Experimental investigation of effect of fingertip stiffness on friction
while grasping an object
Tetsuyou Watanabe, Member, IEEE, and Yoshinori Fujihira

Abstract— In this study, we experimentally investigated theeffect of robot fingertip stiffness on friction during grasping ofan object. To make robots more human-friendly, robotic handswith soft surfaces have been developed. A soft fingertip, i.e., onewith low stiffness, is considered desirable because it produceshigh friction. However, in our experiments, we were able toobtain high friction from a stiff fingertip under a certain
condition. We initially investigated the maximum resistible force
when solid objects with different angled surfaces were graspedby spherical fingertips of different stiffness. When the contact
surface was flat, a stiffer fingertip produced larger frictional
force. When the contact surface was highly convex, themaximum frictional force increased with decreasing fingertip
stiffness. Secondly, we examined the relationships among thecontact area, the load, and the maximum frictional force. We
reformulated the relationship between the load and the
maximum frictional force and, together with our experimental
results, used it to determine the factor that increased the
maximum frictional force.

I. INTRODUCTION

study, we investigated the effect of the fingertip stiffness on
the frictional shear/tangential force.
Analyses of soft fingers were conducted by Kao et al. [8],[11], [12] and Hirai et al. [13], [14]. Xydas and Kao [11]presented the relationship between the normal force and theradius of the contact area when a semispherical fingertip
contacts a flat surface, and used it to develop a model of thefrictional condition. Kao et al. [12] presented the relationshipbetween the normal force and the deformation when asemispherical fingertip contacts a flat surface. Inoue and Hirai
presented a model that considered both the normal and thetangential deformations. Tiezzi et al [8] presented a model ofthe frictional force and examined the effect of the fingertip
compliance. Based on their theoretical and experimental
results, they concluded that, if the fingertip stiffness was low,a large frictional force could be applied. However, as we willshow in this paper, this is not always true. Ho and Hirai
presented a cantilever model of a soft fingertip, but theirinterest was sliding contact.

There have been recent demands for robots that are capableof working among humans. The hands of such robots play anessential role in supporting human activity and replacing
humans in the performance of everyday tasks. For robotic
hands to perform such tasks, planning of the grasp [1] isimportant and several libraries and software have beendeveloped for this purpose. Typical examples are Graspit [2],Openrave [3], and GraspPlugin for Chorenoid [4]. The
frictional conditions are important in grasp planning because
they determine whether the robotic hands would be able tograsp the target object. The frictional conditions are based on
the Amontons-Coulomb friction model. It is valid for contacts
between solid surfaces. However, a robotic hand cannot
always produce sufficiently large frictional force for the stablegrasping of a solid surface. To increase the frictional force
while also taking affinity for humans into consideration,
robotic hands with soft fingertips were recently developed [5],[6]. In this case, the contact is referred to as soft-finger contact[7]. The Amontons-Coulomb model is also considered valid
for this contact. Unfortunately, it is not true for a fingertip withlow stiffness [8]. Furthermore, considering that high fingertip
stiffness affords relatively high manuability and low fingertip
stiffness produces large frictional forces [9], robotic handswith changeable fingertip stiffness have been developed [6],[10]. However, the determination of the low fingertip stiffnessthat will produce a large frictional force is intuitive, and it isuncertain whether a low fingertip stiffness can actually
produce large frictional forces. For reasonable grasp planning,a more detailed analysis of a soft finger is required. In thisIn a study in the field of tribology, the mechanics of thecontact and friction of rubber were analyzed [15]. However,
the interest was kinetic friction and not static friction.
Generally, kinetic friction is more important in the tribology
field. There have been very few studies on static friction in thetribology field. Deladi et al. [16] analyzed the static friction
between rubber and metal objects. However, the stiffness ofthe materials was not considered. In his dissertation [17], thesimilar numerical and experimental results to Tiezzi et al [8]were presented: if the fingertip stiffness was low, a large
frictional force could be applied. As mentioned above, this is
not always true. Stiffness was not his main interest issue andthere is no theoretical analysis on the stiffness. Derler andGerhardt [18] reviewed about friction of human skin, but any
researches on the stiffness were not found.

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).

F. 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).

With this in mind, we experimentally investigated theeffect of fingertip stiffness on frictional force. We examined
the maximum resistible force when grasping a solid object
with several angled surfaces by fingertips of varying stiffness.
We used the results to examine whether the ability of a low
fingertip stiffness to produce a large resistible force depended
on the shape of the contact surface. Specifically, under aparticular condition, the frictional/resistible force increases
with increasing fingertip stiffness. This phenomenon cannot be
explained by conventional theories [8], [17] or a model basedon the Hertz contact theory (for an example, see [19]). The
resistible force consists of the frictional and (tangential) elastic
forces, with the shearing frictional force constituting the majorand fundamental part. We also examined the relationshipbetween the apparent contact area and the load, and thatbetween the maximum frictional/shear force and the load, forvarying fingertip stiffness. We reformulate the relationshipbetween the maximum frictional/shear force and the load and,
together with our experimental results, use it to investigate
which factor increased the frictional force with increasing
fingertip stiffness, and which factor increased the frictional
force with decreasing fingertip stiffness.

Figure 1. Schematic illustration of the experimental set up used toinvestigate the effect of the fingertip surface and the shape of the object
surface on the maximum resistible force
COMPOSITION RATIO AND MATERIAL OF THE FINGERTIPTABLE I.
Fingertip

SiliconHardener

Hardener Volume [%]S1

KE-1308

CAT1300

6

S2

KE-1308

CAT1300L-3

6

S3

KE-1316

CAT1300

10

S4

KE-1300T

CAT1300

10Δd0.00 NF

Fingertip
Flat Plate

Figure 2.

Force gauge

Compression test setup.

Applied force fn [N]

70
S1
S2
S3
S4

60
50
40

S4
S3

30
20
10

S2
S1

0
0

0.5

1

1.5

2

Deformation d [mm]Figure 3. Force-deformation curve.

II. MAXIMUM RESISTIBLE FORCE: A SOLID OBJECT WITH
SEVERAL ANGLED SURFACES IS GRASPED BY SEMISPHERICAL
FINGERTIPS OF VARYING STIFFNESSOne of the most important factors of grasping stability is
the magnitude of the force that the grasp can resist [1].
Regarding this factor, the magnitudes of the generable
frictional and elastic forces in the tangential direction areimportant and are affected by the fingertip stiffness and thesurface conditions. We investigated the variation of the
maximum resistible force in the tangential direction with thefingertip stiffness and the shape of the object.
A. Experimental set up
Fig.1 is a schematic view of experimental set up for theinvestigating the effect of the fingertip stiffness and the shapeof the object surface on the maximum resistible force. The
object was grasped by two fingertips in antipodal postures. The
magnitude of the grasping force was 2[N], which wasmeasured by a load cell and controlled by the positioning stage.
Conversely, an external force was applied to the object fromthe side such that the directions of the grasping force and theapplied external force were perpendicular to each other. The
external force was applied through a force gauge used formeasuring the magnitude of an external force. The force gauge
was attached to the automatic positioning stage. The speed of
the automatic positioning stage was set to 5.0[mm/s] and theexternal force was increased. The external force was increased
until the grasp failed. We measured the maximum external
force at this point, which is the maximum resistible grasping
force. We conducted the same experiment five times for eachpair of fingertips and object.
B. Fingertips and objects
Fingertips of four different stiffness values were used. The
fingertips were identified as S1, S2, S3, and S4. We made themfrom silicon and a harder, both of which were produced by
Shin-etsu Silicone Company. The composition ratios areshown in Table I. The radius of the semi-sphere was 11[mm].
To generate the same tribological surface condition, thefingertips were covered by a thin latex rubber. We conducted
a compression test and experimentally investigated theirstiffness. Fig.2 shows the experimental setup. We fixed thefingertip and pushed and deformed its surface by using a flat
plate attached to a force gauge (IMADA DS2-50N). Fig.3
shows the results. The markers show the experimental results,
whereas the curves are the regression curves obtained using
the equation presented by Kao [12]:


∆





where is the applied force, ∆ is the deformation, and C andare parameters. The values of the parameters were obtainedby the least squares method. It can be seen that the ascendingorder of stiffness is S1, S2, S3, and S4.
Fig.4 shows the photos of the objects being grasped by four
fingertips of different stiffness values. The four objects weredifferent: their surface angles at the contact areas were 180°,
150°, 120°, and 90°, respectively. All the objects were madefrom duralumin and weighed 3.0[g] each. Their shapes were
the same but their contact surfaces were different. The distance
between the apices of the grasping points/areas was 20[mm]and the distance between the other sides was 10[mm].

Conversely, if the fingertip is fixed to investigate the effectof the contact surface angle, different results would beobtained. Considering the case of grasping with the S1
fingertip, the maximum resistible force increases withdecreasing contact surface angle. This might be due to theincrease in the area/volume that the fingertip envelopes withdecreasing contact surface angle. When grasping with theother fingertips, the maximum resistible force decreases withdecreasing contact surface angle (increasing steepness of theobject surface). The rate of the decrease increases withincreasing fingertip stiffness. This suggests that to ensurestable grasping, the corners of the fingertips should not be used
except when they are very soft. As can be seen from Fig.4,
with decreasing softness, the fingertip is more easily able toenvelope the apex of the surface, and can achieve larger
contact area. This might affect the results.
III. INVESTIGATION OF THE CONTACT AREA AND MAXIMUMSTATIC FRICTIONAL FORCE OF A FLAT CONTACT SURFACEAs described in the previous section, we obtained resultsthat contradicted those of conventional studies [8], [17],especially when grasping the flat area of an object. In addition,
the contact between the fingertip and a flat surface isfundamental, and the effect of the elastic force in the tangential
direction can be neglected in the macroscopic range; only thefrictional/shear force need be considered. We therefore
conducted a more detailed investigation of this case byexperimentally examining the contact area and the maximum
frictional/shear force.

Figure 4. Photos of the grasp. The fingertips are identified as S1, S2, S3,
and S4, with the respective numbers corresponding to the magnitudes ofther stiffness (S1 is the lowest and S4 the highest). The objects are of fourtypes and their surface angles in the contact areas are respectively 180°,
150°, 120°, and 90°.

7
S1

Maximum resistible external force [N]C. Experimental results and discussion
Fig.5 shows the results. The mean value and standard
deviation for each setting are shown. When the contact surface
angle of the grasped object was 180°, the maximum resistible
force increased with increasing fingertip stiffness. This
contradicts intuitive expectation and the findings ofconventional studies [8], [17]. When the object with a contact
surface angle of 150° was grasped, the maximum resistible
force decreased with the fingertip stiffness in the order S2, S1,
S3, and S4. Comparison of the results for a contact surface
angle of 180 ° , reveals that the maximum resistible force
decreases drastically when grasping using S3 and S4, whereasthat does not when grasping using S1 and S2. It can be seenfrom Fig.4 that the contact area when grasping the object witha surface angle of 150° using S3 or S4 is much smaller thanthat when grasping the object with a contact surface angle of180°. It is our consideration that the decrease in the contact
area significantly affects the magnitude of the maximum
resistible force. The difference between the contact areas forgrasping using fingertip stiffness of S1 and S2 is not very large,
and the difference between the magnitudes of the maximum
resistible force is also small. When grasping the object with acontact surface angle of 120 ° , the difference between the
maximum resistible forces for S1 and S2 is very small, and thedescending order of the maximum resistible forces is S1/S2,
S3, and S4. When grasping the object with a contact surface
angle of 90 ° , the descending order of magnitudes of the
maximum resistible force is S1, S2, S3, and S4. In this case,the magnitude of the contact area might strongly affect themagnitude of the maximum resistible force (see also Fig.4).
With decreasing contact surface angle (increasing steepness ofthe object surface), the magnitude of the contact area might
become more important to achieving a large resistible force.

6

S2

S3

S4

5
4
3
2
1
0
( i ) 180

( ii ) 150( iii ) 120
Contact surface angle [degree]( iv ) 90

Figure 5. Maximum resistible external force for grasping an object. The
ascending order of the fingertip stffness is S1, S2, S3, and S4, and thecontact surface angles of the objects are respectively 180°, 150°, 120°, and90°.

A. Investigation of the contact area
A schematic illustration of the experimental setup is shownin Fig.6. We daubed the fingertip with colored ink and used it
to touch a sheet placed on the stage so that the area of the sheetthat was colored by the ink corresponded to the contact area.
The load was applied from the upper side using a weight anda linear guide as shown in Fig.6. The applied loads were 5, 10,
20, 30, and 50 [N]. The applied fingertips were the same as
those in the previous section: S1, S2, S3, and S4. After loading,we measured the radius of the colored area (contact area) on
the sheet. Fig.7 shows the results, where the markers are themeasured values and the curves are the regression curves. The
equation of the regression curves was presented by Xydas andKao [11]:






where is the radius of the contact area, and D and areparameters. The parameter values were obtained by the leastsquares method. It can be seen that, if the fingertip stiffness islow, the radius would be large.

Radius of contact area: r [mm]Figure 6. Shematic illustration of the experimental setup for investigating
the contact area. The fingertips contact the flat surface.
14
S1
S2
S3
S4

12
10

Fig.9 shows the results, where the markers indicate theexperimental results and the curves are the regression curves(the equation of the regression curves will be described later).
It can be seen that the maximum frictional/shear force actually
increases with increasing fingertip stiffness.

8
6
4
2
0
0

force gauge is attached on positioning stage, and by controllingthe stage, we applied tangential/shear force to the contact area
between fingertip and the plate (made of duralumin) attachedon the linear guide. Normal force is applied to the contact areaby controlling the weight placed on the plate connected to thetwo other linear guides. The used fingertips are S1, S2, S3 andS4. The applied weight was 0.5, 1.0, 2.0, 3.0 and 5.0 [Kg] for
S1, S2 and S3, and 5.24, 10.24, 20.24 and 30.24 [N] for S4(note that the difference of the setting is due to the usage ofdifferent plate for attaching the fingertip). If increasing theapplied tangential/shear force, the slide occurs at the contact
area. At that time, we can measure maximum tangential/shear
force. We examined the maximum tangential/shear force. We
repeated five times for each set up. It should be noted that theinvestigation of the adhesion force when every fingertip
contacted the plate was targeted at determining the effect ofthe properties of the contact surface such as the roughness. The
measured values ranged between 1 and 3 [mN]. These values
are very small and their effects are hereafter neglected.

10

20

30

40

50

60

Load: fn [N]Figure 7. Load (applied force) versus radius of the contact area.

C. Discussion
According to tribology theory [19], the maximum static
frictional force is given by






where is the maximum frictional force (shear force), isis the real contact area. If thematerial shear stress, andmaterial is a polymer (for example, silicon), the shear stresscan be expressed asFigure 8. Shematic illustration of the experimental setup for investigating
the static maximum frictional force. The fingertips contact the flat surface.



where is the mean pressure on the real contact area , andand are material constants. If represents the apparent
contact area, and the mean pressure on the apparent contact
area , then






The real contact area
increases with increasing load
(normal force) because the likelihood of contact increases
under a high local pressure. Therefore, considering (2), we
suppose that∝; hence
whereobtainandare parameters. From (3), (4), (5), and (6), we
Figure 9. Load (applied force) versus maximum tangential/shear force.

B. Investigation of maximum frictional/shear force
The schematic view of experimental set up is shown in
Fig.8. In the experimental set up shown in Fig.6, we added
another linear stage such that we can measure tangential/shear
force. We connect the added linear guide and force gauge. The







where
. This is the equation of the regression curves
in Fig.9. The parameter values for the regression curves arelisted in Table II. They were obtained using the curve fitting
toolbox in Matlab (MathWorks). If (7) is divided by , weobtainIt should be noted that, here, 0

1, and if
1, (8)

will be the same as the Amontons-Coulomb friction model.
As can be seen from Fig.9 and Table II, the AmontonsCoulomb model cannot be used to represent the phenomenon.
Most grasp planning [1-4] are based on the AmontonsCoulomb model. The presented results suggest the necessityof a careful consideration of friction in grasp planning. Table
II and (8) indicate that, if the load (normal force) becomesvery large,
would converge to , in which case thefingertips with relatively low stiffness produce larger
frictional force. When fingertips with relatively small
stiffness (S1 and S2) are used, the values of and would
not be high, and it is easier for to converge to . As can beseen from Fig.7, the radius of the contact area converges fasterto a constant value with increasing load. This might affect therelatively fast convergence of to . However, if the load
(normal force) is not large, the effects of and would besignificant. The fingertips with relatively high stiffness would
therefore produce larger frictional forces.
Focusing onand , equations (2) and (7) can also be
expressed ascontact area increases with decreasing fingertip stiffness.
Therefore, if the effect of in (10) is relatively strong, themaximum frictional/shear force increases with increasing
fingertip stiffness. This corresponds to the case when thecontact surface of the object is flat (contact surface angle of180° in Figs. 5 and 9). If the effect of in (10) is relatively
strong, the maximum frictional/shear force increases withdecreasing fingertip stiffness. This might be the case for a 90°
contact surface angle in Fig.5. The intermediate case may
correspond to a contact surface angle of 150° or 120° in Fig.5.
It can be seen from Table III that the sign of is positive
when the fingertip stiffness is high, whereas it is negative
when the fingertip stiffness is low. Also, with increasing load,in (9) decreases when the fingertip stiffness is low, andincreases when the fingertip stiffness is high. This suggests
that, if the fingertip stiffness is low, increasing the load would
increase the importance of the contact area in achieving alarge maximum static frictional force.
TABLE II.
CURVES IN FIG.9.



≜ 



We then have




∙



S1

1.17

0.409

0.237

0.996

0.358

S2

1.49

0.290

0.297

0.994

0.457

S3

1.92

0.501

0.218

0.998

0.309

S4

1.61

0.683

0.175

0.994

0.397

TABLE III.

where


RMSE

Fingertip

Here, / is the ratio of the real contact area to theand are power
apparent contact area. Because both
functions of , we can define the following:

PARAMETERS 0 , , AND IN (7) FOR THE REGRESSION( : COEFFICIENT OF DETERMINATION,
RMSE: ROOT MEAN SQUARED ERROR )PARAMETERS

0 AND

IN (9)

Fingertip

,

2 



The values of and for each fingertip can be calculated
from the data in Fig. 7 and Table II. Table III gives thecalculated values. If
0, then (10) becomes the same as themodel presented in [8]. It can be seen from Table III that ≅0 for S1 and S3, for which the model presented in [8] is valid.
However, this is not the case for S2 and S4. It can be seenfrom the results for S1 and S2 in Fig.7 and Fig.9 that therelationship between the load and the maximum
shear/frictional force is close, whereas the relationshipbetween the load and the radius of the contact area is not.
Therefore, the model presented in [8] does not represent thephenomenon in the case of S2. It is also true for S4. It can besaid that the model expressed by (7) comprehensively
represents the phenomenon.
From Table II, it can be seen thatcan be seen. Wein (7). in (9) is relatively
therefore focus on the termlarge when the fingertip stiffness is high because the realcontact area
is related to the magnitude of the local
pressure, whereas the apparent contact area is relatively
small when the fingertip stiffness is high. It can therefore be
said that , defined by (9), increases with increasing fingertip
stiffness. As mentioned above, and from Fig.7, the apparent

S1

0.0188-0.0564

S2

0.0367-0.206

S3

0.07390.0559S40.07970.220

TABLE IV.

PARAMETERS AND IN (11) ( : COEFFICIENT OF
DETERMINATION, RMSE: ROOT MEAN SQUARED ERROR )RMSEFingertip
S1

0.973

0.738

0.994

0.384

S2

1.05

0.744

0.992

0.514

S3

1.74

0.675

0.998

0.350

S4

1.71

0.746

0.994

0.381

D. Approximate relationship between the load and the
maximum static frictional force(7) given in the previous subsection is useful forcomparison and discussion, but practically not easy to copewith since there are multiple terms. Here, we consider anotherrelationship between load and maximum static friction force.
By directly considering (3) and (6), we can have






where and are parameters, the values of which are listed
in Table IV. They were obtained using the curve fitting
and RMSE in
toolbox in Matlab (MathWorks). Comparing
Tables II and III, (11) can be appropriately used to represent
the relationship, although the fitting is poorer than or equal tothat of (7).
E. Remarks on how to deal with the friction condition in
grasp planning
To consider the friction condition in grasp planning, it may
be easier to use (11) than to use (7). Our remarks here arebased on (11). As can be seen from Table IV, in (11) is lessthan 1. Supposing that is the coefficient of friction, when
the normal force is increased, the assumed maximum usable
frictional force is larger than what is actually available. Hence,for grasp planning, the assumed available maximum normal
force should be used. If the value of the maximum normal
force () is set, (11) can be approximated






is constant. Hence, by
It should be noted thatassuming
the frictional coefficient, theconventional grasp planning strategy can be used.
IV. CONCLUSION
In this study, we experimentally investigated the effect offingertip stiffness on the maximum static frictional force, forthe purpose of developing stable object grasping using soft
fingertips. We first showed the experimental results regarding
how a large external force can be resisted by a grasp. We also
noted that for a non-flat contact surface, the maximum
resistible force consisted of the tangential elastic and static
frictional forces. For the experiments, we used objects withdifferent surfaces grasped by fingertips of different stiffness.
We examined the effects of the fingertip stiffness and theshape of the contact surface of the object. We found that when
the contact surface was flat, the maximum static frictional
force (resistible force) increased with increasing fingertip
stiffness. We found that, if the contact surface was convex andits angle steep, the maximum resistible force increased withdecreasing fingertip stiffness. Conversely, we found thatwhen the fingertip was stiff, the maximum resistible force
decreased with increasing steepness of the contact surface
angle. However, when the fingertip was soft, the maximum
resistible force increased with increasing steepness of theobject surface.
We conducted a more detailed experimental investigationof the relationship between the maximum static frictional
force and the normal force using different fingertip stiffness.
The experimental results revealed that the maximum
frictional force depended on the contact area and shearing
parameter defined by (9). If the effect of is strong, themaximum frictional force would increase with increasing
fingertip stiffness. However, if the effect of the apparent
contact area is strong, the maximum frictional force would
increase with decreasing fingertip stiffness.

We also presented a simple relationship between the
maximum static frictional force and the normal force for easy
consideration of friction in grasp planning and made some
remarks about dealing with friction in grasp planning.
Grasp panning also requires the condition of the frictional
moment about the normal direction [1]. A detailed
investigation of cases of objects with convex surfaces was notconducted in this study. We will experimentally analyze suchcases in a future work.
ACKNOWLEDGMENT
The authors would like to thank Mr. Ryosuke Arima andMr. Masahiro Uchida for helping this work by making
experimental setup and conducting experiments.
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