Effects of Presentation of Shear Deformationto Finger Pad on Tracing Movements

Kenya Matsui, Shogo Okamoto, and Yoji Yamada

Abstract— Human sensory inputs and motor outputs mu-tually affect each other. This study focuses on the sheardeformation of a finger pad during tracing movements. A tactileinterface influences the sensory–motor relationships during thetracing movements by manipulating the deformation of thefinger pad. We conducted a preliminary experiment involvingfive participants and confirmed that the moving distancesof the finger increased when the finger pad deformationswere amplified by the tactile device. In addition, accordingto introspection, the participants perceived variations in thefriction of a sheet of paper on which their fingers slid. Weconcluded that the presentation of shear deformation to thefinger pad during tracing affects human motor outputs andthe perceived friction of materials.

I. INTRODUCTION

Human sensory inputs and motor outputs mutually affecteach other [1]. In this study, we pursue the idea that a tactileinterface can influence human motor outputs by interveningin sensory–motor relationships. For example, Nakamoto et al.developed a tactile interface to induce a human’s prehension[2] using the relationship between the perception of slippageon a finger pad and a reflective grasp force control [3].Watanabe et al. studied a tactile interface for altering walkingcycles by vibrotactile stimulation to feet [5]. Vibrotactilestimuli to the sole are known to translate the center of gravityand a its awareness of a person standing still [6]–[8]. Forexample, humans feel that their center of gravity moves tothe right by the presentation of stimuli to the right sole.The abovementioned studies showed that presentations ofeffective stimulation to the human body by tactile interfacesalmost unconsciously affect human motor outputs. As well asthese studies, we investigate how stimulation induces move-ments rather than whether such inductions are unconsciousor not.

We address tracing tasks as the sensory–motor relation-ships. A tracing movement is where a human traces charac-ters or figures on a sheet of paper using his or her fingerpad. The tracing movements cause shear deformation ofthe finger pad, and such deformations have been analyzed[9]. The objective of this study is to intervene in therelationships between the shear deformation of the fingerpad and the tracing movements by a tactile interface andto investigate how the interface influences the tracing move-ments and related sensations. Here, related sensations include

This work was in part supported by MEXT KAKENHI 22800030 and23135514,and Kayamori Foundation of Information Science Advancement.

The authors are with the Department of Mechanical Science and Engi-neering, the Graduate School of Engineering, Nagoya University, Furocho,Chikusa-ku, Nagoya, Aichi, 464-8603, Japan

skin sensations such as the perception of friction and deepsensations such as the perception of force. If the presentationof shear deformation to the finger pad influences the tracingmovements, applications such as inducing tracing movementsof a touch-panel interface user by using the tactile interfacecan be developed in the future. Clarifying what kind of tactilestimulus induces what kind of human movement can lead tothe development of novel tactile interfaces.

II. SENSORY–MOTOR RELATIONSHIPSUNDERLYING EXPERIMENT

A. Basic model of sensory–motor relationships during trac-ing movements

Fig. 1 shows an example of the speculated sensory–motorrelationships between the tracing movements and shear de-formation of the finger pad. Humans input a target trajectoryxd on a plane into their own internal models I(xd, µk) ofthe body and environment and decide the finger’s generativeforces F . The internal model is given by as an equation ofmotion of a finger sliding on a frictional plane:

I(xd, µk) = F = mxd + sign(xd)µkFn (1)

where m, µk, and Fn are the finger’s mass, kinetic frictioncoefficient between the finger and floor, and the finger’snormal force on the plane, respectively. The generative forceF determines the tracing movements x as a result of theinteraction between the person’s own body and environment.We describe this operation as x = B(F ). The shear forcefs to the finger pad and shear deformation ds of the fingerpad are determined by this tracing movement x. From the

Actual

trajectoryx

Body &

Environment

Shear deformation

of finger pad

＋＋

Presentation of shear deformation

to finger pad

Estimation of

friction coefficient

x�

∆��= D(�� )

�� = -sign(�� )����/��

��� + ∆���

F +∆F = I(x�，��� + ∆��� )F +∆F

x = ��

��� + ∆��� = E (�� � ∆��)

Internal model of

generative force to finger

x

Target

trajectory

m: finger mass, K�: finger pad stiffness

/ �

Fig. 1. Relationships between shear deformation of the finger pad andtracing-movement. Black: closed loop without presentation of shear defor-mation. Red: closed loop with presentation of additional shear deformation(△ds) by tactile interface.

978-1-4577-2137-3/11/$26.00 © 2011 IEEE

Finger’s

moving direction

��

���� �

��

(a) Normal condition

Finger’s

moving direction

�� �

�Δ �� �

����

(b) During application ofadditional shear deformation

Fig. 2. Shear deformation to finger pad by tactile interface and perceivedfriction coefficient

Amontons–Coulomb law, the shear force is given by

fs = −sign(x)µkFn. (2)

These force and shear deformation are illustrated in Fig. 2a.The shear deformation is given by

ds =fs

Kf= − sign(x)µkFn

Kf(3)

where Kf is the stiffness of the human’s finger pad. Thisshear deformation can be used by a person to estimate thefriction coefficient µk of the surface [10]. We express theseestimation processes as

µk = E(ds). (4)

Humans feed back this perceived friction to their owninternal model of the finger’s equation of motion. They thendecide the generative forces to realize the desired trajectories.

B. Effect of additional shear deformation to finger pad ontracing movement

In the experiment, as shown in Fig. 1, we applied theshear deformation ∆ds = D(x) to the participant’s fingerpad using the tactile interface; this is mentioned later. Usingthis device, the shear deformation of the finger pad improvesto ds + ∆ds, as shown in Fig. 2b. We speculate that thecoefficient of friction perceived by humans also improves to

µk +∆µk = E(ds +∆ds). (5)

The person feeds back this augmented coefficient of frictionto their own internal model and increases the finger force to

F +∆F = I(xd, µk +∆µk). (6)

As mentioned above, humans perceive the growing frictionby the applied shear deformation to the finger pad, andthen the finger’s generative force improves. Due to suchan underlying mechanism, we speculate that the tracingmovements are influenced by the tactile interface.

The abovementioned mechanism is one possible example.In this study, this possibility is not necessarily presumed. Theobjective of this study is not to identify such mechanisms butto empirically verify and observe whether the presentationof the shear deformation to the finger pad affects the tracingmovements.

Fabric

band

Motor

Ch0

Tracing

Marker

Z

Y

Motor

Pulley

Acrylic

plate

String

Motor

Tracing

Marker

FingerCh0 Ch1

Z

X

(a) Side view (b) Front view

Fig. 3. Device to present shear deformation to finger pad

Fabric

band

Motor

Antiskid

sheath

Pulley Acrylic

plate

(a) Side view (b) Front view

Fig. 4. Photograph of device to present shear deformation to finger pad

III. EXPERIMENTAL SYSTEM

Figs. 3 and 4 show the tactile interface developed topresent the shear deformation to the finger pad. The devicedrove an acrylic plate placed beneath the finger pad byactivating two DC motors to which strings were fastened.The motors (RE-140, MABUCHI) produced a maximumtorque of 7.31 mN·m with an applied voltage of 3.0 V. Twomotors were independently-controlled. The device presentedthe shear deformations along the X-axis. The device itselfhardly moved the finger because the sum of internal forcesapplied by the device to the finger was zero as a whole.We confirmed that the drive of the device shifted the fingerby only 0.3 mm when the finger was still. This value isnegligible compared to the spontaneous finger movementinduced by the manipulation of the shear deformation, whichis approximately 7 mm on average (see Sec. IV-B).

A camera (320 × 240 pixels, 30 fps, Playstation eye,Sony Computer Entertainment Inc.) measured the positionof the attached marker on the device. The resolutions of theposition were 0.85 mm and 1.05 mm in experiments 1 and 2,respectively. We calculated the velocities of the finger using aSavitzky–Golay filter of filter length 5 [11]. The calculatedvelocities were transformed to a device–control computer.The computer controlled the motor torques of the device witha control cycle of 0.2 ms based on the equations presentedin Secs. IV-A.3 and V-A.3.

IV. EXPERIMENT 1: LINEAR TRACE

We investigate the effects of the presentation of sheardeformation to the finger pad on the tracing movements while

the finger linearly traces a 150-mm line drawn on a sheet ofpaper.

A. Method

1) Participant: Participants were five right-handed univer-sity students (P1–P5) from our laboratory; we did not includeourselves in the group. They were told to close their eyes sothey could not see, and aurally blocked by listening to thepink noise through headphones.

2) Task: The participants wore the tactile device on theirright index finger and sat down on a chair in front of thesystem to measure the tracing movements. They traced a lineusing the index finger, as shown in Fig. 5. They conducted asingle line trace with the sound of a metronome at 0.75 Hzand a reciprocating motion for two sounds. They repeatedthis reciprocation three times in a single trial. They practicedfollowing the metronome for a few minutes before theexperiment until they felt familiar with the task. They wereinstructed to trace the 150-mm as accurately as possible.During the trial, they maintained the finger’s posture so thatit would follow the Y -axis. They visually confirmed theposition of the line at the beginning of each trial and placedtheir fingers on the far right of the line, which was designatedas the starting position.

3) Stimuli: We randomly presented three types of sheardeformations to the participant’s finger pad. We did notgive them information about these stimuli. Ten trials wereperformed for each stimulus. The three types of shear defor-mations were as follows:

• amplify condition: the finger pad’s shear de-formations were amplified along the X-axis(Fig. 6a);

• reverse condition: the shear deformations werereversed along the X-axis (Fig. 6b); and

• normal condition: the shear deformations werenot presented.

150 mm

Fig. 5. Experimental setup

Ch1Ch0

Finger’s

moving direction

��

Z

X

Ch1Ch0

Finger’s

moving direction

��

Z

X

(a) Amplify condition (b) Reverse condition

Fig. 6. Shear deformation to finger pad in linear tracing-task

a) Amplify condition: When humans trace a line, theirfinger pads commonly undergo shear deformations in thedirection opposite to the finger’s velocity. Under the amplifycondition, the motor’s torque increased to amplify the sheardeformation of the finger pad. Basically, the motors outputtorques were Tmaxor Tmin. Only when the velocity wasrelatively small, the motors’ torques linearly changed in orderto retain the smoothness of the changes in torques. When afinger was moved in the positive direction along the X-axis,as shown in Fig. 6, and the velocity of the tracing movementwas vx, the tensions exerted on the string of the plate were

T0 =

Tmin if 0 ≤ vx < 10

α(|vx| − 10) + Tmin if 10 ≤ vx < 150

Tmax if 150 ≤ vx

(7)

T1 = Tmin (8)

where α, Tmax, and Tmin were 5.75×10−3 N·s/mm, 1.07 N,and 0.31 N, respectively. We chose α so that the devicewould be likely to effectively influence the tracing move-ment. Tmax was the maximum tension that this motor couldgenerate. We set Tmin as maintaining the string tension. T0

reached Tmax at vx = 150 mm/s. When the finger was movedin the negative direction along the X-axis , the tensions weregiven by

T0 = Tmin (9)

T1 =

Tmin if − 10 ≤ vx < 0

α(|vx| − 10) + Tmin if − 150 < vx ≤ −10

Tmax if vx ≤ −150.

(10)

We get these equations simply by switching T0 and T1 in (7)and (8). When the velocity of the tracing movement was nearzero, the direction of the force applied to the plate tendedto switch frequently, and the deformation presented to thefinger pad behaved vibrationally. In order to prevent this, weset an insensitive zone of ±10 mm/s.

b) Reverse condition: This condition transposed T0 andT1 of the amplify condition.

c) Normal condition: Under this condition, the devicedid not present shear deformation to the finger pad. Themotor outputs were controlled so that the normal forceexerted to the finger pad along the Z-axis became equal tothose in the amplify and reverse conditions. Tensions were

0

150

300

5 6 7 8 9 10 11 12 13

X-a

xia

l p

osi

tio

n [

mm

]

Time [s]

Moving distance

Fig. 7. Example of moving distances

-300

0

300

5 6 7 8 9 10 11 12 13

X-a

xia

l v

elo

city

[m

m/s

]

Time [s]

Velocity

peak

Fig. 8. Example of velocity peaks

given by

T0 = T1 =

Tmin if |vx| < 10

1

2((α(|vx| − 10) + 2Tmin) if 10 ≤ |vx|

1

2(Tmax + Tmin) if 150 ≤ |vx|.

(11)

B. Results

Figs. 7 and 8 show examples of the trajectory and velocityof the tracing movements. We extracted moving distances(Fig. 7) and velocity peaks (Fig. 8) as feature quantities forthe analysis. We calculated the differences in the featurequantities for the amplify and reverse conditions with thenormal condition. Figs. 9 and 10 show the averages andstandard deviations of these differences for each condition.Analysis of the variance showed that the finger’s movingdistances (F0(1, 394) = 29.7, p = 9.96×10−8) and velocitypeaks (F0(1, 592) = 8.03, p = 0.0048) for the amplifycondition were larger than those under the normal conditionby an average of 7.1 mm and 7.6 mm/s, respectively. Forall participants, the distances tended to be larger than thoseunder the normal condition (Fig. 11). For the reverse con-dition, the distances (F0(1, 394) = 7.03, p = 0.0083) andvelocity peaks (F0(1, 592) = 12.0, p = 0.0006) were alsolarger than those under the normal condition by an average of3.9 mm and 9.7 mm/s, respectively. However these increasesdepended on the participants and did not show a uniformtrend (larger for P1, P3, and P5, smaller for P2 and P4). Thevelocity peaks for the amplify and reverse conditions showedsignificant differences from those for the normal condition.

*** **

-20

0

20

Amplify

-Normal

Dif

fere

nce

s in

mo

vin

g d

ista

nce

s [m

m]

Reverse

–Normal

Fig. 9. Average and standard deviation of differences in finger movingdistances for the amplify and reverse conditions with the normal conditionin Exp. 1, ∗∗ significance level of 1%. ∗∗∗ significance level of 0.1%.

** ***

-50

0

50

Amplify

-Normal

Dif

fere

nces

in

Peak

velo

cit

ies

[mm

/s]

Reverse

–Normal

Fig. 10. Average and standard deviation of difference in finger’s peakvelocity for the amplify and reverse conditions with the normal conditionin Exp. 1.

-30

0

30

Dif

fere

nce

s in

mo

vin

g d

ista

nce

s [m

m]

P1 P2 P3 P4 P5

Amplify

Reverse

Amplify

Reverse

Amplify

Reverse

Amplify

Reverse

Amplify

Reverse

Fig. 11. Comparison of moving distances for individuals

However their effect sizes were small (d = 0.15 and 0.19for the amplify and reverse conditions, respectively).

C. Introspective report

The participants reported their introspections in the formof free description and by answering questions after theexperiment.

1) Free description: P1: I felt that the plate was movingand sliding out of the finger pad. I may have increased thefinger’s normal force in order to keep the plate just beneaththe finger. P2: I felt that my finger’s velocity changed whenthe shear deformation was presented. P4: It was difficult to

maintain my finger’s velocity to follow the metronome. P5:Tracing with the device provided me with sensations differentfrom those obtained when tracing with a bare finger becausethe finger contacted the paper by way of a plate.

2) Question form: After the experiment, the participantsexperienced the amplify and reverse conditions and answeredthe following questions.

Q. Amplify condition: Did you feel a change in friction?P1: I felt the paper was more sticky, as if my finger had beenslipping the rubber. P2 and P3: I did not feel any changesin the friction. P4 and P5: I felt that the paper’s frictionchanged.

Q. Amplify condition: Did you feel a change in thefinger’s heaviness or external forces? P1: I felt large sheardeformations of the finger pad caused by the device. I alsofelt that my finger moved more quickly than when thedeformation was not applied. P2: I felt that my finger’snail was pushed to the moving direction of the finger. P3:I felt that my finger’s velocity became slow. The finger paddeformed in an unusual way. P5: I felt the finger to beheavier.

Q. Reverse condition: Did you feel a change in friction?P1–P3: I did not feel changes in the paper’s friction. P4: Ifelt that the paper turned slippery. P5: I felt as if my fingerslid on lubricated glass.

Q. Reverse condition: Did you feel a change in the finger’sheaviness or external forces? P1: I felt that my finger waspulled in the direction of the forward movement. P2 and P4:I felt that my finger received external force. P3: I felt thatmy finger’s velocity became very fast several times. P5: Imay have slowed down the speed of my finger because I feltmy finger was sliding significantly.

D. Discussion

The moving distances under the amplify condition werelarger than those under the normal condition. We attemptto explain this phenomenon based on a mechanism shownin Sec. II-B where presentation of the additional sheardeformation alters the tracing movements . Under the amplifycondition, when the device presents the additional sheardeformation ∆ds to the finger pad, the coefficient of frictionperceived by the participants increases as shown in (5). Theythen feed back the perceived coefficient to their internalmodel and generate the augmented finger force, as shown in(6), to maintain their desired finger trajectories. The partici-pants perceived the increased friction by the amplified sheardeformation of the finger pad. Based on such an underlyingmechanism, we speculate that the moving distances of thetracing movements increased under the amplify condition.

Under the reverse condition, the device applied sheardeformation to the finger pad in the direction of the finger’smotion, which is implausible for natural physical phenom-ena. Because the reverse condition was the opposite of theamplify condition, we imagined that the changes in thefinger’s motions would cause dissimilar results to those underthe amplify condition. However, the moving distances ofthe tracing movements became larger for three participants

(P1, P3 and P5) and smaller for two participants(P2 andP4) compared to the movements for the normal condition.The influences varied between individuals. Pursuing theseindividual variations is a future challenge.

In summary, the amplify condition resulted in increasesof the moving distances for all participants. Three of thefive participants reported increases in the paper’s perceivedfriction. The effects of the reverse condition varied forindividuals.

V. EXPERIMENT 2: CIRCULAR TRACE

In Exp. 1, we showed that the presentation of the shear de-formation to the finger pad influences the tracing movementsalong the axis parallel to the applied shear deformation. InExp. 2, we show that it also affects the tracing movementsperpendicular to the applied shear deformation when tracinga circle.

A. Method

1) Participant: Participants were five right-handed (P1，P2，P4 and P7) and one left-handed (P6) university studentsfrom our laboratory; we did not include ourselves.

2) Task: The participants traced a circle of 150 mm indiameter for each beat of the 0.5-Hz metronome. They tracedthe circle three times in a single trial. At the beginning ofeach trial, they visually confirmed the position of the circleand placed their fingers on the far bottom of the circle, whichwas designated as the starting position.

3) Stimuli: We randomly presented five types of sheardeformations to the participant’s finger pad. Five trials wereconducted for each stimulus. We added two new conditionsto the three conditions used in Exp. 1. The two new con-ditions presented a shear deformation along the X-axis in

Y

X

Finger’s

moving direction

Ch1

��

Ch0

��

Ch0

Ch1

Force applied

to finger padb)

a)

Acrylic

plate

Fig. 12. Shear deformations to finger pad in circular tracing-task: outercondition

accordance with the finger’s velocity along the Y -axis. Thefive conditions were as follows:

• amplify condition: the finger pad’s shear de-formations along the X-axis were amplifiedin response to the finger’s X-axial velocity(Fig. 6a),

• reverse condition: the shear deformationsalong the X-axis were reversed in responseto the finger’s X-axial velocity (Fig. 6b),

• normal condition: the shear deformations werenot presented,

• outer condition: deformation was applied out-ward from the circle in response to the finger’sY -axial velocity (Fig. 12), and

• inner condition: deformation was applied in-ward from the circle in response to the finger’sY -axial velocity.

a) Outer condition: The motor’s torque was controlledin response to the finger’s Y -axial velocity. As a result, thedevice applied the deformation outward from the circle. Forexample, when the finger moved in the positive directionalong the Y -axis, as shown in Fig. 12 a), the tensions exertedon the strings of the plate were

T0 =

Tmin if 0 ≤ vy < 10

α(|vy| − 10) + Tmin if 10 ≤ vy < 150

Tmax if 150 ≤ vy

(12)

T1 = Tmin (13)

where α, Tmax, and Tmin were 5.75×10−3 N s/mm, 1.07 N,and 0.31 N, respectively, similar to Exp. 1. The variablevy was used in (12) instead of (7) in vx. When the fingerwas moved in the negative direction along the Y -axis, as inFig. 12 b), the tensions were given by

T0 = Tmin (14)

T1 =

Tmin if − 10 ≤ vy < 0

α(|vy| − 10) + Tmin if − 150 < vy ≤ −10

Tmax if vy ≤ −150.

(15)

vy was used in (15) instead of vx in(10).b) Inner condition: This condition transposed T0 and

T1 of the outer condition and presented the shear deformationinward from the circle.

B. Results

We extracted the moving distances of the trajectories alongthe X- and Y -axes as feature quantities for the analysis.We calculated the differences in the feature quantities forthe amplify, reverse, outer, and inner conditions with thenormal condition. Figs. 13 and 14 show the averages andstandard deviations of the differences for each condition.Analysis of the variance showed that the finger movingdistances along X-axis (F0(1, 194) = 11.6, p = 8.17×10−4)and Y -axis (F0(1, 194) = 13.0, p = 3.89 × 10−4) for theamplify condition were larger than those under the normalcondition by average of 5.8 and 5.7 mm, respectively. For the

*** **

-20

0

20

Dif

fere

nce

s in

X–

axia

l m

ov

ing

dis

tan

ces

[mm

]

Amplify

-Normal

Reverse

-Normal

Outer

-Normal

Inner

-Normal

Fig. 13. Average and standard deviation of finger’s X-axial movingdistances

*** ***

-20

0

20

Dif

fere

nce

s in

Y–

axia

l m

ov

ing

dis

tan

ces

[mm

]

Amplify

-Normal

Reverse

-Normal

Outer

-Normal

Inner

-Normal

Fig. 14. Average and standard deviation of finger’s Y -axial movingdistances

individual participants, other than P4 along the Y -axis, thedistances tended to be larger than those under the normalcondition, as shown in Figs. 15 and 16. For the outercondition, the distances along the X-axis (F0(1, 194) =8.30, p = 4.42× 10−3) and Y -axis (F0(1, 194) = 24.8, p =1.37 × 10−6) were larger than those under the normalcondition by average of 4.7 and 7.7 mm, respectively. Forthe individual participants, other than P2 and P4 alongthe X-axis, the distances tended to be larger than thoseunder the normal condition. For the reverse condition, thedistances along X-axis (F0(1, 194) = 0.25, p = 0.6169)and Y -axis (F0(1, 194) = 2.24, p = 0.136) did not showany significant differences from those under the normalcondition. The changes in the moving distances dependedon each participant and did not exhibit a uniform trend.Finally, for the inner condition, the distances along X-axis(F0(1, 194) = 0.89, p = 0.3453) and Y -axis (F0(1, 194) =0.42, p = 0.5154) did not show significant differences fromthose under the normal condition. The distances dependedon each participant and did not exhibit a uniform trend.

C. Discussion

Similar to the linear trace, the circular trace under theamplify condition caused the finger’s moving distances alongthe X-axis to become larger than those under the normal con-dition. This can be interpreted by the mechanism introducedin Sec. II-B. Increases in the distances were also observedalong the Y -axis. We speculate that this was because theparticipants assumed the isotropic frictional properties of thepaper. The participants might have perceived the increases

-20

0

20

Amplify

Outer

Inner

Amplify

Outer

Inner

Amplify

Outer

Inner

Amplify

Outer

Inner

Amplify

Outer

Inner

Dif

fere

nce

s in

X–

axia

l m

ov

ing

dis

tan

ces

[mm

]

P1 P2 P4 P6 P7

Reverse

Reverse

Reverse

Reverse

Reverse

Fig. 15. Comparison of X-axial moving distances for individuals

-20

0

20

Amplify

Outer

Inner

Amplify

Outer

Inner

Amplify

Outer

Inner

Amplify

Outer

Inner

Amplify

Outer

Inner

Dif

fere

nce

s in

Y–

axia

l m

ov

ing

dis

tan

ces

[mm

]

P1 P2 P4 P6 P7

Reverse

Reverse

Reverse

Reverse

Reverse

Fig. 16. Comparison of Y -axial moving distances for individuals

in friction along both the X- and Y -axes. Hence, not onlythe X-axial distances but also the Y -axial distances wereinfluenced by the shear deformations applied by the tactiledevice.

We do not interpret the results of the reverse, outer andinner conditions as being based on the mechanism describedin Sec. II-B because these conditions are implausible inour daily lives. However, almost all of the participantswere affected by the presentation of the shear deformations,even though the effects varied for individuals. For the outercondition, the participant’s tracing distances tended to beuniformly increased, which suggests the existence of aspecific mechanism besides the one described in Sec. II-B.The pursuit of such a mechanism is the next challenge. Forthe reverse and inner conditions, the changes in the movingdistances depended on each participant and did not exhibita uniform trend.

VI. CONCLUSIONS

We investigated how the presentation of shear deformationto the finger pad affects tracing movements. We employedlinear and circular motions as tracing tasks. In the linear trace(Exp. 1), the finger’s moving distances increased when theshear deformation of the finger pad was amplified by the tac-tile device (amplify condition). Three of the five participantsreported an increase in the perceived friction of the sheet ofpaper they slid their finger on. In the circular trace (Exp.

2), the finger’s moving distances increased for the amplify,and outer conditions where the deformations were appliedoutward from the circle for the later. These results showedthat the presentations of shear deformations to the fingerpad influenced even the finger’s motions perpendicular to theapplied deformations. Further elucidation of the interactionbetween the tracing movements and shear deformations ofthe finger pad is expected to enhance the development ofhuman–assistive haptic interfaces.

References are important to the reader; therefore, eachcitation must be complete and correct. If at all possible,references should be commonly available publications.

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