This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2024.3352042

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1

Effect of Normal Force Intensity on Tactile Motion
Speed Perception based on Spatiotemporal Cue
Yusuke Ujitoko, Yuko Takenaka, and Koichi Hirota

Abstract—While the relative motion between the skin and objects in contact with it is essential to everyday tactile experiences,
our understanding of how tactile motion is perceived via humantactile function is limited. Previous studies have explored theeffect of normal force on speed perception under conditions
where multiple motion cues on the skin (spatiotemporal cue,tangential skin deformation cue, and slip-induced vibration cue)were integrated. However, the effect of the normal force on speed
perception in terms of each motion cue remains unclear since
the multiple motion cues have not been adequately separated in
the previously reported experiments. In this study, we aim toelucidate the effect of normal force in situations where the speed
perception of tactile motion is based solely on a spatiotemporalcue. We developed a pin-array display which allowed us to vary
the intensity of the normal force without causing tangential forces
or slip-induced vibrations. Using the display, we conducted two
psychophysical experiments. In Experiment 1, we found that the
speed of the object was perceived to be 1.12-1.14 times faster
when the intensity of the normal force was doubled. In Experiment 2, we did not observe differences in the discriminabilityof tactile speed caused by differences in normal force intensity.
Our experimental results are of scientiﬁc signiﬁcance and offer
insights for engineering applications when using haptic displaysthat can only provide spatiotemporal cues represented by normal
forces.
Index Terms—Speed perception, Tactile motion, Normal force,
Pin-array display, Spatiotemporal cue, Haptic, Tactile.

I. I NTRODUCTION
The relative motion between our skin and objects in contact
with it is fundamental to our tactile experience. When we
actively explore and manipulate objects, our hands inevitably
move across their surfaces, generating a relative motion between our hands and the objects. This relative motion allows
us to perceive the haptic properties of the objects, including
their shape, material, and texture [1], [2], [3]. Furthermore,
relative motion itself plays a crucial role in our everyday
interactions with the environment, as evidenced by our ability
to grasp and manipulate objects effectively. For instance, when
initially grasping an object, our ability to detect unexpected
tactile motion on the object’s surface triggers an automatic
reinforcement of the grip [4]. Furthermore, it is known that wehave the ability to perceive the speed of such motion throughtouch [5].
Yusuke Ujitoko is with the NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Atsugi, Japan. E-mail:yusuke.ujitoko@gmail.com
Yuko Takenaka and Koichi Hirota are with the Graduate School of Informations and Engineering, The University of Electro-Communications, 182-8585
Chofu, Japan. E-mail: {takenaka yuko, hirota}@vogue.is.uec.ac.jp
Manuscript received XXXXX XX, 2023

Despite the importance of tactile motion in our daily lives,
our understanding of motion perception in human tactile
function is limited. Tactile motion perception involves various
motion cues (spatiotemporal cues, slip-induced vibration cues,and tangential skin deformation cues), which add to its complexity [6]. Most previous studies have investigated perceptual
characteristics of tactile motion in the particular situation of areal object sliding across the skin [7], [8], [9]. In this scenario,
the multiple motion cues are integrated into tactile motion
perception. However, since these studies have not isolated
motion cues in their experiments, the role of individual cues
on speed perception remains unclear. For example, a previous
study showed that the discriminability of tactile motion speed
was improved under conditions where a larger normal force
was applied [8]. While this was attributed in that study to the
suppression of slip-induced vibration, the role of other motion
cues, such as spatiotemporal cues, is unclear for conditions
where a larger normal force is applied.
This study focuses on the role of the normal force in asituation where humans perceive tactile motion speed based
only on spatiotemporal cues. We anticipated that the intensityof the normal force would have an effect on speed perception
based on the following conjecture. It is assumed that motion
is computed based on the sequential activation of nerve ﬁbers
with spatially displaced receptive ﬁelds [10]. The mean ﬁring
rates of nerve ﬁbers tends to increase as stimuli move faster
across the skin, implying that motion speed information is
encoded in these ﬁring rates [11], [12]. It is known thatmean ﬁring rates are modulated when stroking the skin with a
stiffer and less stiff brush, indicating that the intensity of thenormal force may modulate mean ﬁring rates [11]. Thus, we
speculated that the intensity of the normal force may be related
to speed perception in situations where that speed perception
is based solely on spatiotemporal cues.
We developed a pin-array display for our experiments.
Our pin-array display was capable of varying the intensity
of normal force without altering shear force or slip-induced
vibration when representing object motion on the skin. We
conducted two psychophysical experiments which involved
varying the intensity of normal force using the pin-array
display. In Experiment 1, we investigated the effect of normal
force intensity on the magnitude of perceived speed. In Experiment 2, we investigated the effect of normal force intensity
on the discriminability of perceived speed.
Our experimental ﬁndings hold both scientiﬁc signiﬁcanceand offer valuable insights for engineering applications. In
virtual reality (VR), tactile motion perception is crucial forperceiving the haptic properties of virtual objects (e.g., shape

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This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2024.3352042

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and texture), enabling dexterous manipulation of virtual objects, or facilitating communication with other people via
affective touch [13]. In the context of representing motion
on the skin for VR applications, one of the more common
methods involves the use of a haptic presentation device (e.g.,
pin-arrays [14]) capable of exerting forces in the normal
direction. For such devices, determining the intensity of thepresented normal force is a key design consideration. Improved
knowledge about the role of normal force intensity on tactile
speed perception will be valuable for determining optimallevels of the force to be applied to users’ skin through suchhaptic displays.
II. R ELATED W ORK
In order to characterize motion speed perception based ontactile information, comparisons have been made with motion
speed perception based on other types of cue. In [15], participants estimated the speed of a moving object either solely fromtactile cues (i.e., motion across the skin) while keeping theirhand stationary or solely from kinesthetic cues by tracking
the object with a guided arm movement. Participants tended
to overestimate motion speed when relying on tactile cues
compared to kinesthetic cues. Other studies have comparedvisual and tactile motion speed perception [16], and exploredthe speciﬁc inﬂuence of visual motion on tactile motion
speed perception [17], [18]. There has been a report of visual
pursuit eye movements introducing bias to the perception of
speed [19].
Previous studies have aimed to identify the speciﬁc tactile
cues that impact the perception of motion speed. It has
been shown that spatiotemporal cues originating from an
object’s surface (e.g., the spatial distance between surface dots
and the periodicity of the dots) inﬂuence the perception of
motion speed [7], [20]. The material types of the surfaces
also inﬂuenced speed perception [12]. The material-dependent
effects seemed to be related to the intensity of slip-induced
vibrations. Vibrations originating from relative motion havebeen shown to inﬂuence the discrimination of motion speed
perception [21]. This may be related to the fact that motion
speed inﬂuences the intensity and frequency compositionof slip-induced vibrations [22]. The effect of slip-induced
vibration on speed perception has been suppressed by thepresentation of masking vibrations. However, discriminationof smooth textures was shown to be poor when masking vibrations were presented. Addressing this problem, the applicationof a substantial normal force has been shown to mitigate
the inﬂuence of masking vibrations [8]. While various cues
inﬂuencing tactile motion speed perception have been studied,the speciﬁc impact of the normal force in isolation, without
alterations in shear force or slip-induced vibrations, remains
unexplored, and constitutes the central focus of this study.
Previous research investigating the perception of tactile
motion speed using real objects, has focused on two stimulus
scenarios in which (1) the contact area moves on the skin(e.g., [5]), and (2) the contact area remains ﬁxed while thespatiotemporal pattern of the stimulus presented on the skinis varied (e.g., [7]). For example, in the former scenario, the2hand is stroked with a brush while in the latter scenario, a
relatively moving surface continuously stimulates the same
skin area. This study employed the former stimulus type in our
experiments since it represents one of the most basic stimuli
that can be presented with a pin-array display. A pin-array
display can also replicate the stimulus in the latter scenario
by spatially reproducing the stimulus presented in the former
scenario.
III. A PPARATUS
A. System Overview
We developed an experimental system consisting of a
pin-array display, an air pressure controller, and a PC (seeFig. 1(A)). The system architecture was the same as that in
our previous study [14].
B. Pin-array display
Fig. 1(B) shows the pin-array display. Participants were
instructed to place their right hand on an ABS resin basewhich had on its surface a hand-shaped dent and a series of pinholes with a 2 mm diameter (see Fig. 1(C)). The pin holes andhand-shaped dent in the resin base were created using CNC
machining (Original Mind, Qt100). The hand-shaped dent was
designed to ensure that the participant’s hand and the pins
would make good contact without any gaps between them,and it was modeled on the surface shape of a hand modelobtained from BodyParts3D [23]. To prevent the participants’ﬁngers, particularly the thicker ones, from becoming lodged
in the dent of the display, we scaled down the thickness ofthe hand model by half during the modeling of the dent. The
maximum depth of the dent was 3.9 mm.
Cylindrical pins were created using Clear Resin with a 3D
printer (FormLab, Form3). Pins with a 1.9 mm diameter werearranged in a grid pattern with a 3 mm spacing between theircenters. Our experiments utilized only the pins enclosed by
the blue line in Fig. 1(B). The air pressure applied to each pin
was independently controlled. Calibration was performed foreach pin to ensure the accurate delivery of the target pressure
stimulation within a pressure range up to 0.06 MPa.
To evaluate the temporal resolution of the display, we
manipulated the stimulus onset asynchrony (SOA) of adjacentpins with 3 mm spacing and measured it using high-speed
camera (SONY, RX0M2). The evaluation result showed thatpin control was achievable in the millisecond order. Please see
details in Supplementary Note 1 and Supplementary Figure 1.
C. Other Components
The experimental software running on the PC transmitted
control values to the FPGA (Xilinx, XC7S50) in the airpressure controller through USB serial communication. The
air pressure controller’s internal regulator (SMC, VY1B00)
controlled the valves. To efﬁciently generate the air needed
for the system, two air compressors (RYOBI, ACP-50 and
ACP-60) were employed as air sources for the regulator. The
regulator operated at a response time of 30 ms.

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This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2024.3352042

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3

A. ParticipantsAPC

air pressure controller
FPGA

regulator
air

air
…

pressurecontrolvalue

pin-array display
…

air

skin
pin
tube

air
compressor
airB

only these 53 pins wereused in our experiment

156 mmTen male participants took part in the experiment; all wereright-handed and had a mean age of 23.3 (SD: 1.3) years.
All participants were naive to the purpose of the study andreported no sensorimotor disorders. The experiment lasted
approximately 45 minutes, and the participants were paid
about 1,200 Japanese yen (equivalent to about 8 USD) for
their participation. Ethical approval for this study was obtained from the ethics committee of the University of Electrocommunications (approval number: 23007). The experiments
were conducted following principles that have their origin in
the Helsinki Declaration.
Participants were comfortably seated in chairs. They wore
earplugs and noise-canceling headphones that played white
noise to block out external sounds. The participants rested theirright arms on the armrests, with their right hands placed on
the pin-array display. A cardboard barrier was positioned over
the right hand to prevent participants from seeing the pin-array
display (Fig. 1(C)). We measured the size of the participants’hands along a straight line following the pin layout and foundthat the average was 175.5 (SD: 5.0) mm.

B. Stimulus

C

card
board

pin-arraydisplay

Fig. 1. (A) Components of experimental system and data ﬂow. (B) Pin-array
display. In total, a straight line of 53 pins was used in our experiment. (C)The participant’s right hand was located on the pin-array display. A cardboard
barrier was positioned to prevent participants from seeing their right hand.

IV. E XPERIMENT 1: E FFECT OF N ORMAL F ORCEI NTENSITY ON P ERCEIVED S PEED OF TACTILE M OTION
In this experiment, we investigated the effect of normal
force intensity on the magnitude of perceived speed of tactile
motion. The experiment followed a within-participants design.

The pin-array display simulated a virtual moving object
with a constant speed, spanning a width of 3 mm in aline from the ﬁngertip to the wrist, as illustrated in Fig. 2.
Pressure was applied to push out the pin when any part ofthe virtual object overlapped with the center positions of thepins. The rationale for setting the object’s width to 3 mm
was to ensure a consistent normal force as the object moved
along the pin-array with its 3 mm spacing between the pins.
Setting the width over 3 mm would result in a momentary
simultaneous actuation of two adjacent pins. Setting the width
below 3 mm would result in a brief period of time during
which no actuation of any pins would occur. In both scenarios,
unintended variations in normal force intensity would occur,
which would be clearly unsuitable for a study investigating
the effects of normal force intensity.
To prevent participants from judging speed based on either
the global distance of movement or the duration, for each stimulus we randomly selected one of the nine pins near the ﬁngertip to be the starting point for the object’s movement. Likewise,
we randomly selected one of the nine pins near the wrist to
be the endpoint of the object’s movement. Consequently, theshortest movement distance covered 108 mm (37 pins), while
the longest movement distance spanned 156 mm (53 pins).
This implementation, involving the random assignment ofstarting and ending points for the movement stimulus, wasrelated to the deﬁnition of the stimulation area we wanted toadopt in this experiment. Unlike previous studies that focusedsolely on stimulating the ﬁngertip area (e.g., [7]), we wanted to
conduct stimulation across both the ﬁnger and palm areas. By
activating a series of pins over this extended area, we increased
the pool of pins available for random selection as startingand ending points, thereby enhancing the randomization of
the movement distance.

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JOURNAL OF LATEX CLASS FILES, VOL. XX, NO. X, XXXXXX 2023

start point was randomly
chosen from nine pins

moving object
3 mm

end point was randomly
chosen from nine pins

Fig. 2. A moving object (colored in orange) was represented by the pin-array
display in the experiment.

To clarify the effect of normal force intensity, we conﬁgured
two conditions of intensity per pin: 0.015 MPa (0.0425 N)
and 0.03 MPa (0.085 N). The rationale for this conﬁguration
is as follows. We aimed to explore the impact across awide range of normal force intensities. However, when we
represented relatively high motion speeds (e.g., 0.12 m/s) withthe developed display, we found that intensities exceeding
0.03 MPa per pin caused pain for the human subject. To
prevent a perception of pain from inﬂuencing the results, we
capped the maximum pressure condition at 0.03 MPa. Also,
we found that intensities below 0.015 MPa were sometimes
too weak to be perceived clearly. Therefore, we selected arange of 0.015 MPa and 0.03 MPa for pin intensity in thisexperiment.
C. Procedure
At the beginning of the experiment, participants were
provided with written instructions explaining the details of
the experiment and were asked to provide informed consent
in writing. Then, they moved on to the practice and main
sessions.
In each trial during the practice and main sessions, participants were sequentially presented with two stimuli: a reference
stimulus (0.015 MPa for each pin) and a comparison stimulus(0.015 MPa or 0.03 MPa for each pin). Participants wereasked to judge whether the second stimulus (the comparison
stimulus) was faster than the ﬁrst stimulus (the reference
stimulus) and were required to make a two-alternative forced
choice by pressing a foot button. We informed participants inadvance that the global distance of the object’s movement was
randomized and instructed them not to base their judgment of
motion speed on the global distance of movement or duration.
Once they had made their choice, they could proceed to thenext trial.
We employed a randomly interleaved staircase methodwith two staircases. One of the reference stimuli (0.04 m/s,
0.08 m/s, and 0.12 m/s) was assigned to the two staircases.

4

The presentation order of the two staircases was randomized:
in one staircase, the initial speed of the comparison stimulus
was 0.025 m/s faster than that of the reference stimulus, whilein the other staircase, the initial speed was 0.025 m/s slower
than that of the reference stimulus. We increased or decreased
the speed of the comparison stimulus by 0.005m/s in the next
step of the staircase in response to participants’ “slow” or“fast” responses, respectively. The experiment was terminatedwhen the responses in both staircases had been reversed six
times.
The range of speeds for the reference stimuli (ranging
from 0.04 m/s to 0.12 m/s) was selected based on priorstudies [7], [12]. The main session comprised six blocks, eachcorresponding to one of the three reference stimulus speeds
and one of the two comparison stimulus intensities. The orderof the six blocks was randomized. Before each block started, apractice session was conducted, during which the participants
performed only ﬁve trials. The speed of the reference stimulus
and the intensity of the comparison stimulus in the practicesession were the same as those in the subsequent block. The
procedure was the same for the practice as it was for the main
sessions.
D. Data Analysis
For each block and participant, we ﬁtted the responses withpsychometric functions of the form,
Φ−1 [P (Y = 1)] = β0 + β1 vcomp

(1)

−1

where Φ is the probit link function and P is the probability of Y = 1. The response variable Y takes the value 1 if
the participant reported that the object was moving faster inthe comparison stimulus than in the reference and 0 otherwise.
On the right side of the equation, vcomp is the speed of thecomparison stimulus, and β0 and β1 are the intercept and theslope of the linearized equation, respectively. We analyzed
the data for each participant using a generalized linear model(GLM).
We evaluated the accuracy of the responses to address
our research question: whether the intensity of normal force
affected the perceived motion speed. To this end, we computed
the point of subjective equality (PSE = -β0 /β1 ) corresponding
to the stimulus value yielding a response probability of 0.5.
To determine whether the PSE changed with two factors(speed of reference stimulus and force intensity of comparison stimulus), we conducted a two-way repeated measures
ANOVA using the two factors. If there was a violation of
normality as determined by the Shapiro-Wilk test, we conducted an ART on the data and then conducted the ANOVA
on the aligned ranks. Since other conventional nonparametricstatistical tests (e.g., Kruskal–Wallis test and Mann-Whitney
U test) cannot test the effect of multiple factors and theirinteraction, we adopted the ART procedure (see details in thepaper on ART [24]).
While we could also calculate just noticeable difference(JND) from the psychometric function, the analysis of the
JND value in this experiment would not provide any insights
relevant to our purpose and thus, we did not use it.

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This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2024.3352042

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E. Result

PSE [m/s](Speed of comparison stimulus perceptually equal to
speed of reference stimulus)

Fig. 3 shows the distribution of PSE estimates for eachcombination of reference speed and comparison stimulus intensity. We conducted a two-way ANOVA on the PSE data.
There were signiﬁcant main effects of reference stimulus speed[df = 2, F = 277.6, p < 0.001, ηp2 = 0.91] and comparison
stimulus force intensity [df = 1, F = 16.5, p < 0.001,
ηp2 = 0.23]. There was no signiﬁcant interaction effect between
them [df = 2, F = 1.5, p = 0.23, ηp2 = 0.05]. See posthoc multiple comparisons between conditions of reference
stimulus speeds in Supplementary Note 2 (this analysis does
not fall within the main scope of our study).
The result shows that the perceived speed was faster whena larger normal force was presented than when a smaller one
was presented. Speciﬁcally, when the intensity of normal force
doubled, the median perceived speed increased by 1.12 times
at a reference stimulus speed of 0.04 m/s, and by 1.14 times
at reference stimulus speeds of 0.08 m/s and 0.12 m/s. The
difference in PSE values due to normal force intensity were0.0047 m/s at a reference stimulus speed of 0.04 m/s, 0.0098
m/s at a reference stimulus speed of 0.08 m/s, and 0.0155 m/s
at a reference stimulus speed of 0.12 m/s.
intensity of comparison stimulus
0.015 MPa (control)
0.03 MPa

5

The length of the participants’ hands on a straight line along
the pin layout was 175.1 (SD: 8.6) mm. All participants were
naive to the purpose of the study and reported no sensorimotor
disorders. The experiment lasted approximately 45 minutes,
and the participants were paid about 1,200 Japanese yen(approximately 8 USD). The stimuli were the same as inExperiment 1.
A. Procedure
The procedure was basically the same as in Experiment 1
and here we describe only the differences. In Experiment 2, theintensities of the normal force for both the reference stimulus
and the comparison stimulus were the same. This is because
we aimed to estimate the discriminability of tactile motion
speeds at constant force levels, and to determine whether thediscriminability was dependent on the force level. There were
two conditions for the intensity of the normal force: 0.015 MPa
and 0.03 MPa. There were three conditions for the speed of
the reference stimulus (0.04 m/s, 0.08 m/s, and 0.12 m/s),
which was the same as in Experiment 1. In total, there were
six blocks. The order of the blocks was random. Before theﬁrst block started, a practice session was conducted, during
which the participants performed only ten trials. The speed of
the reference stimulus and the intensity of the normal force ofstimuli in the practice session were randomly assigned. The
procedure was the same for the practice as it was for the main
sessions.
B. Data Analysis

Speed of reference stimulus (0.015 MPa) [m/s]Fig. 3. Result of Experiment 1 (N=10). Box plots indicate PSEs for each
speed of reference stimulus and each intensity of comparison stimulus. The
asterisks denote statistical signiﬁcance for the difference in PSEs due to theintensity of the comparison stimulus at each reference speed. The black point
denotes the PSE for each participant.

V. E XPERIMENT 2: E FFECT OF N ORMAL F ORCE ON
D ISCRIMINABILITY OF TACTILE M OTION S PEEDIn this experiment, we investigated the effect of normal
force intensity on the discriminability of tactile motion speed.
We regarded the JND in speed for tactile motion at a certain
force intensity as the discriminability. We compared the JND
at a small normal force intensity and also at a larger normal
force intensity. This experiment was conducted in a withinparticipants design.
Ten male participants took part in this experiment; all wereright-handed and had a mean age of 23.6 (SD: 1.2) years.

For each block and participant, we ﬁtted the responses withpsychometric functions as shown in the expression (1). We
determined whether the intensity of normal force affected thediscriminability of perceived tactile motion speed. To this end,
we computed the JND from the psychometric functions (JND
= 0.675/β1 , where 0.675 is the 75th percentile of a standard
normal distribution). We estimated the JND for each condition
and identiﬁed whether there was a signiﬁcant difference in
JND between conditions of different intensities of normal
forces at each reference speed.
To determine whether JND changed with two factors (speedof reference stimulus and intensity of stimulus), we conducted
a two-way repeated measures ANOVA using the two factors.
If there was a violation of normality as determined by the
Shapiro-Wilk test, we conducted an ART on the data and thenconducted the ANOVA on the aligned ranks.
While we could also have calculated the PSE from thepsychometric functions, the analysis of the PSE values in thisexperiment would not provide any insights relevant to our
purpose since the force levels of the reference and comparison
stimuli were the same.
C. ResultFig. 4 shows the distribution of JND estimates. We conducted an ART on the data and then a two-way ANOVA
using the two factors on the aligned ranks. There was asigniﬁcant main effect of reference stimulus speed [df = 2,This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/

This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2024.3352042

JOURNAL OF LATEX CLASS FILES, VOL. XX, NO. X, XXXXXX 2023

F = 7.6, p = 0.001, ηp2 = 0.22]. There was no signiﬁcantmain effect of stimulus force intensity [df = 1, F = 0.1,
p = 0.92, ηp2 = 0.0002] and interaction effect [df = 2,
F = 1.0, p = 0.38, ηp2 = 0.036]. See post-hoc multiple
comparisons between conditions of reference stimulus speedsin Supplementary Note 3 (this analysis does not fall within
the main scope of our study). The results suggest that thediscriminability of the motion speed did not change due tothe intensity of normal force.
The median JND values for normal force intensity of 0.015
MPa were 0.0027 m/s at a reference stimulus speed of 0.04
m/s, 0.0054 m/s at a reference stimulus speed of 0.08 m/s, and
0.0048 m/s at a reference stimulus speed of 0.12 m/s. TheseJND values were smaller than the difference in quantiﬁed
speeds due to stimulus intensity at each reference speed inExperiment 1. This indicates that the difference in perceived
speed due to the doubled stimulus intensity in Experiment 1
is perceptible to humans.

intensity of stimulus

6

perceptible to humans. Our results may be due to the inabilityof humans to completely separate signals related to speed
and normal force at the level of mechanoreceptor ﬁring rates,
although this is only a conjecture. It is known that information
about motion speed is encoded in nerve ﬁring rates [11]. It isalso known that a large normal force increases the ﬁring rate ofmechanoreceptor nerve ﬁbers. This leads us to speculate thatwhen speed perception relies on spatiotemporal cues, there isa possibility that signals based on intensive normal force may
be incorrectly attributed to a higher speed.
Another conjecture relating to our ﬁrst ﬁnding is that alarger normal force could have increased the skin’s deformation area per pin, potentially resulting in an increased estimateof the local distance traveled by the virtual object within agiven time period (see Fig. 5). There exists a potential scenario
where speed computation may be performed via the estimatedlocal distance, which increased due to larger deformation. Itshould be noted, however, that it is unclear whether local
distance perception would be changed by this. It is also unclear
whether speed would be computed based on local distanceperception.

0.015 MPa

JND [m/s]

0.03 MPa
small normal force

large normal force

perceived
distance

perceived
distance

…

pin

…

skin

pin

Fig. 5. The deformation area of the skin is enlarged when a larger normal
force is applied by a pin. This might make participants perceive a longer
travel distance, leading to a larger perceived speed.

Speed of reference stimulus [m/s]Fig. 4. Result of Experiment 2 (N=10). Box plots indicate JNDs for each
speed of reference stimulus and each intensity of normal force. The black
point denotes JND for each participant.

VI. D ISCUSSION
A. Interpretation of the Main Results
In this study, we developed a pin-array display that could
systematically manipulate normal force intensity without causing slip-induced vibrations or tangential forces. The display
enabled us to investigate the effect of normal force intensity
on the perception of tactile motion speed in a situation
where participants perceive tactile motion based solely on
spatiotemporal cues. We made several previously undiscoveredﬁndings.
Our ﬁrst ﬁnding was a signiﬁcant effect of normal force
intensity on the magnitude of perceived speed. Within our
stimulus range, when the intensity of normal force was doubled, the motion speed was perceived to be 1.12-1.14 times
faster. The difference in perceived speed due to the difference
in normal force intensity was below the JND, and thus isThis ﬁnding apparently contradicts the results of a previous study, which suggested that speed magnitude remained
unaffected by contact force when a ﬁnger is pressed against
a textured surface with varying contact forces [7]. In thisprevious study, the tangential force and slip-induced vibrations
changed concomitantly with variations in contact force. It isconceivable that participants in the previous study were better
able to accurately estimate motion speed by utilizing these
multiple cues, which were not available in our experiment.
Another factor to consider is that differences in how motion
is presented to participants may inﬂuence the results. In our
experiment, the stimulus moved across the skin, whereas in
the previous study, the skin area being stimulated remained
ﬁxed.
Our second ﬁnding was that there was no signiﬁcant difference in the discriminability of speed when the intensities ofnormal force differed. This result also apparently contradicts
the ﬁndings of previous work, which suggested that discriminability increased with greater normal force when a ﬁnger
was pressed against a textured surface on a moving substratewith varying normal force [8]. The two factors mentioned
in the previous paragraph are also possible reasons for thisinconsistency. For example, the tangential force and slipinduced vibrations may have contributed to discriminability,
but normal force may not have.

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This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2024.3352042

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B. Implications for Future Research and Application Scenarios
It is crucial to determine whether the effect of stimulus
intensity on speed perception is speciﬁc to spatiotemporalcues represented by normal pushing force or whether it iscommon to spatiotemporal cues represented by other types ofstimuli. Stimuli representing spatiotemporal cues such include
vibrations [25] and electrical stimuli [26] in addition to normal
force. Investigating whether similar results can be obtained
when the intensity of such other stimuli increases would allow
us to understand the underlying mechanisms. For instance, if
the phenomenon of faster speed perception were not observed
when applying electrical skin stimulation with higher intensity
than usual, our explanations attributing the increased speed
perception to larger skin deformation in this paper (see Fig. 5)
could be seen as more plausible.
Future experiments that more deeply investigate tactile
motion speed perception based on spatiotemporal cues shouldtake into account the intensity of normal force. Speciﬁcally,
when comparing multiple conditions based on a speciﬁc factor(e.g., differences in spatiotemporal cues originating from thepin layout), the intensity of normal force should be preadjusted across the conditions. Otherwise, the effect of thenormal force intensity cannot be eliminated.
By adopting a research design similar to our study, it would
be possible to elucidate the contribution of normal force
intensity in situations where only other motion cues (e.g.,tangential skin deformation) are available for speed perception.
For example, when generating tangential skin deformation by
moving a real object relative to the skin, the intensities oftangential force and normal force are inevitably correlated,making it challenging to separate their individual contributions. However, by developing a tactile display that allows
for the separate manipulation of tangential force intensity andnormal force intensity, it would be possible to clarify thecontribution of normal force intensity when perceiving speed
using only the motion cue of tangential force.
Finally, let us consider application scenarios involving therepresentation of tactile motion in VR space. In such scenarios,
it is common to use haptic displays that can only present forcesin the normal direction [14]. The perception of tactile motion
may inﬂuence various aspects, including the perception of
haptic properties of virtual objects in relative motion, dexterity
in grasping, and the pleasantness of affective touch. Our results
suggest that, depending on the normal force intensity setting,the perception of speed may vary, potentially impacting thephenomena mentioned above. It should be noted that thequestion of whether the normal force intensity setting does
indeed affect such phenomena requires further investigation.
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