IEEE TRANSACTIONS ON HAPTICS, VOL. ***, NO. ***, *** 20201

Effect of Material Hardness on Friction
Between a Bare Finger and Dry and Lubricated Artiﬁcial Skin
Koki Inoue, Shogo Okamoto, Yasuhiro Akiyama and Yoji Yamada

Abstract—Understanding the tribological phenomena when ﬁngers
slide over soft surfaces such as skin is important for many practicalapplications. Therefore, this study analyzed the coefﬁcients of friction
for a bare ﬁnger sliding over artiﬁcial skin with different hardness
under dry and lubricated surface conditions. This study contrasts withprevious research that predominantly analyzed the contact between skinand hard surfaces or probes. Under dry conditions, the coefﬁcient offriction was constant for artiﬁcial skins that were harder than the ﬁnger
pad, irrespective of the normal force of the ﬁnger. However, the coefﬁcientof friction decreased with increasing normal force for softer artiﬁcialskins. When the surface of the artiﬁcial skin model was lubricated withmica, the coefﬁcient of friction exhibited normal-force dependence only
for soft artiﬁcial skins, similar to the observations under dry conditions.
This effect was due to the deformation friction; thus, the coefﬁcient offriction increased as the normal force increased. Conversely, when themodel was lubricated with TiO2 , the coefﬁcient of friction depended on
the normal force for all hardness levels. These ﬁndings provide insights
into the friction experienced during skin-skin or skin-soft material contact
under dry and lubricated conditions that can easily occur in daily life.
Thus, the results of this study can be useful for the development of skincare products or assistive robots involving human-robot contact.

I. I NTRODUCTION
UMANS regularly touch their skin using their ﬁngers. Therefore, it is important to understand the tribological phenomenathat occur when ﬁngers slide over soft surfaces such as skin for thedevelopment of products such as cosmetics. Speciﬁcally, this study
focuses on the relationships between the coefﬁcient of friction (cof),
the normal force, and the sliding speed when an artiﬁcial skin surface
is rubbed by a human ﬁnger.
Previous studies have investigated these relationships between skinand rigid probes. They found that the cof generally decreases withincreasing normal force at the point of contact between the humanskin and the rigid probe by a power of approximately −1/3 of thenormal force (e.g. [1], [2], [3], [4], [5], [6]). However, the normalforce dependence of the cof differs depending on the probes andother conditions used in the experiment. For example, Wei et al.
slid a polypropylene ball along the forearm and reported that cof
increases with increasing normal force of 0.1–0.9 N [7]. Conversely,
Naylor et al. reported a constant cof between the skin surface anda polyethylene probe of approximately 0.5 for a normal force range
of 2–7 N [8]. Furthermore, Egawa et al. measured a constant cof on
the forearm when the normal force ranged from 0.244–0.589 N [9].
These results [8], [9] support Amontons’ law that the cof does notdepend on the normal force.
Some studies have analyzed the cof under different surface lubrication conditions. For example, Adams et al. measured the friction
between the forearm and glass or polypropylene hemisphere probes
under dry and wet conditions. For both probes, the cof did not varywith normal force under dry conditions, whereas the cof decreased
with increasing normal force under wet conditions [10]. In the workof Dzidek et al., under dry conditions, the cof between a ﬁnger

H

Department of Mechanical Systems Engineering, Nagoya University, Furocho, Chikusaku, Nagoya 464-8603, Japan.
This study was in part supported by MEXT Kakenhi (17H04697).
This study was approved by the institutional review board of the School ofEngineering, Nagoya University (#15-12).

and a glass decreased as the normal force increased, whereas thecof between a ﬁnger and a smooth polypropylene surface increased
with increasing normal force. Furthermore, when the surface waswet with sweat, the cof decreased with increasing normal force forboth materials. In contrast, the cof between a ﬁnger and a roughpolypropylene surface was constant regardless of the normal force
under both dry and wet conditions [11]. Derler et al. measured thefriction between rough or smooth glass plates and human skin under
dry and wet conditions. They found that the cof did not depend on thenormal force in one case and decreased with the increasing normal
force in another case [12]. The effects of moisturization on the skintribological system have also been studied in [11], [13]. As mentioned
above, for skin-object contact, the effects of normal force on the cof
depend on the material and other conditions such as wetness androughness. Most of these studies employed a rigid probe to rub humanor artiﬁcial skin or utilized a ﬁnger on rigid surfaces. However, only
a few studies have examined the normal-force dependence of the cof
when a bare ﬁnger slides on a soft material such as skin.
Therefore, this study conducts experiments to measure the friction
caused by a ﬁnger sliding over the surface of artiﬁcial skin models
that imitate the surface asperity and seven hardness levels of humanskin. These experiments replicate the conditions of a ﬁnger touchingskin. We then investigate how the cof depends on the material
hardness, the normal force, and the sliding speed. Three surface
conditions are analyzed: dry skin and skin lubricated with mica andtitanium dioxide powders. The observed phenomena are explained
according to the normal-force dependence of the contact area, whichis unique to pressing with a ﬁnger and does not occur when pressing
with a rigid probe. The contact area is expressed as a power functionof the normal force, where the exponent changes with normal force
during ﬁnger pushing.
II. M ODEL FOR THE NORMAL - FORCE DEPENDENCE OF THE
COEFFICIENT OF FRICTION

A. Hertzian contact theory
When considering the contact area during ﬁnger touching, theHertzian contact theory is used, which describes the relationshipbetween the deformation, contact surface, and reaction force for two
elastic bodies in contact. This theory is based on various assumptions
such as the occurrence of a small strain when two elastic bodies
come into contact. Therefore, this theory is not strictly applicable tohuman ﬁngers but is often used to obtain a general understanding of
the tribological phenomenon.
Fig. 1 shows the state of a sphere imitating a ﬁnger pad touching
the elastic plane. When a sphere with a radius of Rf (imitating aﬁnger pad) pushes an elastic plane with a load fn , the contact surfaceof the two elastic bodies is a circle with a radius of r. Here, theapparent contact area A of the two elastic bodies is expressed as:
A

=
=

πr2
(
)2
2
3R 3
π
fn 3 ,
4E ∗(1)

where E ∗ is the effective elastic modulus given by the elastic moduli
and the Poisson’s ratios of the two elastic bodies. R is the effective

IEEE TRANSACTIONS ON HAPTICS, VOL. ***, NO. ***, *** 20202

2/3 power of the normal force fn ; i.e., the gradient of the graphin Fig. 2 is approximately 0.66. However, when the normal force
is small, the gradient is greater than 0.66, and when the normal
force is larger than approximately 1 N, the gradient is less than 0.66.
Therefore, during frictional rubbing with a ﬁnger, the exponent β is
not constant but can change with the normal force. Such nonlinearity
is a phenomenon peculiar to pushing with a ﬁnger and has not been
discussed in friction studies using a rigid probe.

Rf
Sphere(Finger)r

ObjectApparent contact area A (mm2)Fig. 1: Contact plane between a ﬁnger and a ﬂat surface as described by
Hertzian contact theory

1000

D. Coefﬁcient-of-friction model considering the normal-force dependence of the ﬁngertip
For the case where a ﬁnger slides on a surface, we propose a novel
cof model as follows:Ϭ͘ϲϲµ = afn bfn +c + dv,
100

10

1
0.01

0.1

10
1
Contact load ݂௡ (N)100

Fig. 2: Relationship between contact load and apparent contact area of
the ﬁnger pad, adapted from Kuilenburg [17]radius, which is determined by the radius of the two elastic spheres.
The effective radius R is equal to Rf if the elastic body pushed by
the ﬁnger is a plane.

(5)

where the power function of the normal force in the equation represents the change of gradient between the apparent contact area andthe normal force, as in Fig. 2. Here, v indicates the sliding velocity. In(5), the exponent is a function of the normal force expressed using
b and c. Using this exponent function, a phenomenon speciﬁc topressing with a ﬁnger is expressed. Here, a represents the magnitudeof the cof and depends on the material hardness, as described in(2). Furthermore, d is the component of speed dependence. In manycases, the cof monotonically increases or decreases with the sliding
velocity [4], [5], [7], [14], [18], [19] or exhibits a peak at a moderatesliding velocity depending on the condition [18]. Under the condition
used herein, the cof monotonically changed with the sliding velocity;
thus, we expressed the effect of velocity as a linear function. As in
the latter experiment, the effect of sliding velocity is signiﬁcant andthis component is necessary.
III. EXPERIMENTS

B. Coefﬁcient-of-friction model based on Hertzian contact theory
Adhesion friction is the dominant type of friction between the skinand a ﬂat surface [6], [14], [15]. This type of friction is based on
the concept that the adhesion of the real contact area Ar is broken
with interfacial shear strength τ . When the apparent contact area andthe real contact area are the same, the cof is simply modeled to be
proportional to the −1/3 power of the normal force fn as follows:
µ

=
=
∝

τ Ar
fn
(
)2
2
3R 3
fn 3 −1
τπ
4E ∗1fn − 3 .

(2)(3)

Thus, in this coefﬁcient-of-friction model, the cof is described as thepower function of the normal force:µ = αfn β ,(4)where α and β; i.e., the exponent of the normal force, are constantvalues. Note that in the ﬁnger contact, the real contact area is not thesame as the apparent contact area because of the ﬁnger ridges andsurface roughness [16].

A. Two-axial force and sliding speed measurement
The cof generated between the ﬁnger and the artiﬁcial skin andthe sliding speed during touching were measured using a two axial
force sensing unit assembled by the authors’ research group [20].
An overview of the device is shown in Fig. 3. The normal force
was measured using two uniaxial force sensors (9313AA2, Kistler,
Switzerland) installed in the lower part of the device, and the shear
force was measured using a uniaxial high-sensitivity force sensor(9217A, Kistler, Switzerland) ﬁxed to two metal pieces in the upper
part of the device. The signals from both the normal and shear
force sensors were ampliﬁed by two charge ampliﬁers (5073A2 and
5015, Kistler, Switzerland, nominal drifts: 0.005 N/s and 0.0003 N/s,
respectively). We did not use low-pass ﬁltering functions of theampliﬁers. Fig. 5 shows examples of raw force data. Then, the cof
was calculated as the ratio of the shear force to the normal force.
Finger movement was measured using two wired encoders (MTL12, MTL Co., Japan) by winding a wire attached to the encoders
around a ﬁnger. The resolution of ﬁnger movement measurement isapproximately 0.01 mm. The sampling frequency was set to 2 kHz
for the two axial forces and the ﬁnger movement measurements.
B. Artiﬁcial skins used in the experiment

C. Normal-force dependence of the contact area
Fig. 2 shows the simpliﬁed double-logarithmic graph summarized
by Kuilenburg [17], which describes the experimental relationshipbetween the normal force and the apparent contact area when aﬁnger is pressed against a rigid surface. According to Hertzian contact
theory, as in (1), the apparent contact area A is proportional to theArtiﬁcial skins (Bioskin, Beaulax Ltd., Japan) with seven levelsof hardness were employed, with the hardest level being 1 and thesoftest level being 7. All skins were 5 mm thick and their surfaces
were covered with a thermoplastic polyurethane thin ﬁlm, the surface
asperity of which simulates that of human skin (roughness value, Ra :7.6±1.9 µm [21]).

Artificial skin
(Bioskin, Beaulax)

Leaf spring

3

Shear force (N)Linear encoder(MLS-12, MTL)

3

Normal force (N)IEEE TRANSACTIONS ON HAPTICS, VOL. ***, NO. ***, *** 2020

2
1
0
0

60 mm

5
Time (s)

10

3
2
1
0
0

5
Time (s)10Fig. 5: Raw data of normal and shear forces
Shear force sensor Normal force sensor(9217A Kistler) (9313AA2 Kistler)

instructed to slide their index ﬁnger as if feeling the quality ofthe material. There were no instructions regarding the ﬁnger speed
and force. Seven types of skin model were tested in a randomizedorder, and each hardness level was tested three and ten times for dry
and lubricated conditions, respectively. There were fewer participants
assigned to test the lubrication conditions than those for the dry
conditions. In order to increase the reliability of the data, thelubrication experiment was performed 10 times. Before each trial,
participants’ ﬁngers and the material surfaces were wiped with a dry
cloth. The experimental setup is shown in Fig. 4.

100 mmFig. 3: Measurement setup

D. Participants
Eleven males aged 20–29 participated in the experiment under dry
conditions and eight males and one female aged 20–29 participated in
the experiment under lubrication conditions. All participants provided
informed consent and were unaware of the objectives of the study
before the experiments.
Fig. 4: Experimental setup

E. Data processing

The shore AO hardness, which is a scale for soft rubbers, of theartiﬁcial skins was measured using a durometer (GS-721N, Teclock,Japan) in accordance with ISO 7619-1. An artiﬁcial skin was placedon a hard plane and the needle of the durometer was placed in static
contact. A load of 200 gf was applied to the artiﬁcial skin, and thedurometer reading was taken immediately after application of theload. This measurement was performed ﬁve times for each material
and the median value was adopted. The hardness of each participants’ﬁnger was measured by the same process. Table I shows the resultof the measurement. The value for the ﬁnger pad shows the averageand standard error among all participants.
The experiment was conducted under three lubrication conditions:dry (no lubrication) and lubrication with two types of powder. Mica(mean particle size: 2 µm) and titanium dioxide (TiO2 , mean particle
size: 0.25 µm) were used as the lubricants, which are commonly usedin cosmetic products. Mica reduces friction and TiO2 powder adheresto the skin.
C. Task
Participants rubbed the surface of the artiﬁcial skin attached tothe measurement instrument for 10 s in a single trial. They were
TABLE I: Hardness of artiﬁcial skin models and human ﬁngers.
Shore AO hardness values conforming to ISO 7619-1. The
unit is arbitrary. Higher values indicate harder materials.
Hardness lv.
Hardness
Hardness lv.
Hardness

1
AO 19.1
5
AO 9.6

2
AO 18.0
6
AO 7.8

3
AO 16.9
7
AO 3.2

4
AO 11.0
Finger
AO 9.0±2.1

Before the main signal processing, we removed a linear drift
component that was deﬁned by the zero force levels before and aftera trial. To analyze the kinetic friction, only data when the ﬁnger
was clearly sliding on the skin model were used for the analysis.
Speciﬁcally, only the observation points where both the normal force
and shear force were at least 0.05 N and the sliding velocity v wasat least 20 mm/s was used.
The relationship between µ, fn , and v was approximated in theform of (5) for each trial using Curve Fitting Toolbox of MATLAB
2019a (e.g., Fig. 6). The success or failure of the ﬁtting was judged
on the basis of the determination coefﬁcient R2 ; trials in which R2
was less than 0.35, which was determined arbitrarily, were excluded
from the analysis due to low accuracy. For dry condition, in termsof the mean R2 value, among the hardness levels, the highest was
R2 = 0.52 for hardness level 1 and the smallest was R2 = 0.46
for hardness level 4. Among the participants, the mean R2 ranged
0.42–0.56. For mica lubricated condition, among the hardness level,
the highest was R2 = 0.63 for hardness level 6 and the smallest
was R2 = 0.50 for hardness level 1. Among the participants, themean R2 ranged 0.42–0.70. For TiO2 lubricated condition, among
the hardness level, the highest was R2 = 0.55 for hardness level 5
and the smallest was R2 = 0.47 for hardness level 1. Among theparticipants, the mean R2 ranged 0.40–0.56.
The variation of ﬁnger motions was substantial as follows. Evenfor the ﬁve trials with the smallest variations of normal force or
speed, the mean and standard deviation of the range (difference
between the maximum and minimum values) of the normal force
was 1.31±0.41 N, which was observed for a trial for hardness level4, and those of the sliding speed was 108±14.3 mm/s for hardness
level 7 of the dry condition. These ranges are comparable to thoseduring tactile exploration observed in a previous report [22].

IEEE TRANSACTIONS ON HAPTICS, VOL. ***, NO. ***, *** 2020

ሺܽሻ

ሺܾሻ

4

independent of the normal force. In the case of softer materials (levels
5–7), the cof was dependent on the normal force.
d was positive for all materials, and there were signiﬁcant differences between harder materials (levels 1 and 2) and softer materials(levels 6 and 7). Under mica-lubricated conditions, the speed dependence of the cof was larger for soft materials. However, this speed
dependence was smaller compared to that under dry conditions.
C. Results under TiO2 -lubricated conditions

Fig. 6: Data plots and ﬁtting results showing the relationship between
coefﬁcients of friction and normal force. Red dots are observed
data. Colored curved planes are the ﬁtting surface. (a) R2 = 0.60.
The power of fn is positive. (b) R2 = 0.36. The power of fn isnegative.

One-way ANOVA was conducted to determine the statistical differences among the seven levels of material hardness for a, b, c, andd. p = 0.05 was used to determine the statistical signiﬁcance, above
which every hardness pair was tested with no adjustment of p. Notethat µ values were not statistically compared among the hardness
levels because they do not depend on only the material hardness but
also depend on fn and v.
IV. R ESULTS
The means and standard errors of µ and a to d are shown in Fig. 7
for each lubrication condition and hardness level. Here, µ was simply
computed as a ratio of the shear to normal forces. The statistics are
summarized in the supplemental material.
A. Results under dry conditions
Softer materials generally exhibited greater a values, which isconsistent with (2), where the cof is proportional to the negative
power of the elastic modulus.
The b and c values must be analyzed in conjunction because theyboth determine the normal-force dependence of the cof. According to
Fig. 7, both b and c were almost zero for hardness levels 1 to 3; i.e.
for material that was harder than the ﬁnger. The cof did not dependon the normal force in these cases. For material that was comparable
to or softer than the ﬁnger pad, b was negative and c was positive.
As the normal force increased, the power function decreased, and thecof decreased.
d was signiﬁcantly positive for all hardness levels; as the sliding
speed increased, the cof increased. Also, d was relatively small for
harder materials (levels 1–3) but relatively large for softer materials.
These results suggest that the speed dependence of the cof is greaterfor softer materials, although this was only partly supported by thestatistical results.
B. Results under mica-lubricated conditions
a increased with decreasing material hardness, except for hardness
level 1. Under mica-lubricated conditions, the cof is proportional
to the negative power of the elastic modulus. Also, mica exhibits
lubrication properties because the a and cof values are smaller thanthose under dry conditions.
b was negative only for the softest material (level 7) and almost
zero for all other hardness levels. The values of c were close to zerofor harder materials (levels 1 and 2) and positive for softer materials(levels 5–7). In the case of harder materials (levels 1, 2, and 4),
the exponent of the normal force was close to zero and the cof was

For the softest material (level 7), a was larger than those forthe other materials. For the other hardness levels, the cof exhibited
negligible dependence on the material hardness under TiO2 -lubricatedconditions.
b was negative and c was positive regardless of the material
hardness, except for hardness level 4. The cof depended on the normal
force for all hardness levels, in contrast to dry and mica-lubricatedconditions, where it depended on the normal force only for softer
materials.
The d value was small for all materials and there was no signiﬁcantdifference between materials.
V. D ISCUSSION
Under dry conditions, the cof was independent of the normal
force when the artiﬁcial skins were harder than the ﬁnger pad. The
adhesion friction between a ﬁnger and a plane is proportional to
the real contact area Ar . During contact between a rough surface
and a sphere, the real contact area is proportional to the normal
force fn due to the effects of surface asperities [23]. Furthermore,
it is possible that the real contact area is proportional to the normal
force even during contact between a ﬁnger and human skin due tothe effects of ﬁngerprints and obvious topographical features on theskin [10]. Therefore, the normal-force independence of the cof canbe understood using the following equation:
µ

=
∝
=

τ Ar
fn
τ fn
fn
τ,

(6)

where the real contact area Ar is proportional to fn ; thus, the cof
related to adhesion is constant. On the other hand, during complete
contact between a ﬁnger and a surface that is as soft as or softer thanthe ﬁnger pad, the real and apparent contact areas almost coincide dueto the small amount of interfacial water acting as an adhesive liquid
bridge [13], [24]. Hence, for softer materials, (5) is valid and the cof
depends on the normal force; i.e., it decreases as the normal force
increases. As discussed above, the normal-force dependence of thecof depends on the material hardness. Speciﬁcally, when rubbing asoft surface with a ﬁnger, the normal-force dependence of the contact
area should be considered, which is a phenomenon unique to pushingwith a ﬁnger.
Under TiO2 -lubricated conditions, the cof depended on the normal
force regardless of the material hardness, unlike under dry conditions.
This may be because ﬁne particles of TiO2 adhere to the ﬁnger
or the artiﬁcial skin model and ﬁll the grooves; therefore, the realcontact area might coincide with the apparent contact area even when
the object is hard. Hence, the true contact area would change inproportion to the power of the normal force, as shown in Fig. 2, andthe cof would depend on the normal force according to (5).
Under mica-lubricated conditions, the cof was independent of thenormal force for harder artiﬁcial skins (levels 1–4). Furthermore,unlike the above cases, the cof did not depend on the normal force

IEEE TRANSACTIONS ON HAPTICS, VOL. ***, NO. ***, *** 2020

1
0.5

Hard

2

3

4

5

6

Hardness Level

coefficient of friction

coefficient of friction

coefficient of friction

1.5

1

TiO2-lubricatedcondition

Mica-lubricatedcondition

Dry condition

0

5

1.5
1
0.5
0

7

1
Hard

Soft

2

3

4

5

6

Hardness Level

1.5
1
0.5
0

7
Soft

1

2

3

4

5

6

Hardness Level

Hard

7
Soft

Ύ
Ύ

ΎΎ

1

1

0.8
0.6

1.2

ΎΎ

1

Ύ

0.8
0.6

ΎΎ

0.4
0.2

0.4
0.2
0

ΎΎ

a (N-1)

1.2

1.2

a (N-1)a (N-1)

Ύ

1

2

3

4

5

6

Hard

Hardness Level Soft

0

7

0.4
0.2
1
Hard

2

3

4

5

6

Hardness Level

0

7

1

2

Hard

Soft

3

4

5

6

Hardness Level

7
Soft

1

ΎΎ

1

1

ΎΎ

0.8
0.6

ΎΎ

0

0

-0.5

-0.5
-1

0.5

0.5

b (N-1)Ύb (N-1)b (N-1)

0.5

1

2

3

4

5

6

-1

7

-0.5
1

2

3

4

5

6

-1

7

1

2

Hard

Hardness Level Soft

3

4

5

6

7

1.5

1.5

Ύ

Ύ
ΎΎ

Hardness Level Soft
Hard

Hardness Level Soft
Hard
1.5

0

Ύ

1

0.5

2

Hard

Hardness Level Soft

0.5

5

6

7

-0.5

4
2
0
2

3

4

1

2

3

4

5

6

7

Hard

Hardness Level Soft

5

6

7

Hardness Level Soft
Hard

Ύ

4

Ύ
ΎΎ

2
0
-2

-0.5

1

2

Hard

Hardness Level Soft

3

4

5

6

7

1

2

Hard

Hardness Level Soft

[ʹ10-3]6[ʹ10-3]
6

ΎΎ

1

0

d (s/mm)4d (s/mm)d (s/mm)3Ύ[ʹ10-3]
6

-2

Ύ

0
1

Ύ

Ύ

0.5

0
-0.5

1

ΎΎ

c

c

c

1

4
2
0

1

2

3

4

5

6

7

Hardness Level Soft
Hard

-2

3

4

5

6

7

Fig. 7: Means and standard errors of cof, a, b, c, and d for each hardness level of the artiﬁcial skin model. The orange and blue bars are signiﬁcantly
positive and negative values tested by the t-test with p < 0.05, whereas the white bars are not statistically different from zero, *: p < 0.05,**: p < 0.01. Left, middle, and right columns represent dry, mica-lubricated, and TiO2 -lubricated conditions, respectively.

IEEE TRANSACTIONS ON HAPTICS, VOL. ***, NO. ***, *** 2020

TABLE II: Cof when the normal force increases

Dry
Mica
TiO2

Material is harderthan a ﬁnger
Constant
Constant
Decrease

Material is softer
than a ﬁnger
Decrease
Increase
Decreaseand b was almost zero for softer artiﬁcial skins; b was negative only
for the softest skin model (level 7). For the majority of hardness levels(levels 1–6), the exponents of the normal force were zero or positive.
When the exponent is negative, adhesion friction is dominant; whenthe exponent is positive, deformation friction is dominant [14]. Hence,mica diminished the effect of adhesion friction, except for the softest
material.
The above-mentioned tendencies are summarized as in Table II.
VI. C ONCLUSIONS
Experiments were conducted to determine the effects of material
hardness on the friction between a human ﬁnger and artiﬁcial skinmodel. Under dry conditions, when the artiﬁcial skin model was
harder than a ﬁnger, the cof did not depend on the normal force.
Conversely, when the skin model was as soft as, or softer thana ﬁnger, the cof decreased with increasing normal force. Whenthe surface was lubricated with mica, which reduces friction, thecof again depended on the normal force for softer materials. Thisdependency was mainly caused by the deformation friction, whereby
the cof increases as the normal force increases. Under TiO2 -lubricatedconditions, normal-force dependence was observed even with hardermaterials. These differences in normal-force dependence might bedue to the lubrication conditions affecting the real contact area or
the dominant friction system. The hardness dependence of the cof
varies according to the surface conditions. Therefore, the relationshipbetween the apparent contact area and the normal force should beconsidered when determining the friction experienced by a ﬁnger
touching soft materials, especially when the materials are softer
than the ﬁnger. Furthermore, even when the material is harder thanthe ﬁnger, it should be considered depending on the lubrication
conditions. These ﬁndings may provide insights into the friction
experienced by a ﬁnger rubbing a soft surface such as skin andadvance the design of products such as assistive robots involving
human-robot body contact as well as skin care and cosmetic products.
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[2] R. K. Sivamani, J. Goodman, N. V. Gitis, and H. I. Maibach, “Friction
coefﬁcient of skin in real-time,” Skin Research and Technology, vol. 9,
no. 3, pp. 235–239, 2003.
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