Virtual Reality

Surface Acoustic
Wave Tactile
DisplayDeveloping realistic tactile displays for virtual reality has been challenging. Tangible displays are increasingly important interfaces not
only for augmenting the reality of computer graphics
but also for conveying graphical information to persons
with visual impairments. Researchers have used various actuators for displays such as miniature loud speakers,1 a pin array,2 pneumatic actuators,3 and ultrasonicvibrators.4 Researchers have also proposed methods
based on the processing properties of human tactile
information. Humans feel tactile
sensations via mechanoreceptive
units that are classiﬁed into four catWe propose a tactile display
egories—rapidly adapting I and II(RAI and RAII) and slowly adapting
using surface acoustic
I and II (SAI and SAII), whose end
organs are Meissner corpuscles,
waves. We can continuously
Pacinian corpuscles, Merkel cellneurite complexes, and Rufﬁni endchange the fineness of theings,
respectively.5
Shinodasurface’s grain by controlling developed a tactile display that
stimulates each mechanoreceptor
selectively, using the human skin’s
the SAWs’ burst frequency.
elastic transfer property.6
However, because the researchers didn’t clarify theparameters that characterize roughness, rigidity, andmaterial quality, they weren’t able to show a principle
for systematic control of tactile sensations by the previously mentioned devices. This resulted in using adhoc stimulation in the displays for creating particularsensations. Furthermore, the researchers didn’t consider the mechanisms for the mechanoreceptors’
motion.
Clarifying the receptors’ mechanical properties lets
us obtain a more effective method for stimulating theprocessing system of human tactile sensation. Thus, inthis article, we ﬁrst analyze which skin deformations
the RA-type mechanoreceptors detect. Based on the
result of the analysis, we clarify a ﬂow of tactile information from the objects’ parameters to the receptors’
deformation, which leads to a proposal for the surface
acoustic wave (SAW) tactile display.

56

November/December 2001

Takaaki Nara, Masaya Takasaki, Taro Maeda,
Toshiro Higuchi, Shigeru Ando, and Susumu Tachi
University of Tokyo, Japan

Models of mechanoreceptors and skinIn this section, we analyze the properties ofmechanoreceptors and skin from the viewpoint of skindeformation to which the mechanoreceptors are sensitive. This analysis suggests the principle of the SAW tactile display.

Meissner and Pacinian corpuscles
Meissner corpuscles, which have a relatively low characteristic frequency of about 40 Hz, are localized in thepapillary dermis with a height of around 150 µm and adiameter of 40 to 70 µm. A structural feature is their
coiled axons7 on which Ca2+ ion channels exist.8
Guharay et al.9 showed that a probability of generalmechanosensitive ion channels being open depends onthe energy of deformation expressed as U = K/2 ⋅(∆A/A)2 ⋅ A, where K is the channel’s elastic modulus
and A is the channel’s size. Thus, we must analyze theaxon surface’s deformation when stress by skin isapplied to the corpuscles.
Transmission of deformation by a coil. We
ﬁrst clarify a coiled structure’s mechanical properties.
As Figure 1 shows, we set an x axis along the wire of thecoil and y, z axes in a section of the wire. When we apply
normal (Figure 1a) and shear (Figure 2a) stresses to the
top and bottom of the coil, a torsional moment Mx andbending moments My, Mz are applied to the section of
the wire in Figures 1a and 2a. Note that only the torsional moment is generated when we apply P to the coil.
As a result, only shear deformation on a coil surface isgenerated when we apply normal stress to the coil (Figure 1b), while stretch deformation—in addition to shear
deformation—is created on the surface when we apply
shear stress to the coil (Figure 2b).
Because activating the axon depends on the ratio ofchange of the channel size, the shear stress to the coil—which generates stretch deformations on the coil surface—changes the surface’s size to increase theprobability of the channel being open. Therefore, wehypothesized that the coiled axon of Meissner corpuscles is sensitive to shear stress in the skin. To verify this0272-1716/01/$10.00 © 2001 IEEE

P

Q

x

z

Mx

Section 1

x

Mz

y
Mx

(a)

(b)

sional moment Mx is generated at a cross-section of thewire, (b) which creates a shearing deformation at thewire’s surface.

statement, we show next that we can derive the corpuscles’ tuning curve on the basis of the coiled axon’s
shearing resonant character.

(b)

2 When we apply shear stress to the coil, (a) in addition to a torsional moment Mx, bending moments My,
Mx are generated at cross-sections of the wire, (b)which creates shearing and stretch deformations at thewire’s surface.

500

nD2

2ρ

,

ωx
ωz

=

(

2 1+ ν

) H 2
1 + 12 2 + ν  
D

(

(1)

)

where d is the diameter of the coil’s wire, µ is the rigidity of the wire, ρ is the density of the wire, and ν is the
Poisson’s ratio of the wire. Assuming that ν is approximately 0.5 and H/D =150 µm/50 µm as in the Meissner corpuscles,
ωx
ωz

=

1

(2)

10

Thus, we can consider that the corpuscles’ characteristic frequency derives from the shearing resonant frequency as the coiled axon’s minimum resonant
frequency. In fact, with parameters observed in medical
experiments,7 ωx/2π = 44 Hz, which corresponds to thereal characteristic frequency. Moreover, we can derive
the tuning curve from the energy of the coil’s shearing
deformation, which depends on the shear stress in theskin, as Figure 3 shows. Although our analysis here is
too simpliﬁed and we should further investigate the roleof the Schwann cells and the collagen ﬁbers of the corpuscles for detecting normal stress of the skin, our discussion suggests that Meissner corpuscles might easily
detect shearing, equivoluminal deformation in the skin.
Also, as for Pacinian corpuscles (the other RA-typemechanoreceptors), we’ve shown that the structure of
the layered lamellae of Pacinian corpuscles might easily detect skin’s equivoluminal deformation with a coupled pendulum model verified by deriving tuning
curves.11 In this way, we suggest that dynamic, shear,equivoluminal deformation inside skin is an importantfactor for stimulating the RA-type mechanoreceptors.

Threshold (µm)

µ

y
Mx

(a)

Dynamic properties of a coil. We can express acoil’s longitudinal resonant frequency of ωz and a shearing resonant frequency of ωz as
d

My

z

My

Section 2

1 When we apply vertical stress to the coil, (a) a tor-

ωz =

x

x

100
50

10
5
Experiment
Theory510

50 100Frequency (Hz)3 The tuning curve of the Meissner corpuscles.10
Assuming that the Meissner corpuscles detect shear
stress of the skin, we can derive the tuning curve fromthe shearing resonant characteristic of the coiled axon.
We drew the experimental curves according to the
Talbot’s data.10

Equivoluminal deformation as invariant
In this section, we investigate the equivoluminal deformation’s meaning from the viewpoint of an invariant ofskin deformation. Although here we consider an idealized skin model of an isotropic, homogeneous, and inﬁnite elastic body, this discussion shows importantcomponents of deformation for mechanoreceptors in tactile displays. We can completely express an elastic body’s
deformation by the stress tensor’s six components. However, the tensor’s components depend on the coordinates’
direction. Thus, unless mechanoreceptors with sphericalasymmetric shapes are set in a uniform direction in skinor a central nerve system calibrates the directions of all
the mechanoreceptors, the brain can’t process tensor
components consistently from spatially distributed
mechanoreceptors. Actually, the mechanoreceptors aren’t
always distributed in the uniform direction in skin. Then,

IEEE Computer Graphics and Applications

57

Virtual Reality

4 Orthogonal
decompositionof a principal
stress. Any
deformation isdecomposed
into dilatationand distortion
according to
the decomposition of a principal stress into amean stresscomponent andan octahedral
shear stresscomponent.

σ1

J1
3

√J 2′ e2θ

e1 =previous section, we expressed modes that the Meissner and Pacinian corpuscles are sensitive to as


0 1
, σ 1 0 (7)τ
0 −11 0

e1

1
1
1

in 2D problems, where τ and σ are proportional to √J ′2
representing equivoluminal deformation. Also, as for
the SA-type mechanoreceptors, Srinivasan12 showed aninteresting result that strain energy density,1  1−2v s 2
φ=
J1 +2 J2′ (8)
4µ s  3(1+ v s )σ31e2 = −1
0

1
−1
0

θ

σ2

let’s consider a diagonal component of deformation of
σ x

τ xy
 τ xz

τ xy
σy
τ yz

σ 1 0τ xz τ yz  = Q −1  0 σ 2
 0 0σ z 0
0 Q
σ 3 

(3)

where νs is Poisson’s ratio and µs is rigidity of skin, is acandidate to be the relevant stimulus for SAI.
The relevant stimulus for the RA-type mechanoreceptors should be investigated by physiological experiments. However, our discussion suggests the importanceof equivoluminal deformation, which is easily detectedby the RA-type mechanoreceptors, as an independent
component of skin deformation. Next, we investigate
how equivoluminal deformation inside skin is generated in active touch.

Skin distortion in active touchthat the central nerve system can detect in spite of themechanoreceptors’ directions. The eigen values σ1, σ2,
σ3—the principal stress—are independent of the coordinates’ direction. Here, we can decompose a vector
composed of (σ1, σ2, σ3) as
σ 
1
1
 1 J   1σ2  = 1 + J2′ −1  3   
σ 3 
1
1
 
 
 θ

(4)
q= s +

where J1, J′2 are the ﬁrst-order stress invariant and thesecond-order stress deviation invariant, respectively.
The first term of (1, 1, 1) corresponds to an isotropic
deformation with a coefﬁcientJ1 σ 1 + σ 2 + σ 3
=
3
3

(5)

which is proportional to dilatation. On the other hand,the second term of (1, −1, 0)θ, which is rotated from (1,−1, 0) with an angle of θ on a plane perpendicular to (1,1, 1), corresponds to equivoluminal deformation with a
coefﬁcient
J2′ =

3
2

τoct

(6)

November/December 2001

σβp, p =

E σ
⋅
π β

(9)

where Eo, Es is Young’s ratio of the object and the skin,respectively; ν0 is Poisson’s ratio of the object; 1/E=
(1−v2s)/Es+(1−v2o)/Eo, s, and s′ are the skin’s static andkinetic shear strength; σ is the topography’s standard
deviation; and β is the topography’s mean radius of projections. Then, during the exploration, we can show thatthe stress q and p to the skin surface can be temporally
vibrated in a stick-slip motion with a stick-slip frequency fss expressed as
fss−1 =
R=

where τoct is an octahedral shear stress. As Figure 4
shows, these two terms are perpendicular in the vector
space composed of principal stress. Thus, if the central
J′2) in thenerve system can detect invariants (J1/3, √elastic skin, it can realize an effective sensing of principal stress that’s independent of the mechanoreceptors’
direction because they’re the independent components
of an orthogonal decomposition. In our analysis in the58

We analyzed contact and relative motion between theﬁnger and an object by a spring (k)–mass (m) model ofthe ﬁnger moving on an object’s Gaussian surface withconstant velocity (U) of exploration.13 By the Hertz contact theory, we can approximately express the normal
stress p and shear stress q to the skin surface generated
at the positions of the projections as2ω0( π −tan−1 R + R )(10)(µ s −µ c )P

(11)

mω0U

µ s −µ c =π( s − s′ )βEσ, ω0 =km(12)

where P is a total normal pressure by the skin. Figure 5
shows the relationship between an object’s parameters
and the stick-slip frequency, which is a key relationshipfor displaying material quality in the next section. As an
example, we drew Figure 5 with P = 1 Newton (N), m =1 gram, k = 500 N/m, and U = 4 cm per second.

ƒSS(Hz)

Under these boundary conditions at the skin surface,100
let’s consider deformation inside the skin. At the80
moment of the shift from the stick state to the slip state,normal and shear stress begins to move suddenly on the
60skin surface. As a result, elastic waves are created inside40
the skin, and these are dominant deformations because
amplitudes are much greater than the stationary defor20
mation generated during the stick state or the slip state.
µs − µc0Now, consider skin deformation with a 2D elastic skin
0
0.5
1
1.5
2
model when normal and shear stress that vary with timeas the Heaviside unit-step function
is applied to the skin surface.
Remarkably, the polarity of the S17 mm
wave’s amplitudes, which are muchlarger than the P-wave’s amplitude,
63 mmturns over along the skin surface by
the normal stress in contrast to theconstant polarity by the shear
1 mmstress.11 As a result, the S-waves byReflector
many normal sources distributed
over the skin surface are canceled,Thin tapewhile the S-waves by the distributed
SliderSteelballs
shear sources become large becauseof a constructive interference. In thisIDTway, we can show that primal surface stress, which creates dominant
deformation inside the skin, is disLiNbO3 substratepersed shear stress. The following
represents our analysis, which wesummarized as a flow of tactile
information:■ The sources of shear stress can be temporally modulated with a stick-slip frequency fss determined by the
1. Parameters of the object to be touched and theparameters of the object to be displayed.
motion of an active touch: (E0, νo, σ, β) × (P, U).
Although many previous tactile displays have used
2. Stress on the skin surface:
Dispersed sources of shear stress, q = s + E/π ⋅ (σ/β)2, stimuli perpendicular to the skin surface,1-3 several disand stick-slip frequency, fss = 1/Tss in Equations 10 plays can control parallel force to the skin surface byusing ultrasonic vibration4 or piezoelectric actuators.14
through 12.
3. Equivoluminal deformation inside the skin due to As used in S-wave gnerators in geophysical prospecting,the constructive interference.
a method using phase-inverted perpendicular vibra4. Meissner and Pacinian corpuscles: Detection of the tions6 is also equal to controlling shear stress to the skin.
equivoluminal deformation. The ratio of the conHowever, because relative motion between the skintribution of both corpuscles is changed by fss.
and real objects hasn’t been analyzed until now, it’sunclear how to temporally modulate shear stress. It’s
also impossible to control a sensation of roughness systematically as though diameters of small projections on
SAW tactile display
In this section, we develop the SAW tactile display, a rough surface change continuously. We propose to use
which can effectively stimulate the mechanoreceptors SAWs to generate sources of shear stress that satisfy theinside skin. We show an experiment of controlling ﬁne- three prerequisites for tactile control.
ness of grain and its several applications.

5 Relationshipbetween a
parameter ofµs − µc and a
stick-slip frequency.

6 Schematic
description of
the SAW tactile
display.

DeviceShear sources method
Based on our discussion in the previous section, we
can derive the prerequisites for tactile control—especially for stimulating the RA mechanoreceptors—as follows:■ Sources of shear stress should be applied to the skinsurface to create equivoluminal distortion detectedby the mechanoreceptors.
■ The sources of shear stress can be spatially dispersedon the ﬁnger surface.

SAWs have recently attracted attention for sources ofdriving force for linear motors15 in addition to their practical application as a ﬁlter for telecommunication equipment. We use SAWs for tactile control.
Figure 6 schematically shows the SAW tactile display’s
structure. On a Lithium Niobate (LiNbO3) 128-degree
Y-cut substrate whose size is 17 mm × 63 mm × 1 mm,
alternating voltage to an interdigital transducer (IDT)
generates a SAW. A SAW’s wavelength is about 265 µm
with the driving frequency of 15 MHz. One of the prominent advantages of the display is the substrate’s thin-

IEEE Computer Graphics and Applications

59

Virtual Reality

ness (1 mm) for creating stimuli to the ﬁnger.
We placed IDTs at both ends of the substrate. To generate progressive waves, we applied an alternating
voltage to one side of the IDTs. To generate standing
waves, we applied the voltage to both sides of the IDTs
and set open-metal-strip arrays (OMSA) after the IDTs
as reﬂectors.
In our tactile display, users can explore the substratewith a slider shown in Figures 7 and 8. The slider has
approximately 100 steel balls with a diameter of 800 µm
on a thin tape. We chose to use a slider because of the following:

7 Detail of theslider.

■ By pressing steel balls with the ﬁnger, a driving force

can be effectively transmitted to the ﬁnger.
■ Steel balls can provide distributed
points to which stress is appliedon the finger surface, assumingthat the tape is satisfactorily thinand soft.

Principle
Here we describe the principle forgenerating sources of shear stressthat are distributed spatially andmodulated temporally.
When users explore the substrate
without SAWs with their ﬁngers—
via the slider—kinetic friction by thesubstrate is applied to the steel balls,
thus creating sources of shear stresson the fingers’ surface at the positions of all the steel balls distributed
spatially (Figure 9a).
By generating SAWs, we candescrease the friction between thesteel balls and the substrate compared to the substrate without SAWs
because there’s a

8 The SAW
tactile display.

Shear stressDirection of
the exploration

Finger■ decrease in contact time between

the balls and the substrate,
Tapeexists between the balls and thesubstrate, and■ parallel movement of the wave
crest (only in using progressive
waves).

Steel
balls

9 Generationof sources ofshear stress thatcan be modulated temporally
by burst wavesof SAW.

(a)Kinetic friction

Shear stress becomes smaller

Tape
Squeeze force

(b)

60

Driving force
by the crest

November/December 2001

■ squeeze-ﬁlm effect by the air that

Steel
balls

SAW

As a result, when we either generatea progressive or standing SAW in thesubstrate, shear stress to the skinbecomes smaller (Figure 9b) thanshear stress without a SAW. Thus, byusing a burst waves of SAW, we canmodulate the sources of shear stressapplied to the skin surface with aburst frequency. The moment when
the wave suddenly appears corresponds to the moment when the
stick state changes into the slip statebecause the friction suddenlyFriction

Friction
1.56
1.4

t (msec)
0100

10 Experimental data of friction
between the substrate and theslider. Generating SAWs reduces
friction. Thus, a burst standing SAW
can create a virtual stick-slip vibration of friction.

Input burst signal

decreases. Therefore, we can control the stick-slip frequency virtually by changing the burst frequency. In thisway, we obtain distributed sources of shear stress thatare modulated with a stick-slip frequency determinedby the object’s solidity and roughness.

Experiments
We performed experiments to control the roughnessof objects by changing the frequency of the modulationof the shear stress’ distributed sources.

Table 1. Scales of the real and virtual objects’ roughness.
Real Objects (Sandpaper)
Number
Scale
#60
#120
#240
#320

−1.125−0.3750.375
1.125

Virtual Objects (Display)
fb
Scale
20 Hz
40 Hz
80 Hz
200 Hz−1.125
−0.5
0.5
1.125

Evaluation
Generation of virtual stick-slip
Figure 10 shows an input signal of a burst wave to the
IDTs and the resulting temporal friction change. The
burst wave has a carrier frequency of 15 MHz and a duty
ratio of 40 percent. The input power is 2 to 3 watts forstanding waves and 100 watts for progressive waves. In
this experiment, we used standing waves. We measured
normal pressure to the slider and friction between theslider and the substrate by strain gauges force sensors.
In the curve of the measured data of friction, we conﬁrmed a 89 percent decrease of friction from 1.56 N to
1.4 N under a normal pressure of 11.7 N during the generation of a SAW. This is a virtual stick-slip vibration offriction. The burst frequency, denoted fb, is a variablefor controlling a tactile sensation in the next section.

Obtained tactile sensation
First of all, when the finger stops on the substrate,
a user doesn’t feel the vibration of the standing SAW
perpendicular to the skin surface at all. However,
exploring the substrate generates a sensation ofroughness that’s variable by the burst frequency fb as
follows. When fb is less than 30 Hz, the surface feels
bumpy as though there existed a row of small solid
projections with an interval of a few millimeters.
When fb is greater than 30 Hz but not more thanaround 100 Hz, the surface feels rough. With anincrease of fb, the roughness decreases as though thesize and the intervals of the projections became smaller. When fb is greater than 1 kHz, the surface feels
smooth or slippery with low friction.

We used the paired comparison method for a pilot
evaluation of the tactile display. We presented four real
objects and four virtual rough objects in the display to
ﬁve male subjects 25 to 30 years old. The real objects
are sandpaper #60, #120, #240, and #320, whosemean radius of projections are 180 µm, 80 µm, 48 µm,
and 34 µm, respectively. We presented the virtual roughobjects by changing the burst frequency to 20 Hz, 40 Hz,
80 Hz, and 200 Hz. We instructed the subjects to explore
the surfaces with their index ﬁngers and compare theroughness of the presented pairs. The subjects evaluated the difference of the roughness of the pairs in fivegrades. Each subject made 12 comparisons for the real
objects and 12 for the virtual objects. Then we constructed scales of the roughness of the real and virtualsurfaces by Scheffé’s method (see Table 1). The correlation between the scales of the real and the virtual
objects is 0.98.
This experiment is a preliminary evaluation, which
only shows that the SAW tactile display can produce several distinct sensations that users can subjectively compare the level of roughness such as a bumpy surface witha frequency of 20 Hz and a smooth one with a frequency of 200 Hz. Although the high correlation is due to few
stimuli that are far apart, we can consider the qualitative
correspondence of the subjective sensation of roughness to the objects’ parameters as follows. The variable
fb in the experiment corresponds in the real case to a
stick-slip frequency fss. As Figure 5 shows, fss increases
when β, one of the parameters of roughness, decreases.
The experimental result that smoothness increases

IEEE Computer Graphics and Applications

61

Virtual Reality

to a designated line on the screen on
the SAW tactile display, a sinusoidal
signal modulated by one pulse isapplied to the IDTs, which results increating a sensation of exploring astring raised in relief on the screen.
Thus, when users explore the SAW
tactile display, they feel as though
they have crossed several strings at
the designated positions on thescreen. Here, we’ve discovered aninteresting phenomenon: when thepulse length gets longer, users perceive two strings. This might be dueto the change of friction at the
beginning and end of the pulse. By
using a triangle wave as a modulation signal, users feel only one
string precisely.

11 Regionswith different
granularities offineness.

12 Lines at thedesignatedpositions are
tangible asthough thestrings areraised in relief.

Conclusion

when fb increases justiﬁes this fact. More precisely, as aparameter of the material’s quality, we can represent a
stick-slip frequency determined by Eσ/β in the SAW tactile display by a burst frequency fb. In future work, weplan to control fb by Equations 10 through 12 with theparameters measured in real surfaces.

Application with position feedback
By placing a slide rheostat’s position sensor with sufﬁciently low friction on the linear guide, we can generate tactile sensation according to the ﬁnger’s position.
Figure 11 shows a spatial control application ofregions with different granularities of fineness. We
divided a region on the screen with the same size as thesubstrate of the SAW tactile display into three parts—
the left, central, and right regions. The buttons on thebars controls the size and position of three regions. Bychanging the burst frequency in each region, the ﬁneness of the grain changes according to the region. Whenusers explore the SAW tactile display’s substrate fromthe left end to the right, they can feel the regions’ levelof roughness on the screen by their ﬁngers.
Also, by checking the Randomness button, the burst
frequency and the amplitude of the burst signal varyrandomly with a designated central burst frequency andcentral amplitude. By introducing randomness, we canenhance the reality of roughness as if a user explored asurface with ﬁne, randomly distributed scratches.
Figure 12 shows an application of tangible lines on ascreen. A mouse cursor moves on the screen according
to the motion of a finger on the SAW tactile display.
Users can freely choose the number and position oflines. When users explore the position corresponding

62

November/December 2001

We developed surface acoustic
wave tactile display, which cancontinuously change the finenessof the surface’s grain. In the future,by fabricating a 2D position sensor
on the substrate of a 3-inch wafer,
we’ll create a 2D tangible screenthat has windows with different
levels of roughness and sensible edges in a 2D SAW
tactile display.
■

References
1. R.D. Howe et al., “Remote Palpation Technology,” IEEE Eng.
in Medicine and Biology, vol. 14, no. 3, May/June 1995, pp.
318-323.
2. Y. Ikei et al., “Texture Presentation by Vibratory Tactile Display,” Proc. IEEE Virtual Reality Ann. Int’l Symp. (VRAIS
96), IEEE CS Press, Los Alamitos, Calif., 1996, pp. 199-205.
3. A. Sato et al., “Development of Non-Constrained Arm with
Tactile Feedback Device,” Proc. IEEE Int’l Conf. Advanced
Robotics (ICAR), IEEE Robotics and Automation Soc., Piscataway, N.J., 1991, pp. 334-338.
4. T. Watanabe et. al., “A Method for Controlling Tactile Sensation of Surface Roughness Using Ultrasonic Vibration,”
Proc. IEEE Int’l Conf. Advanced Robotics (ICAR), IEEE
Robotics and Automation Soc., Piscataway, N.J., 1995,
pp. 1134-1139.
5. R.S Johansson et al., “Tactile Sensory Coding in the
Glabrous Skin of the Human Hand,” Trends in Neurosciences, vol. 6, no. 1, Jan. 1983, pp. 27-32.
6. N. Asamura, N. Yokoyama, and H. Shinoda, “Selectively
Stimulating Skin Receptors for Tactile Display,” IEEE Computer Graphics and Applications, vol. 18, no. 6, Nov./Dec.
1998, pp. 32-37.
7. K.H. Andrew et al., “Morphology of Cutaneous Receptors,”
Handbook of Sensory Physiology, vol. II, Springer-Verlag,
Berlin, 1973, p. 16.
8. T. Tachibana et al., “Ultrastructural Localization of Calcium in Mechanoreceptors of the Oral Mucosa,” J. Neurocy-tology, vol. 21, no. 10, Oct. 1992, pp. 745-753.
9. F. Guharay et al., “Stretch-Activated Single Ion Channel
Currents in Tissue-Cultured Embryonic Chick Skeletal
Muscle,” J. Physiology, vol. 352, 1984, pp. 685-701.
10. W. Talbot et al., “The Sense of Flutter-Vibration,” J. Neurophysiology, vol. 31, no. 2 Mar. 1967, pp. 301-334.
11. T. Nara et al., “Surface Acoustic Wave Tactile Display Basedon Properties of Mechanoreceptors,” Proc. IEEE Virtual
Reality (VR2001), IEEE CS Press, Los Alamitos, Calif., 2001,
pp. 13-20.
12. M.A. Srinivasan et al., “An Investigation of the Mechanicsof Tactile Sense Using Two-Dimensional Models of the Primate Fingertip,” Trans. ASME, J. Biomechanical Engineering, vol. 118, no. 1, Feb. 1996, pp. 48-55.
13. T. Nara et al., “An Application of SAW to a Tactile Display
in a Virtual Reality,” Proc. IEEE Ultrasonics Symp., IEEE
Press, Piscataway, N.J., 2000, pp. 1-4.
14. V. Hayward et al., “Tactile Display Device Using Distributed Lateral Skin Stretch,” Proc. American Soc. MechanicalEngineers (ASME), vol. DSC-69-2, American Soc. Mechanical Engineers, New York, 2000, pp. 1309-1314.
15. M. Kurosawa et al., “Ultrasonic Linear Motor Using Surface
Acoustic Waves,” IEEE Trans. Ultrasonics, Ferroelectrics, andFrequency Control, vol. 43, no. 5, Sept. 1996, pp. 901-906.

Takaaki Nara is a research fellow
at the Japan Society for the Promotion of Science. His research interests
include modeling of processing system of human tactile sensation,
development of tactile displays, andanalysis of inverse source problems.
He has a BE, ME, and PhD in mathematical engineeringand information physics from the University of Tokyo.

Masaya Takasaki is a research
associate at Saitama University. His
research interests include SAW
devices, ultrasonic motors and magnetic levitation. He has a BE, ME, and
PhD in precision machinery engineering from the University of Tokyo.

Taro Maeda is an assistant professor at the University of Tokyo. His
research interests include psychophysics, modeling of brain byneural networks, man–machineinterface for telexistence, and virtual reality. He has a BE and a PhD in
mathematical engineering and information physics fromthe University of Tokyo. He is a member of IEEE, ARVO,
and SFN.

Toshiro Higuchi is a professor in
the Department of Precision Machinery Engineering at the University ofTokyo. His research interests include
mechatronics, electrostatic actuators, magnetic bearing, bioengineering, SAW sensors and actuators, andmanufacturing. He has a BS, MS, and DrEng in precision
machinery engineering from University of Tokyo.

Shigeru Ando is a professor in the
Department of Information Physics
and Computing at the University ofTokyo. He works on research andeducation on sensors, image processing, optical and acoustic sensing,measurement, and electrical circuits.
His interests are on intelligent and smart sensing structure
and artiﬁcial implementation of sensing and perceptionof human being. He has a BE, MS, and PhD from the University of Tokyo. He has received the Outstanding ResearchAward from the Society of Instrument and Control Engineers. He is a member of IEEE, the Optical Society of America, the Acoustical Society of America, the steeringcommittee of Conference of Solid-State Sensors and Actuators (Transducers), the Institute of Electrical Engineersof Japan, the Acoustical Society of Japan, the Optical Society of Japan, and the Society of Instrument and Control
Engineers.

Susumu Tachi is a professor in the
Department of Information Physics
and Computing at the University ofTokyo. He is a founding director of
the Robotics Society of Japan, a fellow of the Society of Instrument andControl Engineers, and is the president of the Virtual Reality Society of Japan. He also serves
as chairman of the International Measurement Confederation (IMEKO) Technical Committee 17 on Measurementin Robotics. His present research covers telexistence, realtime remote robotics (r-cubed), and virtual reality. He has
a BE, MS, and PhD in mathematical engineering and information physics from the University of Tokyo.
Readers may contact Nara at the Ando Lab., Dept. ofInformation Physics and Computing, Graduate School ofInformation Science and Technology, University of Tokyo,
7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan, email
nara@alab.t.u-tokyo.ac.jp.

For further information on this or any other computing
topic, please visit our Digital Library at http://computer.
org/publications/dlib.

IEEE Computer Graphics and Applications

63