Surface Acoustic Wa ve (SAW) Tactile Display
Based on Properties of Mechanoreceptors
Takaaki NARA, Masay a TAKASAKI, T aroMAEDA,
T oshiro HIGUCHI,Shigeru ANDO, and Susumu T A
CHIGraduate School of Engineering
The University of Tokyo
Bunkyo-ku, T okyonara@alab.t.u-tokyo.ac.jp

Abstract

In this p aper, we rst analyze dynamic properties of
rapidly adapting mechanoreceptors in order to derive a
principle of tactile displays. It is shown that Meissnercorpuscles with coile d axons and Pacinian corpuscles
with layered lamellae are suite d to detect equivoluminal
distortion of a skin. Combining these analyses with amodel of a contact and a relative motion between an
obje ct and the skin, it is shown that a prerequisite fortactile displays is to gener atesour ces of shear stressthat can be spatially disperse d at the skin surface andtemporally modulate d with a stick-slip frequency determined by parameters of the object to b e displayed. As adevic e that satisfys this prerequisite, we prop ose a tactile display using Surface Acoustic Waves(SAW). The
roughness of the surfac ecan be changed continuously
by c ontr olling the burst fr
equency of the SAW.

1

Introduction

Development of realistic tactile displays has beena great challenge in Virtual Reality. V ariedactuators suc h as miniature loudspeakers[1], a single micropin[2], a pin array[3], pneumatic actuators[4], and ultrasonic vibrators[5] have been used for displays.
Methods based on the processing properties of human tactile information ha ve also been proposed.
T actile sensations are generated by activation of
mechanoreceptive units that are classi ed into four
categories, namely rapidly adapting I and II (RAI,
RAII) and slowly adapting I, II (SAI, SAII), whose
end organs are Meissner corpuscles, Pacinian corpuscles, Merkel cell-neurite complexes, and RuÆni endings, respectively[6]. Shinoda developed a tactile displa y that stimulates each mechanoreceptor selectively,
using an elastic transfer property of a skin[7]. Kajimoto conducted electrical selective stimulation to thereceptors[8].

How ever, because parameters that characterizeroughness, rigidit y,and material qualit yfor generalobjects were not clari ed in detail, a principle for displa ying general objects by the above devices was notshown, which resulted in using ad hoc stimulation in
the displays for creating particular sensations.
F urthermore, the mechanisms for the motion of
the mechanoreceptors have not been considered atall. Clarifying mechanical properties of the receptors
should enable us to obtain a more e ective method
for stimulating the processing system of human tactile sensation.
Thus, in this paper, we rst derive models of Meissner and P aciniancorpuscles that play an importantrole in active touch. In section 2 w eanalyze what
they detect inside the skin. In section 3, w eexpress
dominant skin deformation detected by the receptors
in terms of the speci c parameters of objects. By
combining these analyses, a ow of tactile informationfrom the parameters of objects to the deformation of
the receptors is speci ed. This ow leads to the creation of a principle that shows e ective stimulation fortactile control. Based on this principle, we propose anovel tactile display using SAW in section 4.
2
2.1

Models of mechanoreceptors
Meissner corpuscles

Meissner corpuscles, which have a relativ ely low ercharacteristic frequency of about 40[Hz], are localized in the papillary dermis with a height of around150[m] and a diameter of 4070[m]. A structuralfeature is their coiled axons[9] on which Ca2+ ion channels exist[10]. It is kno wn[11] that an open probabilit y of general mechanosensitive ion channels depends on energy of deformation expressed as U =K=2  (A=A)2  A, where K is an elastic modulusof the channel and A is the size of the channel. Thus,

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it is necessary to analyze deformation of the axon surface when stress by skin is applied to the corpuscles.
We discuss below the role of coiled axons of Meissnercorpuscles for detecting mechanical deformation of the
skin.
2.1.1

T ransmission ofdeformation by a coil

We rst clarify mechanical properties of a coiled structure. As sho wnin Fig.1, w eset an x axis along theline of the coil and y; z axes in a section of the line.
When normal(Fig.1a)) and shear(Fig.2a)) stresses areapplied to the coil, a torsional moment of Mx andbending moments of My ; Mz It is noteworth y that only
the torsional moment is generated when P is applied
to the coil. As a result, only shear deformation is generated on a coil surface when normal stress is applied
to the coil(Fig.1b)), while stretch deformation, in addition to shear deformation, is created on the surface
when shear stress is applied to the coil(Fig.2b)).

Figure 1: When vertical stress is applied tothe coil,a) a torsional moment Mx is generated at a cross section of the line, b) which results in the creation of ashearing deformation at the line's surface

Figure 2: When shear stress is applied to the coil, a) in
addition to a torsional moment Mx, bending moments
My ; Mz are generated at cross sections of the line, b)
which results in the creation of shearing and stretch
deformations at the line's surface
Considering that activation of the axon depends on
the ratio of change of the channel size!$only the shear
stress to the coil, which generates stretch deformations
on the coil surface, changes the size of the surface so as

to increase the open probability of the channel. Therefore, a hypothesis that the coiled axon of Meissner corpuscles detects shear stress in the skin is derived. F ora veri cation of the statement, w eshow next that atuning curve of the corpuscles can be derived on thebasis of the shearing resonant character of the coiled
axon.
2.1.2

Dynamic properties of a coil

A coil's longitudinal resonant frequency of !z and ashearing resonant frequency of !x are expressed assr
2(1 +  ) ; (1)!xd;=!z = 2nD 2
!z
1 + 12(2 +  ) HD 2
where d:the diameter of the line of the coil!$:therigidit y of the line, :the densit yof the line!$ :theP oisson's ratio of the line.Assuming that   0:5 and
H=D = 150[m]=50[m] as in the Meissner corpuscles,
!x
1:
=
(2)
!z
10
Thus, it is supposed that the characteristic frequencyof the corpuscles derives from the shearing resonant
frequency as the minimum resonant frequency of thecoiled axon. In fact, with parameters observed in medical experiments[12 ], !x=2 = 44[Hz]!$which corresponds to the real characteristic frequency. Moreover,
the tuning curve itself can be driven from the energyof the shearing deformation of the coil, which depends
on the shear stress in the skin, as shown in Fig.3. In
this w ay,it is hypothesized that Meissner corpuscles
might easily detect shearing, equivoluminal deformation in the skin.

Figure 3: The tuning curve of the Meissner corpuscles:- - -:experiment[13] ||:theory Assuming that the
Meissner corpuscles detect shear stress of the skin, thetuning curve can be driven from the shearing resonant
characteristic of the coiled axon

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2.2

Pacinian corpuscles

We next consider another RA-type mechanoreceptor, the P acinian corpuscle. The structure of the
corpuscle is that an inner core including an axon issurrounded by concentric 2070-ply layered lamellae as the section is schematically drawn in Fig.4.
Neighboring lamellae are connected by collagen bers.
Gaps betw een the neighboring lamellae are lled withliquid[14].

Figure 4: A schematic description of a section of a
P acinian corpuscle
Although models of P acinian corpuscles are proposed by Loewenstein[15] and Bell[16], only the simplest deformation(Fig.5; m=2), or a certain speci c
deformation, is giv en to the outermost lamella as aboundary condition for a correspondence to physiological experiments[17 ].

Figure 5: 'Modes' of deformations of Pacinian corpuscles: Arbitrary deformation applied to the corpuscle
inside the skin is represented as a summation of modes
T o consider arbitrary deformation
insidethe skin,w eexpress displacements and external forces in the
; r directions of the n-th lamella at r = an by a summation of the m-th order mode(Fig.5) expressed as
Yn = Yn;m  sin m; Xn = Xn;m  cos m (3)p = (Fn;m + Tn;m) sin m; pr = (Fn;m + Sn;m ) cos m; (4)where Fn;m:an elastic force by collagen bers, andTn;m; Sn;m :shear and normal stresses by liquid. An
isotropic stretch represented b ym = 0 is excluded because the corpuscles contain incompressible liquid. A
parallel movement of m = 1 is also excluded here. On

the assumption that a lamella is a cylindrical shell, by
substituting (3), (4) into Donnell's equations as
C @ 2Yn @Xn+ @ + p = 0;
(5)
a2n @2
D @ 4 Xn C @Yn@2X+
X
M 2n =0; (6)n + pr
4
4
2
an @
an @
@t
w e obtain an equation about the displacement of Xn;min the r direction as
1 Tn;m ; (7)m 1
Fn;m + Sn;mM X n;m = kn Xn;m +mmwhere :the density of the shell!$d:the thickness of theshell, M = d, C = Ed=(1  2):the shell's rigidityof stretch!$D = Ed3=12(1 2 ):the shell's rigidity
4
4of bending, and kn = m D=an is a shell's equivalentspring constant. Here, it can be shown that the elastic
force b y collagen bers is expressed as
Fn;m =Gn+1 (Xn+1;m Xn;m ) Gn (Xn;m Xn 1;m); (8)and the force by viscosity of liquid is represented as
1 Tn;m = Rn;m( mX_ n+1;m 2X_ n;m + mX_ n 1;m);Sn;mm
2
where Rn;m = 2  m 1 anm
4m + m 2m+2 m 2m 2 1
4m m2 2m+2 + 2(m2 1) 2m m2 2m 2 + 1 ;
2m
2m 2
m+1
 4(mm++m1) 2m+2 mm 2m 2 1 1 ;m = 22m
2 (m + 1)m 1
 4m + m+2m
; (9)
m = 2
m+2
m 2m 2 1
:viscosit y,and = an+1 =an !%Thus, by solving simultaneous equations of (7) for n = 1::N (n = 1:theinmost lamella!$n = N :the outermost lamella), lamel-lae's amplitudes in a sinusoidal vibration can be obtained. Fig. 6 depicts a relation betw eenthe orderof the mode and an amplitude of the inmost lamellawith a frequency of 100[Hz]. It can be seen thatthe
amplitude of only the mode of m = 2 reaches the innercore.
This model is veri ed by a deriv ationof a tuning curve of Pacinian corpuscles(Fig.7) in the mode of
m = 2 according to the physiological experiment[17].
P arametersused2 here[14][15] are  = 103[kg/m5 3],  2=
3
0:6  10 [Ns/m ](40 !n), N = 40, E = 5  10 [N/m ],d = 1[m], a0 = 10[m], and = 1:083. Because it
is indicated that a mechanical lter by lamellae contributes to the tuning curve below the characteristic frequency[16]!$validit y of the model that coincides

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the mode of m = 2 reaches the axon

Figure 7: The tuning curve of Pacinian corpuscles: - -: Experiment[18 ] ||: Theory
with the experimental curve below the characteristicfrequency can be con rmed.
In this w ay,the structure of the layered lamellaeof P acinian corpuscles can detect skin's equivoluminal
deformation of the minimum order of m = 2.
3

Skin distortion in active touch

It is necessary for a deriv ationof a principle oftactile displays, besides the analysis of properties ofmechanoreceptors, to clarify deformation of a skin in
activ e touc h.
F rom the analysis[20] of a contact and a relative motion betw een a skin and an object which has a Gaussian surface, it is sho wnthat normal stress of p andshear stress of q to the skin surface at the positions of
the projections are
q = s + p;

p=

E 
 ;


(10)

which vibrate temporally with a stick-slip frequencyof fss expressed as
2  tan 1 R + R ; (11)
f 1 =
ss

R

=

!0
(s c)P ;
m!0 U

(12)

=

(s s0 ); !0 =
E

r

k
;
m

(13)

where Eo; Es :Young's ratio of the object and the skin,respectively!$o; s :Poisson's ratio of the object andthe skin0 !$respectively, 1=E = (1 s2)=Es +(1 o2)=Eo,s and s are the static and kinetic shear strength of theskin, :standard deviation of the topography, :mean
radius of projections of the topography, P :a total normal pressure by the skin, U :a velocit y of the motion,m; k:mass and elasticity of the skin. The relation betw eenthe parameters of an object and the stick-slip
frequency, which is a key relation for displaying material qualit yin section 4, is drawn in Fig.8 with,for example, P = 1[N], m = 1[g], k = 500[N/m],
U = 4[cm/s].

Figure 8: A relation betw een a parameter ofs cand a stick-slip frequency
Under these boundary conditions at the skin surface, let us consider deformation inside the skin. A t
the moment of the shift from the stick state to the slip
state, the normal and the shear stresses begin to movesuddenly on the skin surface. As a result, elastic waves
are created inside the skin[21], which are dominant deformations because amplitudes are much greater thanthe other stationary deformation. Displacements inside the skin are drawn in Figs. 9 and 10 when thenormal and shear stresses that vary with time as the
Heaviside unit function are applied to the skin surface(We call these surface stresses 'the normal source' and'the shear source').
The remarkable point is that the polarit y of
the S-wave's amplitudes in Fig.b), which are muc hlarger than the P-wave's amplitude in Fig.a), turns
over along the horizontal axis by the normal source(Fig.9b)) in contrast to the constant polarit yby theshear source(Fig.10b)). As a result, the S-wavesby
many normal sources distributed over the skin surface
are canceled as in Fig.11a), while the S-waves by the
distributed shear sources become large due to a constructive interference as in Fig.11b). In this way, it isshown that primal surface stress, which creates dominant deformation inside the skin, is dispersed shear
stress.

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The analyses in sections 2 and 3 are summarized asa ow of tactile information as in Fig.12.

4

4.1

SAW tactile display

Shear sources method

F rom the above discussion, the prerequisites for tactile con trol, especially for stimulating RA mechanoreceptors, can be driven as follows:
Figure 9: Amplitudes of P and S w avesinside the Sources of shear stress should be applied to theskin when a normal source of P is applied to the skin
skin surface in order to create equivoluminal dissurface: The horizontal axis is a distance along thetortion detected by mechanoreceptors.
skin surface from the point where the stress is applied The sources of shear stress can be spatially dispersed on the nger surface
 The sources of shear stress can be temporally
modulated with a stick-slip frequency of fss determined by the parameters of the object to be
displayed.
Though previous tactile displays have used varied
Figure 10: Amplitudes of P and S waves when a shear actuators([1][2][3 ][4]and so on), almost all stimulationis perpendicular to the skin surface with the excepsource of Q is applied to the skin surface
tion of tw omethods. The rst method, which controls the parallel force to the skin surface, uses ultrasonic vibrations[5]. A frictional force betw eena
metal plate and a nger, which is a shear stress to theskin surface, can be con trolledby a squeeze- lm effect. The display succeeded in creating a sensation as
if the surface were smooth by a stationary vibration,or as if a small projection w erecreated on the surface by a momentary vibration. The second method,which is supposed to be equal to control shear stress to
Figure 11: Amplitudes of S-waves by several sources the skin, uses a several phase-inverted perpendiculardispersed at the intervals of 1[mm] on the nger sur- vibrations[7]. In geophysical exploration, two phaseface: a)By normal sources b)By shear sources
inverted P-wave vibrators are used asa source of an
S-wave[22]. The fact that two vertical vibrators drivenout of phase create an S-wave can be con rmed by the1) P arametersof the object to be touc hedand thespatialpattern of amplitudes in Fig.9b). The display
motion of an active touch: (E0; o; ; )  (P; U )cancreatea sensation as if a smooth surface, a sponge,
"or
a
pin
moved
on the skin.
2) Stress on the skin surface
How
ever,
becausethe relative motion between the2
Dispersed sources of shear stress!’q = s + E=  (= ) skin and a real object has
not been analyzed until now,
Stic k-slip frequency!’fss = 1=Tss in (11)  (13)
it is unclear how to temporally modulate shear stress,"and it is impossible to control a sensation of roughness3)Equivoluminal deformation inside the skinsystematically as if diameters of small projections on(Fig.11b))
a rough surface changed continuously. We propose"to use SAW to generate sources of shear stress that
4)Meissner and Pacinian corpuscles : Detection of thesatisfy the above three prerequisites for tactile control.
equivoluminal deformation (sec.2). The ratio of the 4.2 Device
con tribution of both corpuscles is changed by fss .
SAW has recently attracted attention for sources ofdriving
force for linear motors[23], in addition to its
Figure 12: A ow of tactile information
practical application as a lter for telecommunication

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equipment. We use SAW as sources of shear stress toa nger surface for tactile control.
The structure of the tactile display is shown
schematically in Fig.13. In a LiNbO3 Y-cut substrate
whose size is 17[mm] 63[mm]1[mm], SAW is generated by an alternative voltage to an interdigital transducer(IDT). The wavelength of SAW is about 265[m]with the driving frequency of 15[MHz]. One of theprominent advantages of the display is the thinnessof the substrate of 1[mm] for creating stimuli to thenger.
IDTs are placed at both ends of the substrate. According to the use of progressive w aves or standing
w aves, it is decided to apply an alternative voltage
to one side or both sides of the IDTs. F orgenerating standing waves e ectively, Open Metal Strip Array(OMSA) are set after IDTs as re ectors.

Figure 13: Sc hematic description of the SAW tactile
displayIn our tactile display, the substrate is explored witha 'slider' shown in Fig.16 in the last page. The slider
has around 100 steel balls with a diameter of 800[m]on a thin tape. The reasons to use a slider are as
follo ws: 1) By pressing steel balls with the nger, adriving force can be e ectively transmitted to the nger. 2) Steel balls can pro videdistributed points towhich stress is applied on the nger surface, assumingthat the tape is satisfactorily thin and soft.
4.3

Principle

The principle for generating sources of shear stressthat are distributed spatially and modulated temporally is described in the following text.
When the substrate without SAW is explored by
the nger with the slider, kinetic friction by thesubstrate is applied to the steel balls, thus creating
sources of shear stress on the surface of the ngerat the positions of all the steel balls distributed spatially(Fig.14 a)).
Now, by generating SAW, friction betw een the steel
balls and the substrate is decreased compared to thesubstrate without SAW for the following three reasons: 1) Decrease in contact time betw eenthe balls
and the substrate; 2) A squeeze- lm e ect by the airthat exists betw een the balls and the substrate; and 3)
A parallel movement of the wave crest (only in using
progressive waves). As a result, when either progressive or standing wave of SAW is generated in the substrate, shear stress to the skin becomes smaller(Fig.14b)) than shear stress without SAW.

Figure 14: Generation of sources of shear stress thatcan be modulated temporally by burst SAW
Thus, by using a burst SAW, the sources of shear
stress applied to the skin surface can be modulatedwith a burst frequency. The moment when the wave
appears suddenly corresponds to the moment when
the stick state changes into the slip state because thefriction suddenly decreases. Therefore, the stick-slip
frequency can be controlled virtually by changing the
burst frequency. In this w ay,w eobtain distributed
sources of shear stress that are modulated with astick-slip frequency determined by the solidity and theroughness of the object.
5

Experiments

In this section, we carry out experiments to control
roughness of objects by changing the frequency of themodulation of the distributed sources of shear stress.
5.1

Generation of virtual stick-slip

Fig.15 shows an input signal of a burst wave to IDT
and the resultant temporal change of friction.
The burst wave has a carrier frequency of 15[MHz]and a dut yratio of 40%. An input pow er isaround
10[W] for standing waves and 100[W] for progressive
w aves.We use here standing waves.

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0-7695-0948-7/01Authorized$17.00 licensed© 2001useIEEEIn the curve of the measured data of friction betw een the slider and the substrate, a 89% decrease offriction from 1.56[N] to 1.4[N] under a normal pressure of 11.7[N] can be con rmed during generation of
SAW. This is a virtual stick-slip vibration of friction.
The burst frequency, denoted fb, is a variable for controlling a tactile sensation in the next section.

Figure 15: Experimental data of friction betw een thesubstrate and the slider. F riction is reduced by generating SAW. Thus, burst standing SAW can create
virtual stick-slip vibration of friction.
5.2

Obtained tactile sensation

5.3

Evaluation

First of all, when the nger stops on the substrate,
the vibration cannot be felt at all. How ever, exploring
the substrate generates a sensation of roughness which
is variable by the burst frequency of fb as follo ws.
When fb < 30[Hz], the surface feels bumpy as if
there existed a row of small solid projections with aninterval of a few [mm]. When 30[Hz]< fb < 100[Hz],the surface feels rough. With an increase of fb, theroughness decreases as if the size and the intervalsof the projections had become smaller. When fb >100[Hz], the surface feels smooth or slippery with low
friction.
A Psychophysical experiment called Sche e's
method of pair comparison is carried out for an evaluation of the tactile display. F our real objects and four
virtual roughness in the display are presented to threesubjects. The real objects are sandpaper #60, #120,#240, and #320. The virtual roughness is presented
by changing the burst frequency of 20[Hz], 40[Hz],80[Hz], and 200[Hz]. A scale of the roughness of thereal and the virtual surfaces is constructed by ranking
the roughness of the pair presented. A virtual surface
can be evaluated by a correlation betw een the rankingof the real and the virtual surfaces.
A composed scale of the roughness of the real andthe virtual objects is provided as follows.

Real objects (Sandpapers) Virtual objects (Display)
T he n umber
scale
fb
scale
# 60
-1.125 20[Hz]-1.125# 120-0.375 40[Hz]
-0.5
# 240
0.375
80[Hz]
0.5
# 320
1.125
200[Hz]1.125
The correlation betw een the real and the virtual objects calculated from the above data is 0.98. The highvalue of the correlation is reasonable from a de nitesubjective di erence betw een a bumpy surface with afrequency of 20[Hz] and a smooth one with a frequencyof 200[Hz].
What characteristics of objects are presented in thisSAW tactile display? The variable of fb in the experiment corresponds in the real case to a stick-slip
frequency of fss . As shown in Fig.8, fss increases
when the , which is the parameter of roughness, decreases. The experimental result that smoothness increases when fb increases is justi ed by this fact. Moreprecisely ,as a parameter of the quality of the material, a stick-slip frequency determined by E= canbe represented in the SAW tactile display by a burst
frequency of fb.

6

Conclusion

In this paper, in order to obtain a principle for tactile displays, we rst analyzed dynamic properties ofmechanoreceptors and a skin. The results were as follows: Meissner corpuscles with coiled axons might easily detect shearing deformation of the skin due
to the resultant stretches on the surface of theaxons.
 P aciniancorpuscles might easily detect a minimum order equivoluminal distortion of the skin
due to the rapid decay of the higher modes
through the layered lamellae.
 In a contact and a relativ emotion betw eenan
object and a skin surface, stress generated at theskin surface, which creates dominant deformations inside the skin, is dispersed shear stress dueto the constructive interference of distortion. The
shear stress changes temporally with a stick-slip
frequency determined by the parameters of solidity and roughness of the object.
F romthe above analyses, we obtained a prerequisite for tactile control that a tactile display should
generate sources of shear stress that are spatially distributed and temporally modulated with a stick-slip

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substrate explored by a nger with a slider was produced. In the SAW tactile display, it w as con rmedby psyc hophysical experiments that roughness could
be controlled continuously by changing the burst frequency of SAW.

Figure 16: Slider

Figure 17: The SAW tactile display
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