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1

Vibrotactile Stimuli Applied to Finger Pads as
Biases for Perceived Inertial and Viscous Loads
Shogo Okamoto, Member, IEEE, Masashi Konyo, Member, IEEE, and Satoshi Tadokoro, Fellow, IEEE
Abstract—The perception of the mass and viscosity of an object is based on the dynamic forces applied to our hands when we jiggle
or lift the object [1], [2], [3]. This force is commonly assumed to be sensed by kinetic receptors [4] in our muscles or tendons. Whenjiggling objects, we also experience the cutaneous deformation of our ﬁnger pads. In this study, we show that the dynamic vibrationon the ﬁnger pad inﬂuences our perception of mass and viscosity. We experimentally conﬁrm that the vibration on the ﬁnger pad, thatsynchronizes with the hand’s accelerations or velocities, enhances the perceived changes in the mass or viscosity when the vibrotactile
stimuli and the changes in the mass and viscosity are in the same perceptual direction. For example, when the increased mass andan acceleration-synchronized tactile stimulus–which is a positive bias for the mass–are simultaneously presented to the experimentparticipants, they respond that the perceived increase in the mass is enhanced. In contrast, when the tactile and proprioceptive stimuli
are in perceptually opposite directions, the vibrotactile stimuli cancel the perceived changes in the mass and viscosity. In particular, theeffect of the velocity-synchronized vibration on perception is stronger than the effect of the actual viscosity.
Index Terms—Mass, Viscosity, Vibration, Skin stretch.

✦

1

I NTRODUCTIONW

E estimate the mass of an object from the forces
applied to our hands [1], [2], [3] when we jiggle
or lift the object. Such motions allow us to acquire thehigher ability to discriminate the mass [5]. The forces
exerted on our hands are assumed to be mediated by
the proprioceptive mechanoreceptors in our muscles andtendons, which respond to stretching or tension in ourmuscles or tendons [4]. We also experience the cutaneous
deformations of our ﬁnger pads when we jiggle or lift
the objects. These cutaneous deformations activate thetactile mechanoreceptors in our ﬁnger pads. The tactile
mechanoreceptors can also be innervated by vibrotactile
stimulation. In this study, we show that vibrotactile
stimuli, which are synchronized with the dynamic hand
movements, serve as increasing- or decreasing biases forthe perceived mass and viscosity of the object during the
jiggling tasks.

Possible Applications
One of the clear advantages of the illusion of the mass
and viscosity caused by vibrations is that this illusion
enables the presentation of the mass and viscosity without force feedback displays. It is difﬁcult to install force
feedback displays, which need to be grounded to theenvironment or to parts of the body, on mobile information terminals or computer mice. To avoid this limitation,• S. Okamoto is with the Graduate School of Engineering, Nagoya University, Japan• M. Konyo and S. Tadokoro are with the Graduate School of Information
Sciences, Tohoku University, Japan.
This study was partially supported by grants from MIC SCOPE (082102006),
MEXT KAKENHI (21686024), and the Kayamori Foundation of Informational Science Advancement.

Digital Object Indentifier 10.1109/ToH.2011.36

some studies have used alternatives to force feedback
displays. For example, the sensory discrepancy between
the visual and kinesthetic cues represented the virtualcompliance of an object [6] or surface shapes such as
bumps or holes [7], which are usually presented by theforce feedback displays. A technique that delivers thesense of hard materials, such as metal or wood, using
high-frequency vibration during contact with these materials has been proposed [8], [9]. Konyo et al. proposeda vibrotactile displaying method for the sense of frictionof certain materials. They provided vibratory stimuli
to ﬁnger pads, synchronizing the simulated frictional
vibration between the ﬁnger pads and the explored materials [10]. Methods for presenting the mass or viscosityof an object through tactile vibrations have not yet been
proposed. The vibrotactile biases presented in this study
represent a new alternative method for the sense of mass
and viscosity.
Since the haptic bias effects presented in this study use
vibrotactile stimuli, it may be possible to combine themwith other vibrotactile feedback methods to improve thehaptic interaction of information terminals. For example,
Fukumoto et al. presented a vibrotactile display method
to present the sensations acquired by pressing a virtual
button [11]. The symbolic vibratory stimuli, called haptic
icons [12], and the vibrotactile texture displays for virtual
clothes or roughness [13] were also realized throughvibrotactile stimuli to the ﬁnger pads. These techniques
and the illusory displaying method for the mass andviscosity shown in this study may be realized using thesame vibrotactile actuator on the information terminals.

2

E XPERIMENTAL PARADIGM

Here, we present the paradigm of the experiments. We
will design the vibrotactile stimuli that will become the1939-1412/11/$26.00 © 2011 IEEE

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positive/increasing and negative/decreasing biases forthe perception of the mass and viscosity. The positive
tactile stimuli will increase the perceived mass and viscosity, and the negative stimuli will have the opposite
effects. We will present the inﬂuences of the tactile
stimuli on the perception of the mass and viscosity bydemonstrating that these tactile stimuli bias the perception of the mass and viscosity. First, we will showthat the tactile stimuli enhance the perceived changes in
the mass and viscosity. For example, when the increasein the actual mass and the positive tactile stimuli are
simultaneously presented to the participants, the perceived increase in the mass becomes stronger. Second,
we will show that the tactile stimuli cancel or weaken theperceived changes in the mass and viscosity, given thatthese changes can be detected by the participants without the tactile biases. For example, when the increasein the actual mass and the negative tactile stimuli are
simultaneously presented, the perceived increase in themass is canceled or weakened.

3

A PPARATUS

To independently manipulate the vibrotactile and proprioceptive stimuli, which correspond to the mass andviscosity of an object, we prepared an actuated slider
with a vibrotactile stimulator. The participants haptically explored the mass and viscosity of an impedancecontrolled slider (Fig. 1a). The slider was driven horizontally, and its position (x(t)) was controlled by
Fx (t) = mẍ(t) + cẋ(t).

(1)

The actuated slider behaved as if it was a frictionless
object with mass (m) and viscosity (c). The participants
exerted a force (F x (t)) on the slider with the right index
ﬁnger. They moved the slider as if they were jiggling theobject to the right or left (Fig. 1b). A piezo stack actuator
was installed on the slider as a vibrotactile stimulator.
The actuator stimulated the ﬁnger pad of the participants
by producing a vibratory displacement of 280 Hz and7.2 μm peak-to-peak amplitude along the Z-axis (Fig. 1c;also, see discussion about the usage of this frequency insection 8.2). The amplitudes could change and details
are described in section 4.3.
The product information for the actuated slider, force
sensor and tactile stimulator is the following: MR12T,
Yamaha, Hamamatsu, Japan; ThinNANO1.2/1, BL AUTOTEC, Kobe, Japan; and ASB510C801P0, NEC/TOKIN,
Sendai, Japan, respectively. The slider was driven bya shaft motor that did not produce any noticeable vibrations while the slider was in motion. The 280 Hz
vibrations of the stimulator did not inﬂuence the outputof the force sensor because these vibrations were far
above the cut-off frequency (100 Hz) of the force sensor.
The sampling and control frequencies for the force sensor
and the actuated slider were 1 kHz. The output rate of
the tactile stimuli was 2 kHz. The contactor of the tactile
stimulator was 11.6 mm in diameter. The output force ofFig. 1. a. Actuated slider, force sensor, and vibrator. b.
The jiggling movement. c. The tactile vibration applied tothe ﬁnger pad.
the stimulator was approximately 800 N, which is muchlarger than the force exerted by a human ﬁnger.

4

V IBROTACTILE S TIMULI THAT S ERVE AS B I ASES FOR I NERTIAL AND V ISCOUS L OADS
4.1

General Design

To design vibrotactile stimuli that could serve as biases
for inertial and viscous loads, we analyzed the lateral
deformation of the ﬁnger pad that occurs when the handis jiggling an object. If the object mass increases and thehand movement is maintained, the lateral deformationof the ﬁnger pad increases as a result of the increased
external force on the ﬁnger pad (see section 4.2). Suchincreases are signiﬁcant when the hand acceleration islarge. With the increase in the cutaneous deformation,
the activities of the RA and SA receptors of the ﬁnger
pad increase (see section 8.2). In order to mimic theincrease of the RA receptors’ activities, the amplitudeof the vibrotactile stimuli is increased in synchronization
with the acceleration of the hand. If the mass of the object
decreases, the activity level of the mechanoreceptors will
be lower than that in the case of a larger mass. In orderto mimic the decrease in the RA receptors’ activities,
the amplitude of the vibrotactile stimuli is decreased insynchronization with the hand acceleration.
The change in lateral deformation on the ﬁnger pad
due to the change in viscosity of the object is prominent
when the hand velocity is large (see section 4.2). In orderto mimic the change in the activities of the RA receptors

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Fig. 2. Skin model for the numerical analysis of the lateral
deformation of a ﬁnger pad in jiggling a frictionless 1-DOF
object. Left. Schematic model of a ﬁnger and a virtual
object with no friction. Right. Symbolic version of the theﬁgure on the left.

that is caused by an increase or decrease of the viscosity,
the amplitude of the vibrotactile stimuli is increased or
decreased in synchronization with the hand velocity.
4.2

Numerical Simulation of Lateral Skin Stretch

We will consider the certain case in which a human ﬁnger moves a frictionless virtual object (Fig. 2). When theﬁnger moves the object, a dynamic lateral deformation
occurs on the ﬁnger pad. This deformation depends onthe mechanical impedance of the object and the hand
movement. In the model, the skin surface and the object
are ﬁxed and do not slide. The ﬁnger is expressed asa mass point (mb ) with a spring (kf ) and damper (cf )connected. The force (f (t)) that the ﬁnger produces isapplied to the mass of the ﬁnger. The object is represented by its mass (mi ) and viscosity (ci ). The equationof motion is given bymi x¨s + (ci + cf )x˙s + kf xs = cf x˙b + kf xb ,mb x¨b + cf x˙b + kf xb = cf x˙s + kf xs + f (t),

(2)
(3)

where xb (t) and xs (t) are the position of the ﬁnger’s
mass and the position of the object, respectively. The
lateral skin stretch is expressed as xb (t) − xs (t). The
values of the parameters used for the computation are
as follows. The mechanical impedance of the object was
mi = 0.2 kg, and ci = 0.5 N·s/m; these values were also
used in the experiments conducted in this study. The
physical parameters of the skin were kf = 400 N/m,and cf = 2.0 N·s/m, based on the report of Nakazawa
et al. [14], in which they estimated the spring coefﬁcientand viscosity of the ﬁnger pad when lateral forces wereapplied to its surface. The model of the ﬁnger used intheir study is very similar to our skin model. The massof the ﬁnger was set to mb = 0.01 kg. The ﬁnger force(f (t)) exerted to jiggle the object was approximated as asinusoidal function: f (t) = F sin (ωt), with ω = 2π rad/s.
The magnitude of the force (F = 0.5 N) was determinedfrom actual data observed using the same equipmentthat was used in the present study.

We now look at the effects of mass change on lateralskin stretches. For instance, Fig. 3 shows the differencein the skin stretches between the case of mi = 0.2 kg
and 0.3 kg. The phase difference between the change
in skin stretch due to the change in mass and theﬁnger velocity is approximately π/2 rad. This is close
to the phase of the acceleration of the ﬁnger. The phasedifference (θ) between the change in skin stretch and theﬁnger velocity is θ = 1.79 rad (102.6◦). If we change
the mechanical parameters of the skin, this relationshipremains approximately the same. For example, when kf
and cf change by a factor of 0.5 to 2 and m b changes by
a factor of 0.1 to 10, θ changes by 1.69 to 1.80 rad.
Fig. 4 shows the difference in skin stretches between
the cases of ci = 0.5 N·s/m and 0.6 N·s/m. The phaseof the difference in skin stretches is close to that of
the hand velocity (θ = 0.36 rad, 20.9 ◦). If we change
the mechanical parameters of the skin, this relationshipremains approximately the same. For example, when kf
and cf change by a factor of 0.5 to 2 times and m bchanges by a factor of 0.1 to 10, θ changes by 0.23 to
0.38 rad.
From these analyses, it is predicted that the manipulation of the lateral skin stretch of the ﬁnger pad that issynchronized with the ﬁnger’s acceleration will lead tothe perception of mass change. Also, the manipulation ofskin stretch in synchronization with the ﬁnger’s velocity
will inﬂuence the perception of viscosity change. In thisstudy, instead of the skin stretches, we apply vibrotactile
stimuli to the ﬁnger pad and investigate the effects of thestimuli on the perception of changes in the inertial andviscous loads.
4.3

Equations of Tactile Stimuli

The displacement of the tactile stimuli was given byy(t) = A(t) sin (2πf t). The vibratory frequency was
f = 280 Hz for both the reference and test stimuli inthe experiments. For the reference stimuli, the amplitudeof the displacement was constant: A(t) = 3.6 μm. The
amplitude of the tactile stimuli intended to affect the perception of the mass–these stimuli were used for Exp. 1–changed in synchronization with the hand acceleration.
The amplitudes were determined by⎧⎨ A(t) = αiif |ẍ(t)| < Bi ,|ẍ(t)| − Bi
(4)
⎩ A(t) = αi (1 ±) if |ẍ(t)| ≥ Bi ,Di
where αi , Bi and Di are the amplitude of the stimuli
when the hand is at rest, the width of the insensitive
range of hand acceleration in which the amplitude did
not change, and the rate of amplitude change, respectively: αi = 3.6 μm, Bi = 0.4 m/s2 , and Di = 1.0 m/s2 .
These values were determined by the researchers to
represent one condition that was likely to be the bias
for the perception of the inertial load. The insensitive
range was introduced so that these amplitude changes
were not driven by the small movement of the linear

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Fig. 3. Skin stretch change caused by an increase in themass, (xb (t) − xs (t)|mi =0.2 kg ) − (xb (t) − xs (t)|mi =0.3 kg ).
The solid line is the change in lateral skin stretches causedby an increase in object mass. The dashed line is theﬁnger velocity. The phase of the skin-stretch change isapproximately π/2 apart from that of ﬁnger velocity, and it
is close to that of the ﬁnger acceleration.

Fig. 4. Skin stretch change caused by an increasein the viscosity, (xb (t) − xs (t)|ci =0.5 N·s/m ) − (xb (t) −xs (t)|ci =0.6 N·s/m ). The solid line is the change in lateralskin stretches caused by an increase in the viscosity. The
dashed line is the ﬁnger velocity. The phase of the skinstretch change is close to that of ﬁnger velocity.

slider along the X-axis when the participant placed hisor her ﬁnger on the tactile stimulator at the beginningof every experimental trial. In other words, this value
was intended to ensure that the tactile biases weregenerated only by the jiggling movements of the hand.
The “±” sign in (4) corresponds to “+” for increasing theperceived mass, and “−” for decreasing the perceived
mass.
The amplitudes of the tactile stimuli intended to affectthe perception of viscosity–these stimuli were used forExp. 2–changed in synchronization with the hand velocity. The amplitudes were determined by

5.1⎧⎨ A(t) = αv

|ẋ(t)| − Bv
⎩ A(t) = αv (1 ±)Dv

if |ẋ(t)| < Bv ,if |ẋ(t)| ≥ Bv ,(5)

where αv , Bv and Dv are the amplitude of the stimuli
when the hand is at rest, the width of the insensitive
range of the hand velocity, and the rate of amplitudechange, respectively: αv = 3.6 μm, Bv = 40 × 10−3 m/s,
and Dv = 120 × 10−3 m/s.

5

E XPERIMENTS

Two types of experiments were conducted. In Exp. 1, theeffects of the tactile stimuli given in (4) on the perceptionof the inertial load were investigated. In Exp. 2, theeffects of the tactile stimuli given in (5) on the perceptionof viscous load were investigated.

5.1.1

Experiment 1 (Biases for Mass)
GeneralExp. 1 was designed to investigate the effects of theacceleration-synchronized tactile stimuli on the perception of the virtual object’s mass. Eight participants explored the mass by jiggling the slider with his or her
ﬁnger following the sounds of a metronome at 1.42 Hz.
They compared the reference and test stimuli and noted
whether the mass of the test stimulus had increased or
decreased compared with the reference mass. For the test
stimuli, the mass was increased or decreased from thereference mass. The tactile stimulus was either the sameas that of the reference stimulus or its amplitude wasincreased (served as a positive bias) or decreased (served
as a negative bias) in synchronization with the ﬁnger’s
acceleration.
5.1.2

Groups of Test Stimuli

The test stimuli were divided into three groups withdifferent combinations of inertial and tactile stimuli(Table 1). Group (i), in which only the mass was manipulated, was prepared in order to verify that theparticipants would be able to detect the change in mass(conditions 1 and 2). Group (ii), in which the mass andthe tactile stimuli were manipulated so as to be perceived
in the same direction, was prepared in order to verify
that the tactile stimuli would enhance the perceptionof mass change (conditions 3 and 4). Group (iii), in
which the mass and tactile stimuli were manipulated
in opposite directions, was prepared in order to verify
that the tactile stimuli would prevent the perception

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IEEE TRANSACTIONS ON HAPTICS, VOL. X, NO. X, XX 20XXof mass change (conditions 5 and 6). The effects ofthe tactile stimuli were investigated by comparing theanswer ratings in the above three stimuli groups.
In conditions 1 and 2, a constant vibration–identicalto the one used in the reference stimulus–was used as atactile stimulus. In condition 1, the mass was increased
from that of the reference stimulus. In condition 2,
the mass was decreased. In condition 3, the mass wasincreased and the amplitude of the tactile stimulus wasincreased in synchronization with the hand acceleration,
so that both the inertial and tactile stimuli would beperceived as a mass increase. In condition 4, the mass
and vibrotactile stimulus were decreased. In condition 5,
the mass was increased but the vibrotactile stimulus wasdecreased, so that the proprioceptive and tactile stimuli
affected the perception in opposite directions. In condition 6, the mass was decreased while the vibrotactile
stimulus was increased.
5.1.3 Expected Results
Fig. 5 presents the comparison scheme for the results.
It shows the average correct answer ratings for eachstimulus group. Here, a correct answer indicates the casein which the participants’ answer matched the change
in the inertial stimulus. Before investigating the main
point, we will look at the answer ratings for group (i).
An average rate that is larger than the chance levelof 0.5 implies that the participant correctly detected
the changes in mass when the constant vibration wasapplied to his or her ﬁnger. We focus on the differencesin ratings between the groups. If there is no difference
observed in the ratings, we infer that the vibrotactile
stimuli do not inﬂuence the perception of mass. If theratings of group (ii) are higher than those of group (i), we
conclude that the tactile stimuli enhance the perceived
change in mass. If the ratings of group (iii) are smaller
than those of group (i), we infer that the tactile stimuli
prevent the perception of the mass change. We also focus
on whether the ratings of group (iii) are lower than the
chance level; if they are lower, we infer that the effect of
the tactile stimuli dominates the actual mass change inthe participants’ perception of the mass change.
5.1.4 Vibrotactile and Inertial Stimuli
For the reference stimulus, the inertial and viscous stimuli were m = 0.2 kg and c = 0.5 N·s/m, respectively. The
tactile stimulus was a sinusoidal displacement of 280 Hzwith a peak-to-peak amplitude on the Z-axis of 7.2 μm.
This stimulus was presented to the ﬁnger pads of theparticipants.
In the test stimuli, the changes in mass (Δm) presented
to the participants were determined for each individual
participant in the preliminary experiment so that thechanges in mass were just noticeable to the participant.
If the mass difference between the reference and test
stimuli is much larger than the effect of the tactile stimuli, the above-mentioned experimental design cannot
verify the effect of tactile stimuli on the perception of

5

TABLE 1
Test stimuli in Exp. 1 (Biases for Mass).
Stimuli
Group(i)
Mass Only(ii) Tactile & Mass,
Same Direction(iii) Tactile & Mass,
Opposite Direction

Condition #
1
2
3
4
5
6

Mass
Increased
Decreased
Increased
Decreased
Increased
Decreased

Accel.-Synch.
Tactile Stimuli
Constant
Constant
Increased
Decreased
Decreased
Increased

TABLE 2
Test stimuli in Exp. 2 (Biases for Viscosity).
Stimuli
Group(iv)
Viscosity Only(v) Tactile & Visc.,
Same Direction(vi) Tactile & Visc.,
Opposite Direction

Condition #
7
8
9
10
11
12

Viscosity
Increased
Decreased
Increased
Decreased
Increased
Decreased

Velocity-Synch.
Tactile Stimulus
Constant
Constant
Increased
Decreased
Decreased
Increased

Fig. 5. Comparison of results. Correct answer ratings foreach stimulus group. The stimuli in group (ii) are designed
to enhance the perceived change of mass. Hence, theratings for group (ii) are expected to be higher than thoseof group (i). The stimuli in group (iii) are designed tocancel the perceived change of mass. Hence, the ratingsfor group (iii) are expected to be smaller than those ofgroup (i).
mass. Before the main experiments, the magnitudes ofthe mass changes or viscosity changes were determinedfor each participant. Such just noticeable changes were
determined by the method of limits. In this method,
ascending and descending series were presented to eachparticipant twice for each series. The step sizes of thestimuli were 0.01 kg (Exp. 1) and 0.02 N·s/m (Exp. 2).
The thresholds of the four series were averaged. Throughthese investigations with all the participants, the values

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of Δm used as test stimuli were determined to be 0.025
to 0.065 kg when an increased mass was presented(conditions 1, 3, and 5). When a decreased mass waspresented (conditions 2, 4 and 6), Δm values were−0.015 to −0.04 kg.
5.1.5 Tasks and Participants
Before the experiments, the participants practiced moving the linear slider in accordance with the sounds of a
metronome. In the main trial, after the reference stimulus, one of the six types of test stimuli was randomly presented to participants with an interval of 3 s. While thesestimuli were presented, the participants tried to maintainthe contact status between their ﬁngers and the stimulator. After comparing the two stimuli, they released theirﬁngers from the stimulator and orally responded regarding whether the mass of the test stimulus was larger orsmaller than that of the reference stimulus. Each type oftest stimuli was presented 20 times; thus, 120 trials were
performed for each participant. The participants moved
their hands with the beat of a metronome that had arhythm of 1.42 Hz (85 beats per minute) in the manner of
one beat for one stroke and two beats for one right-to-leftreciprocation. The metronome was not used for strictly
restricting the jiggling movements of the participants but
for approximately determining their hand movements.
As a result, the participants moved their hands at a
maximum speed of approximately 220 mm/s with astroke of approximately 50 mm. For most of the trials, theparticipants responded after two or three reciprocations.
Eight paid participants took part in Exp. 1. They
were students of Tohoku University in their twenties.
All had given their informed consent. In order to shutout the sounds produced by the tactile stimulator, theylistened to pink noise through headphones during theexperiments. The participants did not know the possible
effects of the tactile stimuli before the experiments. The
experiment lasted approximately 40 min.
5.2

Experiment 2 (Biases for Viscosity)

In Exp. 2, the combinations of test stimuli and tasks
were the same as in Exp. 1. In the test stimuli, theviscosity of the object was manipulated, and the velocitysynchronized tactile stimuli were presented to eight newparticipants (Table 2). An increased viscosity was presented with Δc values of 0.10 to 0.26 N·s/m (condition
7, 9, and 11), and the decreased viscosity was presented
with Δc values of −0.16 to −0.32 N·s/m (conditions 8,
10 and 12).

6

R ESULTS

6.1

Results of Exp. 1 (Biases for Mass)

Regarding the experimental results, Fig. 6a and 6b show
the answer ratios of the participants in Exp. 1 and Exp. 2,
respectively. First, we looked at the results of group (i)in Exp. 1 (Fig. 6a). The ratios of group (i) were higher

Fig. 6. Experimental Results. a. the answer ratios inExp. 1 (mass). b. the answer ratios in Exp. 2 (viscosity).
The answer ratios are shown for each stimuli group. The
blank diamonds are the results of test stimuli with whichmass or viscosity increased (conditions 1, 3, 5, 7, 9, and11). The ﬁlled diamonds are the results of test stimuli withwhich mass or viscosity decreased (conditions 2, 4, 6,
8, 10, and 12). In Exp. 2 (Fig. 6b), one participant did
not show the effects of tactile stimuli. The results of thisparticipant are shown as gray diamonds.
than the chance level (t-test, t0 (15) = 6.60, p = 8.4 ×
10−6 , two-tailed). The participants responded correctly
to the directions of mass changes when the constantvibrations existed. Second, we focused on the differencein the answer ratios between groups (i) and (ii). The
ratios of group (ii) were higher than those of group(i) (Steel-Dwass test, q0 (3, ∞) = 4.73, p = 2.4 × 10−3 ).
This result indicates that the acceleration-synchronizedtactile stimuli enhanced the perceived change in mass.
Finally, we focused on the difference between groups(i) and (iii). The ratios in group (iii) were smaller thanthose in group (i) (Steel-Dwass test, q0 (3, ∞) = 5.75,

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p = 1.4 × 10−4 ). Also, the ratios in group (iii) wereas low as the chance level (average of 0.42, standard
deviation of 0.21). These results indicate that the tactile
stimuli canceled the perceived change in mass. Fromthese analyses, we may conclude that the tactile stimuli
increased and decreased the perceived changes in mass
when tactile and inertial stimuli of the perceptuallysame directions were imposed. When tactile and inertial
stimuli of perceptually opposite directions were used,
the perceived changes were canceled. The accelerationsynchronized tactile stimuli were perceived as a positive
and negative bias of the mass.
6.2

Results of Exp. 2 (Biases for Viscosity)

Fig. 6b shows the results of Exp. 2, in which the viscosity
was manipulated. The answer ratios in group (iv) werehigher than the chance level (t-test, t0 (15) = 10.70,
p = 2.0 × 10−8 , two-tailed)．The participants correctly
identiﬁed the directions of the viscosity changes whenconstant vibrations were applied. The ratios in group(v) were higher than those in group (iv) (Steel-Dwass
test, q0 (3, ∞) = 5.60, p = 2.2 × 10−4 ). This indicatesthat the velocity-synchronized tactile stimuli enhanced
the perceived change in viscosity. The ratios in group(vi) were smaller than those in group (iv) (Steel-Dwass
test, p0 (3, ∞) = 6.15, p = 4.1 × 10−5 ). The tactile stimuli
canceled the perceived change in viscosity. The ratios
in group (vi) were lower than the chance level (t-test,
t0 (15) = 3.87, p = 1.5 × 10−3 ). This shows that theeffect of the tactile stimuli dominated the participants’
perception of viscosity over the proprioceptive viscosity.
From these analyses, we conclude that the velocitysynchronized tactile stimuli were perceived as a positiveor negative bias of viscosity. Individual differences wereobserved in the results. The results of one of the eightparticipants did not exhibit the effect of the tactile stimuli(Fig. 6b, gray diamonds).
6.3

Summary of Results

In both Exp. 1 (mass) and Exp. 2 (viscosity), the vibrotactile stimuli on the ﬁnger pad enhanced the perceived
change in the mass and viscosity when the changes
in the mass and viscosity and the effects of the tactile stimuli were in the same perceptual direction. In
contrast, the vibrotactile stimuli canceled the perceived
changes in the mass and viscosity when the changes inmass and viscosity and the effects of the tactile stimuli
were in opposite directions. The tactile stimuli worked
as both positive and negative biases of the mass andviscosity. The tactile stimuli in which the amplitudechanged in synchronization with the ﬁnger acceleration
were perceived as a bias of the mass. The velocitysynchronized tactile stimuli were perceived as a bias ofthe viscosity. The velocity-synchronized tactile stimuli
dominated the change in the actual viscosity. Although it
is known that various information [15]–including visual

7

cues [16]; static pressure on the skin [5], [17]; motor commands [18]; an object’s geometrical shape [19]; surface
textures [20], [21]; and sense of effort [22], [23], [24], [25]–affects the process of perceiving the mass of an object ora force, in this study, it was found that the vibrotactile
stimuli to the ﬁnger pad also affect the perceived mass
and viscosity of an object.

7

F OLLOW-U P E XPERIMENT: D ISCRIMINA TION OF ACCELERATION - AND V ELOCITY S YNCHRONIZED V IBRATION
Both the acceleration- and velocity-synchronized vibrotactile stimuli may become perceptual biases for boththe mass and viscosity. For instance, the accelerationsynchronized stimuli may become not only the inertial, but also the viscous biases. Also, the velocitysynchronized stimuli may become both the inertial andviscous biases. Both types of vibrotactile stimuli may
play the role of perceived heaviness in the same manner.
To counteract this possibility, we experimentally conﬁrmed that these two vibrotactile stimuli are recognizeddifferently. As well as the experiments in the previous
sections, the participants placed their ﬁngers on thestimulator and moved their hands following the rhythmof a metronome in order to compare the reference andtest stimuli. For the test stimuli, the amplitudes of thevibrotactile stimuli increased in synchronization witheither the hand velocity or the hand acceleration. Eight
new participants answered regarding whether the massor the viscosity of the test stimuli increased comparedwith the reference stimulus; this occurred in the mannerof a two-alternative forced choice.
7.1 Trainings regarding Impedance-Controlled Massand Viscosity
Prior to the experiment, we conﬁrmed that the participants discerned the increases in the mass and viscosity of the jiggled object. To this end, they compared
two types of test stimuli in which either the mass or
viscosity increased compared to the reference stimulus
while the vibrotactile stimuli were constantly presented
to the participants. The mechanical parameters of thevirtual object were (m, c) = (0.2 kg, 0.5 N · s/m) for thereference stimulus. For the test stimulus, its mass wasincreased to m = 0.25 kg or its viscosity was increased toc = 0.7 N·s/m. For three of the eight participants, larger
mechanical parameters were used for the test stimuli
because they claimed that the differences between thereference and test stimuli were too small to discern.
Five of the eight participants did not successfully
discriminate the increases in the mass and viscosity. We
taught them a helpful technique, as follows: In regards tothe increase in the object’s mass, we are especially able
to perceive the resistance when the hand accelerationis large, or when the directions of hand movementschange during the jiggling motions. In regard to theThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
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88D ISCUSSIONS

8.1

Finger pad as dynamic force sensor

increased viscosity, we perceive the resistance when thehand velocity is large. With these techniques the participants repeated practices until they correctly responded
to the test stimuli ﬁve times in a row. Finally, all theparticipants discerned the increases in the mass andviscosity, and they took part in the main experimentdescribed in the following subsection.

This study suggests that, in addition to using the proprioceptive force sensors, we use our ﬁnger pads as
dynamic force sensors when estimating the mass andviscosity of an object. In the present experimental setup,these cutaneous sensors functioned more dominantly
than the proprioceptive sensors, especially in the sensing of small viscous forces. The ﬁnger pad may beable to play the role of a force/torque sensor when
the central nervous system estimates the applied force
from its cutaneous deformations. Birznieks et al. andJohansson et al. supported this possibility through neurophysiology by showing that the nervous activities of
cutaneous mechanoreceptors code the direction of force
applied to the ﬁnger pad [26], [27]. From a psychophysical point of view, enforced displacements of ﬁnger pads
were shown to inﬂuence the perception of a virtual
object’s mass in lifting motions [28]. These studies andour experiments indicate that, in a dynamic way, ourﬁnger pads function as force sensors and help to estimate
the kinetic characteristics of the mass and viscosity of an
object.

7.2

8.2 Why do 280 Hz vibratory stimuli affect the perceived mass and viscosity?

Fig. 7. Ratios at which participants discriminate theacceleration- and velocity-synchronized vibrotactile stimuli

Tasks of Main Experiment

The participants jiggled the virtual object following therhythm of a metronome as in the previous experiments.
They compared the reference and test stimuli. It should
be noted that for both stimuli, the mass and viscosity ofthe object were maintained: (m, c) = (0.2 kg, 0.5 N · s/m).
For the test stimuli, the amplitudes of the vibrotactile
stimuli increased in synchronization with either the handacceleration or the hand velocity; the amplitudes corresponded to (4) and (5), respectively. The participants
answered regarding whether the mass or viscosity of thetest stimuli was larger than that of the reference stimulus. Each participant conducted 40 trials; each of themass and viscosity was increased 20 times, respectively.
7.3

Results

Fig. 7 shows the answer rates of the participants in themain experiments. The ﬁgure shows the ratios at which
the participants answered that the mass and viscosity
increased for the test stimuli in which the accelerationand velocity-synchronized vibrotactile amplitudes, respectively, were presented. Because the answer ratios
were signiﬁcantly higher than the chance level (averageof 0.866, standard deviation of 0.123, t-test, t 0 (7) =8.40, p = 6.68 × 10−5 , two-tailed), the acceleration- andvelocity-synchronized stimuli were recognized as different stimuli. From the above results, we speculate that thetwo types of vibrotactile stimuli affect the perception ofloads differently: the acceleration-synchronized stimuli
are the biases for the inertial load, and the velocitysynchronized stimuli are the biases for the viscous load.

The frequency of vibrotactile stimuli used in the present
study was 280 Hz. We informally conﬁrmed that otherfrequencies also cause the bias effects; however, on account of the frequency characteristics of the stimulator,
we used frequencies higher than tens of hertz. In thesefrequency bands, FAII units preferentially respond to thevibrations.
SAI and SAII units respond to sustained pressure orindentation [4], [29]. Given that the weight indents theﬁnger pads, these receptors mediate the perception of thelifted weight. Thus, SAI and SAII units are commonly
supposed to be related to the perception of loads. In
the case of dynamic cutaneous deformations, fast adaptors also respond to the stimuli. At the moment thatdynamic deformations are applied to the ﬁnger pad–such as in prehension–FAII, FAI, and SAI units could be
activated [30] ．Birznieks and Johansson et al. reported
that FAI units were innervated by the lateral deformationon the ﬁnger pad, though they did not mention FAII
units [26], [27]. These reports imply that fast adaptors
also respond to dynamic skin deformations, such as
those that could have happened during the jiggling
motions in the present study. One speculation from theseneurophysiological studies is that in the case of dynamic
conditions such as jiggling motions, fast adaptors may
also contribute to the perception of applied forces.
8.3 Is directional information about skin stretches
necessary for the perception of mass and viscosity?
The vibrotactile stimuli used in this study were considered to affect the activity level of FA units; however, theThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
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stimuli did not present information about the direction of
the lateral deformation or the external force on the ﬁnger
pad. One may doubt whether the directional informationof forces applied to the ﬁnger pad inﬂuences the perception of the mass and viscosity, but their magnitudes
certainly do so. Our experiments do not answer thisquestion; however, we consider that both the direction
and magnitude of the applied force inﬂuence the perception of the mass and viscosity. We make this conclusion
because, during the experiments, the vibrotactile stimuli
were applied to the participants’ ﬁnger pads while theirﬁnger pads were laterally deformed. The participants
must have been able to estimate the directions of theforces based on the directions of the lateral deformationsof their ﬁnger pads. Hence, the results of this study do
not imply that the directions of skin stretches do notcontribute to the perception of inertial and viscous loads
during jiggling motions.

9

C ONCLUSIONSWe showed that the vibrotactile stimuli on our ﬁnger
pads inﬂuence the perception of the mass and viscosityof the object when it is jiggled by the ﬁnger. From thenumerical analyses of the skin stretches of the ﬁnger
pad, it was predicted that the increase or decrease in
the cutaneous mechanoreceptors’ activity level in synchronization with the hand acceleration would affect theperception of the mass. Also, we predict that the changes
in the mechanoreceptors’ activity in synchronization
with the hand velocity would affect the perception of
the viscosity. The experiments were conducted using
an apparatus that could manipulate the proprioceptive
stimuli, which corresponded to the mass and viscosity ofthe virtual object, and the vibrotactile stimuli applied tothe ﬁnger pad. As a result, the acceleration-synchronizedand velocity-synchronized vibrotactile stimuli biased theperception of the mass and viscosity, respectively. The
tactile stimuli increased and decreased the perceived
changes in inertial and viscous loads when the loads
and the tactile biases were imposed in the same perceptual direction. Through the paradoxical test stimuli–
for example an increased actual viscosity and the tactile
stimuli of a negative bias for the viscosity–that were simultaneously presented to the participants, it was foundthat the tactile stimuli canceled the perceived changes in
the mass and viscosity. We expect that these vibrotactile
biases will become alternative force displays and will
expand the applications of vibrotactile displays in termsof haptic interactions.

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Shogo Okamoto received the BS degree inengineering from Kobe University in 2005, andthe MS and Ph.D. degree in information sciencesin 2007 and 2010 from Graduate School of Information Sciences, Tohoku University, respectively. He was a JSPS research fellow for young
scientists since 2007 to 2010. Since 2010, He
has been an assistant professor at the Graduate
School of Engineering, Nagoya University. His
research interests include haptic interfaces. He
received the Dean’s Award, GSIS, Tohoku University in 2007 and 2010, ROBOMEC award in 2007, 2008, and 2009
from Robotics and Mechatronics division, JSME, Best Poster Award at
WorldHaptics’07, IEEE RAS Japan Chapter Young Award (ICRA’08) in
2008, Award for the Best Hands on Demo at EuroHaptics’08, Young
Investigation Excellence Award from RSJ in 2010, etc. He is a memberof the IEEE.

10

Masashi Konyo received the BS, MS, and PhD
degree in engineering from Kobe University in
1999, 2001, and 2004, respectively. In 2004,
he was a postdoctoral fellow at the BioRobtics
Laboratory, Keio University, and an assistantprofessor of GSIS, Tohoku University since 2005
to 2009. Since 2009, he has been an associate
professor of the Graduate School of Information Sciences, Tohoku University. His current
research interests include haptic perception, tactile interfaces, and human cooperative robotics.
He received the Paper Award from the Virtual Reality Society of Japan
in 2002 and 2007, the Best Poster Award at the WorldHaptics2007,
the Best Hand-on-Demo Award at the EuroHaptics’08, the Best Paper
Award of the Journal of Robotics and Mechatronics in 2010, etc. He is amember of the IEEE.

Satoshi Tadokoro (M’89-SM’06-F’09) received
the B. E. degree in precision machinery engineering in 1982, the M. E. degree in 1984 fromthe University of Tokyo, and the D. E. degreein 1991 from Kobe University. He has been aprofessor of Graduate School of Information Sciences, Tohoku University since 2005. He wasa project leader of MEXT DDT Project on rescue robotics in 2002-2007 having contributionof more than 100 professors nationwide. He
established RoboCupRescue in 1999, TC on
Rescue Engineering of SICE in 2000 (the ﬁrst chair), IEEE Robotics
and Automation Society TC on Safety, Security and Rescue Robotics in2001 (the ﬁrst chair), and International Rescue System Institute (IRS)
in 2002. He was IEEE RAS Japan Chapter Chair in 2003-2005. He
is at present President of IRS, trustee of The RoboCup Federation,
Chair of JSME Robotics Mechatronics Division, and IEEE Robotics andAutomation Society AdCom member. He received The Robot Award
2008, FDMA Commissioner Highest Award in 2008, JSME Funai Awardin 2007, Best Book Author Award from AEM Society in 2006, RMD
Academic Achievement Award in 2005, etc. His research interest is in
rescue robotics, virtual reality and new actuators.