Experimental Investigation of Effect of Fingertip Stiffness on
Resistible Force in Grasping
Yoshinori Fujihira, Kensuke Harada, Member, IEEE, Tokuo Tsuji, Member, IEEEand Tetsuyou Watanabe, Member, IEEE

Abstract— In this study, we experimentally investigated theeffect of robot fingertip stiffness on the maximum resistible
force. The maximum resistible force is defined as the maximum
tangential force at which the fingertip can maintain contact
when applying and increasing tangential/shearing force. We
include in the definition of this term the effect of fingertip
deformation. In contrast to our previous study [11], cylindricalfingertips with flat surfaces were used in this study so that thecontact area would remain the same when there was notangential/shearing force. This made it possible to see the effectof fingertip stiffness more clearly. We also investigated the effectof curvature of the contact surface, which was not investigatedin depth in [11]. The main findings are as follows. 1) Harderfingertips produce larger resistible forces, irrespective of the
shape of the contact surface (flat or curved). 2) For harderfingertips, the maximum resistible force depends largely on the
shape of the contact surface, while for softer fingertips, theshape has little effect. 3) For softer fingertips, the magnitude of
the resistible force changes little even when the normal force
increases.

[9]. However, these conditions do not apply to fingertips withlow stiffness [10]. In addition, the relation between stiffness
and friction is unclear. With this in mind, we experimentallyinvestigated this relation in a previous study [11]. We foundthat harder fingertips produce larger frictional (resistible)
forces on flat surfaces than softer fingertips. However, theresults obtained are very limited. In the experiments,
semispherical fingertips were used, so the contact area
depended on the fingertip stiffness. The contact area is closely
related to the frictional forces achieved. Therefore, it remained
unclear whether fingertip stiffness was a significant and direct
factor in the results obtained. In addition, deformation in thetangential contact direction was not considered. We also did
not investigate the effect of curvature of the contact surfaces indetail. We investigated cases in which contact surfaces wereangled, but the normal force/load was fixed at 2 [N].
Furthermore, we did not consider cases in which the contact
surfaces were curved, which the surfaces of many articles thatmust be manipulated by hand in everyday life are.

I. INTRODUCTION

With this in mind, in this study, we experimentallyinvestigated the resistible forces that result when cylindricalfingertips of various stiffnesses with flat contact surfaces arein contact with flat and curved surfaces. The contact area was
the same irrespective of the magnitude of the normal force(load) and the stiffness when a tangential/shearing force was
not applied. When the normal force was applied, thecylindrical silicone fingertips swelled to the shape of a barrel,
while deformation of the contact surface was negligible due tothe contact constraints.

In recent years, robots have been required to be capable ofworking in human society. Among the key functions of suchrobots are activities, including everyday tasks that humans
perform with their hands. A basic hand task is grasping, andgrasp planning [1, 2] is important for robotic hands. Several
libraries and softwares for grasp planning have beendeveloped. Graspit [3], Openrave [4], and GraspPlugin for
Chorenoid [5] are well known. In grasp planning, friction is a
key issue because friction is embedded in criterion function
associated with grasp stability in grasp planning [1, 2]. The
well-known Amontons–Coulomb friction model is widelyused in grasp planning. Early application of this model tograsp planning pertained to contact between solid surfaces.
More recently, robotic hands with soft fingertips have beendeveloped to increase friction and affinity for humans [6], [7],[8]. Therefore, frictional conditions for soft fingertips must be
developed. Frictional conditions for soft fingertips, based on
the Amontons–Coulomb friction model, have been proposed
Y. Fujihira is with the Graduated school of Natural science andTechnology, Kanazawa University, Kakuma-machi, Kanazawa, 9201192,
Japan (e-mail: fuji3134@stu.kanazawa-u.ac.jp).
K. Harada is with Intelligent Systems Research Institute, National
Institute of Advanced Industrial Science and Technology (AIST), Tsukuba,
Japan (e-mail: kensuke.harada@aist.go.jp)
T. Tsuji, Faculty of Information Science and Electrical Engineering,
KyushuUniversity,
Fukuoka,
819-0395,Japan(e-mail:tsuji@ait.kyushu-u.ac.jp)
T. Watanabe is with the College of Science and Engineering, Kanazawa
University, Kakuma-machi, Kanazawa, 9201192 Japan (corresponding
author to provide e-mail: te-watanabe@ieee.org).

In fingertips with low stiffness, deformation in thetangential contact direction could occur and affect themagnitude of the maximum static frictional force. Unlike instudies focused only on the contact area, in grasping or robotic
hands, fingertips have volume, and thus, deformation of
fingertips affects the magnitude of the maximum tangential
force, which is the maximum force at which the fingertip canmaintain contact while applying and increasing atangential/shearing force. Whether the effect should be
included in the frictional force is a divisive issue. In this paper,
we define the maximum resistible force as the maximum
tangential force at which the fingertip can maintaincontact. The resistible force could include not only thefrictional force but also the force resulting from fingertip
deformation. For the purposes of grasp planning, we want toknow how much the magnitude of an external force can bebalanced, i.e., how heavy an object can be grasped. Thus, theforce that a grasp planner needs to know is not the frictional
force without the force resulting from fingertip deformation
but rather the resistible force. The focus of this investigationwas therefore the resistible force. The main findings obtained
are as follows:
1. Harder fingertips produce larger resistible forces,
irrespective of the shape of the contact surface (flat or
curved).
2. For harder fingertips, the maximum resistible force
depends largely on the shape of the contact surface, while
for softer fingertips, the shape has little effect.
3. For softer fingertips, the magnitude of the resistible forcechanges little even when the normal force increases.
A. Related works
In the robotics, analyses of soft fingers, including
modeling and experimental investigations, have been
conducted by Kao et al. [9], [12], [13], Hirai et al. [14], [15],Ciocarlie et al. [16] and Watanabe et al. [8], [11], [17]. Except
in [9] and in our previous study [11], the relationship between
the finger stiffness and the resistible/frictional force has notbeen examined. In contrast to our previous study [11], Tiezzi
et al. reported that a low fingertip stiffness produces a large
frictional force. In the tribology field, Persson [18] has
analyzed the kinetic friction between rubber and metal objects,
and Deladi et al. [19] have analyzed the static friction between
rubber and metal objects. In general, kinetic friction is more
important in the tribology field. Hence, in the tribology field,
there have been very few studies of static friction, which ismore important in grasping than kinetic friction is. Deladi [20]presented numerical and experimental results similar to thoseobtained by Tiezzi et al. [10] that showed that low fingertip
stiffnesses produce large frictional forces. As mentioned
above, this is not consistent with our previous experimental
results [11]. However, fingertip stiffness was not the main
focus of that study, and no detailed analysis of fingertip
stiffness was conducted as a part of that study. One reason forthis discrepancy might be that in these studies [10], [11] theeffects of deformation around/near the contact surfaces could
be neglected. Derler and Gerhardt [21] reviewed of theliterature on human skin friction but did not find any studies
on the relationship between fingertip stiffness and frictional
force.
II. MAXIMUM RESISTIBLE FORCE BETWEEN FINGERTIP AND
FLAT CONTACT SURFACEIn this study, we examined the maximum resistible force
produced when soft fingertips with various stiffnesses pressedon a flat surface. The maximum resistible force is defined as
the maximum external force on the surface (object) underwhich the fingertip can maintain contact [1]. The resistible
force basically corresponds to the frictional force. However, if
the fingertip or object is soft, deformation of either also affects
the resistible force. In this case, we should consider not thefrictional force but the resistible force for real grasping
problems. Therefore, we use the term “resistible force” todistinguish the resistible force from the frictional force. In ourprevious study [11], we investigated the maximum resistible
force produced when semispherical fingertips with various
stiffnesses pushed several edged surfaces. Whensemispherical fingertips are used, the contact area changes
with the fingertip stiffness and the normal forces. A change inthe contact area makes the effect of fingertip stiffness onfriction unclear. To eliminate the effect of changes in thecontact area, cylindrical fingertips, which have constantcontact areas irrespective of the fingertip stiffnesses andnormal forces, were used in this experiment.
A. Experimental Setup
Fig. 1 is a schematic view of the experimental setup used
to investigate the effect of fingertip stiffness on the maximum
resistible force when a fingertip pushes on a flat surface. Fig. 2
is a photograph of the experimental setup. In a typical test, afingertip was pressed vertically downward on an acryl plate
while a tangential force was applied to the acryl plate. An
automatic positioning stage was used to press the fingertip
against the acryl plate. The fingertip was attached to ahand-made load cell unit (0–50 [N]) attached to the automatic
positioning stage. The load cell unit was used to measure andcontrol the magnitude of the pressing force, which is thenormal force. The fingertips used were made of silicone.
Another automatic positioning stage was used to apply thetangential force to the acryl plate. A force gauge (IMADA
DS2-50N) was attached to the positioning stage to measure themagnitude of the tangential force on the acryl plate. As shownin Fig. 2, the acryl plate was transparent, which made it
possible to observe the contact area using a camera positioned
under the acryl plate.
We increased the tangential/shearing force by moving theautomatic positioning stage at a speed of 1 [mm/s] untilslippage occurred. We defined the measured tangential/shear
force at that time as the maximum resistible force. The normal
force levels applied were 1, 2, 5, 10, 15, and 20 [N].
Automatic
positioning stage

PC

Force data
Position data
Image data

Load cell unit

Normal force
Fingertip(Silicone)

Tangential force

Acryl plate
Force gauge

CameraLinear guide

Automatic positioning stage

Figure 1. Schematic illustration of the experimental setup for investigating
the effect of fingertip stiffness on the maximum resistible force when thefingertips push against a flat surface.

Automatic
positioning stage

Load cell unit
Acryl plate
Force gauge

Linear guide

Automatic
positioning stage

Figure 2. Photo of the actual experimental setup

Figure 4. Compression test setup for the measurement offingertip stiffness

We repeated each test three times. The frictional force ofthe linear guide attached to the acryl plate was measured
beforehand to eliminate its effect.
B. Fingertip and Surface Shape
We used the silicone fingertips shown in Fig. 3 in thisstudy. Based on the size of the semispherical finger used in theprevious study [11], we chose to use fingertips with diametersand heights of 22 [mm] and 11 [mm], respectively. We madethe fingertips from base materials and hardeners, both ofwhich were produced by the Shin-etsu Silicone Company.
Fingertips with different stiffnesses can be made by changing
the ratios of the component materials used. To makeobservation of the contact area easier, the fingertips werecolored red.

obtained using the model form proposed by Watanabe [11]:𝑓𝑡 = 𝜏0 𝑓𝑛𝛼 + 𝑎𝑓𝑛 





where 𝑓𝑡 is the maximum resistible force, and 𝛼 and 𝑎 areparameters. The values of the parameters were obtained by theleast squares method and are shown in Table II.
As Fig. 7 shows, higher fingertip stiffness resulted inlarger resistible forces. This trend is similar to that observed
for semispherical fingertips in our previous study [11]. We
discussed this trend in [11] and associated differences in thecontact area with differences in fingertip stiffness. In thisexperiment, cylindrical fingertips were used, so the contact
areas were constant when there was no tangential force (in theinitial state). However, when the fingertip and the acryl plate

We conducted compression tests, as illustrated in Fig. 4, tomeasure the stiffnesses of the fingertips. Fig. 5 shows theresults of the compression tests. The markers represent theexperimental results, whereas the curves are regression curves
obtained using the model form proposed by Kao [13]:𝑓𝑛 = 𝐶 ∆𝑥 𝜁 where 𝑓𝑛 is the applied normal force, 𝛥𝑥 is the deformation,
and 𝐶 and ζ are parameters. The values of the parameters wereobtained by the least squares method and are shown in Table I.
It can be seen that the ascending order of stiffness is S1, S2, S3,
and S4.
C. Experimental Results and Discussion
Fig. 6 is an example of time series data for the tangential
force for S2. The arrows point to the first peak of each curve,
which is the point at which the fingertip and the acryl platestarted to slip. We obtained the maximum resistible force fromthe tangential force at this peak. After this peak, stick–slip canbe seen from Fig. 6. Fig. 7 shows the normal force versus the
maximum resistible force. The markers correspond to theexperimental results, whereas the curves are regression curves

Figure 5. Force-deformation curve for the fingertip stiffness. Note that themeasurement limit for the force gauge is 50 [N], and the experiments were
stopped when the normal force exceeded this limit.
TABLE I.
STIFFNESS PARAMETERS C AND 𝜁 IN (1) FOR THE
REGRESSION CURVES SHOWN IN FIG. 5 (𝑅 2 : COEFFICIENT OF
DETERMINATION, RMSE: ROOT MEAN SQUARED ERROR )Fingertip
type

C

𝜻

𝑹𝟐

RSME

S1

3.13

1.46

0.973

1.07

S2

7.58

1.97

0.998

0.107

S3

14.0

2.52

0.997

0.600

S4

20.1

2.39

0.997

0.575

6

8

[N]

20
15

Tangential force

Figure 3. Silicone fingertips used in the experiments, S1, S2, S3, and S4,
shown in ascending order of fingertip stiffness from left to right (see Fig. 5).

10

5
0
0

2

4
Time [s]Figure 6. Time series data for the tangential force for S2.
The first peak (indicated by the red arrow for each curve) is defined as the
maximum resistible force..

Figure 7. Normal force versus maximum resistible force. Note that when
S4 was used to apply normal forces of 15 and 20 [N], the tangential force
exceeded the measurement limit of the force gauge.
TABLE II.
PARAMETERS 𝜏0 , 𝛼, AND 𝑎 IN (2) FOR THE REGRESSIONCURVES SHOWN IN FIG. 7. 𝑓𝑡 = 𝜏0 𝑓𝑛 𝛼 + 𝑎𝑓𝑛 (𝑅 2 : COEFFICIENT OF
DETERMINATION, RMSE: ROOT MEAN SQUARED ERROR )Fingertip
type

𝝉𝟎

𝜶

𝒂

𝑹𝟐

RSME

S1

4.41

0.353

1.47x10-10

0.977

0.483

S2

4.54

0.477

4.48x10-11

0.966

1.10

0.550

6.96x10

-09

0.962

2.90

3.08x10

-13

0.951

2.75

S3
S4

8.53
9.76

0.604

reduce the magnitude of the normal stress and consequently
reduce friction. On the other hand, in terms of the amount of

Figure 9. Tangential forced displacement versus tangential force in forcases of S1 and S4.

tangential/shearing forced displacement, the softer fingertip
offers an advantage, as shown in Fig. 9. The softer finger isthus more suitable when it is necessary to resist a large forced
displacement (see Fig. 9 S1), and the harder finger is suitable
when it is necessary to resist a large tangential/shearing force(see Fig. 9 S4).
III. MAXIMUM RESISTIBLE FORCE WHEN FINGERTIPSPUSHED AGAINST CURVED CONTACT SURFACEIn the real world, there are objects with various shapes.
Contact surfaces are not always flat. We therefore investigatedthe effect of fingertip stiffness on the resistible force when thefingertips were in contact with curved surfaces.
A. Experimental Setup
Fig. 10 is a schematic view of the experimental setup used
to investigate the effect of fingertip stiffness on the maximum
resistible force when the fingertips pushed against curved
surfaces. This setup was basically the same as the setup shownin Fig. 1, except that curve surfaces were used and the camera
was removed. R15 and R25 curved surface parts, shown in Fig.
11, were used. These parts were attached to the acryl plate.
Because these parts’ surfaces are not transparent, the contact
area could not be observed, so the camera was removed. The
same fingertips (S1, S2, S3 and S4) as used in the previous

Figure 8. Photo of the contact areas (areas bordered by lines) when slip
occurred between the fingertip and the acryl plate in the cases of S1 (thesoftest fingertip) and S4 (the hardest fingertip). For the softer fingertip, thedeformation of the contact area and the shearing/bending deformation werelarger.

Automatic
positioning stagePC

Load cell unit

started slipping, the shape and position of the contact areachanged, as shown in Fig. 8. When a forced tangential
force/displacement was applied, deformation by bending andshearing occurred in the fingertip. This deformation affected
the deformation of the contact area and the stress distribution
over the contact area. As Fig. 8 shows, the shearing/bending
deformation and the deformation of the contact area weremore evident for the softest fingertip (S1). For the hardest
fingertip (S4), the change in the contact area was smaller, andshearing/bending deformation was not evident. The
deformations of the softer fingertip (S1) were assumed toForce data
Position data
Fingertip(Silicone)

Normal force
Tangential force

Acryl plate
Force gauge

Linear guide

Automatic positioning stage
Curved surface

Figure 10. Schematic illustration of the experimental setup for investigating
the effect of the fingertip stiffness on the maximum resistible force when thefingertips pushed against R15 and R25 curved surfaces. This setup did notpermit observation of the contact surface because the R15 and R25 curved
surfaces are not transparent.

20
R15
R25
Figure 11. Photos of acryl the curved surface parts having with R15 andR25curvesR25curved surfaces. They were made of acryl

series of tests were used in this series. The experimental
procedure was also the same as that used in the previous seriesof tests. The speed of the positioning stage for applying thetangential force was 1 [mm/s]. We measured the maximum
tangential force, which we considered the maximum resistible
force, at the start of slippage. The normal force levels applied
were 1, 2, 5, 10, 15, and 20 [N]. We repeated each test threetimes. Strictly speaking, the direction of the tangential force inthis setup is only tangential at the initial state. The direction of
the applied, initially tangential force could change according
to the fingertip deformation and curvature of the contact
surface. However, practically speaking, this alteration in
direction does not occur when applying the force in the exact
tangential direction, but given the impact of this directionchange and its interest to many researchers, we believe amodel of this system is worth exploring.
B. Experimental Results and Discussion
Fig. 12 and Fig. 13 show the normal force versus the
maximum resistible force for the R15 and R25 curved surfaces,
respectively. The markers correspond to the experimental
results, whereas the curves are regression curves obtainedusing Equation (2). The values of the parameters wereobtained by the least squares method and are shown in Table
III and Table IV. As the values of the coefficient ofdetermination (R2) and the root mean squared error (RSME)
show, the greater the surface curvature is, the poorer the fit of
the regression equation was. The greater the curvature is, thesmaller the contact area is and the easier it is for a deviation to
occur. As a result, the variance of the maximum resistible
force tends to be larger. This is believed to be the reason forthe poorer fit of the regressions for the more curved surfaces.

Figure 12. Normal force versus maximum resistible force for the R15 curved
surface. Testing using S1 was stopped at 10 [N] because the normal
deformation was excessive and breaking was observed when normal forcesof 15 and 20 [N] were applied.

Figure 13. Normal force versus maximum resistible force for the R25 curved
surface. Testing using S1 was stopped at 10 [N] because the normal
deformation was excessive and breaking was observed when normal forcesof 15 and 20 [N] were applied. For S3 and S4, application of normal forces of
15 and 20 [N] resulted in the tangential force exceeded the measurement limitof the force gauge.
TABLE III.
PARAMETERS 𝜏0 , 𝛼, AND 𝑎 IN (2) FOR THE REGRESSIONCURVES SHOWN IN FIG. 12 (R15). 𝑓𝑡 = 𝜏0 𝑓𝑛 𝛼 + 𝑎𝑓𝑛 (𝑅 2 : COEFFICIENT OF
DETERMINATION, RMSE: ROOT MEAN SQUARED ERROR )Fingertip
type

𝝉𝟎

𝜶

𝒂

S1

3.47

0.284
0.472

S2
S3
S4

3.72
5.76
5.97

0.535
0.504

𝑹𝟐

RSME

1.72x10-12

0.856

3.19

2.03x10

-09

0.943

20.7

9.53x10

-09

0.976

31.3

1.31x10

-10

0.935

80.0

TABLE IV.
PARAMETERS 𝜏0 , 𝛼, AND 𝑎 IN (2) FOR THE REGRESSIONCURVES SHOWN IN FIG. 13 (R25). 𝑓𝑡 = 𝜏0 𝑓𝑛 𝛼 + 𝑎𝑓𝑛 (𝑅 2 : COEFFICIENT OF
DETERMINATION, RMSE: ROOT MEAN SQUARED ERROR )Fingertip
type

𝝉𝟎

𝜶

𝒂

S1

4.73

0.248
0.426

S2

3.75

𝑹𝟐

RSME

4.04x10-11

0.891

2.96

6.64x10

-10

0.970

7.37

-09

0.988

22.7

0.980

51.6

S3

7.49

0.726

1.53x10

S4

7.85

0.757

7.39x10-11

As in the case of contact with a flat surface, the harderfingertips (S3 and S4) resisted higher tangential forces than
the softer fingertips (S1 and S2) in both cases, as shown in Fig.
12 and Fig. 13. Fig. 14 and Fig. 15 are side-view photographsof the S1 (softest) and S4 (hardest) fingertips. Fig. 14 and Fig.
15 show that bending/shearing deformation (see Fig. 8 for thedefinition) occurred. The contact areas and bending/shearing
deformation of the softer fingertips were larger than those of
the harder fingertips. As shown in Fig. 16, with curved
surfaces, large bending/shearing deformations can progress toslippage because of the moment produced by the deformationand the deviation of contact in the normal direction (i.e., partof the original normal force can act as a tangential force). In
addition, a large contact area indicates a small normal
stress/pressure on the contact area. These factors might be thereasons for harder fingertips producing larger resistible forces.

[N]

[N]

(a) S1 fingertip
Figure 16. Schematic illustration of the states of softer and harder fingertips
when pushing against a curved surface.

[N]

[N]

(b) S4 fingertip
Figure 14. Photo of side views of the fingertip using the R15 curved surface:initial states (left) and slip occurrence (right)
Figure 17. Comparison of maximum resistible force versus normal force forthe two fingertips, S1 and S4, and the three contact surfaces: flat (solid lines),
R15 (dotted lines), and R25 (dashed lines).

[N]

Other interesting points are that the ranges of the maximum
resistible forces were very different and that the differences in
the maximum resistible forces between S3 and S4 were small.
[N](a) S1 fingertip
[N]

[N]

(b) S4 fingertip
Figure 15. Photo of side views of the fingertip using the R25 curved surface:initial states (left) and slip occurrence (right)

Fig. 17 illustrates the effect of the shape of the contact
surface and shows the rearranged results for the S1 (softest)
and S4 (hardest) fingertips. The results show that the softer
fingertip was not greatly affected by the shape of the contact
surface, while the harder fingertip was greatly affected. The
maximum resistible force for the softer fingertip was not
greatly affected by an increase in the normal force. As Fig. 16
shows, part of the original normal force can act as a tangential
force because of large bending/shearing deformations incurved contact surfaces with softer fingertips. This might
explain why the maximum resistible force does not increasemuch even when the normal force increases.
For hardest fingertip, the maximum resistible force for theR25 curved surface was the largest, while it was the smallest
for R15. As Fig. 14 (b) and Fig.15 (b) (at 𝑓𝑛 = 10 [N]), part ofthe contact with the R15 surface occurred along the curved
surface, and part of the original normal force can act as atangential force in this area. This was not observed with theR25 surface (Fig. 15 (b)). These results indicate that there is asuitable curvature of the contact surface that maximizes theresistible force when a soft fingertip (with a relatively large
stiffness) pushes against a curved surface.

IV. CONCLUSION
In this study, we experimentally investigated the effect offingertip stiffness on the maximum resistible force produced
when a cylindrical fingertip with a flat contact surface was incontact with a flat or curved surface. The maximum resistible
force is defined as the maximum tangential force at which thefingertip can maintain contact when applying and increasing atangential/shearing force. We include in the definition of thisterm the effect of fingertip deformation. The main findings are
as follows.
1. Harder fingertips produce larger resistible forces,
irrespective of the shape of the contact surface (flat or
curved). The results for curved surfaces were somewhat
different from those observed in our previous study [11].
When semispherical fingertip contacts with angled
surfaces were tested in the previous study [11], softer
fingertips were found to produce larger resistible force fora contact angle of 90 [degrees]. Although the experimental
setups used in the two studies were different (for example,
the magnitude of the normal force was fixed in [11] but
varied in this study), as were the shapes of the fingertips,
more detail investigations may be needed and will be
conducted in our future research.
2. For harder fingertips, the maximum resistible force
depends largely on the shape of the contact surface, while
for softer fingertips, the shape has little effect. Of the threesurfaces used in this study (one flat and two curved
surfaces), the surface with the middle curvature resulted in
the largest maximum resistible force for harder fingertips.
How the magnitude of curvature affects the maximum
resistible force will be examined in greater detail in our
future research.
3. For softer fingertips, the magnitude of the resistible forcechanges little even when the normal force increases. Thisfinding is very important from the perspective of grasp
planning because conventional frictional coefficientscannot be used directly. The development of a new
frictional model will also be a topic of our future research.
In addition to the future research needs identified above,
investigation of frictional moments will be part of our future
research. Both contact forces and contact moments cancontribute to object grasping. Therefore, in grasp planning,both frictional forces and moments must be considered.
Modeling and analytical investigations based on theexperimental results will also be a part of our future work.
ACKNOWLEDGMENT
The authors would like to thank Mr. Masahiro Uchida for
helping this work by designing experimental setup.
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