Estimation of Finger Pad Deformation
based on Skin Deformation
Transferred to the Radial Side
Yoichiro Matsuura, Shogo Okamoto, and Yoji Yamada ⋆Abstract. Techniques to measure the deformation of finger pad when rubbing
material surfaces are important for the analysis of textural sensations and development of tactile texture displays. However, such measurements are difficult
because when the finger pad is in contact with the material surfaces, it is not
exposed for measurement. We developed a technique to estimate finger pad shear
deformation by using the skin deformation transferred to the side of the fingertip. Good agreement was shown between measured finger pad accelerations andthose estimated by our method. The skin deformation of the finger side can beeffectively used to estimate that of the finger pad with an average accuracy of0.93.
Keywords: Accelerometer, Transfer function, Skin impedance

1Introduction

Texture sensations are evoked during mechanical interaction between finger pads andmaterial surfaces. Hence, measurement of finger pad deformation or shear force during
rubbing motion is important for the analysis of tactile sensations and development oftactile texture displays. For example, as a representative display technique, the vibrotactile texture display presents the sense of materials by controlling the spectrum orfrequency components of vibratory stimuli imparted to the finger pad [1]. Most of thesetechniques are based on the measurement of skin vibration or shear deformation of thefinger pad during rubbing motion. However, such measurement during active touch isdifficult and methods of direct measurement are limited.
The most successful measurement of finger pad slipping on materials appears to
be recording with a camera through transparent materials [2], which is not applicable to general materials. Thus, many researchers have attempted or developed indirect
measurements of finger pads. For example, Wiertlewski et al. measured the interaction forces between a fixed finger pad and materials moved laterally against the finger
pad [3]. The shear displacement of a finger pad can be determined from such force
measurements, given that the finger pad’s mechanical impedance is well specified. The
neighboring skin parts reflect the mechanical deformation of the finger pad. Bensmaı̈aet al. analyzed fingertip vibration during tactile exploration of materials using a Hall effect transducer and magnet [4]. They also attempted to measure the displacement of the⋆ Department of Mechanical Science and Engineering, the Graduate School of Engineering,Nagoya University. Nagoya, Japan. This study is in part supported by KAKENHI Shitsukan(25135717).

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Matsuura, Okamoto, & Yamadaskin near the contact surface using a laser velocity sensor [5]. To estimate the load applied to the finger pad, Nakatani et al. measured the radial deformation of the fingertip
that results from the Poisson effect when the finger pad is pressed [6]. Tanaka et al. measured the skin vibration propagated to the radial side of the fingertip during explorationof materials using the differential output of two accelerometers [7]. As demonstrated bythese studies, it is effective to focus on the skin area close to the finger pad that transfers
mechanical deformation to adjacent tissues. Accelerometers are suitable for measuring
the fast and fine deformation of skin owing to their excellent frequency response [8]. In
a completely different approach, some researchers embedded sensors in pseudo fingers
to investigate the internal physics [9, 10].
As described above, early studies were not adequate for measuring fast and fine finger pad deformation, or measured related quantities that are indirectly linked to finger
pad deformation. In some studies, the attenuation of skin propagation was not considered. In this study, we have developed a fundamental technique to estimate the shear
displacement of a finger pad from the displacement propagated to the radial side of thefingertip. Such a technique will lead to a wearable sensor for finger pad shear deformation caused by active exploration of material surfaces.

2Operating Principle: Transfer Function Between the Side of theFingertip and Finger Pad

Finger pad

AccelerometerkAccelerometermpadcfxpad

msidexsideFig. 1. Spring-mass-damper model of finger skin

As is shown in Fig. 1, deformation of the side of a fingertip accompanies the finger
pad’s shear deformation. Given the transfer characteristics between these two types ofdeformation, it is possible to estimate the shear deformation of the finger pad from thedeformation of the side of the fingertip. With the physical model of the finger pad asshown in Fig. 1, the equations of motion of the finger pad and radial side point massessare:mpad ẍpad (t) = k(xside (t) − xpad (t)) + c(ẋside (t) − ẋpad (t)) + f (t)(1)

mside ẍside (t) = −k(xside (t) − xpad (t)) − c(ẋside (t) − ẋpad (t))(2)

Estimation of Finger Pad Deformation3

where mpad and mside are the point masses of the finger pad and radial side, respectively;
xpad (t) and xside (t) are the respective displacements of the finger pad and radial side; andf (t)is the force that causes the displacement of the finger pad. The transfer function forwhich the input and output respectively are the displacements xpad (t) and xside (t) of thetwo point masses, is expressed by:G(s) = α(cs + k)mside s2 + cs + k(3)where α is a constant value to indicate the transfer ratio between the two skin deformations, which is naturally smaller than 1.0. We use the inverse of this transfer function toestimate xpad (t) from xside (t). Note that the use of G(s)−1 for high frequency bands islimited because G(s) is a proper function. Eventually, these processes are similar to thespecification of lump mechanical properties of the finger tip, which has been attemptedby many research groups thus far (e.g. [11]).

3

Specification of Transfer Characteristics of the Fingertip

3.1

Measurement of the Skin Acceleration

Finger cradle
Accelerometer (side)
Voice coil motor
Accelerometer (pad)Linear slider
Electronic scaleFig. 2. Experimental apparatus for measuring acceleration of a fingertip

Fig. 2 shows an apparatus that generates and measures the acceleration of skin deformation. One accelerometer (2302B, Showa Sokki Co. Ltd., Japan, single degree offreedom) was taped to the radial side of the fingertip, and another was mounted on thevibration generator to which the finger pad was bonded. The vibration was produced bya voice coil motor and its motion was restrained along a low-frictional linear slider. The
accelerometers recorded ẍside (t) and ẍpad (t), respectively, along the direction of vibration at 5 kHz. During the measurement, the proximal interphalangeal joint was fixed tothe base through a clip. The contact force between the finger pad and vibration generator, or pressing force of the finger, was maintained at approximately 1 N by monitoring
an electronic scale. Sinusoidal vibratory stimuli, swept across the frequency range of4Matsuura, Okamoto, & Yamada

10–500 Hz, were applied to the finger pad. This trial was repeated 10 times for each of
the 5 male voluntary participants in their 20’s.
3.2 Frequency Response Characteristics of the Finger Pad
Gain characteristics of the fingertip skin obtained from the five participants are shownin Fig. 3 with a dotted line. These values were computed using the equation G( f ) =20 log 10 (ẍside ( f )/ẍpad ( f )), where f is the frequency. For this computation, the average
gains of all of the trials were used for each individual. The peak of the gain characteristic
was found in the frequency band of approximately 100–300 Hz. This value is similar tothose reported in the literature referenced above [7, 12].
3.3

Curve Fitting of the Transfer Function

Table 1. Identified parameters of transfer function
ParticipantAB
CDE

α
0.783
0.818
0.842
0.805
0.900

mside kg
1.97 × 10−4
1.76 × 10−4
3.83 × 10−4
5.38 × 10−45.01 × 10−4k N/m
5.17 × 102
4.87 × 102
7.09 × 102
8.49 × 102
6.85 × 102

c N·s/m
0.288
0.284
0.731
0.612
0.845

R20.937
0.924
0.946
0.952
0.924

We fitted transfer functions of (3) to the gain curves of each participant in order to
identify the physical parameters mside , k, c, and constant α . Transfer functions obtained
from the gain curves are shown in Fig. 3 with a solid line. Identified values and R2
values for the curve fits are listed in Table. 1.
We cannot compare these parameters to those found in other studies because ourdynamic model of the finger pad is different from those used by other researchers.
However, computed values found in our study are not significantly different from thoseof other researches under similar conditions. Nakazawa et al. reported mean values of
stiffness and damping coefficient of 4.80 × 102 N/m and 2.10 N·s/m, respectively, forthe middle finger [13]. Wiertlewski et al. reported a point mass of 1.27 × 10−4 kg,stiffness of 9.13 × 102 N/m, and damping coefficient of 1.327 N· s/m as mean values.

4Estimation of Finger Pad Deformation from that of the Side ofthe Fingertip

We validated the method for estimating the acceleration of finger pad deformation fromthat of the side of the fingertip using leave-one-out cross-validation. We computed how
well the transfer function performed on the basis of the results of 9 of the 10 trials inSec. 3.1 to estimate the output of the trial that was excluded. The computed mean andstandard deviation of the goodness of estimation are shown in Tab. 2. The mean of thegoodness of estimation was higher than 0.92, which is a high value for each participant.

442200Gain [dB]Gain [dB]

Estimation of Finger Pad Deformation-2-4-6-85-2-4-60100

200 300 400
Frequency [Hz]-80500100(a) Participant A

200 300 400
Frequency [Hz]500(b) Participant B

2420Gain [dB]Gain [dB]0-2-4-2-4-6-8-60100

200 300 400
Frequency [Hz]500

-100100(c) Participant C

200 300 400
Frequency [Hz]500(d) Participant D

Gain [dB]20-2-4-60100

200 300 400
Frequency [Hz]500(e) Participant EFig. 3. Observed and fitted gain curves. Dotted and solid curves are observed and fitted characteristics, respectively.

6Matsuura, Okamoto, & Yamada
Table 2. Result of leave-one-out cross-validation
Participant
AB
CDE

5

Mean R2 ± std. dev.
0.938 ± 2.14 × 10−60.924 ± 2.52 × 10−50.946 ± 8.09 × 10−60.952 ± 1.93 × 10−80.925 ± 4.47 × 10−7Conclusion

We developed a technique for estimating the finger pad shear deformation from the deformation of the radial side of the fingertip due to mechanical strain that propagatesfrom the finger pad. Practically, this technique leads to a small, accelerometer-based
wearable sensor that provides highly accurate estimation of finger pad shear deformation during rubbing motion. We specified the transfer function of skin deformation between the finger pad and radial side of the fingertip and examined the accuracy of estimation by cross-validation. As a result, we found that our approach could estimate thefinger pad shear deformation with an average accuracy of 0.93. In the future, we willfurther sophisticate the experimental equipment and data analysis, and its mechanicalproperties such as the mass of the accelerometer should thoroughly be considered forspecification of the impedance of the finger tip.

References
1. Konyo, M., Tadokoro, S., Takamori, T., Oguro, K.: Artificial tactile feel display using soft gel
actuators. IEEE International Conference on Robotics and Automation (2000) 3416–3421
2. Levesque, V., Hayward, V.: Experimental evidence of lateral skin strain during tactile exploration. Eurohaptics July (2003) 261–275
3. Wiertlewski, M., Losada, J., Hayward, V.: The spatial spectrum of tangential skin displacement can encode tactual texture. IEEE Transactions on Robotics 27(3) (2011) 461–472
4. Bensmaı̈a, S., Hollins, M.: Pacinian representations of fine surface texture. Perception andPsychophysics 67(5) (2005) 842–854
5. Webera, A.I., Saala, H.P., Lieberb, J.D., Chenga, J.W., Manfredia, L.R., Dammann III, J.F.,
Bensmaı̈a, S.J.: Spatial and temporal codes mediate the tactile perception of natural textures.
PNAS 110(42) (2013) 17107–17112
6. Nakatani, M., Shiojima, K., Kinoshita, S., Kawasoe, T., Koketsu, K., Wada, J.: Wearable
contact force sensor system based on fingerpad deformation. IEEE World Haptics Conference (2011) 323–328
7. Tanaka, Y., Horita, Y., Sano, A.: Finger-mounted skin vibration sensor for active touch.
Eurohaptics (2012) 169–174
8. Okamoto, S., Wiertlewski, M., Hayward, V.: Anticipatory vibrotactile cueing facilitates grip
force adjustment. IEEE World Haptics Conference (2013) 525–530
9. Tomimoto, M.: The frictional pattern of tactile sensations in anthropomorphic fingertip.
Tribology International 44 (2011) 1340–1347
10. Mukaibo, Y., Shirado, H., Konyo, M., Maeno, T.: Development of a texture sensor emulating the tissue structure and perceptual mechanism of human fingers. IEEE International
Conference on Robotics and Automation (2005) 2565–2570

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11. Wang, Q., Hayward, V.: In vivo biomechanics of the fingerpad skin under local tangentialtraction. Journal of Biomechanics 40(4) (2007) 851–860
12. Lundstrom, R.: Local vibrations-mechanical impedance of the human hand s glabrous skin.
Biomechanics 17(2) (1984) 137–144
13. Nakazawa, N., Ikeura, R., Inooka, H.: Characteristics of human fingertips in the shearingdirection. Biological Cybernetics 82(3) (2000) 207–214