The original publication is available at www.springerlink.com.
Haptics: Perception, Devices and Scenarios
Lecture Notes in Computer Science, 2008, Volume 5024/2008, 619-629, DOI: 10.1007/978-3-540-69057-3̲79

Alternative Display of Friction Represented by
Tactile Stimulation without Tangential Force
Masashi Konyo, Hiroshi Yamada, Shogo Okamoto, and Satoshi Tadokoro
Graduate School of Information Sciences, Tohoku University,
6-6-01 Aramaki Aza Aoba, Aoba-ku, Sendai 980-8579 Japan{konyo,tadokoro}@rm.is.tohoku.ac.jp
http://www.rm.is.tohoku.ac.jp/

Abstract. A new display method of friction sensation based on tactile stimulation is proposed. In this method, no tangential force on thefingertip is required to represent friction sensation. We focus on the activities of tactile receptors in response to stick-slip contact phenomena
with the fingertip. The proposed method controls the activities of FA II
type receptors using very high frequency vibrations (at 600 Hz) in corresponding to the phase of stick-slip transition. The stick-slip transition
was expressed by a single DOF model with Coulomb’s friction, which
represents the effects of coefficients of dynamic/static friction and hand
movements. The sensory magnitudes of the perceived friction by the
proposed method were evaluated in contrast with a force display. The
experimental results showed that the perceived friction proposed hadhigh correlation with that of the force display in regard to the increase
tendency toward static friction coefficients. The sensory magnitudes of
the tactile perceived friction were about one-seventh smaller than thatof the force display.
Key words: friction display, tactile stimulation, stick-slip friction model,
vibration

1

Introduction

Haptic display of friction in virtual environments is important to represent properties of contact objects and control the objects. Many conventional friction displays generate friction force against operators’ hands or fingers. There are two
methods to generate the friction force. One is use of force displays such as PHANToM to represent actual friction force in the tangential direction of the contact
surface. Many sophisticated haptic rendering methods using force displays haveproposed [1, 2]. Another is changing friction properties of the contact surface using squeeze films generated by ultrasonic vibrations [3] or using thin film sliders
actuated by SAW [5] or electrostatic force [4]. This approach is effective when
the finger and the contact surface can move relatively.
This paper proposes an alternative display method of friction sensation using vibratory stimulation on a fingertip without actual friction forces. No use
of tangential force contributes to reduce large mechanical parts and actuators.
This approach is advantageous to mount on small equipments such as handheld
information devices and game controllers. This approach is also easy to integrate
the tactile friction display with a force feedback device because there is no need2

Alternative Display of Friction Represented by Tactile Stimulation

to move the finger against the contact surface relatively. From the aspect of skinstimulation, effects of skin stretch [6] and rotational sliding [7] were investigated
for the friction display. Comparatively speaking, our approach makes the tactile
display much smaller and simpler because the vibratory stimulation can be generated by a single 1-DOF actuator, such as a piezoelectric vibrator and a voicecoil. In addition, our method can be realized by vibrating the side of contact
objects such as a touch panel of LCDs.
We focus on not deformations of skin but activities of tactile receptors whena finger is stroking on a surface with friction. We have proposed several stimulation methods using mechanical vibrations to control the activities of tactile
receptors selectively based on the frequency response characteristics of them [8,9]. For example, vibration on fingertip at the frequency of 5 Hz could generatepressure sensation by stimulating SA I type receptors [8], and vibration at 30
Hz, which is sensitive for FA I type receptors induced reflective grasping reactionof human [9]. In this paper, we focus on the activities of FA II type receptors,
which are most sensitive against vibrations at the frequency of more than 200
Hz. Although we proposed the similar concept that friction sensation could be
generated by stimulating FA II type receptors using high frequency vibration in[8], the stimulation method was based on heuristics and not be established well.
In this paper, we propose the friction display method based on the stimulationof FA II type receptor integrated with a physical friction model, which canrepresent effects of friction coefficient and finger movements. At first, we describe
the observation of stick-slip phenomena at the contact area of the finger and thesurface. This observation supports our hypothesis of the FA II stimulation. Then,the concept of the stimulation method using FA II stimulation based on stick-slip
transitions is proposed. Next, the applied physical model of stick-slip frictions
is described. Finally, we validate the proposed method in contrast with friction
sensation generated by the force display via a PHANToM.

2

Basic Concepts

Stick-slip Phenomena are highly related to production of friction sensation detected by tactile receptors. We proposed a friction display method based on
the representation of activities of tactile receptors in response to the stick-slip
phenomenon.
2.1

Observations of Stick-Slip Phenomena

At first, we observe actual stick-slip phenomenon with human fingertip. Nahvi
et al. [10] reported that a high frequency vibration at 89 Hz occurred on a human finger pad with contacting objects. We had observed that this phenomenon
depends on a contact condition. In this section, we examine an approximate
appearance condition of stick-slip phenomenon.
In the experiment, deformations of a finger pad marked with dots in contact
with a transparent acrylic pate were measured by a high speed camera at 2000
frame/sec. To keep the skin condition, which is affected by perspiration andfats and oils, the finger pad was cleaned by ethanol and left one minute after
cleaned. One participant stroked the surface with his index finger keeping his
pressing forces at 0.5, 1.0, 2.0 [N] after he was trained to keep the pressing forces
approximately. Three stroking motion at relatively slow, middle, high speedsTitle Suppressed Due to Excessive LengthAppearance

300

Non-appearance

250
200
150
100
50
0
0

50
100
Finger velocity (mm/s)

Appearance rate of stick-slip

Stick-Slip Freqeucncy (Hz)

350

3

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

150

Fig. 1. Figure in the left.

0

1

2

Normal force (N)Fig. 2. Figure in the right.

were performed. Each condition was measured twice. Thus, the number of trials
is 18.
2.2

Friction Display Method Proposed

We focus on the activities of tactile receptors in response to stick-slip transition.
From the observation in the previous section, we confirmed that stick-slip phenomenon occurs at the wide area of finger pad at high frequencies of more than
100 Hz. These results indicates that only FA II type tactile receptors (Pacinian
corpuscles) can detect such stick-slip information because FA II has high responsiveness (À 100 Hz) and large receptive fields (À 10 mm). Several studies
supported the same idea. For example, Howe et al. [11] reported the reason why
Pacinian corpuscles can detect slip information. In this study, we investigate thepossibility of the friction display based on vibratory stimulations on FA II type
receptors in corresponding to stick-slip transitions.
We use selective stimulation method using vibration [8, 9] to control the activities of FA II receptors as mentioned in Introduction. High frequency vibrations
at more than 200 Hz stimulate FA II selectively, because FA II has the mostsensitive response characteristics in such the range than other tactile receptors.
Changing amplitudes of high frequency vibration at a fixed frequency component can control the activities of FA II. Note that changing frequency within thehigher range (> about 300 Hz) have no sensory qualitative difference for FA II.
It just affect on a subjective magnitude of the same vibratory sensation. In thisstudy, we use high frequency vibration at 600 Hz as a stimulation for FA II inorder to separate from the stick-slip frequencies at around 100 Hz adequately,as described in 4.
Fig. 3 illustrates a basic concept of friction display method proposed. Vibratory stimulation at the high frequency is generated in response to the timing ofstick-to-slip transitions. The vibration has a peak just after stick-to-slip transition and damps gradually. Amplitudes of the vibration peak (Ak , Ak+1 ) reflects
on amounts of elastic displacement (dk , dk+1 ) in the stick friction phases. Assuming sampling linear elasticity in static friction, the amplitude A is proportional
to the elastic displacement d. For example, as shown in Fig. 3, Ak > Ak+1 , whendk > dk+1 .
For realizing the proposed concept, the following problems should be considered:

4

Alternative Display of Friction Represented by Tactile Stimulation
Stick-Slip transition

dt+1

dt
Stick

At

Slip

Stick

Slip

Stick

At+1

Vibratory
Stimulationt

Fig. 3. Basic concept of friction display method proposed.

– Modeling of stick-slip friction which represents physical friction parametersof target objects and finger’s forces and movements– Patterning of vibration stimulation corresponding to the activities of FA II
In this paper, the stick-slip friction is expressed by a single DOF model with
Coulomb’s friction, which represents the effects of coefficients of dynamic/static
friction and hand movements as described in the following section. For the pattering of vibration, we conduct in a heuristic way as described in 3.4.

3Stick-Slip Friction Model

3.1

Aanalytical Model

Stick-slip motion is generated by the repetition of ”stick” and ”slip” of mating
surfaces. Stick-slip motion is caused by the deference between static friction coefficient and kinetic coefficient, and it tends to occur with slower sliding velocity
and higher normal load. Some haptic rendering researches proposed establishedfriction models for force feedback device[1, 2]. These models mainly focus on
discontinuity of kinetic friction force around at zero-crossing of velocities anddiscrete time computing. In this paper, we use Nakno’s model [12] which focuses
on representation of stick-slip motion by a simple analytical model.
Nakano’s friction model approximates stick-slip motion as a 1-DOF vibration
system with Coulomb friction, which is consists of an object (mass m), a linear
spring (stiffness k) and a viscous damper (damping coefficient c) as shown in
Fig. 4. The object contacts a floor surface with a normal load W , and the floor
surface side in the x direction with a positive moving velocity V . The object isforced by friction F, which is determined as a function of the relative velocity
between the floor surface and the object, V − ẋ,– static friction (when V − ẋ = 0):
F = Fs ,|Fs | ≤ |Fsmax |,Fsmax = µs W,

(1)
(2)
(3)

– kinetic friction (when V − ẋ 6= 0):
F = sgn(V − ẋ)Fk ,Fk = µk W,

(4)
(5)

Title Suppressed Due to Excessive Length

5

x(t)

k

m
W

F

∆µ

c
0

starting pointof stickx(t)VFig. 4. 1-DOF vibration model of stick-slip motion (revised from [12]).

where Fsmax is maximum static friction, µs is a static friction coefficient, andµk is a kinetic friction coefficient. The difference between the two friction coefficients,∆µ = µs − µk > 0.

3.2

(6)

Stick-to-Slip Transitions

In the stick state, stick-to-slip transitions occurred when,mẍ + cẋ + k(x − x0 ) > Fsmax ,(7)

where x denotes the position of the object, x0 denotes the position of the object
when the spring is in its natural length, and the origin of the x coordinate isdetermined to be the static equilibrium position with the positive kinetic friction
Fk , that is
x0 = −Fk /k.

(8)

At the moment of the stick-to-slip transitions, the object gets the maximum
static friction force. And then the force is suddenly released and the object isoscillated corresponding to the stored elastic displacement. This phenomenon is
expected to be highly related with human cutaneous friction perception. In thispaper, the maximum amplitude of vibratory stimulation Amax at the stick-to-slip
transition is calculated as follows,
Amax = αk(x − x0 ),(9)where α is a constant to convert the elastic force into the amplitude of vibration.
3.3

Slip-to-Stick Transitions

In the slip state, the motion of the object are described as follows,mẍ + cẋ + k(x − x0 ) = Fk , when ẋ < V,mẍ + cẋ + k(x − x0 ) = −Fk , when ẋ > V.

(10)
(11)

In the above slip state, slip-to-stick transitions occur when the velocity of theobject ẋ becomes equal to the velocity of the floor surface V . However, if theAlternative Display of Friction Represented by Tactile Stimulation

Finger’s velocity [mm/s]

60

Vibration amplitude

6

40

4
20

2

0

0
-2

-20

-4
-40
-60
0

-6

Vibration amplitude [V]6Finger’s velocity

0.51Time [s]1.5

2Fig. 5. Vibratory stimulation corresponding to the finger’s velocity（m = 0.00016[kg],k = 10[N/m], µs = 1.0, µk = 0.4).

object has a critical damping or a overdamping, or the floor surface is accelareted,the objects keep slip state and stick-slip phenomena does not occur because ẋ
cannot be equal to V .
Considering a haptic friction display, finger motions correspond to the motionof the floor surface in the model. In this case, the velocity of the object ẋ neverexceed the velocity of the finger because the slip state changes into the stick
state at the time that ẋ became equal to V . Thus, the equation of motion (10)is always held for the slip sate. The motion equation (10) is solved as follows,ẋ = e−pζt {(−ωC1 − pζC2 ) sin ωt + (ωC2 − pζC1 ) cos ωt + pζµk W/k} , (12)where,
C1 = ∆µW/k,
C2 = cµs W/2ωm + V /ω,pp = k/m,√
ζ = c/2 mk,p
ω = p 1 − ζ 2.

(13)
(14)
(15)
(16)
(17)

According to the equation (12), judgments of slip-to-stick transition in the slip
state can be conducted by comparing between ẋ and V . If ẋ become equal to V ,the slip state changes into the stick state.
3.4

Parameter Identification and Patterning of Stimulation

The parameters (m, c, and k) in the friction model have effect on the periodof the stick-to-slip transition. We set the parameters to make the frequency ofthe stick-to-slip transition about 100 Hz at a maximum when the human handstrokes the virtual surface naturally. Fig.5 shows an example of vibration patterngenerated by the model when a finger moves in sinusoidal way. The time constantof damping of vibration is 80 ms. Fig.5 shows that stick-slip phenomena does
not occur when the finger velocity become higher.

Title Suppressed Due to Excessive Length

Force feedback
device7

Gimbals

PiezoelectricVibrator

Fig. 6. System setup.

4

Evaluations of the Tactile Friction Display

4.1

Experimental Setup

Fig. 6 shows the experimental setup to evaluate the friction display. A piezoelectric osseous conduction speaker (NEC Tokin, KDS-UM-01) was used for thevibratory stimulator on skin. The stimulator produces vibration at the amplitude of about 5 µm in the condition of adding a 1.0 N load, when the sinusoidal
voltages of 15 Vpp at the frequency of 600 Hz is applied.
A force feedback device is a PHANToM (SensAble Technologies Inc.). For
testing the proposed tactile friction display, the force feedback device is used
only for producing normal force without any tangential force and measuring
hand movements. The same force feedback device is used as a normal friction
display to compare with friction sensation generated by the tactile stimulation.
The piezoelectric stimulator was attached on the end of the PHANToM withgimbals (Fig. 6). A finger pad of the index finger put on the center of the stimulator supported by thumb from the back side of it as shown in Fig. 6. Finger
movements were tracked at every 3 ms by the PHANToM and the stimulator
was controlled at the frequency of 5 kHz.
4.2

Methods

Sensory magnitudes of the perceived friction presented by the proposed method
are evaluated in contrast with a force display via a PHANToM.
The tactile friction method used same the parameters of the model as describe
in 3.4. The difference between the two friction coefficient ∆µ has effect on the
stick-slip frequency. In this evaluation, we also investigate effects of the twofriction coefficients. Friction coefficients change with keeping ∆µ. Three set of∆µ = 0.1, 0.2, 0.3 were applied. Ten static friction coefficients were selected from0.375 to 0.6. Thus, one set of the friction confidents was 10 × 3.
The force display represents the tangential force on each stick-slip condition
using the same model and the parameters described in 3. In such case, partici-

Alternative Display of Friction Represented by Tactile Stimulation
2.5
Frictionby force∆µ = 0.3∆µ = 0.2∆µ = 0.12
1.5

Frictionby tactile∆µ = 0.3∆µ = 0.2∆µ = 0.1

1
0.5
0
0.35

0.4

0.45

0.5

0.55

0.6

Static friction coefficient µs

Magnitudes of perceived friction

Magnitudes of perceived friction8

2.5

Frictionby force∆µ = 0.3∆µ = 0.2∆µ = 0.12
1.5

Frictionby tactile∆µ = 0.3∆µ = 0.2∆µ = 0.1

1
0.5
0
0

0.1

0.2

0.3

0.4

0.5

0.6

Kinetic friction coefficient µk

Fig. 7. Static friction coefficients vs. per- Fig. 8. Kinetic friction coefficient vs. perceived friction (µs = µk + ∆µ ).
ceived friction (µk = µs − ∆µ ).

pants pick the piezoelectric stimulator in the same manner as the tactile display
but the stimulator makes no vibration.
Magnitude estimation method was applied to evaluate the two friction display. Participants were asked to assign an arbitrary number to quantify theexperience of friction from the viewpoint of subjective strength of friction sensation within 10 seconds. A participant evaluated one set (30 trials) each of boththe tactile display and the force display with a short brake. The participants
were asked to keep the same magnitude scale between the two sets as much as
possible. Orders of stimulation are random. The participants were blindfolded
and wore headphones delivering pink noise. Ten healthy volunteers (9 men and1 woman, aged 22 to 32 years) participated in the experiment.
4.3

Results

The magnitudes of perceived friction were calculated by the geometric averageof all the participants. In order to compare the perceived frictions of the tactile
display and the force display, two kinds of normalizations of data were conducted:(1) Fig. 7 and Fig. 8 are the results with the normalization on all the participantsin both the tactile display and the force display. This way is useful to comparewith the two displays in the same magnitude space. (2) Fig. 9 and Fig. 10 show
the individual normalized results on the two displays. This way is useful todetermine relationships between the friction coefficient and the magnitude oneach display.
Static Friction vs. Kinetic Friction From the results in Fig. 7, both the two
displays successfully increase the perceived friction corresponding to the increaseof the static friction coefficients µs , which was defined in the friction model. Fig.
8 was rearranged from the same data in Fig. 7 in corresponding to the kinetic
coefficients.
Comparing between Fig. 7 and Fig. 8, it is clear that the perceived frictions
were depends on the static coefficients. Therefore, our proposed method could
represent amount of static friction force by using vibratory stimulations.

㻝㻚㻢

㻝㻚㻢

㻝㻚㻠

㻝㻚㻠

㻝㻚㻞
㻝
㻜㻚㻤

Frictionby tactile㻜㻚㻢∆µ = 0.3∆µ = 0.2∆µ = 0.1

㻜㻚㻠
㻜㻚㻞
㻜
0.35

0.4

0.45

0.5

0.55

Static friction coefficient

0.6

Normalized magnitudesof perceived friction

Normalized magnitudesof perceived friction

Title Suppressed Due to Excessive Length

9

㻝㻚㻞
㻝
㻜㻚㻤

Frictionby force㻜㻚㻢∆µ = 0.3∆µ = 0.2∆µ = 0.1

㻜㻚㻠
㻜㻚㻞
㻜
㻜㻚㻟㻡

㻜㻚㻠

㻜㻚㻠㻡

㻜㻚㻡

㻜㻚㻡㻡

㻜㻚㻢

㻜㻚㻢㻡

Static friction coefficientFig. 9. Normalized perceived friction of the Fig. 10. Normalized perceived friction oftactile display.
the force display.

On the contrary, the kinetic friction coefficients were not reflected on the perceive friction well. We consider that the effect of the kinetic friction coefficientswas smaller than that of the static friction confidents in the aspect of magnitudeof perceived friction. More investigations are needed.
Tactile Friction Display vs. Force Friction Display Comparing between
Fig. 9 and Fig. 10, both the increase tendencies of the perceived frictions against
the increase of the friction coefficients were very similar. Correlation coefficients
between the tactile display and the force display on each ∆µ series were very
high (∆µ = 0.3: 0.794, ∆µ = 0.2: 0.950, ∆µ = 0.1: 0.884).
The result in Fig. 7 also showed that the sensory magnitudes of the tactile
perceived friction were about one-seventh smaller than that of the force display.
Although the friction sensation of the tactile display was smaller than that of
the force display, we confirmed that the proposed method could express friction
sensation without actual friction force.

5

Conclusions

A new display method of friction sensation based on tactile stimulation was
proposed. In this method, no tangential force on the fingertip is required torepresent friction sensation. The proposed method controls the activities of FA
II type receptors using very high frequency vibrations in corresponding to thephase of stick-slip transition. The stick-slip transition was expressed by a single
DOF model with Coulomb’s friction, which represents the effects of coefficientsof dynamic/static friction and hand movements.
The sensory magnitudes of the perceived friction by the proposed method
were evaluated in contrast with a force display. The experimental results showedthat the perceived friction proposed had high correlation with that of the force
display in regard to the increase tendency toward static friction coefficients.
The sensory magnitudes of the tactile perceived friction were about one-seventh
smaller than that of the force display.

10

Alternative Display of Friction Represented by Tactile Stimulation

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