Sato et al. Robomech J (2017) 4:19
DOI 10.1186/s40648-017-0087-1

Open Access

RESEARCH ARTICLE

Wearable finger pad deformation
sensor for tactile textures in frequency domain
by using accelerometer on finger side
Shunsuke Sato*, Shogo Okamoto, Yoichiro Matsuura and Yoji Yamada

Abstract
In this study, we set out to develop a method for estimating the fine and fast shear deformation of a finger pad, thatis, the palm side of a fingertip, as it scans the surface of a material. Using a miniature accelerometer, we measured theacceleration at the radial skin, the deformation of which is accompanied by the shear deformation of the finger pad.
Using a transfer function, as specified in a separate experiment, between the pad and side of a finger, we estimatedthe shear deformation of the finger pad in the frequency domain. A comparison between an estimate based on theaccelerometer and another based on a precise force sensor for the tangential component of the interaction force
between the fingertip and material surfaces showed that the estimation accuracy was sufficient for frequencies inexcess of approximately 20–50 Hz and for skin deformation above 10−6 m. Our technique merely requires that anaccelerometer be attached to the side of the fingertip, which allows active texture exploration. These estimates ormeasurements of the finger skin deformation caused by touching materials will help us to comprehend the relation‑
ships between material surfaces and the resulting texture sensations.
Keywords: Tactile sensor, Finger pad, Skin deformation
Introduction
In general, the physical properties of material surfaces
characterize their tactile textures. From this standpoint,
many research groups have investigated the relationships between different types of material properties andthe textures that are perceived by touching them. Suchan approach has significantly contributed to industries
involved with clothing [1]. In contrast, texture perception arises as a result of the skin deformation caused by
the interaction between the finger and material. Hence,
the mechanical properties of the fingertips of individuals influence the textures perceived by those individuals.
A typical example is the moisture content of a fingertip
influencing the friction-induced pleasantness of the surface of a material [2]. Therefore, many researchers haveattempted to link the information related to the deformation of a fingertip and the perceived texture when a finger*Correspondence: sato.shiyunsuke@c.mbox.nagoya‑u.ac.jp
Department of Mechanical Engineering and Science, Nagoya University,
Chikusa‑ku, Nagoya, Japan

touches a material. However, the measurement of a finger
pad’s deformation is not easy because the finger pad is incontact with the material surface and is not exposed toany sensing devices. In this study, we developed a technique for estimating the fast and fine lateral deformationsof a finger pad when a finger actively explores the surface
of a material. To the best of our knowledge, such techniques have not previously been reported.
Many research groups have measured information related to the deformation of a fingertip by using a
range of approaches. Nonetheless, observation througha transparent material such as glass is a very distinctive
way of directly measuring deformation [3, 4]. In principle, this method is applicable only to transparent material. Another approach involves using the differential
outputs of two accelerometers [5] to measure the macroscopic deformation of a finger pad. One accelerometer is attached to the dorsal side of the fingertip andanother is fixed to the surface of the material contacted
by the fingertip. Provided there is no slippage, the difference between the values measured with these two© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license,
and indicate if changes were made.

Sato et al. Robomech J (2017) 4:19

accelerometers will be the acceleration of the deformation of the finger pad. However, this technique cannot beapplied to a finger sliding on the surface of a material.
To date, several indirect measurement methods havebeen employed to overcome the difficulties and limitations of direct measurement. For example, a number of
researchers have exploited the propagation of skin deformations. Any high-frequency deformation at a point on
the skin is transferred to the adjacent elastic skin tissues. Bensmaïa et al. attempted to measure these highfrequency components as a finger was sliding over thesurface of a material by using a Hall-effect transducer
attached to the finger [6]. Similarly, the propagatedvibratory information was acquired using a laser Doppler velocity meter [7, 8], microphones [9], accelerometers [10], and PVDF films [11] attached to the finger close
to the tip, as well as a microphone [12] on the forearm.
Although these vibrations in the adjacent skin originate
from the vibratory deformations of the finger pad, thesemethods were not to measure the deformations of theindividual finger pad.
Many researchers measured the interaction force
between the fingertip and material surfaces as reliable information related to the finger pad’s deformation
because the forces cause the skin to deform [13–19]. For
example, Wiertlewski et al. [13] precisely measured theinteraction forces when a material slid beneath a fingertip. However, they all measured interaction forces thatwere distinct from the skin deformations.
Given the abovementioned background and related
studies, this study set out to develop a technique for estimating the lateral deformation of a finger pad and which
could be applied to situations involving active touching.
We used the propagation of skin deformation, whereby
the lateral deformation of a finger pad leads to otherdeformation of the skin at the radial side of the fingertip.
The skin deformation at the radial side can be measured
by an accelerometer designed for the measurement ofsmall and fast displacements. This study is based on ourprevious publications [20, 21] in which we introduced
the principles of measurement and the linear causality
between the deformations of the pad and the radial sideof a finger. In this paper, we also assess the accuracy of
our method by means of a comparison with a method
based on force sensing after specifying the skin impedance of individuals, as well as describing the principles
used for the estimation. Nakatani et al. [22] employeda similar approach in which they took advantage of the
Poisson effect at a fingertip. They measured the deformation at the side of a fingertip by using strain gauges
to estimate the normal load applied to the finger pad. In
principle, however, their method was not designed to beable to handle rapid changes in the load.

Page 2 of 11

In the present study, we were interested in the intensity or energy of the skin deformation for each frequency
band. In terms of texture and vibrotactile perception, thephases of the skin vibrations were less influential, and thepower or intensity of the spectral density in the frequency
domain are considered important [6, 8, 23–25]. Some
researchers have demonstrated that virtual textures orsurfaces can be presented even without a representationof the phase information of the vibratory signals [26–28]. Furthermore, our method was used to estimate themacroscopic deformation of the finger pad. Actual skindeformations in the contact area between the finger pad
and material surface are not spatially unique and include
phase differences. However, our method does not rely on
estimating the spatial distribution of the deformations in
the finger pad. Therefore, the phase information acquiredby our method may be weakly related to texture perception. Furthermore, the miniature accelerometers used forour method are not responsible for the low frequency
signals, which means that our method cannot acquire
those signals in the time and frequency domains. Hence,in this study, we did not set out to address the phases ortime series data of skin deformations. Rather, we focusedon the magnitudes of the skin deformations within a limited frequency range.

Principles used to estimate finger pad
deformations
Here, we describe the principles on which our estimation
is based. First, we introduce our proposal for estimating afinger pad’s deformation by using the propagation of theskin deformation. Second, for comparison, we describe amethod for estimating a finger pad’s deformation basedon the tangential component of the interaction force
between the finger pad and material.
Estimation via acceleration measured at the sideof the finger

As shown in Fig. 1, the lateral deformation of the finger pad propagates to the radial side through the elastic
body. Matsuura et al. [20] recently confirmed that theFinger tip
Deformationof finger pad
YPropagateddeformation at
the radial side

X
Fig. 1 Propagation of finger skin deformation. The lateral deforma‑tion of finger pad along X-axis propagates to the radial side

Sato et al. Robomech J (2017) 4:19

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deformations at the pad and side of a finger exhibit significant causality that can be repeatedly observed in shaking tests. Hence, the deformation at a finger pad can belinked to that at the side of the finger through the following procedures.
As a calibration procedure, we simultaneously measure the acceleration at the finger pad ẍp (t) and sideẍs (t) through a shaking test. The transfer function G1 (s)between these two types of acceleration is then determined byL[ẍs (t)]A(s)L[ẍp (t)]A(s)Xs (s)=Xp (s)

G1 (s) =(1)

where L and A(s) are the Laplace transformation and gain
characteristics of the accelerometer, respectively. As longas we use the same accelerometers for the finger pad andradial side, their gain characteristics are easily canceled.
In the frequency range where A(s) = 1 (0 dB), we canmake use of this transfer function to estimate Xp (s). The
acceleration at the finger side ẍs1 (t) is measured, and thenthe lateral deformation of the finger pad in the frequency
domain can be estimated by

X̄p1 (s) =1 L[ẍs1 (t)].
s2 G1 (s)(2)

In our method, the acceleration of the hand movement isalso measured by the accelerometer, which may interferewith the estimates of the finger pad’s deformation. However, the frequency of human hand motions is usually afew Hertz at most, which the miniature accelerometers
used in the present study cannot detect, so this range is
excluded from our method. As described later, the accelerometers that we used can respond to frequencies inexcess of 20 Hz.
This method functions on the assumption that thetransfer function of the fingertip does not vary during themeasurement. It is known that the mechanical impedance of a finger pad varies depending on the normalload [29], whereby the stiffness and viscosity of the finger
pad increase by approximately 30% as the load increases
from 1 to 3 N. In our experiments, described below, eachparticipant controlled the load applied with his finger
to maintain a value of 1 N, by referring to an electronic
scale. The actual load may have slightly differed fromthis target value for a brief instant, but we nevertheless assumed that, for the greater part of the measurement, the load was fairly controlled and the change inthe mechanical impedance of the skin was minor, whichallows us to statistically discuss the amplitudes of skindeformation in the frequency domain.

Furthermore, we assumed that the shear deformationof the finger pad is the unique factor that determines theskin deformation at the radial side. This indicates that
only the tangential translation of the finger motion isconsidered, and the rotation around and translation along
the longitudinal axis of the finger should not interferewith the skin deformation at the radial side. In the experiments, only tangential finger motions were allowed. Furthermore, the participants attempted to maintain the
posture of their finger. Nonetheless, the frequency of therotational motion of the finger is smaller than the active
range of the miniature accelerometer that we used.
The abovementioned control of the finger load andmotions does not allow the wearers of the sensor to conduct fully active and free touching; however, these control actions are acceptable for research or investigation
purposes under laboratory conditions.
Estimation based on tangential force applied to finger pad

Some earlier studies successfully expressed the deformation of the skin of a finger pad as caused by the tangential
force on the finger pad by using a spring-mass-damper
model [29–31], indicating a linear relationship between
the deformation and force. This assumption holds provided that the skin deformation is not large and the normal load on the finger is constant. Based on this model,
the finger pad’s deformation can be estimated from thetangential force.
When the finger pad is expressed by the one-degreeof-freedom model shown in Fig. 2 and the displacementof the representative mass point is defined by xp (t), theequation of motion is given by

f (t) = mp ẍp (t) + cẋp (t) + kxp (t)(3)

where f(t), mp, c, and k are the tangential force on thefinger pad, the mass, viscosity, and spring coefficient of
the fingertip, respectively. Hence, the transfer function
between f(t) and xp (t) is

G2 (s) =Xp (s)1=.
F (s)mp s2 + cs + k

Finger tip

(4)

Bone

Material surface
or contactor
Fig. 2 Spring-mass-damper model of the tangential deformation ofa fingertip

Sato et al. Robomech J (2017) 4:19

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When the tangential force f2 (t) is measured, the finger
pad’s deformation can be estimated by(5)

X̄p2 (s) = G2 (s)F2 (s)where F2 (s) corresponds to f2 (t) in the frequency
domain. The mechanical parameters of the finger padwere experimentally identified for individual participantsin the experiments.
To the best of our knowledge, the use of the tangential forces for estimating the finger pad’s deformation asa result of touching material surfaces has not been usedpreviously; nevertheless, experienced researchers would
likely have devised a similar setup.

Experiment 1: Transfer function for fingertip
accelerations
Here, we describe how we experimentally estimated thetransfer function between the accelerations of the padand the side of the finger.
Apparatus

The main components of the experimental apparatus shown in Fig. 3 are two piezoelectric accelerometers [2302B, Showa Sokki Co. Ltd., Japan (onedegree-of-freedom, 1.3 g), valid in 20–1000 Hz] and avibration generator.

One of the accelerometers was fixed to the side of thefinger by using adhesive tape. This attachment of theaccelerometer does not alter either the stiffness or theviscosity of the finger pad, and does not lead to any subjective influences on the textures experienced by wearers. Another was mounted on the contactor on which thefinger pad was placed, to measure the acceleration of thefinger pad’s deformation. The displacement of the vibrating contactor was small, being a maximum of ±2.5 mm,
for which the finger pad does not slip on the contactor. Hence, the displacement of the contactor is in good
agreement with that of the finger pad. The sensitivity of
the accelerometers was set along the X-axis. The outputs
from both accelerometers were recorded at 8 kHz.
The vibration generator, which was based on a voicecoil motor (X-1741, Neomax Engineering Co. Ltd.,
Japan), was used to deform the fingertip at various frequencies. The finger was fixed using a cradle at the proximal interphalangeal (PIP) joint. The accelerations of theapplied vibration were set to approximately ±10 m/s2 at
frequencies in excess of 10 Hz. The accelerations were
smaller than this value at frequencies below 10 Hz.
Procedure

Three male volunteers in their 20s participated in theexperiments after providing informed consent. Theirfinger pads were wiped using cleaning paper before themeasurement. Swept sinusoidal vibrations of 1–500 Hz
were used. Twenty sweeps, including ten rising and fallingseries, were applied to the index finger of each participant.
While the responses of the fingertip were recorded, eachparticipant tried to keep his finger on the cradle while
maintaining a load of 1 N. The participant could monitor
the load by viewing the display of an electronic scale.
Analysis

CradleAccelerometerContactor

YX

Accelerometer
SliderY
X

Direction ofvibration
Linear guideFig. 3 Apparatus used for estimating the transfer function between
the finger pad and radial side. Bottom left Side view. Bottom right Front
view. The sensitivity of the accelerometers and the vibration applied
to the finger pad was along X-axis

We computed the Fourier transform of the outputs from thetwo accelerometers, Ẍs (s) and Ẍp (s), to acquire the accelerations of the skin deformations in the frequency domain.
Following (1), we then computed the transfer function G1 (s)of the fingertip. Note that this transfer function includes
not only the properties of the fingertip but also those of
the accelerometer attached to the finger side. Furthermore,
the coherency between the input Ẍs (s) and output Ẍp (s) of
the transfer function was computed to check the linearity
between the input and output. We applied these computation procedures for the individual participants.

Experiment 2: Estimation of mechanicalparameters of fingertip
As previously mentioned, to estimate the finger pad’s
lateral deformation based on the measured lateral forceand (5), we experimentally determined the mechanicalSato et al. Robomech J (2017) 4:19

Page 5 of 11

parameters in G2 (s). The parameters determined
here were used for the analysis undertaken as part ofExperiment 3.
Apparatus

As shown in Fig. 4, we used a vibration generator with ahigh-precision piezoelectric force sensor [9217A, Kistler,
Switzerland (minimum sensitivity 1 mN)] placed between
the vibrator and finger contactor. The force sensor was
operated with a charge amplifier (5015A, Kistler, Switzerland, with a response of up to 30 kHz) and measured thelateral component (X-direction) of the force applied to
the finger pad. The participant’s fingertip was placed on
the contactor while his PIP joint was fixed to a cradle inthe same way as in Experiment 1. The deformation of thefinger pad along the X-axis was measured by an accelerometer mounted on the contactor. The outputs from both
sensors were recorded at 8 kHz.
Procedure

The same participants as those taking part in Experiment 1 also participated in this measurement. A seriesof 20 swept sinusoidal vibrations of up to 500 Hz were
presented to each participant. The participants were also
instructed to maintain a finger load of 1 N during themeasurement.
Analysis

We analyzed the mechanical impedance of the fingertip
of each participant. When the fingertip was modeled asa spring-mass-damper system, as shown in Fig. 2, themechanical impedance of the fingertip plus the aluminum contactor is given byZ(s) =F (s)Ẋp (s)= mc s + c +

k
.
s

(6)

Fig. 4 Apparatus used for estimating the mechanical impedance
parameters of fingertip. The index fingertip was placed on the con‑tactor and its PIP joint was fixed by a cradle during the measurement

Note that mc is not the mass of the finger pad but the sumof the effective mass of the contactor and that of the masspoint of the finger pad. Because the available data consisted of the accelerations of the finger pad, we converted
this formula, as follows:sZ(s) = s2

F (s)Ẍp (s)2(7)= mc s + cs + k.
By substituting jω for s, this formula can be expressed asjωZ(jω) = (k − mc ω2 ) + jωc(8)where ω is the angular velocity. This equation indicatesthat its real part is characterized by the stiffness and massof the system. Furthermore, the imaginary part is characterized by the viscosity. We computed the real and imaginary parts of this equation by using the measured ẍp (t)and f(t) samples, and then fitted the samples into theequations for the real and imaginary parts by using theleast-squares method to estimate the mc, k, and c values
for individual participants.

Experiment 3: Comparison of acceleration‑and force‑based estimates of lateral deformation
To compare the estimates of the finger pad’s deformation as
determined by the two methods, we simultaneously measured the acceleration at the finger side and the tangential
force while the participant scanned the surface of a material.
Apparatus

As shown in Fig. 5, a fingertip to which the accelerometer
was attached at the radial side was used to scan the surface of a textured material. The material was placed on analuminum plate to which the force sensor [9217A, Kistler,
Switzerland (nominal force threshold: 1 mN, resonancefrequency: greater than 20 kHz)] same as in Experiment
2 was installed to measure the tangential component of
the interaction force. The plate was supported by a pairof leaf springs so that the normal load would not interferewith the force sensor.
Four types of materials were used for the measurement. They were a piece of cotton cloth, a flat and finely
polished aluminum plate, and two types of grating scaleboards made of ABS plastic. The grating scales have alternative ridges and grooves on their surfaces. The width ofeach ridge was 1 mm, with the ridges repeatedly arranged
at intervals of 1 mm (fine) or 9 mm (coarse). The heightof the ridges was also 1 mm in both cases.
Procedure

Each participant participated in this experiment after
the transfer function G1 (s) for his fingertip had beenSato et al. Robomech J (2017) 4:19

Coherency

Gain

Page 6 of 11

1

0.1
1.0

0

100

Gain

Fig. 5 Simultaneous measurement of the acceleration at the finger
side and the tangential component of the interaction force

specified in Experiment 1. Each participant scanned eachtype of material along the X-axis, having been instructedto rhythmically scan a length of 5 cm over 1 s, i.e., 5 cm/s,
for 10 s. In the same way as in the previous experiments,
the finger load was also maintained at approximately 1 N.
Analysis

For each participant, the measured tangential force f2 (t)was converted into the frequency domain by a Fouriertransform and, according to (5), for each combination ofparticipants and materials, we computed X̄p2 (s), that is,
the finger pad’s deformation in the frequency domain. For
this computation, we used the k and c values estimated inExperiment 2 for the individual participants. Because it
was difficult to estimate mp with our experimental setup,
for the analysis in Experiment 3, we used a representativevalue taken from the literature [31]: mp = 0.1 × 10−3 kg.
This value is potentially determined by the weight of local
epidermal tissue of finger pad [31], and it is unlikely tobe affected by the mass of an accelerometer at the finger
side.
Similarly, from the accelerations at the finger side,ẍs1 (t), following (2), we computed X̄p1 (s). We used G1 (s)that was estimated for each participant in Experiment 1
to compute X̄p1 (s) for each participant.
Furthermore, to discuss the accuracy of the estimatedfinger pad’s deformation, we computed the difference inthe magnitudes of these two types of estimates: |X̄p1 (s)|and |X̄p2 (s)|.

Results
Gain of transfer function for fingertip (Experiment 1)

The top part of Fig. 6 shows an example of the gain of thetransfer function between the acceleration of the pad andthe side of the finger for one participant. As previously
mentioned, because we are interested in the magnitudes ofthe skin deformations, the figure shows the magnitude of
G1 (s). The first and second peaks were observed at around70 and 300 Hz, respectively. Typically, in terms of the101
Frequency [Hz]

102

1

0.1
101
102
Frequency [Hz]Fig. 6 Gain (top) and coherence (middle) of the smoothed transfer
function between the accelerations of the finger pad and side for one
participant. Bottom figure compares the gains of the transfer function
for three participants
100

lateral skin deformation of the finger pad, a one degree-offreedom system can be applied, as previously mentioned.
In our setup, however, the mass of the accelerometer at theside of the finger constitutes the system with two degrees
of freedom. As a result, the magnitude of the transfer function showed a few typical features of a system consisting of
two resonances and an anti-resonance between them.
Figure 6 also shows the magnitude of the transfer function for each of the three participants. They were largely
flat up to 80–120 Hz, and then moderately increased followed by a cave for which the bottom peak was between
120–150 Hz. We suggest that the major causes of theindividualities originate from the anatomical individualities of the participants’ fingertips [32] as well as theindividualities of the mechanical impedance of their fingertips. Especially, the nail profile and thickness of thefingertip fatty tissue may influence the transfer function
between the skin deformation at the pad and radial sideof the finger. Given the main goal of the present study,
this was not pursued any further.
For all the participants, the coherence of the transfer
function was sufficiently high, being greater than 0.8,
within a range of 10–450 Hz, indicating that the estimation based on the transfer function is valid within thisfrequency range.
Mechanical parameters of fingertip (Experiment 2)

Figure 7 shows examples of the real and imaginary partsof (8). From the gradient and intercept of a line into which
the measured samples were fitted, the mc and k values

10-4

0

-2
0

Imaginary part [104]Page 7 of 11

Estimated finger pad’s
deformation [m]Real part [105]Sato et al. Robomech J (2017) 4:19

2
4
8
6
Square of angular frequency [106 (rad/s)2]

10-6
10-8
10-10

Cloth
Aluminum
Fine grating scale (2 mm)Coarse grating scale (10 mm)

101

102
Frequency [Hz]Fig. 8 Finger pad’s lateral deformation estimated by the accelera‑
tions at the finger side. Examples of one participant

2
0
-2
0

1000
2000
Angular frequency [rad/s]

3000

Fig. 7 Example of the real and imaginary parts of (8), the impedanceof the mechanical parameters of the finger tip. Dotted curves and solidlines are measured samples and linear approximations, respectively

were estimated. Furthermore, c was estimated from thegradient of the approximated line of the imaginary part.
Table 1 lists the values estimated for individual participants. The mean estimated mc value was 0.029 kg for all
the participants. As previously described, mc was mainly
the effective mass of the contactor and not that of the finger pad. The k and c values estimated here are close to
those reported in other studies in which the mechanicalparameters involved in the lateral deformation of a finger pad were investigated. Nakazawa et al. [29] reported
that k = 310 N/m and c = 2.1 Ns/m while the finger load
was 1 N. Wiertlewski and Hayward [31] reported thatthese values were within a range of 600–1700 N/m and
0.8–2.4 Ns/m for a 0.5 N load. The values estimated inour study are largely consistent with these previously
reported values.
Comparison between the acceleration‑ and force‑based
estimates of finger pad deformations (Experiment 3)
Examples of estimated finger pad deformation

Figure 8 shows the estimated finger pad deformationX̄p1 (s) for each type of material when scanned by any
one participant. The skin deformation includes the wide
Table 1 Mechanical parameters of finger pad estimatedin Experiment 2
Participant

Stiffness: k (N/m)

Viscosity: c (Ns/m)

P1

830

2.1

P2

530

5.1

P3

1300

5.8

range of frequency components as observed in anotherstudy [13]. The deformation for the grating scales, whichhave a surface roughness that is larger than both thecloth and aluminum, is greater than those for the clothand aluminum. Naturally, the greater surface roughness
led to the greater skin deformation when the exploratory
motion of the participant was controlled to be approximately the same across the materials. The profiles of thefrequency responses differ depending on the materials,
although we do not thoroughly discuss the differences
because the active hand movements of the participants
were not precisely controlled. Note that Fig. 8 shows theresults for computational estimation, for which the accuracy is discussed in the latter part of this manuscript.
Because the grating scales have a periodic surface texture, the skin vibration might have also been periodic
to some extent. The estimated lateral skin deformation
for the coarse grating scale, for which the spatial surface period was 10 mm, exhibited a small peak at around
14–20 Hz. Since the participant was instructed to scan
the material over a length of 5 cm in 1 s, the skin vibration
was predicted to concentrate up to 8–10 Hz if the handvelocity was well controlled and followed a sinusoidal or
bell-shaped curve. Unfortunately, these frequencies areout of the range of sensitivity of the accelerometer. However, the expected and observed peak frequencies did not
substantially disagree with each other, taking account of
the moderate control of hand exploration in our study.
Similarly, the skin deformation for the fine grating scale,for which the surface period was 2 mm, was predicted toconcentrate up to 40–50 Hz. The estimated skin deformation for the fine grating scale was mostly greater thanthose for the cloth and aluminum plates below this frequency range, which is consistent with the expectations.
Comparison between the acceleration‑ and force‑based
estimates

Figure 9 shows examples of the time-series data of theaccelerations at the finger side and the tangential forces.

Sato et al. Robomech J (2017) 4:19

Page 8 of 11

Cloth

10-6

0
-0.6

10-8

Grating scales (fine)

Cloth

0.6

10-10

0

10-4

[m/s2]-0.6

Acceleration at finger side:

Xp1( ): Acceleration-based method
Xp2( ): Force-based method

10-4

30

Cloth

-30
30

-30

Grating scales (fine)

0

1

2

Time [s]3

4

5

Fig. 9 Example of the time series data of the accelerations at thefinger side ẍs1 (t) and tangential component of the interaction force
f2 (t) when the finger slid on material surfaces

Estimated finger pad’s deformation [m]Shear force: f(t) [N]

0.6

10-6
10-8
Aluminum
10-10
10-4
10-6
10-8
Grating scale (1 mm)
10-10
10-4
10-6
10-8
Grating scale (10 mm)
10-10

101

102
Frequency [Hz]Fig. 10 Two types of estimates. Solid curves are the finger pad’s
deformation estimated based on the accelerations at the finger side.
Dotted curves are those estimated based on the tangential compo‑
nents of the interaction forces

20
Difference in displacement(dB re 1.0 m)

Apparently, the fine material, which is cloth in the figure, exhibited smaller variations in the accelerations andforces than the rough material, which is the grating scalein the figure. Naturally, the skin accelerations and interaction forces depend on the materials, is as shown inthese time-series data.
Figure 10 shows examples of the magnitudes of thefinger pad deformations estimated using (2) and (5) for
each material. As previously stated, because the linearityof the transfer function G1 (s) was valid for 10–450 Hz,
these estimates are shown for this range. Smaller interaction forces [14] and skin deformations [8] at higher
frequency bands are typical responses of the finger whensliding on a material. For any types of material, the two
types of estimates appear to be in reasonably good agreement with each other. We should note that the humanperceptual threshold to vibrotactile stimulation [33, 34]
is approximately 1­ 0−7 m at the most sensitive frequency.
For shear skin displacements, the threshold may be evensmaller by a few tens of a percentage point [35]. Furthermore, taking the smallest resolution of the force sensor
into account, an estimated skin deformation of less than
­10−7 m may be practically insignificant.
As none of the specific materials involved differencesthat were notably larger than those of the others, we
computed the average differences between the two typesof estimates across all the types of materials and participants, as shown in Fig. 11. The estimated differences forthe representative frequencies are also listed in Table 2.

0

Difference threshold (20%)
Difference threshold (10%)
Difference in displacement

-20
-40
-60
101

102
Frequency [Hz]Fig. 11 Perceptual differential thresholds towards the amplitudes ofvibrotactile stimuli and average difference between the two typesof estimates: |X̄p1 (ω)| and |X̄p2 (ω)|. Differential thresholds are drawn
based on literature [34]Note that we do not know which type of estimate is moreaccurate, although the differences between them becomea criterion whereby we can judge whether the estimates
are reliable. If the difference is significant for some

Sato et al. Robomech J (2017) 4:19

Page 9 of 11

Table 2 Differences in displacements estimated by the two
types of methods at representative frequencies. DT indi‑cates the differential threshold of human vibrotactile per‑ceptionFrequency (Hz)Difference (μm)
DT (10%) (μm)
DT (20%) (μm)

10
4.3
0.68
1.4

30
0.60
0.49
0.98

100

450
−2

2.2 × 10−2

7.0 × 10−1

1.4 × 10

8.7 × 10−4
4.3 × 10−2
8.6 × 10−2

frequency bands, then we cannot rely on the two typesof estimates. As a criterion for judging the accuracy, we
adopted the differential thresholds of human perception
for the vibrotactile stimuli. The differential threshold isthe minimum difference between two physical stimuli
that humans can distinguish. If the differences between
the two types of estimates are smaller than the differential thresholds, then such differences are not significant
to the perception and can be ignored. Because the differential thresholds towards the amplitudes of the vibrotactile stimuli are typically within a range of 10–20% of thestimuli [36, 37], we set 10–20% of the absolute thresholds, as presented by Gescheider et al. [34] as the criteria
for judging a significant difference. As shown in Fig. 11
and Table 2, the differences between the two types of estimates fall below the differential thresholds of 20 and 10%
at frequencies in excess of 23 and 50 Hz, respectively.

Discussion
Using the propagation of skin deformation at a fingertip,
we developed a technique for sensing the shear deformation of a finger pad. Here, we discuss the estimation
accuracy and limitations of our method based on theexperimental results.
Accuracy of the estimates

A comparison, in Experiment 3, of the two types of estimate of a finger pad’s deformation indicated that our
method, based on the accelerations at the finger side,
can be applied to a deformation in excess of 23–50 Hz.
In contrast, skin deformation at less than a few tens ofHertz, at which our method may incur significant errors,
is regarded as being less effective for the perception offine textures [6, 24]; nonetheless, they still influence theperception of coarse surfaces. At the high-frequency
range, in which the deformation is smaller than 10−7 m,because of the limitations of the sensitivity of the force
sensor and the noise level of the accelerometer, the accuracy of our method has not been validated; nonetheless,such a small deformation is unlikely to influence the perception of texture as previously mentioned.
Because of the reasons given below, it is assumed thatthe estimation based on the force sensor and that basedon the accelerometer are, respectively, superior to theother method for a frequency range smaller than a few
tens of Hertz and that greater than 100 Hz.
In the low-frequency range (less than a few tens ofHertz), the normal and tangential deformation of thefinger pad are not decoupled and collectively affect the
deformation at the finger side. The normal deformationof the finger pad also leads to skin deformation at thefinger side. Hence, a large normal deformation in the
low-frequency range may interfere with the estimates of
the tangential deformation of the finger pad. At high frequencies, the adverse effects of the normal deformationon the estimates of tangential deformation are minute,because this effect of normal deformation on the radialside is attenuated [22]. From this aspect, at a frequency
range of less than a few tens of Hertz, the estimation
method based on the tangential force is regarded as being
better than our accelerometer-based method, althoughfurther comparisons would be necessary to draw a firm
conclusion.
In the high-frequency range above 100 Hz, the interaction forces between the finger pad and material are smalland hardly detectable even when using one of the mostsensitive commercially available rigid force sensors. As
shown in Fig. 10, in our experiments, estimates basedon the force sensor were found to change linearly with agradient of −40 dB/dec, indicating that the outputs fromthe sensor were mostly noise of a constant level. There
were no profound signals. On the other hand, because
the acceleration is proportional to the square of the frequency, the accelerometer is good at detecting high-frequency signals, indicating that estimations based on theaccelerometer are suitable at a high-frequency range.
Indeed, the skin deformation estimated by the accelerometer reflected the different surface properties of materials up to 450 Hz, as shown in Figs. 8 and 10.
Effects of whole finger vibration

We did not restrain the finger joints during the measurement in experiment 3. Hence, the finger could rotate inab/adduction at the metacarpophalangeal joint. Ideally,such rotation should be removed throughout the experiments. One may say that the effect of the finger ab/adduction is minor. According to a study [38] in which themechanical impedance of the index fingers in abduction
was measured, the resonance point of the ab/adduction
motion is a few tens of Hertz, above which the rotational
vibration is reduced. This also indicates that the whole
finger vibration may be magnified at low frequencies andadversely affects the estimation based on the accelerometer at the finger side. Indeed, the finger pad deformations
estimated by the accelerometer were greater than thoseresulting from the shear force at low frequency ranges, asSato et al. Robomech J (2017) 4:19

shown in Fig. 10. Bracing the MP joint may lead to thetwo types of estimates being more congruent.
Limitations on usage

In this section, we discuss the limitations of the method
we developed, and present cautions on its use.
First, our method functions at a constant finger load in
the normal direction. Therefore, the method should not
be used when the finger load varies dynamically while
exploring a surface. This is because the profile of thetransfer function of the fingertip depends on the load.
Hence, when our method is used, the finger load has tobe controlled in some way: e.g., instruction followed bypractice. To compensate for this dependence on the finger load, a calibration method involving variations in
the finger load is necessary, which will be the subject ofa future study. In addition, it should be mentioned thatmost of the previously introduced indirect measurement
methods did not consider the changes in the finger load.
Another caution regarding the usage is the effect ofrotation or the gradient of the fingertip while the participants tried to maintain the posture of their finger
during the exploration in our experiments. The acceleration at the finger side is also affected by gravity, whichshould not be confused with that of the skin deformation.
Although we used only one accelerometer, the simultaneous use of a 3-axial accelerometer on the nail would be
able to compensate for any adverse effects of the finger
rotation.
Finally, calibration for an individual fingertip shouldbe performed before measurement by using our method.
The transfer functions vary considerably depending on
the individual. We believe that such individuality originates from the profiles of fingertips and nails as well as
the mechanical characteristics of the finger pad. Hence,
the transfer function for one person cannot be applied
to another. Moreover, as previously mentioned, because
the function depends on the attachment of the accelerometer, calibration should be performed before each use.

Conclusion
We developed a technique for estimating the shear deformation of a finger pad, which is applicable even when
actively touching a material. This technique requires only
an accelerometer attached to the radial side of the fingertip, and the finger pad is not covered with any materials
or devices that disturb the natural touch. The propagation of skin deformation on which our method is based
has been used by some research groups in the past; however, they simply measured skin vibrations or deformations near the fingertip immediately after simple signal
processing, and did not refer to the actual skin deformation of the individual. Therefore, our method is a uniquePage 10 of 11

general technique for measuring the shear deformationof a finger pad when actively touching the surface of amaterial.
As a result of comparing our accelerometer-based
method with another method based on the tangential
component of the interaction force between the fingertip
and material, for a range in excess of higher than approximately 20–50 Hz and 10−6 m, the estimates obtainedwith both methods are found to be in good agreement,with the differences being smaller than the human discrimination thresholds. This indicates that our method iseffective for the analysis of the perception of fine roughness surfaces with which high-frequency skin deformation is mediated.
For practical purposes, it is preferable to solve a few
related problems, such as those related to the variation in
the finger load and further tests of the estimation accuracy for deformation of sub-micro meter. Nonetheless,this technique is expected to impact researchers in thefield of haptics, because skin deformation is the directsource of tactile sensations and thus far, many researchgroups have attempted to link this information on skindeformation with human perceptions.
Authors’ contributions
SS and SO are the main contributors of this study, including formulating theconcepts and principles, conducting experiments and analyses, and editing
the manuscript. YM and YY are credited with the principles of the methods. All
authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
Not applicable.
Ethics approval and consent to participate
Voluntary participants provided written informed consent before experiments.
Funding
This study was partly supported by MEXT KAKENHI Shitsukan 25135717 and
15H05923.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in pub‑lished maps and institutional affiliations.
Received: 4 April 2016 Accepted: 25 July 2017

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