
A fast Fourier transform (FFT) was conducted to analyze thenoise in the contact force signal, and the result is shown in
Fig. 4(a). The noise appeared when the frequency was larger
than 35 Hz. The comparison in Fig. 4(b) indicates that if thecutoff frequency was lower than 35 Hz, the waveform of thecontact force signal was destroyed such that the sharp peakof the contact force was reduced and shifted. Therefore, thecontact force data was denoised using a second-order digital
filter with a cut-off frequency of 35 Hz. The filtered contact
forces of one subject’s palm are shown in Fig. 5.
Figure 5 shows that the tendencies of force variation weresimilar despite differences among the steady-state forces.
Specifically, a peak value of the contact force occurred when
the impactor reached the predetermined compressive displacement. The contact force then gradually decreased to a
constant value (the steady-state force). It can be inferred thatthe steady-state force is influenced by the stiffness or elasticity of the soft tissue, while the peak value of the response
force with its decline shows the viscosity.
III. NONLINEAR VISCOELASTIC MODEL

The dynamic response of the contact force of the threesoft tissues was obtained through the psychophysiological
VOLUME 11, 2023

A. CONVENTIONAL LINEAR VISCOELASTIC MODEL

The five-element Maxwell model is composed of two
Maxwell bodies and one Hookean spring connected in parallel, as shown in Fig. 6, with the definition of the elastic
parameters k1 , k2 , and k3 , and viscous parameters c2 and c3 .
The mathematical expressions of the five-element model are
as follows:(
vt 0 ≤ t < tp
x(t) =,(1)
vtp tp ≤ t




3
X

ki

 k1 vt + ci v 1−exp − t
0≤t<tp


ci


i=2





3 
X
ki
F(t) = k vt +
,
c
v
1−exp
−
t
×
1
p
i
p


c

i

i=2






ki


exp −
t − tp
tp≤t
ci
(2)

Fs = k1 x tp ,(3)
where x denotes the compressive displacement, v the contact
velocity, F the contact force, Fs the steady-state contact force,and tp the peak value timing (or stop timing).
7785

J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

FIGURE 5. Profiles of the contact force variation of one subject’s palm and fitting results by using the nonlinear model in equation (5). The contact
condition of figures from (a) to (f) is: steady-state force of 5, 10, 15, 5, 10, and 15 N, and contact velocity of 10, 10, 10, 250, 250, and 250 mm/s,
respectively. In (d)–(f), the graph on the right side shows the rising phase.

FIGURE 6. Linear and nonlinear five-element generalized Maxwell
models. In (a) and (b), parameters k1 , k2 , and k3 are defined as thestiffness of the three springs, and parameters c2 and c3 are the damping
ratios of the two dampers. In (b), the red arrows indicate that the
stiffness of the three springs is nonlinear.

Equation (2) shows that the variation in the response force
is divided into two parts based on the peak value timing tp ,which coincides with the rising and attenuation phases of thecontact force in Fig. 5. However, the rising phase of the curveof best fit by the linear model was convex and differed fromthat of the experimental results, as shown in Fig. 7. This linear
model fails to express the mechanical properties of humansoft tissue; however, it was first considered for fitting theattenuation phase.
B. PROPOSED NONLINEAR VISCOELASTIC MODEL

Even though the attenuation phase was perfectly matched,a set of generalized parameters that equally describe thecontact force in arbitrary contact conditions was intended
to be revealed. The relationships among five viscoelastic
parameters and contact conditions from one subject’s palm
are summarized statistically in Fig. 8 as an example.
7786

FIGURE 7. Comparison between the experimental data and curve fitting
result of the linear five-element model. The graph on the right side showsdetails of the rising phase of the contact force.

In Fig. 8(a), three elastic parameters were observed tohave an increasing trend with respect to the compressive
displacement. In this case, a square polynomial can perfectly
describe the relation for generalizing elastic parameters as
follows:
ki = γi x 2 (i = 1, 2, 3),(4)

where γi is a constant coefficient for ki . The fitting curve foreach elastic parameter ki was obtained by using Equation (4)and is shown in Fig. 8(a) for comparison.
Because the elastic parameter k1 only contributes to thesteady-state force corresponding to Equation (3), it is only
relative to the compressive displacement. The relationshipbetween k1 and the contact velocity was not considered. Further descriptions worthy of special mention cannot be madefor Figs. 8(b)–(e). Although a downward trend with respect
to the contact velocity was observed in Figs. 8(f) and 8(g),generalizing the relationship between the viscous parametersand contact velocity necessitates additional contact velocity
settings and was not considered.
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J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

FIGURE 8. Relationships between contact conditions and parameters k1 , k2 , k3 , c2 , and c3 .

Considering the nonlinearity of the elastic parameters,
a nonlinear five-element generalized Maxwell model was
obtained and is shown in Fig. 6(b). By inserting Equation (4),Equations (2) and (6) are rewritten as follows:




3
X

γ

γ1(vt)3+ ci v 1−exp − i v2 t 3
0≤t<tp


ci


i=2




3  
X
F(t) = γ vt 3+ c v 1−exp − γi v2 t 3 ×
,
i
1 p

p

c

i

i=2






γi


exp − v2 t 2 t − tp
tp≤t
ci
(5)

3
Fs = γ1 x tp .
(6)
Using the nonlinear five-element generalized Maxwell
model along with the trust region algorithm, the dynamic
response of the contact force was fitted and is presented inFig. 5. Consequently, according to the curve fitting results,
the optimized parameters (γ1 , γ2 , γ3 , c2 , and c3 ) of the threesoft tissues are depicted in Fig. 9, and for comparison, thoseof the three dummies are shown as well.
IV. DUMMY DEVELOPMENT

Based on the quantitative analysis of the impedance properties of the three soft tissues, three dummies were fabricatedusing a polyurethane resin material. TANAC Co., Ltd. provided manufacturing technology support. The polyurethane
resin was fabricated by two agents being mixed together andhardening. The principal agent and hardening agent consistedof a polyol and isocyanate, respectively. The two agentswere poured into a silicone rubber mold, and the bubbles
generated when stirring were eliminated by using a vacuum
VOLUME 11, 2023

environment. The mixed agents were then hardened in adrying furnace. The chemical reaction formula is shown in
Fig. 10.
The viscoelasticity of the polyurethane resin material was
determined only by changing the weight ratio of the principal
agent to the hardening agent: the larger the weight ratio,
the higher is the stiffness of the polyurethane resin. Basedon the steady-state elasticity of the soft tissues analyzed in
Section III, a weight ratio of 100:15 was selected for thedevelopment of the three dummies, with a Young’s modulusof 25 kPa. Dummies I, II, and III corresponded to the palm,
thenar eminence, and forefinger pad, with thicknesses of 15,
20, and 5 mm, respectively. The length and width of eachdummy were 150 and 120 mm, respectively. Dummy I is
depicted in Fig. 10(b).
The viscoelasticities of the dummies were investigated via
two approaches. The first approach entailed a comparison
between the viscoelastic parameters of the dummies andthose of the soft tissues, as described in Section IV-A. The
nonlinear model indicates that the mechanical property ofhuman soft tissues has a steady-state elasticity attributed
to the parameter γ1 and additional attenuated forces fromthe other four parameters. The second approach entailed
curve comparisons to determine whether both the steadystate force and dynamic response of the contact force of thedummies are located at the corresponding ranges enclosedby the calibration curves of the soft tissues, as described in
Sections IV-B and IV-C.
A. VISCOELASTIC PARAMETERS

Using the proposed nonlinear viscoelasticity model, the viscoelasticity values of the soft tissues and dummies were7787

J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

quantified using the five parameters: γ1 , γ2 , γ3 , c2 , and c3 .
The optimization results are shown in Fig. 9 for comparison.
As illustrated by Equation (6), only γ1 is related to thesteady-state elasticity. The magnitude of parameter γ1 ofdummy I was between the largest and smallest γ1 values ofthe palms, and the same result was observed in dummy II.
Dummies I and II show a steady-state elasticity representing the average elasticity of soft tissues. Parameter γ1 ofdummy III was larger than that of the forefinger pads; therefore, dummy III exhibits a large steady-state elasticity compared to the forefinger pads.
Parameters γ2 , γ3 , c2 , and c3 are related to the additional
attenuated force. Parameters γ3 and c3 of dummy II werelarger than those of the thenar eminences. According to thenonlinear model, a large c3 contributes to a large peak value inthe rising phase, and a large γ3 causes a smaller time constantof the attenuation phase. Consequently, a large peak value
and a rapid attenuation tendency appear in the contact force.
This coincides with the observation in Figs. 12(b) and 12(e).
Furthermore, parameters γ2 and c2 of dummy III were smaller
than those of the thenar eminences. A small peak value anda slow attenuation tendency appear, which is observed in
Figs. 12(c) and 12(f). Dummies II and III exhibit a viscositythat differs from that of the soft tissues.

B. STEADY-STATE ELASTICITY

A dummy that mimics the mechanical properties of humansoft tissue needs to first satisfy the steady-state elasticity.
Due to individual differences, the values of γ1 that wereobtained from different human subjects vary within a range.
The average values of parameter γ1 shown in Fig. 9 were used
to compute the steady-state force according to Equation (6).
Figure 11 shows the calibration curves representing the variation of the steady-state force with respect to the compressive
displacement. The light gray region enclosed by the leftmost and rightmost calibration curves denotes a range of thesteady-state force, herein referred to as the steady-state force
range.
To examine the biofidelity of the three dummies, thesteady-state forces were measured using the same experimental apparatus shown in Fig. 2(a) and are depicted in Fig. 11
for comparison. As shown by the error bars in Fig. 11, thetrial error for each of the three trials was small. The steadystate forces of dummies I, II, and III exceeded the curve ofthe largest γ1 when the contact started. Owing to the material
behavior, all three artificial dummies show higher elasticity
than that of the three soft tissues in a contact case of small
compressive displacements. As the compressive displacement increased, the steady-state forces of the three dummies
entered the steady-state force range. All three dummies show
low elasticity under a large compressive displacement.
The steady-state force of dummy III was located near theleft edge of the steady-state force range when the compressive
displacement was large, i.e., dummy III represents the case of
the largest γ1 .
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C. VISCOELASTICITY

The same impact experiments were conducted on the three
dummies to show the performance of the contact force variation. For brevity, the experimental results with the contact
condition of a steady-state force of 10 N are shown in Fig. 12.
The contact force of human subjects was depicted in a highly
generalized manner. According to Equation (5), the averagevalues of parameters γ1 , γ2 , γ3 , c2 , and c3 shown in Fig. 9
were regarded as a set of coefficients for computing thecontact force. Figure 12 shows the calibration curves representing the variation of the contact force with respect to time.
The light gray region enclosed by the uppermost and lowest
calibration curves denotes a range of the contact force, hereinreferred to as the force variation range. The curve comparison
for the dynamic response of the contact force is similar to thatfor the steady-state force.
At the beginning of the rising phase, the contact forcesof the three dummies exceeded those of the human subjects;
however, they entered into the force variation range at the endof the rising phase, as observed in Figs. 12(a)–(c). This is consistent with the observation that all three artificial dummies
show a higher elasticity when the compressive displacement
is small.
Dummies I and III exhibited a small peak in the contact force located in the force variation range, whereas
dummy II exhibited a large peak that almost reached theupper edge of the force variation range. This indicates thatdummy II has a higher viscosity when compared with that ofdummies I and III.
V. DISCUSSIONS
A. PERFORMANCE OF THE NONLINEAR MODEL

Principles for selecting a viscoelastic model were discussed
by Shellhammer et al. [34]. In particular, the viscoelastic
model should have as few terms as possible without losing the performance of fitting viscoelastic behaviors, thatis, the trade-off between the simplicity and accuracy of themodel. To meet this requirement, the curve fitting was also
tested on nonlinear three- and seven-element models. The
three-element model has one Maxwell body, whereas theseven-element model has three Maxwell bodies. As shown in
Fig. 13, the five- and seven-element models had the same
fitting capacity both in the rising and attenuation phases,
whereas the three-element model lost the fitting capacity
in the attenuation phase. The five-element model exhibits
advantages with respect to both simplicity and accuracy compared with seven- and three-element models, respectively.
For the rising phase of the contact force, introducing thenonlinearity of elastic parameters k1 , k2 , and k3 changes
the convexity of the rising phase to concavity, which wasobserved from the curve fitting results of the linear fiveelement model in Fig. 7 and the nonlinear five-element modelin Fig. 13. Both the rising and attenuation phases were wellmatched in trials on different contact areas under different
contact conditions, and the curve fitting results showed that
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J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

FIGURE 9. Optimized parameters of palms and dummy I, thenar eminences and dummy II, and forefinger pads and dummy III. The optimization isconducted by curve fitting using the nonlinear five-element Maxwell model in Equation (5). Contact velocities of (b), (e), and (h) are 10 mm/s, while
those of (c), (f), and (i) are 250 mm/s. The abbreviation ‘‘Subj. 1–5’’ is for ‘‘human subject 1–5’’ in the legend. For the legends of (a)-(c), see (c), (d)-(f),see (f), and (g)–(i), see (i).

FIGURE 10. (a) Chemical reaction formula of the principal agent (polyol),hardening agent (isocyanate), and polyurethane. (b) Photograph ofdummy I with length, width, and thickness equal to 150, 120, and 15 mm,
respectively.

the largest difference of approximately 2.3 N appeared at thepeak contact force in the experiment.
Given that the parameter γ1 is only related to the steadystate force Fs , it represents the elasticity of the human soft
tissue. A large γ1 value indicates high elasticity; for example, the palm of subject 4 is softer than that of subject 3,
as observed in Fig. 9(a). Additionally, an interesting phenomenon was observed in Figs. 9(a), 9(d), and 9(g) withthe magnitudes of the parameters γ2 and γ3 of the fivesubjects that had an identical variation tendency with that
VOLUME 11, 2023of the parameter γ1 . Specifically, the parameters γ1 , γ2 , andγ3 may be inherently related, which may beinterpreted as thatin different subjects, the peak value F tp of contact
 forcecorrelates with the steady-state force Fs , and F tp − Fs <(γ2 + γ3 ) x 3 tp based on equation (5).
The results indicate that parameter c2 is always larger
than c3 , while parameter γ2 is always smaller than γ3 . Given
that a small c2 makes the damper release the contact force
rapidly, a small c2 and a large γ2 provide a rapid attenuationof the contact force, which mainly contributes to the initialattenuation phase of the contact force, and vice versa.
Compared to the quasi-linear viscoelastic model proposedby Fung [19], our nonlinear model has advantages of physical significance, whereas the curve fitting performance forboth models is similar. The quasi-linear viscoelastic model isformed as a convolution operating on a relaxation function
and an instantaneous elastic response. It is a one-layer modeland has no ordinary differential equation form. By contrast,
the nonlinear model is easily understandable by the combination of nonlinear springs and dampers, such as in Fig. 6(b).
Corresponding to the equivalent impedance method, the proposed model can be transformed into multi-layer models,such as a two-layer model [31]. The multi-layer model serves
the development of multi-layer dummies, which results inthe possibility of a high nonlinearity that cannot be realized
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J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

FIGURE 11. Comparison between dummies and human soft tissues on the steady-state force. In (a)-(c), the steady-state forces of dummies were directly
measured, while those of five human subjects were computed using Equation (6) and mean values of parameters γ1 . The light gray region denotes thesteady-state force range. The abbreviation ‘‘Subj. 1–5’’ is for ‘‘human subject 1–5’’ in the legend.

FIGURE 12. Comparison between dummies and human soft tissues on viscoelasticity. The contact condition of (a)=(c) is contact velocity of 10 mm/s andsteady-state force of 10 N, while that of (d)-(f) is 250 mm/s and 10 N. In (a)-(f), contact force variations of the three dummies were obtained bymeasurement, while those of five human subjects were computed using the nonlinear viscoelastic model and mean values of parameters γ1 , γ2 , γ3 , c2 ,and c3 . The light gray region denotes the force variation range. In (d)-(f), the graph on the right side shows the rising phase. The abbreviation ‘‘Subj. 1–5’’
is for ‘‘human subject 1–5’’ in the legend.

FIGURE 13. Comparison between the curve fitting result of the nonlinear
three-, five-, and seven-element models. The graph on the right sideshows details of the attenuation phase of the contact force.

in one layer in practice. According to the illustration of
nonlinear springs and dampers, the proposed model can be
expressed by a block diagram which allows simulations of
the pHRI [35] to be easily realized. This is because, in thecase of an arbitrary compressive displacement, the proposedmodel can be expressed as ordinary differential equations that7790

make the establishment of a simulation easier and require lesscomputing time, compared to that of the convolution form of
the quasi-linear viscoelastic model.
In comparison to the previous study [31], the nonlinearityof stiffness is reasonably expressed by observing the fitting results of the attenuation phase; the proposed nonlinear
model can be expressed by analytical formulas, which provide convenience for curve fitting. Moreover, as reported by
Iki et al. [31], redundancy of the optimal solution existed in
the curve fitting because of two elastic parameters associatedwith the steady-state force. There is no redundancy problem
in this study because only γ1 is related to the steady-state
force, and the other four parameters are determined based on
the principle stated at the beginning of this subsection.
Generally, the average of the viscoelastic parametersindicates the mechanical property of human soft tissue. However, the largest value of the viscoelastic parameters is considered as the optimal value for the dummy development
owing to safety considerations. The dummies with larger
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J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

viscoelasticity contribute to a worse contact case wherein alarger contact force appears under the same contact situation,e.g., higher elasticity leads to a larger steady-state force, andhigher viscosity suppresses the attenuation of contact force.
B. BIOFIDELITY OF THE DUMMIESThis study demonstrates two approaches for testing the biofidelity of dummies: a parametric comparison and calibration by ranges. The two approaches exhibited reliability for
dummies I and II; however, the initial approach failed fordummy III. As indicated by the behavior of parameter γ1 in
Fig. 9(g), dummy III exhibited a larger steady-state elasticity
than that of the forefinger pads, whereas a similar steady-stateelasticity was observed in Fig. 11(c). This is because dummy
III possesses a lower nonlinearity of elasticity than that offorefinger pads when the steady-state force is below 5 N,
and parameter γ1 is increased in the case where the lower
nonlinearity part is used to conduct the curve fitting to optimize γ1 . Therefore, the parametric comparison is not suitablefor examining the biofidelity of the developed dummies.
Nevertheless, it demonstrates simplification and reliability
when the dummy has the same nonlinearity of elasticity as
the human soft tissue.
Considering the importance of the dynamic response of thecontact force as stressed by [9], additional discussions on thecalibration by ranges are presented. The calibration based on
the ranges is more intuitive because it transforms parameterγ1 to the calibration curves of the steady-state elasticity andparameters γ1 , γ2 , γ3 , c2 , and c3 to those of the dynamic
response of the contact force.
An elasticity range was accepted in the development of theHybrid III dummy for the automobile industry [36], and thebiofidelity of dummies is tested based on either the related
injury criterion [14], [15] or the frequency domain [29]. This
study employed a method that is similar to that describing
the range of the elasticity regarding the test method in aprevious study [36] and extended it to the ranges of elasticity
and viscosity. The biofidelity was assessed depending onwhether both the steady-state force and dynamic response of
the contact force of the dummies are located within a steadystate force range and a force variation range, respectively. The
two ranges were provided based on the individual differencesof the human subjects, as shown in Figs. 11 and 12.
All three dummies, particularly dummies I and III, lostthe biofidelity at the beginning of the contact. However,an elasticity exceeding that of the human soft tissue only
appeared when the compressive displacement was small, andthe steady-state force was under 5 N. Such a low biofidelity
does not affect the performance in safety-validation experiments where a large contact force or compressive displacement results in the loss of safety. Moreover, a convexity wasobserved in the rising phase of the dummies when the contact
velocity was 250 mm/s. the linear model may be also used forthe case of high-velocity impact to represent the rising phase.
Dummies exhibit a nonlinearity of elasticity that differsfrom that of soft tissues. However, the high biofidelity of
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all three dummies is embodied in the large compressive
displacement case, or when the steady-state force exceeds
approximately 5 N.
Dummy I represents the average viscoelasticity of the fivehuman subjects. This is observed from the fact that the steadystate force is located at the center of the steady-state force
range, as well as the dynamic response of the contact force.
In general, dummy I shows a more optimized standard forhuman palms.
Because dummy II shows a low steady-state force close
to the lower edge of the steady-state force range, it may
not be precise enough to monitor slight contact in the muchsmaller range of the pain onset level. However, its viscosity
compensates for such low elasticity and enhances the risingphase of its contact force at the upper edge of the force
variation range. Dummy II is expected to be used for studies
involving the total energy injury criterion [11], [12] becausesuch energy variation is calculated through an integral of thecontact force from 0 to that corresponding
to the maximumcompressive displacement x tp in Equation (1), that is, therising phase of the contact force.
Dummy III, with the largest steady-state elasticity, can help
to build a safe–side dummy, coinciding with the safety consideration stressed in Section V-A. Dummy III is a suitable
substitute for the forefinger pad in safety-validation experiments of the pHRI.
Moreover, dummy II has a higher nonlinear curvature thanthose of dummies I and III. This is attributed to the factthat the thickness plays a dominant role in the nonlinearityof the elasticity, and dummy II has the largest thickness(20 mm). This indicates that both the material characteristics
and the thickness of the dummy changes the elasticity, which
gives us more opportunities for developing dummies with themechanical property of high similarity to that of the humansoft tissue.
C. LIMITATION

The proposed experimental methodology cannot guarantee
high repeatability of the impact between the impactor andsoft tissue, because it would necessitate stricter fixation forthe hand. However, a stricter fixation would increase hazards
to the subjects and disregard ethical considerations.
Based on observations, it is inferred that the viscousparameters may have concealed relationships with the contact
velocity. However, owing to the lack of contact velocity settings, the nonlinearity of viscous parameters was not considered in this study. The impedance properties can be acquiredby modeling the contact force in a manner that is dependent
only on inputs, that is, using the compressive displacement
and contact velocity.
To the best of our knowledge, reports on the specificrequirements of the elasticity for dummy development are
rare. A specification, as well as characteristic similarity
requirement for developing dummies, requires statisticalresults based on numerous experiments on human subjects.
Because the number of human subjects, which was five in
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J. Liu et al.: Development of Dummy Based on Impedance Properties of Human Soft Tissue

the study, is small, it is difficult to propose a parametricspecification. Nevertheless, this study emphasizes the development process of dummies, which is expected to promote
quantifiable approaches to the development of dummies.
The biofidelity of the three dummies was embodied in
the displacement–force calibration. The dummies were developed for the safety validation experiment of pHRI, and they
are expected to be impacted in a pHRI environment instead ofhuman soft tissues. The contact force/pressure are regarded as
injury criteria to determine the safety level according to [9].
Therefore, the displacement–force similarity is sufficient forthe dummies to mimic the performance of generating contact
force/pressure. However, the thickness was not taken into
account for the above safety validation, and the strain–stresssimilarity was not adopted in this study.
VI. CONCLUSION

This study devised a development process of high-biofidelity
dummies as substitutes for human soft tissues used in hazardous pHRI experiments. A psychophysiological experiment was designed and conducted to obtain the dynamic
response force of human hands under a worst-case clamping
scenario. The center of the palm, thenar eminence, and forefinger pad were selected as the three specific soft tissues forthe impact experiment. Then, a linear five-element Maxwell
model was employed to fit the attenuation phase of the contact force variation. Consequently, a nonlinear five-element
Maxwell model was proposed based on the observation of thenonlinearity of elastic parameters. The curve fitting results
show unexpected performance in matching the rising phase of
the contact force. Using the proposed nonlinear viscoelastic
model, the viscoelasticity of the three soft tissues was quantified as five viscoelastic parameters.
Based on the viscoelasticity analysis of the three soft tissues, three dummies were fabricated using a polyurethane
resin material. The biofidelity of the dummies was examined
via parametric and curve comparisons. Based on the analysis
of comparisons, the high biofidelity of all three dummies is
embodied in the case where the steady-state force exceeds
approximately 5 N. Dummy I represents the average elasticity
and viscosity of the five human palms, and it shows a more
optimized standard for fabricating the dummy for palms.
Dummy III possesses the largest steady-state elasticity offorefinger pads to contribute to the fabrication of a safe–sidedummy. However, dummy II shows a higher viscosity thanthat of the thenar eminences, thereby failing to fabricate either
the standard dummy or the safe–side dummy.
Future studies will focus on improving the nonlinear
viscoelastic model by revealing the nonlinearity of viscous parameters and enhancing the biofidelity of dummies by regulating the nonlinearity of their elasticity toreach a high similarity based on the strain–stress calibration. Moreover, considering that the shape of bone influences the viscoelasticity of the soft tissue, the structure of
the human body parts will be considered for future dummy
development.
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ACKNOWLEDGMENT

The authors would like to thank TANAC Company Ltd., fortheir manufacturing technology support during the dummy
development.
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YOJI YAMADA (Member, IEEE) received the
Ph.D. degree from the Tokyo Institute of Technology. Since 1983, he has been with the Toyota
Technological Institute, Nagoya, Japan. In 2004,
he joined as a Leader with the Safety Intelligence Research Group, National Institute ofAdvanced Industrial and Science Technology(AIST). In 2009, he joined as a Professor with
the Department of Mechanical Science and Engineering, Graduate School of Engineering, Nagoya
University. In 2022, he joined as the President of the Toyota College, National
Institute of Technology.

JIAN LIU received the M.S. degree in mechanical and electronic engineering from Zhejiang
University, Hangzhou, China, in 2018. He iscurrently pursuing the Ph.D. degree in mechanical systems engineering with Nagoya University,
Nagoya, Japan. His current research interests include robotics, biomechanics, and especially physical human safety in human–robot
coexistence systems.

YUMENA IKI received the B.S. and M.S.
degrees from Nagoya University, Nagoya, Japan,
in 2019 and 2021, respectively.

VOLUME 11, 2023

YASUHIRO AKIYAMA (Member, IEEE) received
the B.E. degree in engineering from the Tokyo
Institute of Technology, Tokyo, Japan, in 2006, andthe M.S. and Ph.D. degrees in engineering fromThe University of Tokyo, Tokyo, in 2008 and 2011,
respectively. From 2016 to 2022, he was an Assistant Professor with Nagoya University, Japan.
He is currently an Associate Professor with Shinshu University. His main research interests include
mechanical safety, human–robot interaction, andbiomechanics.

SHOGO OKAMOTO (Member, IEEE) received
the Ph.D. degree in information sciences fromTohoku University, in 2010. From 2010 to 2021,
he was an Associate Professor with Nagoya University. He is currently an Associate Professor
with the Department of Computer Science, Tokyo
Metropolitan University. His research interests
include haptics, assistive robotics, human-centeredinformatics, and affective engineering.

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