# Influence of finger movement direction on friction-induced vibrations and perception of textured surfaces

Brigitte Camillieri, Jenny Faucheu, Rochelle Ackerley, Nolwenn Le Moing, Marie-Ange Bueno

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Brigitte Camillieri, Jenny Faucheu, Rochelle Ackerley, Nolwenn Le Moing, Marie-Ange Bueno. Influence of finger movement direction on friction-induced vibrations and perception of textured surfaces. Tribology International, 2025, 211, pp.110844. 10.1016/j.triboint.2025.110844. emse-05097245

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# Influence of finger movement direction on friction-induced vibrations and perception of textured surfaces

Brigitte Camillieri<sup>a, ∗</sup>, Jenny Faucheu<sup>b, †</sup>, Rochelle Ackerley<sup>c, ‡</sup>, Nolwenn Le Moing<sup>b</sup>,
Marie-Ange Bueno<sup>a, †</sup>

ARTICLE INFO

Keywords:

Tactile

Friction

Finger orientation

Perception

Textile

A B S T R A C T

Many factors can influence how we touch surfaces, where we adapt our finger exploration strategy to the task, material properties, and texture. We studied the influence of finger movement direction, i.e. anteroposterior or lateral, on friction-induced vibrations during touch and perceptual discrimination differences of spatial periods. Three experiments were carried out: two investigating the vibrations induced in the finger, during different sliding velocities and also in changing the investigated textile surfaces, finger angle, velocity, and normal force, as well as a third experiment investigating the perceptual discrimination of textured surfaces. We found that finger vibrations during moving touch were consistently larger in the anteroposterior dimension, especially for frequencies higher than 100 Hz, regardless of the condition or surface. However, for frequencies below 60 Hz, finger vibrations were smaller, similar or greater in the anteroposterior dimension depending on finger velocity, where the velocity equality threshold for movement direction effect was approximately 40 mm/s. In terms of perception, small differences in spatial periods, i.e. 100 or 200 µm, were better discriminated using lateral movements, while discrimination was significantly better using anteroposterior movements for larger spatial period differences, i.e. 300 µm. These results can be explained by different psychometric curves for the movement direction, representing the response level relative to spatial period differences, where the slopes of the discrimination threshold differ between the anteroposterior and lateral directions. These results are discussed relative to the different vibrational behaviours in anteroposterior and lateral movements due to the influence of fingerprints and arm biomechanical behaviour.

1. Introduction

Natural tactile exploration of a surface can be considered as a pro-
cedure to make a classification in three mechanical dimensions, i.e.
softness/hardness, roughness/smoothness, and stickiness/slipperiness,
and in one thermal dimension, i.e. warm/cool [1,2]. From this explo-
ration, we are able to rapidly discriminate and recognize materials and
textures. During tactile evaluation, the finger can move in different ways
depending on the material and on the task, i.e. the evaluation of soft-
ness/hardness, roughness/smoothness or stickiness/slipperiness, where
it can be static (e.g. exerting downwards pressure), or scan the surface
with various velocities or trajectories (e.g. linear or more complex) [3].
During a whole tactile exploration, linear trajectories have been

identified to be the most common (representing 70 % of touch time
during a tactile task) and are often used for the evaluation of roughness
and slipperiness. The static surface exploration strategy is the least
common (representing 8 % of touch time during a tactile task) and is
preferentially used for hardness assessment. During finger movements in
softness/hardness evaluation, lateral movements tend to dominate,
relative to anteroposterior (AP), i.e. proximal-distal, movements.
Moreover, anteroposterior movements are more commonly used to
explore harder materials and lateral movements for softer materials.
More generally, the task, material properties [4], and texture [5] can all
influence the exploration strategy. The tactile task also influences the
finger movement speed and normal force [6].

Exploration is linked to tactile perception, which is in turn affected

<footnote><sup>a</sup> Université de Haute Alsace, Laboratoire de Physique et Mécanique Textiles (LPMT, UR 4365) École Nationale Supérieure d'Ingénieurs Sud-Alsace, Mulhouse F-68093, France</footnote>

<footnote><sup>b</sup> Mines Saint-Etienne, Univ Lyon, CNRS, UMR 5307 LGF, Centre SMS, Saint-Etienne F-42023, France</footnote>

<footnote><sup>c</sup> Aix Marseille Univ, CNRS, CRPN (Centre de Recherche en Psychologie et Neurosciences - UMR 7077), Marseille, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: marie-ange.bueno@uha.fr (M.-A. Bueno).</footnote>
by the normal force exerted by the finger during touch [7], sliding di-
rection [8], and velocity [9]. During finger movements, fluctuations in
finger-surface interactions can be measured via skin deformation, and
these can depend on the movement direction, i.e. proximal-distal or
medial-lateral (radial-ulnar), and for different normal forces or sliding
velocities [10]. It is known that fingerprint microgeometry plays a role
in shaping tactile perception, where the spatial period of the fingerprint
can shape vibrations elicited in the skin during texture exploration. This
interaction can be observed in friction-induced vibrations during tactile
exploration, with person-specific frequency peaks for a given texture
[11–13]. Consequently, the influence of fingerprints on finger vibra-
tions, due to texture interpenetration, is significant when fingerprints
are parallel to the texture and perpendicular to the sliding movement
[14,15], similar to a ratchet mechanism. However, it has recently been
shown that this influence diminishes and can become negligible when
the explored texture is compressible, i.e. in the perpendicular surface
direction. Therefore with low hardness, as it is often the case for textile
fabrics because of entrapped air and hairiness, the orientation of the
fingerprints relative to the surface texture may have no significant role
for the friction-induced vibrations during their exploration [16].

Even if the interaction between fingerprints and surface texture were
negligible, finger movements can have an influence on friction force,
instantaneous variation, and vibrations induced in the finger. Higher
vibrations have been obtained in distal, rather than proximal, directions
for anteroposterior movements [8]; however this is a generalization, as
proximal direction anteroposterior movements give higher vibrations
than the ulnar direction with lateral movement [17]. In a previous
study, induced finger vibrations in lateral and anteroposterior move-
ments were compared and it was found that: i) below a frequency
threshold of approximately 75 Hz, higher vibrations were observed in
lateral, rather than anteroposterior movements, ii) conversely lower
vibrations in lateral movements were obtained for higher frequencies
[16]. However, this result was observed for a given velocity, normal
force, and finger angle, but these conditions themselves could also in-
fluence the resulting vibrations induced in the finger [9,18].

The objective of the present study was to characterize differences in
vibrations induced in the finger for back-and-forth movements made in
the lateral or anteroposterior directions, considering the influence of
sliding velocity, but also finger angle perpendicular to the surface, and
normal load, for different kinds of textures (textile fabrics and 3D
printed surfaces). The hypothesis was that differences in induced vi-
brations could change the perception of a textured surface. Therefore,
we also aimed to study the influence of finger movement direction, i.e.
lateral or anteroposterior movement, by measuring the discrimination
ability to discern fine geometrical difference in textured surfaces by
human participants.

## 2. Materials and methods

Three experiments were carried out, two investigating the vibrations
induced in the finger, during different sliding velocities (Experiment 1)
and in changing the textile surface, angle, velocity, and normal force
(Experiment 2), as well as a study investigating the perceptual
discrimination of textile surfaces (Experiment 3). These all used a set of
textures that varied on different characteristics.

### 2.1. Investigated surfaces

For the vibration experiment, four different kinds of textile fabrics
were investigated. A Pekin fabric was used for all experiments and a
cotton plain woven, velvet, or polar fabric were occasionally used in
order to diversify the fabrics considered.

Pekin is globally a kind of plain woven fabric with two different warp
yarns: a fine yarn (blue) and a coarser yarn (white). The repeat for warp
is three blue yarns and two white yarns inserted and, during weaving,
the two white yarns are woven together, creating a surface with bumps

(white yarns) and grooves (blue yarns). The spatial period is 7 patterns/
cm, with a similar width of bumps and grooves of 715 µm, with a mean
bump height of 160 µm, measured with a digital microscope (VHX 6000
Keyence, France) (Fig. 1).

The cotton plain woven is an orthotropic fabric with identical weft
and warp yarns, with the same number of yarns per centimetre in both
directions (23 yarns/cm), giving a relatively smooth, i.e. less rough,
surface for a textile fabric (Fig. 2a).

The velvet and polar fabrics are textiles with a large number of hairs
emerging more or less orthogonally from the lower (ground) surface of
the textile, with a main hairiness direction for velvet fabric (Fig. 2b and
c).

In addition, a coarse polymer replica by 3D printing of the Pekin
fabric was tested. The spatial period is 6.3 patterns/cm, with a similar
width of bumps and grooves of 800 µm, and with a mean bump height of
280 µm, measured with a digital microscope (VHX 6000 Keyence,
France) (Fig. 3).

To complement the tribological experiments, a psychophysical
experiment was built to investigate the relationship between the vi-
brations induced by the stimulus and the resulting sensation, in order to
establish the limits of the sensory performance [19]. Such psychophys-
ical experiments use participants who judge the presence or magnitude
of a series of stimuli built through careful adjustments of their physical
attributes. To build this series of stimuli, a fine Pekin polymer replica in
terms of bump and groove widths was created by 3D printing, having
715 µm width for both bumps and grooves, with a bump height of
500 µm. From this reference, two sets of textures with periodical grooves
were designed with a bump height identical to the reference. A set,
named “iso-groove”, with the same groove width as the reference
(715 µm), but with a bump width from 215 to 915 µm in steps of 100 µm
(i.e. 215, 315, 415… to 915 µm) was made and a second set named
“iso-bump” with a bump width of 715 µm, the same as the reference, but
with a groove width from 215 to 915 µm in steps of 100 µm. The spatial
period, i.e. the addition of the reference width and the variable width,
was then in the range between 930 µm and 1630 µm.

The necessary accuracy in terms of bump and groove widths for these
two sets of textured surfaces was not possible to achieve by woven
process, therefore 3D printing was preferred at the expense of bump
height, which is higher than for Pekin woven fabric.

### 2.2. Vibration measurement

In Experiments 1 and 2, a tribometer designed for tactile measure-
ments was used to measure vibrations. It contained a three-axis load cell
(model 3A60-20N, Interface Inc., Scottsdale, Arizona) on which the
sample to be rubbed was fixed. For this research, the slider was the
human finger, during active touch (alternating movement with a sliding
displacement of 40 mm in each direction). An accelerometer (Deltatron
4517-002, Bruël & Kjaer, Mennecy, France) was glued to the skin 3 mm
above the finger nail to measure friction-induced vibration propagation
in the finger [20]. The signals from the three axis load cell forces and
from the accelerometer were recorded with Pulse software and hard-
ware from Bruël & Kjaer at 1000 Hz. The normal force measured by the
load cell was displayed live during the measurement on a screen in front
of the participant, as this was required to maintain a constant force. To
limit fatigue, the participant had two supports on which to place their
arm, one for lateral movements, the other for anteroposterior move-
ments, as well as two rests.

Finger vibrations were analysed in the frequency domain following
the same procedure used in [16]. Finger acceleration was expressed as
the root mean square (RMS) relative to frequency and measurement
giving a spectrum, named autospectrum, which is the average of 14
spectra. To quantify the vibrations on a specific frequency bandwidth,
the spectral power *SP* is calculated as follows:
<figure><img src="image_2.png" /><figcaption>Fig. 1. Pekin woven fabric a) picture (the red arrow represents 1 mm and is oriented in the direction of movement) and b) 3D profile.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. a) Plain woven b) velvet and c) polar fabrics investigated. The red arrow represents 5 mm and is oriented in the direction of movement.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Pekin coarse replica by 3D printing a) picture (the red arrow represents 1 mm and is oriented in the direction of movement) and b) 3D profile.</figcaption></figure>

$$SP(\Delta f) = \sqrt{\frac{1}{C} \sum_{i=1}^{N} RMS_{i}^{2}} \qquad (1)$$

where

f: the frequency in Hz,

Δf: the considered frequency bandwidth [f<sub>1</sub> - f<sub>N</sub>],

RMS<sub>i</sub>: the root mean square of the acceleration at the f<sub>i</sub> frequency, in m/s<sup>2</sup>,

C: factor depending on the weighing window used, in this case, it is a Hanning window and C = 1.5.

## 2.3. Experimental tasks

The experiments were performed in accordance with the 1964 Hel-sinki declaration and its later amendments, apart from pre-registration, as well as with local ethical standards. The participants gave informed consent and provided information about their year of birth. The experiments took place in an air-conditioned room (20 ± 2°C and 65 ± 5 % of relative humidity). Each participant washed and dried her/his hands before each experiment.

Two different approaches were carried out: i) measurement of finger/fabric interactions via vibrations induced in the finger (Experiments 1 and 2) and ii) the perception of tactile discrimination of textured surfaces (Experiment 3).
### 2.3.1. Finger/fabric interaction and induced vibrations

For movement-induced finger vibration measurements, two different experiments were conducted using active touch with an alternating, back-and-forward finger movement, in both anteroposterior and lateral planes. Experiment 1 was the main experiment, which was based on a preliminary, previously published study [16], characterized by an active finger movement with alternating displacement of 40 mm, at an average velocity of 40 mm/s, with the finger inclined at approximately 20° to the surface being touched and a normal contact force of 0.5 N. Experiment 2 is a variation of Experiment 1. In a previous published study [16], differences in finger vibrations from anteroposterior and lateral movements were found around 75 Hz. For the present study, in Experiments 1 and 2, the threshold was found between 65 and 95 Hz depending on the participant. Therefore, the vibrational data processing was adapted to focus on the pertinent frequency bandwidths outside these threshold zones: below 60 Hz, i.e. [10–60 Hz] and above 100 Hz, i.e. [100–800 Hz].

#### Experiment 1: Influence of sliding velocity on induced vibrations in the finger

Ten participants (5 females and 5 males, 24–62 years with an average age of 37; all right-handed) took part in this experiment. For experiment 1, each participant had to maintain a fixed finger angle of approximately 20° to the surface of the fabric during touch and apply a normal force of 0.5 N. The same movement was repeated 4 times for 3 different velocities, i.e. 20, 40 and 50 mm/s. The finger velocity range was chosen in agreement with results obtained in other textile tactile tasks, as which is in the optimal range to activate skin mechanoreceptors [21]. The duration of a measurement was 32 s and the test order of velocity was randomized. Using a metronome, the participant was guided to the correct finger movement velocity, at each top, they had to have covered the 40 mm required distance (two marks were plotted on the surface) and then change the direction of movement, with a smooth movement. A training phase was carried out at the start of the test. For the normal force, the participant had a visual feedback with the indicated target.

In a previous study [16], two fabrics were used, namely the Pekin and the plain fabrics, as described in Section 2.1. As Pekin presented a stronger difference in finger vibration behaviour in lateral and anteroposterior movements, in comparison to plain woven fabric, it was deemed a good candidate for the present experiment. Moreover, the 3D printed coarse polymer replica of the Pekin was used following the same protocol. Both Pekin fabric and coarse replica were tested together, in a random order.

#### Experiment 2: Influence of textile surfaces, angle, velocity, and normal force on vibrations induced in the finger

In a further experiment, different experimental conditions were studied by changing the finger angle, normal force, or velocity, for various textile fabrics for each finger movement, i.e. lateral or anteroposterior. The goal was primarily to test the robustness of the results obtained in terms of lateral versus anteroposterior movements, rather than investigating the specific influence of each of these parameters on movement-induced vibrations. Four participants (2 females and 2 males, 29–63 years with an average age of 47; all right-handed) took part in Experiment 2.

For this experiment, finger velocity, finger angle, or normal force were changed: finger velocity 40 or 80 mm/s, angle approximately 20° or 40°, normal force 0.5 N or approximately 1.5 N. This experiment was carried out on the four fabrics described in Section 2.1, i.e. Pekin, plain woven, velvet, and polar fabrics.

The first half of each recording was made under baseline conditions, i.e. 40 mm/s, 20°, and 0.5 N, and then, at a beep, the participant was asked to change the velocity, angle, or normal force. This protocol was preferred to separate trials for two different conditions, even if the data treatment was longer, because the participants considered it was easier for reproducing the conditions. For each participant, each tested condition was repeated twice; therefore, each participant had 48 tests (4

fabrics, 3 parameters, 2 finger movements, and 2 repeats per condition). The duration of a measurement was 11 s.

### 2.3.2. Perception of finger/textured surface interactions

#### Experiment 3: Perceptual discrimination of textured surfaces

A complementary experiment focused on touch perception, rather than vibrational measures. For Experiment 3, 28 participants (14 females and 14 males with an average age of 33 years ± 14) took part in a two-alternative forced choice (2AFC) test [19], to discriminate which of two fabrics were judged to have the larger line spacing. Fabric samples were installed in a sample case that enabled the participant to touch two samples in a single trial without seeing them. These two samples were presented together and could be explored alternatively by the participant. Table 1 gives the dimensional characteristics of the sample pairs used in the perceptual experiment. Both iso-groove and iso-bump sets of surfaces, described in Section 2.1, were selected to assess the performance of lateral and anteroposterior conditions to discriminate the samples. The pairs were built regarding the width difference of the grooves for the iso-bump pairs and the width difference of the bumps for iso-groove pairs. For both iso-groove and iso-bump pairs, a reference of 215 or 615 µm was chosen that was matched to a different fabric surface with 100, 200, or 300 µm difference (see Table 1 for pair combinations). Participants were asked to use the index finger of their dominant hand to stroke the sample surface, either in the lateral or anteroposterior dimension, then indicate the surface that they perceived had the larger spacings. The finger velocity was not specifically controlled, so that the participant could adapt their finger velocity to best fulfil the task; however, for all participants, finger velocity was observed to be between 30 and 70 mm/s.

### 2.4. Statistical analyses

For Experiments 1 and 2 on finger movement-induced vibrations, Shapiro-Wilk tests (p-value > 0.05) were first conducted on each data set to verify normality, and second, equality of variances for each experiment were compared with Fisher-Snedecor tests (F-test, p-value > 0.05). For data that did not violate these assumptions, means were compared using Student's tests (t-test, p-value > 0.05) for paired data. For violations of one or both assumptions, non-parametric Wilcoxon signed rank tests for paired data were used (p-value > 0.05).

In the perceptual experiment, the ratio of correct answers for each pair of samples was compared to chance level using a binomial test ($P_{\text{chance}} = 50 \%$) with a significance level $\alpha$ set at 5 % (p-value<0.05). In addition, the ratio of correct answers for lateral and anteroposterior conditions was also compared in the same way.

## 3. Results

### 3.1. Finger/fabric interaction and movement-induced vibrations

#### 3.1.1. Influence of finger velocity on movement-induced vibrations

The mean RMS autospectra from all the participants in Experiment 1, for the 3 tested finger velocities, i.e. 20, 40 or 50 mm/s, were calculated and are illustrated in Fig. 4. For both anteroposterior and lateral finger movements, the vibrations increased in spectral power with finger velocity from 20 to 50 mm/s, which is coherent with the literature [11, 22].

Considering the spectral power for all participants over both finger directions, the influence of finger direction (lateral or anteroposterior) was statistically significant (p-value < 0.001). Fig. 5 shows boxplots of the spectral power for the whole frequency bandwidth [3–800 Hz] for the three velocities, where it can be observed that velocity has a significant influence on finger vibrations in both lateral and anteroposterior movement directions, and moreover, stronger vibrations were generated in the finger for anteroposterior than for lateral movements.
<table><caption>**Table 1**
Dimensional characteristics of the sample pairs used in the perceptual experiment.</caption><thead><tr><th rowspan="3">Width difference (µm)</th><th colspan="4">Iso-groove surface set</th><th colspan="4">Iso-bump surface set</th></tr><tr><th colspan="4">Groove width: 715 µm</th><th colspan="4">Bump width: 715 µm</th></tr><tr><th colspan="4">Bump width (µm)</th><th colspan="4">Groove width (µm)</th></tr><tr><th></th><th>Sample 1</th><th>Sample 2</th><th>Sample 1</th><th>Sample 2</th><th>Sample 1</th><th>Sample 2</th><th>Sample 1</th><th>Sample 2</th></tr></thead><tbody><tr><td>Δ100</td><td>215</td><td>315</td><td>615</td><td>715</td><td>215</td><td>315</td><td>615</td><td>715</td></tr><tr><td>Δ200</td><td>215</td><td>415</td><td>615</td><td>815</td><td>215</td><td>415</td><td>615</td><td>815</td></tr><tr><td>Δ300</td><td>215</td><td>515</td><td>615</td><td>915</td><td>215</td><td>515</td><td>615</td><td>915</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Average for all participants of the root mean square (RMS) spectral power of the acceleration due to movement-induced finger vibrations relative to frequency with Pekin fabric for a) anteroposterior (AP) and b) lateral finger movements. The red lines represent 60 Hz (left) and 100 Hz (right).</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Global spectral power boxplots for each velocity with p-values for a) anteroposterior (AP) and b) lateral movements. Crosses represent mean values, middle lines are median values, the lowest line of the box is the 1st quartile Q1 and the highest line is the 3rd quartile Q3, the lowest whisker is the maximum between the minimum datum and Q1 – 1.5 • (Q3 – Q1) and the highest whisker is the minimum between the maximum datum and Q3 + 1.5 • (Q3 – Q1). * corresponds to a significative influence (p-value<0.05) and for a very significative influence ** for p-value< 0.01 and *** for p-value< 0.001.</figcaption></figure>

To analyse this influence more deeply, vibrations were separated for low [10–60 Hz] and high [100–800 Hz] frequency components. The overall effect of finger movement direction (lateral or anteroposterior) on spectral power was not statistically significant for the low frequency range (p-value = 0.984), but was significant for the high frequency range (p-value < 0.001). The influence of velocity was further investigated per frequency range, where it can be seen in Fig. 6 that, regardless

of finger movement direction, the influence of finger velocity was overall stronger in the high frequency range [100–800 Hz], than the lower range [10–60 Hz].

Fig. 7 illustrates the power spectral ratio between anteroposterior and lateral finger vibrations. For frequencies over 100 Hz, the ratio is clearly higher than 1 (Fig. 7b), showing a strong influence of finger movement with higher vibrations for anteroposterior movements.
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Spectral power boxplots for each velocity with p-values for a) and c) anteroposterior and b) and d) lateral movement for the two selected frequency bandwidths: a) and b) [10–60 Hz] and c) and d) [100–800 Hz]. \* corresponds to a significative influence (p-value<0.05) and for a very significative influence \*\* for p-value< 0.01 and \*\*\* for p-value< 0.001.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Spectral power anteroposterior (AP)/lateral ratio boxplots for each finger velocity for a) [10–60 Hz] and b) [100–800 Hz]. The red line corresponds to equal spectral power for anteroposterior and lateral movements.</figcaption></figure>
However, for the lower frequency range [10–60 Hz], the pattern is different, where vibrations for anteroposterior movements were lower than lateral movement at 20 mm/s, similar at 40 mm/s, and higher at 50 mm/s. Thus, 40 mm/s can be considered as a velocity equality threshold for movement direction effects on finger vibrations below 60 Hz. The same phenomenon was also obtained from the coarse polymer replica by 3D printing of the Pekin fabric (Fig. 8).

Overall, for low frequencies [10–60 Hz] at the slower velocity (20 mm/s), texture exploration produced greater finger vibrations for lateral movements, and faster (50 mm/s) exploration gave greater finger vibrations for anteroposterior movements. However, finger vibrations at high frequencies (between 100 and 800 Hz) were always larger in spectral power for anteroposterior than lateral movements.

Due to the significant differences between the Pekin fabric and its coarse replica, in terms of bump height and bump and groove widths, the tribological results obtained from these two surfaces cannot be quantitatively compared.

### 3.1.2. Movement-induced finger vibrations in anteroposterior and lateral directions over various textiles and conditions

Data obtained in Experiment 1, Experiment 2, and from a previous published study [16] were analysed together. This previous study was conducted under approximately similar active touch conditions, on 5 participants, using Pekin and plain fabrics, stroked at 40 mm/s and 0.5 N force, with a finger angle of approximately 30°.

Fig. 9 shows that finger vibrations above 100 Hz were higher for in anteroposterior than lateral movements (p-value < 0.001; Fig. 9b), whereas below 60 Hz, the opposite was found where vibrations were higher for lateral movements (p-value = 0.001; Fig. 9a). Fig. 10 shows data from the coarse polymer replica by 3D printing of the Pekin fabric following Experiment 1 protocol. These results demonstrate a similar tendency for the effect of movement direction on finger vibrations above 100 Hz (p-value < 0.001; Fig. 10b), although this was not significant below 60 Hz (p-value = 0.529; Fig. 10a).

### 3.2. Perceptual experiment

Experiment 3 found that line space texture discrimination performance was also different in lateral and anteroposterior directions, under these conditions. For stimulus pairs with line gap differences of Δ100 and Δ200 (Table 1), regardless of whether iso-grooves or iso-bumps were tested and the results were merged because no difference was observed. Lateral movement discrimination was higher than chance

level ($P_{L,\Delta100} = 61\%$, p-value = 0.03 and $P_{L,\Delta200} = 69\%$, p-value < 0.001), whereas for anteroposterior movements, discrimination was at chance level ($P_{AP,\Delta100} = 47\%$, p-value = 0.10 and $P_{AP,\Delta200} = 56\%$, p-value = 0.07). For pairs with differences of Δ300, i.e. larger gaps, discrimination was better than chance for both directions of movement ($P_{L,\Delta300} = 59\%$, p-value = 0.04 and $P_{AP,\Delta300} = 73\%$, p-value < 0.001).

In a further analysis directly comparing the movement direction, lateral movements gave better discrimination than anteroposterior movements at line gap differences of Δ100 and Δ200 (p-value = 0.023 and p-value = 0.028, respectively), however, at pair differences of Δ300, anteroposterior movements conversely gave better discrimination than lateral movements (p-value = 0.013).

## 4. Discussion

As previously postulated, we found that vibrations induced in finger skin touching different surfaces are influenced by both finger movement direction and velocity. For finger movements in anteroposterior and lateral directions in Experiment 1, we found that finger vibration power increased with movement velocity (cf. Figs. 4 and 5); however, anteroposterior movements gave overall consistently stronger vibrations. When we split the vibration data into lower [10–60 Hz] and higher [100–800 Hz] frequency bands, further differences became apparent. At the lower frequencies, vibrations were of lower spectral power and there was no significant difference between the direction of movement, although, spectral vibration power changed more with velocity for anteroposterior movements (Fig. 6a and b). The larger differences occurred at higher frequencies, i.e. 100–800 Hz, where there was a clear difference between anteroposterior and lateral movements (Fig. 6c and d). For lateral movements, spectral power for the higher frequencies stayed approximately similar to that of the lower frequencies, but there was a large increase for the anteroposterior movements (Fig. 6). Overall, the anteroposterior dimension gave a stronger relation between increasing vibrational power and velocity of movement, with greater differences at higher frequencies. Related to this, the firing frequency of mechanoreceptors in the skin increases with touch velocity [23,24], thus corresponds well with the vibrational signal. However, for lower frequencies, 40 mm/s movement velocity seemed to be a threshold; below this velocity finger vibrations were higher with lateral movements, and above this, finger vibrations were higher with anteroposterior movements (Fig. 7). Further, similar results, with stronger effects for the anteroposterior dimension, were found for both the Pekin fabric and its coarse polymer replica (Figs. 7 and 8).

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** In the case of the coarse Pekin replica by 3D printing, spectral power anteroposterior (AP)/lateral ratio boxplots for each finger velocity for a) [10–60 Hz] and b) [100–800 Hz]. The red line corresponds to equal spectral power for anteroposterior and lateral movements.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 9. Spectral power of anteroposterior (AP) relative to lateral movement from results of Experiment 1, Experiment 2, and a previous study [16] for a) [10–60 Hz] and b) [100–800 Hz] vibrations. The grey line corresponds to anteroposterior equal to lateral.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 10. For the coarse polymer replica of the Pekin fabric, spectral power of anteroposterior (AP) relative to lateral movement spectral power for a) [10–60 Hz] and b) [100–800 Hz] vibrations. The grey line corresponds to anteroposterior equal to lateral.</figcaption></figure>

These results were extended in Experiment 2, where we investigated more conditions, including different fabrics, normal finger force, and finger angle, as well as touch velocity, over the anteroposterior and lateral dimensions. We combined data from three different experiments and found again that anteroposterior movements showed higher spectral vibrational power for the high frequency range [100–800 Hz] and this effect was the same for the Pekin fabric coarse replica (Figs. 9 and 10). Additionally, over this variety of conditions, it was also found that vibrations were conversely greater for lateral movements in the lower range [10–60 Hz]. These additional data support the finding overall that anteroposterior movements generate much more vibrations in finger skin. The next question was to determine whether these vibrational differences could be related to perceptual differences in touching the textures.

Experiment 3 thus probed these differences further, on a perceptual level, which entails the processing of all information generated during touch, and not just skin vibrations. We chose a line space textural discrimination task to identify whether anteroposterior or lateral movements were better to discern differences between textures. For

larger gaps (Δ300), tactile perceptual discrimination was high and significantly better than chance for both anteroposterior and lateral movements, where anteroposterior movements gave a better level of discrimination. Surprisingly, at smaller differences between textures (Δ100 and Δ200, i.e. the task was more difficult), anteroposterior movements did not allow discrimination of line spacing between textures, but lateral movements were significantly better than the chance level for discrimination. Interestingly, no differences were found between iso-groove or iso-bump textures, thus these likely generated similar vibrational patterns in the skin.

Based on these observations, the psychometric curves representing the response level for lateral and anteroposterior touch can be drawn qualitatively, as illustrated in Fig. 11. Psychometric functions set a detection threshold and the response level is positively related to the stimulus level following a typical S-shaped function [25]. The discrimination performances observed for lateral and anteroposterior conditions indicated that the S-shape curve related to the lateral condition increased (from chance level) at lower stimulus level than for the anteroposterior condition, i.e. better discrimination at smaller textural
<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Qualitative representation of response level regarding stimulus level, i. e. difference in the spatial period Δ for touch during lateral (L) and anteroposterior (AP) movements.</figcaption></figure>

spacing for lateral movements. Conversely, it also shows that the S-shaped curve representing the anteroposterior touch should exhibit a larger slope that the one representing the lateral movement. Therefore, it turns out that the two S-shaped curves cross each other for a stimulus level between Δ200 and Δ300.

The discrimination under-performance of the anteroposterior condition for small stimulus levels might be due to the differences in terms of induced vibrations between movements conditions. During finger movement over a surface, the spatial periods of this surface are included in the induced vibrations, therefore the smaller the spatial periods, the higher the corresponding frequency peaks [11,12]. From the tested surfaces in Experiment 3, i.e. the 3D printed surfaces, due to the total spatial period between 930 and 1630 microns and the participant finger velocity between 30 and 70 mm/s, the frequency of the structure should be between 18 and 75 Hz, i.e. less than 100 Hz. This frequency range for the given velocities corresponds to the case where the friction-induced vibrations are similar or lower for lateral than for anteroposterior movement directions. Moreover, the difference of frequencies due to the difference of spatial periods for Δ100 pairs are between 2 and 7 Hz, 3 and 13 Hz for Δ200 pairs and 4 and 18 Hz for Δ300 pairs. We postulate that the higher induced vibrations in anteroposterior direction might override the induced vibrations that carry useful information related to the texture topography, i.e. small difference of frequency and then reduce the discrimination performance. On the other hand, at low frequencies, the induced vibrations are sensitive to the finger velocity which means that the participant has the opportunity to tune her/his finger velocity to best fulfil the discrimination task under free-finger velocity task [6,9,26]. It is also likely that changes in finger velocity can impact the perception.

Taking all of our experiments together, we find that the vibrations induced in the finger skin on touching a texture are clearly influenced by the direction of finger movement, and further, that this can have effects on the perception of the texture. Although finger vibrations were much greater using anteroposterior movements, especially at higher vibrational frequencies, this did not relate to a better perceptual capacity. The participants were less able to judge textural differences in the anteroposterior direction; thus, it seems that to discern finer differences textures, lateral finger movements are more suited to the task. Below, we explore potential explanations of this.

The two types of movement, anteroposterior and lateral, are biomechanically different, which could influence the vibrational and perceptual results. Presently, participants were relatively free to move their finger, hand, and to some extent their arm as well, meaning that anteroposterior and lateral movements engaged different sets of

muscles. Lateral movements were more typically constrained to the finger, using more the intrinsic dorsal interossei muscles, for side-to-side movements. Conversely, anteroposterior movements tended to be somewhat larger, using the arm, as well and implicating the extrinsic flexor and extensor muscles located in the forearm, and even small shoulder movements. Although these movements were not quantified, they were clearly different, which may have given an increased range of movement and/or force in the anteroposterior dimension, thus inherently increasing the vibrations generated in the skin. Furthermore, in lateral dimension for the low velocity (20 mm/s), stick-slip could occur inducing higher spectral vibrations in the 10–60 Hz frequency range.

Another reason for differences between anteroposterior and lateral touch may be due to fingerprints. Why fingerprints exist has long been debated in the scientific literature, but it is evident that they play a role in shaping touch. From the association of type I mechanoreceptors (fast-adapting Meissner and slowly-adapting Merkel types) with individual papillary ridges of the fingerprints [27], to the relationship between decreased width of papillary ridges and increased tactile sensitivity [28], it is clear that the papillary ridges of the fingerprint are an interface between the body and a surface that are a key determinant of the interaction. In our present study, participants touched surfaces with their fingertip, meaning that the majority of touch was on the upper half, which typically consists of rounded, parallel lines in the skin across the radial-ulnar, mediolateral direction. This impacts on touch as it means that moving the skin in the anteroposterior direction would produce an inherently different vibrational pattern over the papillary ridges, as compared to the lateral plane. We found evidence for this in Experiments 1 and 2, where anteroposterior movements were more amplified, possibly due to the increased bumping over the ridges.

However, how these explanations relate to the perceptual results in Experiment 3 are unclear. Concerning muscle control, we have a larger range of movement possible with anteroposterior finger bending, whereas lateral, side-to-side movements are more constrained. Experiments 1 and 2 show a benefit to anteroposterior movements for increasing the amplitude of vibrations elicited in the finger, which also related to a better coding of velocity in the vibrations, especially for higher frequencies. These signal advantages did not translate directly to a better performance in tactile discrimination. When the texture differences were larger (Δ300), the anteroposterior movements gave an improved performance, likely due to a large vibratory signal. However, for smaller texture differences (Δ100 and Δ200), the lateral movements were better, potentially because the fingerprint ridges were less involved and thus giving a cleaner vibratory signal. Therefore, the fingerprint may enhance tactile discrimination under certain conditions, but also decrease it under others.

There are limitations to the present work, such as that the results may be different for more complex movements, such as of different trajectories, forces, or velocities, or with other textures, thus should be interpreted with care. Naturalistic exploratory touch is often much more complex than simply anteroposterior and lateral movements [29]. Further, although not explored here, future work could include analyses of movement trajectory and force, as well as imaging skin-surface interactions to observe differences in papillary ridge movements. Another interesting point for future studies is that the spread of results was maximal at 40 mm/s, in the range between 20 and 50 mm/s. Therefore, this velocity, giving more variable results, should possibly be avoided in some applications, such as tactile rendering of real surfaces from a tactile device; in that case the tactile feeling has to be as uniform as possible for different users [30,31].

## 5. Conclusion

In the present study, vibration of the finger during textured surface touch was investigated relative to the movement direction, i.e. anteroposterior or lateral, and to finger velocity, over different conditions, i. e. by changing the normal load, finger angle, and textured surface. The
results showed that the finger vibrations during moving touch were different with anteroposterior or lateral movements. Regardless of the condition, finger vibrations were consistently higher in anteroposterior dimension, especially for frequencies higher than 100 Hz. In terms of perception, small differences in spatial periods, i.e. 100 or 200 µm, for surfaces with spatial periods between approximately 1–1.6 mm were better discriminated using lateral movements, while discrimination was significantly better using anteroposterior movements for spatial period difference of 300 µm. These perceptual discrimination differences may have been due to differences in the kinetics of the biomechanical movement and/or due to the different vibrations given by the fingerprints.

## Statement of originality

In the last decade a lot of studies concerned the influence of fingerprints, surface texture orientation and sliding movement on the finger induced vibrations. Among them, a few studies consider the finger in both lateral and anteroposterior orientations or with an alternating movement. In a previous published manuscript, we proved the influence of movement direction on induced vibrations independently of fingerprints. However, it was in particular conditions of finger velocity, normal force and angle and for particular surfaces. The present work goes further this previous study by considering different conditions and surfaces; the differences of tribological behaviour are more precisely highlighted. Moreover, the finger induced vibrations are related to tactile perception.

## CRediT authorship contribution statement

**Marie-Ange Bueno:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Le Moing Nolwenn:** Validation, Investigation, Formal analysis. **Brigitte Camillieri:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Rochelle Ackerley:** Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Investigation, Formal analysis. **Jenny Faucheu:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors thank all the participants to this study from the Laboratory of Textile Physics and Mechanics (University of Haute Alsace) and the Laboratory Georges Friedel (Mines Saint Etienne) and the GDR CNRS TACT 2033 and ANR-20-CE28-0010 COMTACT for the scientific discussions. R. Ackerley is funded by a European Research Council (ERC) Consolidator grant under the European Union's Horizon 2020 research and innovation programme [grant agreement No. 772242].

## Data availability

Data will be made available on request.

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