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Wearable finger pad deformation sensor for tactile textures in frequency domain by using accelerometer on finger side

Wearable finger pad deformation sensor for tactile textures in frequency domain by using... In this study, we set out to develop a method for estimating the fine and fast shear deformation of a finger pad, that is, the palm side of a fingertip, as it scans the surface of a material. Using a miniature accelerometer, we measured the acceleration 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 estimated the shear deformation of the finger pad in the frequency domain. A comparison between an estimate based on the accelerometer 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 in −6 excess of approximately 20–50 Hz and for skin deformation above 10 m. Our technique merely requires that an accelerometer be attached to the side of the fingertip, which allows active texture exploration. These estimates or measurements 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 touches a material. However, the measurement of a finger Introduction pad’s deformation is not easy because the finger pad is in In general, the physical properties of material surfaces contact with the material surface and is not exposed to characterize their tactile textures. From this standpoint, any sensing devices. In this study, we developed a tech- many research groups have investigated the relation- nique for estimating the fast and fine lateral deformations ships between different types of material properties and of a finger pad when a finger actively explores the surface the textures that are perceived by touching them. Such of a material. To the best of our knowledge, such tech- an approach has significantly contributed to industries niques have not previously been reported. involved with clothing  [1]. In contrast, texture percep- Many research groups have measured informa- tion arises as a result of the skin deformation caused by tion related to the deformation of a fingertip by using a the interaction between the finger and material. Hence, range of approaches. Nonetheless, observation through the mechanical properties of the fingertips of individu - a transparent material such as glass is a very distinctive als influence the textures perceived by those individuals. way of directly measuring deformation  [3, 4]. In princi- A typical example is the moisture content of a fingertip ple, this method is applicable only to transparent mate- influencing the friction-induced pleasantness of the sur - rial. Another approach involves using the differential face of a material  [2]. Therefore, many researchers have outputs of two accelerometers  [5] to measure the mac- attempted to link the information related to the deforma- roscopic deformation of a finger pad. One accelerom - tion of a fingertip and the perceived texture when a finger eter is attached to the dorsal side of the fingertip and another is fixed to the surface of the material contacted *Correspondence: sato.shiyunsuke@c.mbox.nagoya‑u.ac.jp by the fingertip. Provided there is no slippage, the dif - Department of Mechanical Engineering and Science, Nagoya University, ference between the values measured with these two Chikusa‑ku, Nagoya, Japan © 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 Page 2 of 11 accelerometers will be the acceleration of the deforma- In the present study, we were interested in the inten- tion of the finger pad. However, this technique cannot be sity or energy of the skin deformation for each frequency applied to a finger sliding on the surface of a material. band. In terms of texture and vibrotactile perception, the To date, several indirect measurement methods have phases of the skin vibrations were less influential, and the been employed to overcome the difficulties and limita - power or intensity of the spectral density in the frequency tions of direct measurement. For example, a number of domain are considered important  [6, 8, 23–25]. Some researchers have exploited the propagation of skin defor- researchers have demonstrated that virtual textures or mations. Any high-frequency deformation at a point on surfaces can be presented even without a representation the skin is transferred to the adjacent elastic skin tis- of the phase information of the vibratory signals  [26– sues. Bensmaïa et  al. attempted to measure these high 28]. Furthermore, our method was used to estimate the frequency components as a finger was sliding over the macroscopic deformation of the finger pad. Actual skin surface of a material by using a Hall-effect transducer deformations in the contact area between the finger pad attached to the finger  [6]. Similarly, the propagated and material surface are not spatially unique and include vibratory information was acquired using a laser Dop- phase differences. However, our method does not rely on pler velocity meter  [7, 8], microphones  [9], accelerome- estimating the spatial distribution of the deformations in ters [10], and PVDF films [11] attached to the finger close the finger pad. Therefore, the phase information acquired to the tip, as well as a microphone  [12] on the forearm. by our method may be weakly related to texture percep- Although these vibrations in the adjacent skin originate tion. Furthermore, the miniature accelerometers used for from the vibratory deformations of the finger pad, these our method are not responsible for the low frequency methods were not to measure the deformations of the signals, which means that our method cannot acquire individual finger pad. those signals in the time and frequency domains. Hence, Many researchers measured the interaction force in this study, we did not set out to address the phases or between the fingertip and material surfaces as reli - time series data of skin deformations. Rather, we focused able information related to the finger pad’s deformation on the magnitudes of the skin deformations within a lim- because the forces cause the skin to deform [13–19]. For ited frequency range. example, Wiertlewski et  al.  [13] precisely measured the interaction forces when a material slid beneath a finger - Principles used to estimate finger pad tip. However, they all measured interaction forces that deformations were distinct from the skin deformations. Here, we describe the principles on which our estimation Given the abovementioned background and related is based. First, we introduce our proposal for estimating a studies, this study set out to develop a technique for esti- finger pad’s deformation by using the propagation of the mating the lateral deformation of a finger pad and which skin deformation. Second, for comparison, we describe a could be applied to situations involving active touching. method for estimating a finger pad’s deformation based We used the propagation of skin deformation, whereby on the tangential component of the interaction force the lateral deformation of a finger pad leads to other between the finger pad and material. deformation of the skin at the radial side of the fingertip. The skin deformation at the radial side can be measured Estimation via acceleration measured at the side by an accelerometer designed for the measurement of of the finger small and fast displacements. This study is based on our As shown in Fig.  1, the lateral deformation of the fin - previous publications  [20, 21] in which we introduced ger pad propagates to the radial side through the elastic the principles of measurement and the linear causality body. Matsuura et  al.  [20] recently confirmed that the between the deformations of the pad and the radial side of a finger. In this paper, we also assess the accuracy of our method by means of a comparison with a method Finger tip based on force sensing after specifying the skin imped- ance of individuals, as well as describing the principles Deformation Propagated used for the estimation. Nakatani et  al.  [22] employed of finger pad deformation at a similar approach in which they took advantage of the the radial side Poisson effect at a fingertip. They measured the defor - mation 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 be Fig. 1 Propagation of finger skin deformation. The lateral deforma‑ tion of finger pad along X ‑axis propagates to the radial side able to handle rapid changes in the load. Sato et al. Robomech J (2017) 4:19 Page 3 of 11 deformations at the pad and side of a finger exhibit signif - Furthermore, we assumed that the shear deformation icant causality that can be repeatedly observed in shak- of the finger pad is the unique factor that determines the ing tests. Hence, the deformation at a finger pad can be skin deformation at the radial side. This indicates that linked to that at the side of the finger through the follow - only the tangential translation of the finger motion is ing procedures. considered, and the rotation around and translation along As a calibration procedure, we simultaneously meas- the longitudinal axis of the finger should not interfere ure the acceleration at the finger pad x ¨ (t) and side with the skin deformation at the radial side. In the experi- x ¨ (t) through a shaking test. The transfer function G (s) ments, only tangential finger motions were allowed. Fur - s 1 between these two types of acceleration is then deter- thermore, the participants attempted to maintain the mined by posture of their finger. Nonetheless, the frequency of the rotational motion of the finger is smaller than the active L[x (t)]A(s) s range of the miniature accelerometer that we used. G (s) = L[x¨ (t)]A(s) The abovementioned control of the finger load and (1) motions does not allow the wearers of the sensor to con- X (s) duct fully active and free touching; however, these con- X (s) trol actions are acceptable for research or investigation where L and A(s) are the Laplace transformation and gain purposes under laboratory conditions. characteristics of the accelerometer, respectively. As long as we use the same accelerometers for the finger pad and Estimation based on tangential force applied to finger pad radial side, their gain characteristics are easily canceled. Some earlier studies successfully expressed the deforma- In the frequency range where A(s) = 1 (0  dB), we can tion of the skin of a finger pad as caused by the tangential make use of this transfer function to estimate X (s). The force on the finger pad by using a spring-mass-damper acceleration at the finger side x ¨ (t) is measured, and then model  [29–31], indicating a linear relationship between s1 the lateral deformation of the finger pad in the frequency the deformation and force. This assumption holds pro - domain can be estimated by vided that the skin deformation is not large and the nor- mal load on the finger is constant. Based on this model, 1 L[x¨ (t)] s1 the finger pad’s deformation can be estimated from the X (s) = . (2) p1 s G (s) tangential force. In our method, the acceleration of the hand movement is When the finger pad is expressed by the one-degree- also measured by the accelerometer, which may interfere of-freedom model shown in Fig.  2 and the displacement with the estimates of the finger pad’s deformation. How - of the representative mass point is defined by x (t), the ever, the frequency of human hand motions is usually a equation of motion is given by few Hertz at most, which the miniature accelerometers f (t) = m x¨ (t) + cx˙ (t) + kx (t) p p p p (3) used in the present study cannot detect, so this range is excluded from our method. As described later, the accel- where f(t), m , c, and k are the tangential force on the erometers that we used can respond to frequencies in finger pad, the mass, viscosity, and spring coefficient of excess of 20 Hz. the fingertip, respectively. Hence, the transfer function This method functions on the assumption that the between f(t) and x (t) is transfer function of the fingertip does not vary during the X (s) measurement. It is known that the mechanical imped- G (s) = = . 2 (4) F (s) m s + cs + k ance of a finger pad varies depending on the normal load [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, each Finger tip Bone participant 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 from this target value for a brief instant, but we neverthe- less assumed that, for the greater part of the measure- ment, the load was fairly controlled and the change in Material surface or contactor the mechanical impedance of the skin was minor, which allows us to statistically discuss the amplitudes of skin Fig. 2 Spring‑mass‑ damper model of the tangential deformation of a fingertip deformation in the frequency domain. Sato et al. Robomech J (2017) 4:19 Page 4 of 11 When the tangential force f (t) is measured, the finger One of the accelerometers was fixed to the side of the pad’s deformation can be estimated by finger by using adhesive tape. This attachment of the accelerometer does not alter either the stiffness or the X (s) = G (s)F (s) (5) p2 2 2 viscosity of the finger pad, and does not lead to any sub - where F (s) corresponds to f (t) in the frequency jective influences on the textures experienced by wear - 2 2 domain. The mechanical parameters of the finger pad ers. Another was mounted on the contactor on which the were experimentally identified for individual participants finger pad was placed, to measure the acceleration of the in the experiments. finger pad’s deformation. The displacement of the vibrat - To the best of our knowledge, the use of the tangen- ing contactor was small, being a maximum of ±2.5  mm, tial forces for estimating the finger pad’s deformation as for which the finger pad does not slip on the contac - a result of touching material surfaces has not been used tor. Hence, the displacement of the contactor is in good previously; nevertheless, experienced researchers would agreement with that of the finger pad. The sensitivity of likely have devised a similar setup. the accelerometers was set along the X-axis. The outputs from both accelerometers were recorded at 8 kHz. Experiment 1: Transfer function for fingertip The vibration generator, which was based on a voice accelerations coil motor (X-1741, Neomax Engineering Co. Ltd., Here, we describe how we experimentally estimated the Japan), was used to deform the fingertip at various fre - transfer function between the accelerations of the pad quencies. The finger was fixed using a cradle at the proxi - and the side of the finger. mal interphalangeal (PIP) joint. The accelerations of the applied vibration were set to approximately ±10  m/s at Apparatus frequencies in excess of 10  Hz. The accelerations were The main components of the experimental appa - smaller than this value at frequencies below 10 Hz. ratus shown in Fig.  3 are two piezoelectric acceler- ometers [2302B, Showa Sokki Co. Ltd., Japan (one Procedure degree-of-freedom, 1.3  g), valid in 20–1000  Hz] and a Three male volunteers in their 20s participated in the vibration generator. experiments after providing informed consent. Their finger pads were wiped using cleaning paper before the measurement. Swept sinusoidal vibrations of 1–500  Hz were used. Twenty sweeps, including ten rising and falling series, were applied to the index finger of each participant. While the responses of the fingertip were recorded, each participant 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 We computed the Fourier transform of the outputs from the ¨ ¨ two accelerometers, X (s) and X (s), to acquire the accel- s p erations of the skin deformations in the frequency domain. Following (1), we then computed the transfer function G (s) of the fingertip. Note that this transfer function includes Accelerometer Cradle not only the properties of the fingertip but also those of the accelerometer attached to the finger side. Furthermore, Contactor ¨ ¨ the coherency between the input X (s) and output X (s) of s p the transfer function was computed to check the linearity Accelero- between the input and output. We applied these computa- meter tion procedures for the individual participants. Slider Direction of Experiment 2: Estimation of mechanical vibration Linear guide parameters of fingertip Fig. 3 Apparatus used for estimating the transfer function between As previously mentioned, to estimate the finger pad’s the finger pad and radial side. Bottom left Side view. Bottom right Front lateral deformation based on the measured lateral force view. The sensitivity of the accelerometers and the vibration applied to the finger pad was along X ‑axis and (5), we experimentally determined the mechanical Sato et al. Robomech J (2017) 4:19 Page 5 of 11 parameters in G (s). The parameters determined Note that m is not the mass of the finger pad but the sum 2 c here were used for the analysis undertaken as part of of the effective mass of the contactor and that of the mass Experiment 3. point of the finger pad. Because the available data con - sisted of the accelerations of the finger pad, we converted Apparatus this formula, as follows: As shown in Fig.  4, we used a vibration generator with a F (s) high-precision piezoelectric force sensor [9217A, Kistler, sZ(s) = s Switzerland (minimum sensitivity 1 mN)] placed between X (s) (7) the vibrator and finger contactor. The force sensor was = m s + cs + k. operated with a charge amplifier (5015A, Kistler, Switzer - land, with a response of up to 30 kHz) and measured the By substituting jω for s, this formula can be expressed as lateral component (X-direction) of the force applied to jωZ(jω) = (k − m ω ) + jωc (8) the finger pad. The participant’s fingertip was placed on the contactor while his PIP joint was fixed to a cradle in where ω is the angular velocity. This equation indicates the same way as in Experiment 1. The deformation of the that its real part is characterized by the stiffness and mass finger pad along the X-axis was measured by an acceler - of the system. Furthermore, the imaginary part is charac- ometer mounted on the contactor. The outputs from both terized by the viscosity. We computed the real and imagi- sensors were recorded at 8 kHz. nary parts of this equation by using the measured x ¨ (t) and f(t) samples, and then fitted the samples into the Procedure equations for the real and imaginary parts by using the The same participants as those taking part in Experi - least-squares method to estimate the m , k, and c values ment 1 also participated in this measurement. A series for individual participants. of 20 swept sinusoidal vibrations of up to 500  Hz were presented to each participant. The participants were also Experiment 3: Comparison of acceleration‑ instructed to maintain a finger load of 1  N during the and force‑based estimates of lateral deformation measurement. To compare the estimates of the finger pad’s deformation as determined by the two methods, we simultaneously meas- Analysis ured the acceleration at the finger side and the tangential We analyzed the mechanical impedance of the fingertip force while the participant scanned the surface of a material. of each participant. When the fingertip was modeled as a spring-mass-damper system, as shown in Fig.  2, the Apparatus mechanical impedance of the fingertip plus the alu - As shown in Fig. 5, a fingertip to which the accelerometer minum contactor is given by was attached at the radial side was used to scan the sur- face of a textured material. The material was placed on an F (s) Z(s) = aluminum plate to which the force sensor [9217A, Kistler, X (s) Switzerland (nominal force threshold: 1  mN, resonance (6) frequency: greater than 20  kHz)] same as in Experiment = m s + c + . s 2 was installed to measure the tangential component of the interaction force. The plate was supported by a pair of leaf springs so that the normal load would not interfere with the force sensor. Four types of materials were used for the measure- ment. They were a piece of cotton cloth, a flat and finely polished aluminum plate, and two types of grating scale boards made of ABS plastic. The grating scales have alter - native ridges and grooves on their surfaces. The width of each ridge was 1 mm, with the ridges repeatedly arranged at intervals of 1  mm (fine) or 9  mm (coarse). The height of the ridges was also 1 mm in both cases. Procedure Fig. 4 Apparatus used for estimating the mechanical impedance Each participant participated in this experiment after parameters of fingertip. The index fingertip was placed on the con‑ tactor and its PIP joint was fixed by a cradle during the measurement the transfer function G (s) for his fingertip had been 1 Sato et al. Robomech J (2017) 4:19 Page 6 of 11 0.1 1.0 0 1 2 10 10 10 Frequency [Hz] 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 each 0.1 type of material along the X-axis, having been instructed 0 1 2 10 10 10 to rhythmically scan a length of 5 cm over 1 s, i.e., 5 cm/s, Frequency [Hz] for 10 s. In the same way as in the previous experiments, Fig. 6 Gain (top) and coherence (middle) of the smoothed transfer the finger load was also maintained at approximately 1 N. 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 Analysis For each participant, the measured tangential force f (t) was converted into the frequency domain by a Fourier transform and, according to (5), for each combination of lateral skin deformation of the finger pad, a one degree-of- participants and materials, we computed X (s), that is, freedom system can be applied, as previously mentioned. p2 the finger pad’s deformation in the frequency domain. For In our setup, however, the mass of the accelerometer at the this computation, we used the k and c values estimated in side of the finger constitutes the system with two degrees Experiment 2 for the individual participants. Because it of freedom. As a result, the magnitude of the transfer func- was difficult to estimate m with our experimental setup, tion showed a few typical features of a system consisting of for the analysis in Experiment 3, we used a representative two resonances and an anti-resonance between them. −3 value taken from the literature [31]: m = 0.1 × 10  kg. Figure 6 also shows the magnitude of the transfer func- This value is potentially determined by the weight of local tion for each of the three participants. They were largely epidermal tissue of finger pad  [31], and it is unlikely to flat up to 80–120 Hz, and then moderately increased fol - be affected by the mass of an accelerometer at the finger lowed by a cave for which the bottom peak was between side. 120–150 Hz. We suggest that the major causes of the Similarly, from the accelerations at the finger side, individualities originate from the anatomical individu- x (t), following (2), we computed X (s). We used G (s) alities of the participants’ fingertips  [32] as well as the s1 p1 1 that was estimated for each participant in Experiment 1 individualities of the mechanical impedance of their fin - to compute X (s) for each participant. gertips. Especially, the nail profile and thickness of the p1 Furthermore, to discuss the accuracy of the estimated fingertip fatty tissue may influence the transfer function finger pad’s deformation, we computed the difference in between the skin deformation at the pad and radial side the magnitudes of these two types of estimates: |X (s)| of the finger. Given the main goal of the present study, p1 and |X (s)|. this was not pursued any further. p2 For all the participants, the coherence of the transfer Results function was sufficiently high, being greater than 0.8, Gain of transfer function for fingertip (Experiment 1) within a range of 10–450 Hz, indicating that the estima- The top part of Fig.  6 shows an example of the gain of the tion based on the transfer function is valid within this transfer function between the acceleration of the pad and frequency range. the side of the finger for one participant. As previously mentioned, because we are interested in the magnitudes of Mechanical parameters of fingertip (Experiment 2) the skin deformations, the figure shows the magnitude of Figure  7 shows examples of the real and imaginary parts G (s). The first and second peaks were observed at around of (8). From the gradient and intercept of a line into which 70 and 300  Hz, respectively. Typically, in terms of the the measured samples were fitted, the m and k values Gain Coherency Gain Sato et al. Robomech J (2017) 4:19 Page 7 of 11 -4 -6 Cloth -2 -8 Aluminum Fine grating scale (2 mm) 0 2 4 8 Coarse grating scale (10 mm) 6 2 -10 Square of angular frequency [10 (rad/s) ] 1 2 10 10 Frequency [Hz] Fig. 8 Finger pad’s lateral deformation estimated by the accelera‑ tions at the finger side. Examples of one participant -2 range of frequency components as observed in another 0 1000 2000 3000 study [13]. The deformation for the grating scales, which Angular frequency [rad/s] have a surface roughness that is larger than both the Fig. 7 Example of the real and imaginary parts of (8), the impedance of the mechanical parameters of the finger tip. Dotted curves and solid cloth and aluminum, is greater than those for the cloth lines are measured samples and linear approximations, respectively and aluminum. Naturally, the greater surface roughness led to the greater skin deformation when the exploratory motion of the participant was controlled to be approxi- mately the same across the materials. The profiles of the were estimated. Furthermore, c was estimated from the frequency responses differ depending on the materials, gradient of the approximated line of the imaginary part. although we do not thoroughly discuss the differences Table  1 lists the values estimated for individual partici- because the active hand movements of the participants pants. The mean estimated m value was 0.029 kg for all were not precisely controlled. Note that Fig. 8 shows the the participants. As previously described, m was mainly results for computational estimation, for which the accu- the effective mass of the contactor and not that of the fin - racy is discussed in the latter part of this manuscript. ger pad. The k and c values estimated here are close to Because the grating scales have a periodic surface tex- those reported in other studies in which the mechanical ture, the skin vibration might have also been periodic parameters involved in the lateral deformation of a fin - to some extent. The estimated lateral skin deformation ger pad were investigated. Nakazawa et al. [29] reported for the coarse grating scale, for which the spatial sur- that k = 310 N/m and c = 2.1 Ns/m while the finger load face period was 10 mm, exhibited a small peak at around was 1  N. Wiertlewski and Hayward  [31] reported that 14–20  Hz. Since the participant was instructed to scan these values were within a range of 600–1700  N/m and the material over a length of 5 cm in 1 s, the skin vibration 0.8–2.4  Ns/m for a 0.5  N load. The values estimated in was predicted to concentrate up to 8–10  Hz if the hand our study are largely consistent with these previously velocity was well controlled and followed a sinusoidal or reported values. bell-shaped curve. Unfortunately, these frequencies are out of the range of sensitivity of the accelerometer. How- Comparison between the acceleration‑ and force‑based ever, the expected and observed peak frequencies did not estimates of finger pad deformations (Experiment 3) substantially disagree with each other, taking account of Examples of estimated finger pad deformation the moderate control of hand exploration in our study. Figure  8 shows the estimated finger pad deformation Similarly, the skin deformation for the fine grating scale, X (s) for each type of material when scanned by any p1 for which the surface period was 2 mm, was predicted to one participant. The skin deformation includes the wide concentrate up to 40–50  Hz. The estimated skin defor - mation for the fine grating scale was mostly greater than those for the cloth and aluminum plates below this fre- Table 1 Mechanical parameters of  finger pad estimated quency range, which is consistent with the expectations. in Experiment 2 Participant Stiffness: k (N/m) Viscosity: c (Ns/m) Comparison between the acceleration‑ and force‑based P1 830 2.1 estimates P2 530 5.1 Figure  9 shows examples of the time-series data of the P3 1300 5.8 accelerations at the finger side and the tangential forces. 4 5 Imaginary part [10 ] Real part [10 ] Estimated finger pad’s deformation [m] Sato et al. Robomech J (2017) 4:19 Page 8 of 11 -4 Cloth X ( ): Acceleration-based method p1 0.6 X ( ): Force-based method p2 -6 -8 -0.6 Grating scales (fine) 0.6 Cloth -10 -4 -0.6 -6 Cloth -8 Aluminum -10 -30 Grating scales (fine) -4 -6 -8 -30 Grating scale (1 mm) 01 2 3 4 5 -10 Time [s] 10 -4 Fig. 9 Example of the time series data of the accelerations at the finger side x ¨ (t) and tangential component of the interaction force s1 -6 f (t) when the finger slid on material surfaces 2 10 -8 Grating scale (10 mm) -10 Apparently, the fine material, which is cloth in the fig - 1 2 10 10 ure, exhibited smaller variations in the accelerations and Frequency [Hz] forces than the rough material, which is the grating scale Fig. 10 Two types of estimates. Solid curves are the finger pad’s in the figure. Naturally, the skin accelerations and inter - deformation estimated based on the accelerations at the finger side. Dotted curves are those estimated based on the tangential compo‑ action forces depend on the materials, is as shown in nents of the interaction forces these time-series data. Figure  10 shows examples of the magnitudes of the finger pad deformations estimated using (2) and (5) for each material. As previously stated, because the linearity Difference threshold (20%) of the transfer function G (s) was valid for 10–450  Hz, Difference threshold (10%) these estimates are shown for this range. Smaller inter- Difference in displacement action forces  [14] and skin deformations  [8] at higher frequency bands are typical responses of the finger when -20 sliding on a material. For any types of material, the two types of estimates appear to be in reasonably good agree- -40 ment with each other. We should note that the human perceptual threshold to vibrotactile stimulation  [33, 34] -60 −7 is approximately 10 m at the most sensitive frequency. 10 10 For shear skin displacements, the threshold may be even Frequency [Hz] smaller by a few tens of a percentage point [35]. Further- Fig. 11 Perceptual differential thresholds towards the amplitudes of more, taking the smallest resolution of the force sensor vibrotactile stimuli and average difference between the two types into account, an estimated skin deformation of less than ¯ ¯ of estimates: |X (ω)| and |X (ω)|. Differential thresholds are drawn p1 p2 −7 10  m may be practically insignificant. based on literature [34] As none of the specific materials involved differences that were notably larger than those of the others, we Note that we do not know which type of estimate is more computed the average differences between the two types accurate, although the differences between them become of estimates across all the types of materials and partici- a criterion whereby we can judge whether the estimates pants, as shown in Fig.  11. The estimated differences for are reliable. If the difference is significant for some the representative frequencies are also listed in Table  2. Acceleration at finger side: [m/s ] Shear force: f(t)[N] Difference in displacement Estimated finger pad’sdeformation [m] (dB re 1.0 m) Sato et al. Robomech J (2017) 4:19 Page 9 of 11 Table 2 Differences in displacements estimated by the two on the accelerometer are, respectively, superior to the types of  methods at  representative frequencies. DT indi‑ other method for a frequency range smaller than a few cates the differential threshold of human vibrotactile per‑ tens of Hertz and that greater than 100 Hz. ception In the low-frequency range (less than a few tens of Hertz), the normal and tangential deformation of the Frequency (Hz) 10 30 100 450 finger pad are not decoupled and collectively affect the −2 −4 Difference (μm) 4.3 0.60 2.2 × 10 8.7 × 10 deformation at the finger side. The normal deformation −2 −2 DT (10%) (μm) 0.68 0.49 7.0 × 10 4.3 × 10 of the finger pad also leads to skin deformation at the −1 −2 DT (20%) (μm) 1.4 0.98 1.4 × 10 8.6 × 10 finger 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 fre - frequency bands, then we cannot rely on the two types quencies, the adverse effects of the normal deformation of estimates. As a criterion for judging the accuracy, we on the estimates of tangential deformation are minute, adopted the differential thresholds of human perception because this effect of normal deformation on the radial for the vibrotactile stimuli. The differential threshold is side is attenuated  [22]. From this aspect, at a frequency the minimum difference between two physical stimuli range of less than a few tens of Hertz, the estimation that humans can distinguish. If the differences between method based on the tangential force is regarded as being the two types of estimates are smaller than the differen - better than our accelerometer-based method, although tial thresholds, then such differences are not significant further comparisons would be necessary to draw a firm to the perception and can be ignored. Because the differ - conclusion. ential thresholds towards the amplitudes of the vibrotac- In the high-frequency range above 100 Hz, the interac- tile stimuli are typically within a range of 10–20% of the tion forces between the finger pad and material are small stimuli  [36, 37], we set 10–20% of the absolute thresh- and hardly detectable even when using one of the most olds, as presented by Gescheider et al. [34] as the criteria sensitive commercially available rigid force sensors. As for judging a significant difference. As shown in Fig.  11 shown in Fig.  10, in our experiments, estimates based and Table 2, the differences between the two types of esti - on the force sensor were found to change linearly with a mates fall below the differential thresholds of 20 and 10% gradient of −40 dB/dec, indicating that the outputs from at frequencies in excess of 23 and 50 Hz, respectively. the sensor were mostly noise of a constant level. There were no profound signals. On the other hand, because Discussion the acceleration is proportional to the square of the fre- Using the propagation of skin deformation at a fingertip, quency, the accelerometer is good at detecting high-fre- we developed a technique for sensing the shear defor- quency signals, indicating that estimations based on the mation of a finger pad. Here, we discuss the estimation accelerometer are suitable at a high-frequency range. accuracy and limitations of our method based on the Indeed, the skin deformation estimated by the acceler- experimental results. ometer reflected the different surface properties of mate - rials up to 450 Hz, as shown in Figs. 8 and 10. Accuracy of the estimates A comparison, in Experiment 3, of the two types of esti- Eec ff ts of whole finger vibration mate of a finger pad’s deformation indicated that our We did not restrain the finger joints during the measure - method, based on the accelerations at the finger side, ment in experiment 3. Hence, the finger could rotate in can be applied to a deformation in excess of 23–50  Hz. ab/adduction at the metacarpophalangeal joint. Ideally, In contrast, skin deformation at less than a few tens of such rotation should be removed throughout the experi- Hertz, at which our method may incur significant errors, ments. One may say that the effect of the finger ab/adduc - is regarded as being less effective for the perception of tion is minor. According to a study  [38] in which the fine textures  [6, 24]; nonetheless, they still influence the mechanical impedance of the index fingers in abduction perception of coarse surfaces. At the high-frequency was measured, the resonance point of the ab/adduction −7 range, in which the deformation is smaller than 10   m, motion is a few tens of Hertz, above which the rotational because of the limitations of the sensitivity of the force vibration is reduced. This also indicates that the whole sensor and the noise level of the accelerometer, the accu- finger vibration may be magnified at low frequencies and racy of our method has not been validated; nonetheless, adversely affects the estimation based on the accelerome - such a small deformation is unlikely to influence the per - ter at the finger side. Indeed, the finger pad deformations ception of texture as previously mentioned. estimated by the accelerometer were greater than those Because of the reasons given below, it is assumed that resulting from the shear force at low frequency ranges, as the estimation based on the force sensor and that based Sato et al. Robomech J (2017) 4:19 Page 10 of 11 shown in Fig.  10. Bracing the MP joint may lead to the general technique for measuring the shear deformation two types of estimates being more congruent. of a finger pad when actively touching the surface of a material. Limitations on usage As a result of comparing our accelerometer-based In this section, we discuss the limitations of the method method with another method based on the tangential we developed, and present cautions on its use. component of the interaction force between the fingertip First, our method functions at a constant finger load in and material, for a range in excess of higher than approxi- −6 the normal direction. Therefore, the method should not mately 20–50  Hz and 10   m, the estimates obtained be used when the finger load varies dynamically while with both methods are found to be in good agreement, exploring a surface. This is because the profile of the with the differences being smaller than the human dis - transfer function of the fingertip depends on the load. crimination thresholds. This indicates that our method is Hence, when our method is used, the finger load has to effective for the analysis of the perception of fine rough - be controlled in some way: e.g., instruction followed by ness surfaces with which high-frequency skin deforma- practice. To compensate for this dependence on the fin - tion is mediated. ger load, a calibration method involving variations in For practical purposes, it is preferable to solve a few the finger load is necessary, which will be the subject of related problems, such as those related to the variation in a future study. In addition, it should be mentioned that the finger load and further tests of the estimation accu - most of the previously introduced indirect measurement racy for deformation of sub-micro meter. Nonetheless, methods did not consider the changes in the finger load. this technique is expected to impact researchers in the Another caution regarding the usage is the effect of field of haptics, because skin deformation is the direct rotation or the gradient of the fingertip while the par - source of tactile sensations and thus far, many research ticipants tried to maintain the posture of their finger groups have attempted to link this information on skin during the exploration in our experiments. The accelera - deformation with human perceptions. tion at the finger side is also affected by gravity, which Authors’ contributions should not be confused with that of the skin deformation. SS and SO are the main contributors of this study, including formulating the Although we used only one accelerometer, the simultane- concepts and principles, conducting experiments and analyses, and editing the manuscript. YM and YY are credited with the principles of the methods. All ous use of a 3-axial accelerometer on the nail would be authors read and approved the final manuscript. able to compensate for any adverse effects of the finger rotation. Competing interests Finally, calibration for an individual fingertip should The authors declare that they have no competing interests. be performed before measurement by using our method. The transfer functions vary considerably depending on Availability of data and materials Not applicable. the individual. We believe that such individuality origi- nates from the profiles of fingertips and nails as well as Ethics approval and consent to participate the mechanical characteristics of the finger pad. Hence, Voluntary participants provided written informed consent before experiments. the transfer function for one person cannot be applied Funding to another. Moreover, as previously mentioned, because This study was partly supported by MEXT KAKENHI Shitsukan 25135717 and the function depends on the attachment of the acceler- 15H05923. ometer, calibration should be performed before each use. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in pub‑ Conclusion lished maps and institutional affiliations. We developed a technique for estimating the shear defor- mation of a finger pad, which is applicable even when Received: 4 April 2016 Accepted: 25 July 2017 actively touching a material. This technique requires only an accelerometer attached to the radial side of the finger - tip, and the finger pad is not covered with any materials or devices that disturb the natural touch. The propaga - References tion of skin deformation on which our method is based 1. Kawabata S, Niwa M (1989) Fabric performance in clothing and clothing manufacture. 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In: Isokoski P, Springare J (eds) Haptics: perception, devices, 38:1441–1449 mobility, and communication, vol 7283. Lecture Notes in Computer Sci‑ 31. Wiertlewski M, Hayward V (2012) Mechanical behavior of the fingertip in ence. Springer, Berlin, pp 169–174 the range of frequencies and displacements relevant to touch. J Biomech 11. Tanaka Y, Nguyen DP, Fukuda T, Sano A (2015) Wearable skin vibration 45(11):1869–1874 sensor using a PVDF film. Proceedings of IEEE World Haptics Conference, 32. Nohara K, Tada M, Umeda K, Mochimaru M (2007) Synthesizing possible pp 146–151 variations of finger structure using principal component analysis for 12. Delhaye B, Hayward V, Lefèvre P, Thonnard JL (2012) Texture‑induced non‑rigid volume registration results. In: Proceeding of 3rd international vibrations in the forearm during tactile exploration. Front Behav Neurosci symposium on measurement, analysis and modeling of human function, 6:37 pp 247–253 13. 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Lecture Notes in Computer Science. Springer, Berlin, pp 313–319 21. Sato S, Okamoto S, Yamada Y (2015) Wearable finger pad sensor for tactile textures using propagated deformation at finger side: assessment of accuracy. In: Proceedings of IEEE international conference on systems, man, and cybernetics, pp 892–896 22. Nakatani M, Shiojima K, Kinoshita S, Kawasoe T, Koketsu K, Wada J (2011) Wearable contact force sensor system based on fingerpad deformation. In: Proceedings of IEEE World Haptics Conference, pp 323–328 23. Bensmaïa SJ, Hollins M (2000) Complex tactile waveform discrimination. J Acoust Soc Am 108:1236–1245 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ROBOMECH Journal Springer Journals

Wearable finger pad deformation sensor for tactile textures in frequency domain by using accelerometer on finger side

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Springer Journals
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Copyright © 2017 by The Author(s)
Subject
Engineering; Robotics and Automation; Mechatronics; Artificial Intelligence (incl. Robotics); Control; Computational Intelligence
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2197-4225
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10.1186/s40648-017-0087-1
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Abstract

In this study, we set out to develop a method for estimating the fine and fast shear deformation of a finger pad, that is, the palm side of a fingertip, as it scans the surface of a material. Using a miniature accelerometer, we measured the acceleration 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 estimated the shear deformation of the finger pad in the frequency domain. A comparison between an estimate based on the accelerometer 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 in −6 excess of approximately 20–50 Hz and for skin deformation above 10 m. Our technique merely requires that an accelerometer be attached to the side of the fingertip, which allows active texture exploration. These estimates or measurements 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 touches a material. However, the measurement of a finger Introduction pad’s deformation is not easy because the finger pad is in In general, the physical properties of material surfaces contact with the material surface and is not exposed to characterize their tactile textures. From this standpoint, any sensing devices. In this study, we developed a tech- many research groups have investigated the relation- nique for estimating the fast and fine lateral deformations ships between different types of material properties and of a finger pad when a finger actively explores the surface the textures that are perceived by touching them. Such of a material. To the best of our knowledge, such tech- an approach has significantly contributed to industries niques have not previously been reported. involved with clothing  [1]. In contrast, texture percep- Many research groups have measured informa- tion arises as a result of the skin deformation caused by tion related to the deformation of a fingertip by using a the interaction between the finger and material. Hence, range of approaches. Nonetheless, observation through the mechanical properties of the fingertips of individu - a transparent material such as glass is a very distinctive als influence the textures perceived by those individuals. way of directly measuring deformation  [3, 4]. In princi- A typical example is the moisture content of a fingertip ple, this method is applicable only to transparent mate- influencing the friction-induced pleasantness of the sur - rial. Another approach involves using the differential face of a material  [2]. Therefore, many researchers have outputs of two accelerometers  [5] to measure the mac- attempted to link the information related to the deforma- roscopic deformation of a finger pad. One accelerom - tion of a fingertip and the perceived texture when a finger eter is attached to the dorsal side of the fingertip and another is fixed to the surface of the material contacted *Correspondence: sato.shiyunsuke@c.mbox.nagoya‑u.ac.jp by the fingertip. Provided there is no slippage, the dif - Department of Mechanical Engineering and Science, Nagoya University, ference between the values measured with these two Chikusa‑ku, Nagoya, Japan © 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 Page 2 of 11 accelerometers will be the acceleration of the deforma- In the present study, we were interested in the inten- tion of the finger pad. However, this technique cannot be sity or energy of the skin deformation for each frequency applied to a finger sliding on the surface of a material. band. In terms of texture and vibrotactile perception, the To date, several indirect measurement methods have phases of the skin vibrations were less influential, and the been employed to overcome the difficulties and limita - power or intensity of the spectral density in the frequency tions of direct measurement. For example, a number of domain are considered important  [6, 8, 23–25]. Some researchers have exploited the propagation of skin defor- researchers have demonstrated that virtual textures or mations. Any high-frequency deformation at a point on surfaces can be presented even without a representation the skin is transferred to the adjacent elastic skin tis- of the phase information of the vibratory signals  [26– sues. Bensmaïa et  al. attempted to measure these high 28]. Furthermore, our method was used to estimate the frequency components as a finger was sliding over the macroscopic deformation of the finger pad. Actual skin surface of a material by using a Hall-effect transducer deformations in the contact area between the finger pad attached to the finger  [6]. Similarly, the propagated and material surface are not spatially unique and include vibratory information was acquired using a laser Dop- phase differences. However, our method does not rely on pler velocity meter  [7, 8], microphones  [9], accelerome- estimating the spatial distribution of the deformations in ters [10], and PVDF films [11] attached to the finger close the finger pad. Therefore, the phase information acquired to the tip, as well as a microphone  [12] on the forearm. by our method may be weakly related to texture percep- Although these vibrations in the adjacent skin originate tion. Furthermore, the miniature accelerometers used for from the vibratory deformations of the finger pad, these our method are not responsible for the low frequency methods were not to measure the deformations of the signals, which means that our method cannot acquire individual finger pad. those signals in the time and frequency domains. Hence, Many researchers measured the interaction force in this study, we did not set out to address the phases or between the fingertip and material surfaces as reli - time series data of skin deformations. Rather, we focused able information related to the finger pad’s deformation on the magnitudes of the skin deformations within a lim- because the forces cause the skin to deform [13–19]. For ited frequency range. example, Wiertlewski et  al.  [13] precisely measured the interaction forces when a material slid beneath a finger - Principles used to estimate finger pad tip. However, they all measured interaction forces that deformations were distinct from the skin deformations. Here, we describe the principles on which our estimation Given the abovementioned background and related is based. First, we introduce our proposal for estimating a studies, this study set out to develop a technique for esti- finger pad’s deformation by using the propagation of the mating the lateral deformation of a finger pad and which skin deformation. Second, for comparison, we describe a could be applied to situations involving active touching. method for estimating a finger pad’s deformation based We used the propagation of skin deformation, whereby on the tangential component of the interaction force the lateral deformation of a finger pad leads to other between the finger pad and material. deformation of the skin at the radial side of the fingertip. The skin deformation at the radial side can be measured Estimation via acceleration measured at the side by an accelerometer designed for the measurement of of the finger small and fast displacements. This study is based on our As shown in Fig.  1, the lateral deformation of the fin - previous publications  [20, 21] in which we introduced ger pad propagates to the radial side through the elastic the principles of measurement and the linear causality body. Matsuura et  al.  [20] recently confirmed that the between the deformations of the pad and the radial side of a finger. In this paper, we also assess the accuracy of our method by means of a comparison with a method Finger tip based on force sensing after specifying the skin imped- ance of individuals, as well as describing the principles Deformation Propagated used for the estimation. Nakatani et  al.  [22] employed of finger pad deformation at a similar approach in which they took advantage of the the radial side Poisson effect at a fingertip. They measured the defor - mation 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 be Fig. 1 Propagation of finger skin deformation. The lateral deforma‑ tion of finger pad along X ‑axis propagates to the radial side able to handle rapid changes in the load. Sato et al. Robomech J (2017) 4:19 Page 3 of 11 deformations at the pad and side of a finger exhibit signif - Furthermore, we assumed that the shear deformation icant causality that can be repeatedly observed in shak- of the finger pad is the unique factor that determines the ing tests. Hence, the deformation at a finger pad can be skin deformation at the radial side. This indicates that linked to that at the side of the finger through the follow - only the tangential translation of the finger motion is ing procedures. considered, and the rotation around and translation along As a calibration procedure, we simultaneously meas- the longitudinal axis of the finger should not interfere ure the acceleration at the finger pad x ¨ (t) and side with the skin deformation at the radial side. In the experi- x ¨ (t) through a shaking test. The transfer function G (s) ments, only tangential finger motions were allowed. Fur - s 1 between these two types of acceleration is then deter- thermore, the participants attempted to maintain the mined by posture of their finger. Nonetheless, the frequency of the rotational motion of the finger is smaller than the active L[x (t)]A(s) s range of the miniature accelerometer that we used. G (s) = L[x¨ (t)]A(s) The abovementioned control of the finger load and (1) motions does not allow the wearers of the sensor to con- X (s) duct fully active and free touching; however, these con- X (s) trol actions are acceptable for research or investigation where L and A(s) are the Laplace transformation and gain purposes under laboratory conditions. characteristics of the accelerometer, respectively. As long as we use the same accelerometers for the finger pad and Estimation based on tangential force applied to finger pad radial side, their gain characteristics are easily canceled. Some earlier studies successfully expressed the deforma- In the frequency range where A(s) = 1 (0  dB), we can tion of the skin of a finger pad as caused by the tangential make use of this transfer function to estimate X (s). The force on the finger pad by using a spring-mass-damper acceleration at the finger side x ¨ (t) is measured, and then model  [29–31], indicating a linear relationship between s1 the lateral deformation of the finger pad in the frequency the deformation and force. This assumption holds pro - domain can be estimated by vided that the skin deformation is not large and the nor- mal load on the finger is constant. Based on this model, 1 L[x¨ (t)] s1 the finger pad’s deformation can be estimated from the X (s) = . (2) p1 s G (s) tangential force. In our method, the acceleration of the hand movement is When the finger pad is expressed by the one-degree- also measured by the accelerometer, which may interfere of-freedom model shown in Fig.  2 and the displacement with the estimates of the finger pad’s deformation. How - of the representative mass point is defined by x (t), the ever, the frequency of human hand motions is usually a equation of motion is given by few Hertz at most, which the miniature accelerometers f (t) = m x¨ (t) + cx˙ (t) + kx (t) p p p p (3) used in the present study cannot detect, so this range is excluded from our method. As described later, the accel- where f(t), m , c, and k are the tangential force on the erometers that we used can respond to frequencies in finger pad, the mass, viscosity, and spring coefficient of excess of 20 Hz. the fingertip, respectively. Hence, the transfer function This method functions on the assumption that the between f(t) and x (t) is transfer function of the fingertip does not vary during the X (s) measurement. It is known that the mechanical imped- G (s) = = . 2 (4) F (s) m s + cs + k ance of a finger pad varies depending on the normal load [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, each Finger tip Bone participant 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 from this target value for a brief instant, but we neverthe- less assumed that, for the greater part of the measure- ment, the load was fairly controlled and the change in Material surface or contactor the mechanical impedance of the skin was minor, which allows us to statistically discuss the amplitudes of skin Fig. 2 Spring‑mass‑ damper model of the tangential deformation of a fingertip deformation in the frequency domain. Sato et al. Robomech J (2017) 4:19 Page 4 of 11 When the tangential force f (t) is measured, the finger One of the accelerometers was fixed to the side of the pad’s deformation can be estimated by finger by using adhesive tape. This attachment of the accelerometer does not alter either the stiffness or the X (s) = G (s)F (s) (5) p2 2 2 viscosity of the finger pad, and does not lead to any sub - where F (s) corresponds to f (t) in the frequency jective influences on the textures experienced by wear - 2 2 domain. The mechanical parameters of the finger pad ers. Another was mounted on the contactor on which the were experimentally identified for individual participants finger pad was placed, to measure the acceleration of the in the experiments. finger pad’s deformation. The displacement of the vibrat - To the best of our knowledge, the use of the tangen- ing contactor was small, being a maximum of ±2.5  mm, tial forces for estimating the finger pad’s deformation as for which the finger pad does not slip on the contac - a result of touching material surfaces has not been used tor. Hence, the displacement of the contactor is in good previously; nevertheless, experienced researchers would agreement with that of the finger pad. The sensitivity of likely have devised a similar setup. the accelerometers was set along the X-axis. The outputs from both accelerometers were recorded at 8 kHz. Experiment 1: Transfer function for fingertip The vibration generator, which was based on a voice accelerations coil motor (X-1741, Neomax Engineering Co. Ltd., Here, we describe how we experimentally estimated the Japan), was used to deform the fingertip at various fre - transfer function between the accelerations of the pad quencies. The finger was fixed using a cradle at the proxi - and the side of the finger. mal interphalangeal (PIP) joint. The accelerations of the applied vibration were set to approximately ±10  m/s at Apparatus frequencies in excess of 10  Hz. The accelerations were The main components of the experimental appa - smaller than this value at frequencies below 10 Hz. ratus shown in Fig.  3 are two piezoelectric acceler- ometers [2302B, Showa Sokki Co. Ltd., Japan (one Procedure degree-of-freedom, 1.3  g), valid in 20–1000  Hz] and a Three male volunteers in their 20s participated in the vibration generator. experiments after providing informed consent. Their finger pads were wiped using cleaning paper before the measurement. Swept sinusoidal vibrations of 1–500  Hz were used. Twenty sweeps, including ten rising and falling series, were applied to the index finger of each participant. While the responses of the fingertip were recorded, each participant 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 We computed the Fourier transform of the outputs from the ¨ ¨ two accelerometers, X (s) and X (s), to acquire the accel- s p erations of the skin deformations in the frequency domain. Following (1), we then computed the transfer function G (s) of the fingertip. Note that this transfer function includes Accelerometer Cradle not only the properties of the fingertip but also those of the accelerometer attached to the finger side. Furthermore, Contactor ¨ ¨ the coherency between the input X (s) and output X (s) of s p the transfer function was computed to check the linearity Accelero- between the input and output. We applied these computa- meter tion procedures for the individual participants. Slider Direction of Experiment 2: Estimation of mechanical vibration Linear guide parameters of fingertip Fig. 3 Apparatus used for estimating the transfer function between As previously mentioned, to estimate the finger pad’s the finger pad and radial side. Bottom left Side view. Bottom right Front lateral deformation based on the measured lateral force view. The sensitivity of the accelerometers and the vibration applied to the finger pad was along X ‑axis and (5), we experimentally determined the mechanical Sato et al. Robomech J (2017) 4:19 Page 5 of 11 parameters in G (s). The parameters determined Note that m is not the mass of the finger pad but the sum 2 c here were used for the analysis undertaken as part of of the effective mass of the contactor and that of the mass Experiment 3. point of the finger pad. Because the available data con - sisted of the accelerations of the finger pad, we converted Apparatus this formula, as follows: As shown in Fig.  4, we used a vibration generator with a F (s) high-precision piezoelectric force sensor [9217A, Kistler, sZ(s) = s Switzerland (minimum sensitivity 1 mN)] placed between X (s) (7) the vibrator and finger contactor. The force sensor was = m s + cs + k. operated with a charge amplifier (5015A, Kistler, Switzer - land, with a response of up to 30 kHz) and measured the By substituting jω for s, this formula can be expressed as lateral component (X-direction) of the force applied to jωZ(jω) = (k − m ω ) + jωc (8) the finger pad. The participant’s fingertip was placed on the contactor while his PIP joint was fixed to a cradle in where ω is the angular velocity. This equation indicates the same way as in Experiment 1. The deformation of the that its real part is characterized by the stiffness and mass finger pad along the X-axis was measured by an acceler - of the system. Furthermore, the imaginary part is charac- ometer mounted on the contactor. The outputs from both terized by the viscosity. We computed the real and imagi- sensors were recorded at 8 kHz. nary parts of this equation by using the measured x ¨ (t) and f(t) samples, and then fitted the samples into the Procedure equations for the real and imaginary parts by using the The same participants as those taking part in Experi - least-squares method to estimate the m , k, and c values ment 1 also participated in this measurement. A series for individual participants. of 20 swept sinusoidal vibrations of up to 500  Hz were presented to each participant. The participants were also Experiment 3: Comparison of acceleration‑ instructed to maintain a finger load of 1  N during the and force‑based estimates of lateral deformation measurement. To compare the estimates of the finger pad’s deformation as determined by the two methods, we simultaneously meas- Analysis ured the acceleration at the finger side and the tangential We analyzed the mechanical impedance of the fingertip force while the participant scanned the surface of a material. of each participant. When the fingertip was modeled as a spring-mass-damper system, as shown in Fig.  2, the Apparatus mechanical impedance of the fingertip plus the alu - As shown in Fig. 5, a fingertip to which the accelerometer minum contactor is given by was attached at the radial side was used to scan the sur- face of a textured material. The material was placed on an F (s) Z(s) = aluminum plate to which the force sensor [9217A, Kistler, X (s) Switzerland (nominal force threshold: 1  mN, resonance (6) frequency: greater than 20  kHz)] same as in Experiment = m s + c + . s 2 was installed to measure the tangential component of the interaction force. The plate was supported by a pair of leaf springs so that the normal load would not interfere with the force sensor. Four types of materials were used for the measure- ment. They were a piece of cotton cloth, a flat and finely polished aluminum plate, and two types of grating scale boards made of ABS plastic. The grating scales have alter - native ridges and grooves on their surfaces. The width of each ridge was 1 mm, with the ridges repeatedly arranged at intervals of 1  mm (fine) or 9  mm (coarse). The height of the ridges was also 1 mm in both cases. Procedure Fig. 4 Apparatus used for estimating the mechanical impedance Each participant participated in this experiment after parameters of fingertip. The index fingertip was placed on the con‑ tactor and its PIP joint was fixed by a cradle during the measurement the transfer function G (s) for his fingertip had been 1 Sato et al. Robomech J (2017) 4:19 Page 6 of 11 0.1 1.0 0 1 2 10 10 10 Frequency [Hz] 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 each 0.1 type of material along the X-axis, having been instructed 0 1 2 10 10 10 to rhythmically scan a length of 5 cm over 1 s, i.e., 5 cm/s, Frequency [Hz] for 10 s. In the same way as in the previous experiments, Fig. 6 Gain (top) and coherence (middle) of the smoothed transfer the finger load was also maintained at approximately 1 N. 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 Analysis For each participant, the measured tangential force f (t) was converted into the frequency domain by a Fourier transform and, according to (5), for each combination of lateral skin deformation of the finger pad, a one degree-of- participants and materials, we computed X (s), that is, freedom system can be applied, as previously mentioned. p2 the finger pad’s deformation in the frequency domain. For In our setup, however, the mass of the accelerometer at the this computation, we used the k and c values estimated in side of the finger constitutes the system with two degrees Experiment 2 for the individual participants. Because it of freedom. As a result, the magnitude of the transfer func- was difficult to estimate m with our experimental setup, tion showed a few typical features of a system consisting of for the analysis in Experiment 3, we used a representative two resonances and an anti-resonance between them. −3 value taken from the literature [31]: m = 0.1 × 10  kg. Figure 6 also shows the magnitude of the transfer func- This value is potentially determined by the weight of local tion for each of the three participants. They were largely epidermal tissue of finger pad  [31], and it is unlikely to flat up to 80–120 Hz, and then moderately increased fol - be affected by the mass of an accelerometer at the finger lowed by a cave for which the bottom peak was between side. 120–150 Hz. We suggest that the major causes of the Similarly, from the accelerations at the finger side, individualities originate from the anatomical individu- x (t), following (2), we computed X (s). We used G (s) alities of the participants’ fingertips  [32] as well as the s1 p1 1 that was estimated for each participant in Experiment 1 individualities of the mechanical impedance of their fin - to compute X (s) for each participant. gertips. Especially, the nail profile and thickness of the p1 Furthermore, to discuss the accuracy of the estimated fingertip fatty tissue may influence the transfer function finger pad’s deformation, we computed the difference in between the skin deformation at the pad and radial side the magnitudes of these two types of estimates: |X (s)| of the finger. Given the main goal of the present study, p1 and |X (s)|. this was not pursued any further. p2 For all the participants, the coherence of the transfer Results function was sufficiently high, being greater than 0.8, Gain of transfer function for fingertip (Experiment 1) within a range of 10–450 Hz, indicating that the estima- The top part of Fig.  6 shows an example of the gain of the tion based on the transfer function is valid within this transfer function between the acceleration of the pad and frequency range. the side of the finger for one participant. As previously mentioned, because we are interested in the magnitudes of Mechanical parameters of fingertip (Experiment 2) the skin deformations, the figure shows the magnitude of Figure  7 shows examples of the real and imaginary parts G (s). The first and second peaks were observed at around of (8). From the gradient and intercept of a line into which 70 and 300  Hz, respectively. Typically, in terms of the the measured samples were fitted, the m and k values Gain Coherency Gain Sato et al. Robomech J (2017) 4:19 Page 7 of 11 -4 -6 Cloth -2 -8 Aluminum Fine grating scale (2 mm) 0 2 4 8 Coarse grating scale (10 mm) 6 2 -10 Square of angular frequency [10 (rad/s) ] 1 2 10 10 Frequency [Hz] Fig. 8 Finger pad’s lateral deformation estimated by the accelera‑ tions at the finger side. Examples of one participant -2 range of frequency components as observed in another 0 1000 2000 3000 study [13]. The deformation for the grating scales, which Angular frequency [rad/s] have a surface roughness that is larger than both the Fig. 7 Example of the real and imaginary parts of (8), the impedance of the mechanical parameters of the finger tip. Dotted curves and solid cloth and aluminum, is greater than those for the cloth lines are measured samples and linear approximations, respectively and aluminum. Naturally, the greater surface roughness led to the greater skin deformation when the exploratory motion of the participant was controlled to be approxi- mately the same across the materials. The profiles of the were estimated. Furthermore, c was estimated from the frequency responses differ depending on the materials, gradient of the approximated line of the imaginary part. although we do not thoroughly discuss the differences Table  1 lists the values estimated for individual partici- because the active hand movements of the participants pants. The mean estimated m value was 0.029 kg for all were not precisely controlled. Note that Fig. 8 shows the the participants. As previously described, m was mainly results for computational estimation, for which the accu- the effective mass of the contactor and not that of the fin - racy is discussed in the latter part of this manuscript. ger pad. The k and c values estimated here are close to Because the grating scales have a periodic surface tex- those reported in other studies in which the mechanical ture, the skin vibration might have also been periodic parameters involved in the lateral deformation of a fin - to some extent. The estimated lateral skin deformation ger pad were investigated. Nakazawa et al. [29] reported for the coarse grating scale, for which the spatial sur- that k = 310 N/m and c = 2.1 Ns/m while the finger load face period was 10 mm, exhibited a small peak at around was 1  N. Wiertlewski and Hayward  [31] reported that 14–20  Hz. Since the participant was instructed to scan these values were within a range of 600–1700  N/m and the material over a length of 5 cm in 1 s, the skin vibration 0.8–2.4  Ns/m for a 0.5  N load. The values estimated in was predicted to concentrate up to 8–10  Hz if the hand our study are largely consistent with these previously velocity was well controlled and followed a sinusoidal or reported values. bell-shaped curve. Unfortunately, these frequencies are out of the range of sensitivity of the accelerometer. How- Comparison between the acceleration‑ and force‑based ever, the expected and observed peak frequencies did not estimates of finger pad deformations (Experiment 3) substantially disagree with each other, taking account of Examples of estimated finger pad deformation the moderate control of hand exploration in our study. Figure  8 shows the estimated finger pad deformation Similarly, the skin deformation for the fine grating scale, X (s) for each type of material when scanned by any p1 for which the surface period was 2 mm, was predicted to one participant. The skin deformation includes the wide concentrate up to 40–50  Hz. The estimated skin defor - mation for the fine grating scale was mostly greater than those for the cloth and aluminum plates below this fre- Table 1 Mechanical parameters of  finger pad estimated quency range, which is consistent with the expectations. in Experiment 2 Participant Stiffness: k (N/m) Viscosity: c (Ns/m) Comparison between the acceleration‑ and force‑based P1 830 2.1 estimates P2 530 5.1 Figure  9 shows examples of the time-series data of the P3 1300 5.8 accelerations at the finger side and the tangential forces. 4 5 Imaginary part [10 ] Real part [10 ] Estimated finger pad’s deformation [m] Sato et al. Robomech J (2017) 4:19 Page 8 of 11 -4 Cloth X ( ): Acceleration-based method p1 0.6 X ( ): Force-based method p2 -6 -8 -0.6 Grating scales (fine) 0.6 Cloth -10 -4 -0.6 -6 Cloth -8 Aluminum -10 -30 Grating scales (fine) -4 -6 -8 -30 Grating scale (1 mm) 01 2 3 4 5 -10 Time [s] 10 -4 Fig. 9 Example of the time series data of the accelerations at the finger side x ¨ (t) and tangential component of the interaction force s1 -6 f (t) when the finger slid on material surfaces 2 10 -8 Grating scale (10 mm) -10 Apparently, the fine material, which is cloth in the fig - 1 2 10 10 ure, exhibited smaller variations in the accelerations and Frequency [Hz] forces than the rough material, which is the grating scale Fig. 10 Two types of estimates. Solid curves are the finger pad’s in the figure. Naturally, the skin accelerations and inter - deformation estimated based on the accelerations at the finger side. Dotted curves are those estimated based on the tangential compo‑ action forces depend on the materials, is as shown in nents of the interaction forces these time-series data. Figure  10 shows examples of the magnitudes of the finger pad deformations estimated using (2) and (5) for each material. As previously stated, because the linearity Difference threshold (20%) of the transfer function G (s) was valid for 10–450  Hz, Difference threshold (10%) these estimates are shown for this range. Smaller inter- Difference in displacement action forces  [14] and skin deformations  [8] at higher frequency bands are typical responses of the finger when -20 sliding on a material. For any types of material, the two types of estimates appear to be in reasonably good agree- -40 ment with each other. We should note that the human perceptual threshold to vibrotactile stimulation  [33, 34] -60 −7 is approximately 10 m at the most sensitive frequency. 10 10 For shear skin displacements, the threshold may be even Frequency [Hz] smaller by a few tens of a percentage point [35]. Further- Fig. 11 Perceptual differential thresholds towards the amplitudes of more, taking the smallest resolution of the force sensor vibrotactile stimuli and average difference between the two types into account, an estimated skin deformation of less than ¯ ¯ of estimates: |X (ω)| and |X (ω)|. Differential thresholds are drawn p1 p2 −7 10  m may be practically insignificant. based on literature [34] As none of the specific materials involved differences that were notably larger than those of the others, we Note that we do not know which type of estimate is more computed the average differences between the two types accurate, although the differences between them become of estimates across all the types of materials and partici- a criterion whereby we can judge whether the estimates pants, as shown in Fig.  11. The estimated differences for are reliable. If the difference is significant for some the representative frequencies are also listed in Table  2. Acceleration at finger side: [m/s ] Shear force: f(t)[N] Difference in displacement Estimated finger pad’sdeformation [m] (dB re 1.0 m) Sato et al. Robomech J (2017) 4:19 Page 9 of 11 Table 2 Differences in displacements estimated by the two on the accelerometer are, respectively, superior to the types of  methods at  representative frequencies. DT indi‑ other method for a frequency range smaller than a few cates the differential threshold of human vibrotactile per‑ tens of Hertz and that greater than 100 Hz. ception In the low-frequency range (less than a few tens of Hertz), the normal and tangential deformation of the Frequency (Hz) 10 30 100 450 finger pad are not decoupled and collectively affect the −2 −4 Difference (μm) 4.3 0.60 2.2 × 10 8.7 × 10 deformation at the finger side. The normal deformation −2 −2 DT (10%) (μm) 0.68 0.49 7.0 × 10 4.3 × 10 of the finger pad also leads to skin deformation at the −1 −2 DT (20%) (μm) 1.4 0.98 1.4 × 10 8.6 × 10 finger 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 fre - frequency bands, then we cannot rely on the two types quencies, the adverse effects of the normal deformation of estimates. As a criterion for judging the accuracy, we on the estimates of tangential deformation are minute, adopted the differential thresholds of human perception because this effect of normal deformation on the radial for the vibrotactile stimuli. The differential threshold is side is attenuated  [22]. From this aspect, at a frequency the minimum difference between two physical stimuli range of less than a few tens of Hertz, the estimation that humans can distinguish. If the differences between method based on the tangential force is regarded as being the two types of estimates are smaller than the differen - better than our accelerometer-based method, although tial thresholds, then such differences are not significant further comparisons would be necessary to draw a firm to the perception and can be ignored. Because the differ - conclusion. ential thresholds towards the amplitudes of the vibrotac- In the high-frequency range above 100 Hz, the interac- tile stimuli are typically within a range of 10–20% of the tion forces between the finger pad and material are small stimuli  [36, 37], we set 10–20% of the absolute thresh- and hardly detectable even when using one of the most olds, as presented by Gescheider et al. [34] as the criteria sensitive commercially available rigid force sensors. As for judging a significant difference. As shown in Fig.  11 shown in Fig.  10, in our experiments, estimates based and Table 2, the differences between the two types of esti - on the force sensor were found to change linearly with a mates fall below the differential thresholds of 20 and 10% gradient of −40 dB/dec, indicating that the outputs from at frequencies in excess of 23 and 50 Hz, respectively. the sensor were mostly noise of a constant level. There were no profound signals. On the other hand, because Discussion the acceleration is proportional to the square of the fre- Using the propagation of skin deformation at a fingertip, quency, the accelerometer is good at detecting high-fre- we developed a technique for sensing the shear defor- quency signals, indicating that estimations based on the mation of a finger pad. Here, we discuss the estimation accelerometer are suitable at a high-frequency range. accuracy and limitations of our method based on the Indeed, the skin deformation estimated by the acceler- experimental results. ometer reflected the different surface properties of mate - rials up to 450 Hz, as shown in Figs. 8 and 10. Accuracy of the estimates A comparison, in Experiment 3, of the two types of esti- Eec ff ts of whole finger vibration mate of a finger pad’s deformation indicated that our We did not restrain the finger joints during the measure - method, based on the accelerations at the finger side, ment in experiment 3. Hence, the finger could rotate in can be applied to a deformation in excess of 23–50  Hz. ab/adduction at the metacarpophalangeal joint. Ideally, In contrast, skin deformation at less than a few tens of such rotation should be removed throughout the experi- Hertz, at which our method may incur significant errors, ments. One may say that the effect of the finger ab/adduc - is regarded as being less effective for the perception of tion is minor. According to a study  [38] in which the fine textures  [6, 24]; nonetheless, they still influence the mechanical impedance of the index fingers in abduction perception of coarse surfaces. At the high-frequency was measured, the resonance point of the ab/adduction −7 range, in which the deformation is smaller than 10   m, motion is a few tens of Hertz, above which the rotational because of the limitations of the sensitivity of the force vibration is reduced. This also indicates that the whole sensor and the noise level of the accelerometer, the accu- finger vibration may be magnified at low frequencies and racy of our method has not been validated; nonetheless, adversely affects the estimation based on the accelerome - such a small deformation is unlikely to influence the per - ter at the finger side. Indeed, the finger pad deformations ception of texture as previously mentioned. estimated by the accelerometer were greater than those Because of the reasons given below, it is assumed that resulting from the shear force at low frequency ranges, as the estimation based on the force sensor and that based Sato et al. Robomech J (2017) 4:19 Page 10 of 11 shown in Fig.  10. Bracing the MP joint may lead to the general technique for measuring the shear deformation two types of estimates being more congruent. of a finger pad when actively touching the surface of a material. Limitations on usage As a result of comparing our accelerometer-based In this section, we discuss the limitations of the method method with another method based on the tangential we developed, and present cautions on its use. component of the interaction force between the fingertip First, our method functions at a constant finger load in and material, for a range in excess of higher than approxi- −6 the normal direction. Therefore, the method should not mately 20–50  Hz and 10   m, the estimates obtained be used when the finger load varies dynamically while with both methods are found to be in good agreement, exploring a surface. This is because the profile of the with the differences being smaller than the human dis - transfer function of the fingertip depends on the load. crimination thresholds. This indicates that our method is Hence, when our method is used, the finger load has to effective for the analysis of the perception of fine rough - be controlled in some way: e.g., instruction followed by ness surfaces with which high-frequency skin deforma- practice. To compensate for this dependence on the fin - tion is mediated. ger load, a calibration method involving variations in For practical purposes, it is preferable to solve a few the finger load is necessary, which will be the subject of related problems, such as those related to the variation in a future study. In addition, it should be mentioned that the finger load and further tests of the estimation accu - most of the previously introduced indirect measurement racy for deformation of sub-micro meter. Nonetheless, methods did not consider the changes in the finger load. this technique is expected to impact researchers in the Another caution regarding the usage is the effect of field of haptics, because skin deformation is the direct rotation or the gradient of the fingertip while the par - source of tactile sensations and thus far, many research ticipants tried to maintain the posture of their finger groups have attempted to link this information on skin during the exploration in our experiments. The accelera - deformation with human perceptions. tion at the finger side is also affected by gravity, which Authors’ contributions should not be confused with that of the skin deformation. SS and SO are the main contributors of this study, including formulating the Although we used only one accelerometer, the simultane- concepts and principles, conducting experiments and analyses, and editing the manuscript. YM and YY are credited with the principles of the methods. All ous use of a 3-axial accelerometer on the nail would be authors read and approved the final manuscript. able to compensate for any adverse effects of the finger rotation. Competing interests Finally, calibration for an individual fingertip should The authors declare that they have no competing interests. be performed before measurement by using our method. The transfer functions vary considerably depending on Availability of data and materials Not applicable. the individual. We believe that such individuality origi- nates from the profiles of fingertips and nails as well as Ethics approval and consent to participate the mechanical characteristics of the finger pad. Hence, Voluntary participants provided written informed consent before experiments. the transfer function for one person cannot be applied Funding to another. Moreover, as previously mentioned, because This study was partly supported by MEXT KAKENHI Shitsukan 25135717 and the function depends on the attachment of the acceler- 15H05923. ometer, calibration should be performed before each use. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in pub‑ Conclusion lished maps and institutional affiliations. We developed a technique for estimating the shear defor- mation of a finger pad, which is applicable even when Received: 4 April 2016 Accepted: 25 July 2017 actively touching a material. This technique requires only an accelerometer attached to the radial side of the finger - tip, and the finger pad is not covered with any materials or devices that disturb the natural touch. The propaga - References tion of skin deformation on which our method is based 1. Kawabata S, Niwa M (1989) Fabric performance in clothing and clothing manufacture. 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