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Relative contribution ratios of skin andproprioceptive sensations in perception of force
applied to fingertip
Kenya Matsui, Shogo Okamoto, and Yoji Yamada, Member, IEEE
Abstract—Humans perceive a force applied to their fingertips by integrating skin and proprioceptive sensations. In this study, weinvestigated the relative contribution ratios of these sensations using two approaches. Decoupled forces were applied to the finger pad
and proximal interphalangeal joint of the index finger of the participants. First, we calculated the ratios from the point of subjective
equality between the skin and the proprioceptive perceptions. Second, we obtained discrimination limens of the two perceptions tocompute their contribution ratios. The results of these two approaches showed good agreement. Additionally, we investigated how themagnitudes of forces, which were 1.0 and 0.3 N, applied to a fingertip affect the relative contribution ratios of the two sensory channels.
When humans perceived the force of 1.0 N, the relative contribution ratios of skin and proprioceptive sensations were 16–28% and 72–
84%, respectively. In contrast, when humans perceived the force of 0.3 N, the relative contribution ratios were 37–55% and 45–63%,
respectively. These relative contribution ratios can be utilized for the design of efficient haptic interfaces.
Index Terms—Skin stretch, Sensory integration, Force perception.

✦

1

I NTRODUCTION

Humans integrate both skin and proprioceptive sensations to estimate the properties of an object while
exploring it with their ﬁngers. For example, these two
sensations provide information about the weight [1],[2], [3], hardness [4], [5], and length [6] of the object.
Furthermore, links between these two sensations havebeen suggested to play a role in the perception of thesurface shape [7], [8]. Knowledge of the relative contribution ratios of skin and proprioceptive sensations is ofgreat importance. Such knowledge should lead to not
only the clariﬁcation of the perceptual mechanism but
also the development of haptic displays. For example,
an interface that applies shear deformation to the ﬁnger
pad can impart sensations of force and weight as analternative to a kinesthetic sense display. Provancher andSylvester demonstrated that a force and shear deformation imparted to the human ﬁngertip affect the humanestimation of friction [9]. The design guidelines or implementation for such a display were presented [10],[11]. Kurita et al. developed an interface that presented
the weight and friction coefﬁcient of grasped objects bycontrolling the shear deformation of the human ﬁnger
pad [12]. Minamizawa et al. demonstrated that shear
and normal force feedback to ﬁnger pads by wearable
haptic interfaces provided a good approximation of the• The authors are with the Department of Mechanical Science and Engineering, Nagoya University, Japan.
• This work was in part supported by MEXT KAKENHI 22800030 and
23135514.
• We thank Dr. Jonathan Platkiewicz, Prof. Susumu Hara and Dr. Yasuhiro
Akiyama for advice and discussions.

Digital Object Indentifier 10.1109/ToH.2013.71

haptic interaction with virtual objects [13]. Similar effects
can be expected only by the application of normal orrotational forces to ﬁnger pads [14], [15]. Feeding backa shear force to the ﬁnger pad potentially improves
the performance of a task involving manipulation ofan object in the virtual space [16]. As shown in suchinterfaces, the application of one or both of the forces andshear deformation to the ﬁnger pad is effective in designing haptic interfaces. Forces applied to the ﬁnger pads
should be manipulated as precisely as those applied tothe hands because studies in the ﬁeld of psychophysics
suggest that humans can accurately estimate the force
applied to the ﬁnger pad [17].
Despite the wide use of force feedback to ﬁnger pads,
the relative contribution ratios of the two sensory channels when a force is applied to a ﬁngertip have notyet been studied in adequate detail. Provancher andSylvester focused on the relationship between the skindeformation and the friction stimuli applied to the ﬁngertip [9]. Minamizawa et al. [13] and Giachritsis et al. [3]

݂መ௦௣

݂௣
݂௦

Fig. 1. Integration of perceived force. The proprioceptive
force (fp ) and the finger pad force (fs ) are decoupled, andthe perceived force (fˆsp ) is the integration of these twoforces.

1939-1412/13/$31.00 © 2013 IEEE

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investigated the roles of skin and proprioceptive cues in
the weight perception of an object gripped by the thumband the index ﬁnger. These studies did not directly discuss the contribution ratios of the cues, or they addressed
the weight perception via a two-ﬁngered grip underwhich the roles of skin sensations tend to be greaterin the force perception (see also the ﬁrst paragraph ofsec. 5.1). In addition, active and passive grip conditions
were mixed in some cases. We investigate the contribution ratios for one ﬁnger, which is a more general condition. Furthermore, we adopt two approaches–a pointof subjective equality (PSE) approach and one basedon the discrimination limen (DL)–for investigating thecontribution ratios of the two perceptual cues in orderto obtain more reliable conclusions.
The objective of this study is to examine the relative
contribution ratios of skin and proprioceptive sensationsin the perception of a force applied to a ﬁngertip. Humans apply an equal-sized force to the ﬁnger pad andthe entire ﬁnger when they manipulate objects. In thisstudy, the two sensations were decoupled. As shown in
Fig. 1, the two sensations were independently imparted
by the skin (shear deformation to the ﬁnger pad) and the
proprioceptive (force on muscles and tendons of ﬁnger)
stimuli although some interference with each cue existed. First, we obtain the relative contribution ratios byidentifying the PSE of the stimuli. Second, we specify theDLs of the two sensations and then calculate the ratios ofthe sensory channels. Additionally, we investigate how
the magnitudes of forces (1.0 N and 0.3 N) applied toa ﬁngertip affect the relative contribution ratios of thetwo sensory channels. Generally, as the force applied tothe ﬁngertip decreases, the skin sensation becomes more
dominant [18]. All experimental procedures were admitted by the ethical committee of the Graduate School ofEngineering at Nagoya University.

wp1 (fˆs1 , fˆp1 ) = wp1 (fˆs2 , fˆp2 ). This equation, then, can be
rewritten as

2

Under the assumption of a linear cue combination, theintegrated force perception fˆsp is given bywith ﬁxed fˆp1 . When fˆs1 is close to fˆs2 , it is approximated that ws2 (fˆs1 , fˆp1 ) = ws2 (fˆs2 , fˆp1 ) andwp2 (fˆs1 , fˆp1 ) = wp2 (fˆs2 , fˆp1 ). Subtracting (7) from (6)givesσ̂sp = ws2 (fˆs1 , fˆp1 )σ̂s ,(8)fˆsp = ws1 (fˆs , fˆp )fˆs + wp1 (fˆs , fˆp )fˆp ,where σ̂sp = fˆsp1 − fˆsp2 and σ̂s = fˆs1 − fˆs2 . Similarly,

T WO APPROACHES FOR RESOLUTION OF

RELATIVE CONTRIBUTION RATIOS

2.1 Approach based on point of subjective equality(1)

where fˆs and fˆp are the perceived forces applied tothe skin and proprioceptive cues, respectively, and ws1
and wp1 are the relative weights when fˆs and fˆp are
integrated [19]. As previously described, these weights
depend on the force applied to the ﬁngertip. Additionally, ws1 and wp1 are related by ws1 + wp1 = 1. Two
subjectively equivalent stimuli are described by
ws1 (fˆs1 , fˆp1 )fˆs1 + wp1 (fˆs1 , fˆp1 )fˆp1= ws1 (fˆs2 , fˆp2 )fˆs2 + wp1 (fˆs2 , fˆp2 )fˆp2 .

(2)When fˆs and fˆp values are close, respectively, we
can approximate that ws1 (fˆs1 , fˆp1 ) = ws1 (fˆs2 , fˆp2 ) andws1 (fˆs1 , fˆp1 )Δfˆs + wp1 (fˆs1 , fˆp1 )Δfˆp = 0,(3)

where Δfˆs = fˆs1 − fˆs2 and Δfˆp = fˆp1 − fˆp2 . Based on therelationship ws1 + wp1 = 1 and (3), the relative contribution ratios for the skin and proprioceptive sensations are
given byΔfp
ws1 (fˆs1 , fˆp1 ) =,(4)
Δfp − Δfs
wp1 (fˆs1 , fˆp1 ) = 1 − ws1 (fˆs1 , fˆp1 ).

(5)

2.2 Approach based on discrimination limen
A representative DL-based approach is the maximum
likelihood estimation (MLE) or the minimum varianceestimation (MVE) model that determines the contribution ratios based on the variance of perception [19], [20].
By deﬁnition, the minimization of variance maximizes
the reliability of the integrated information.
When the DL of one cue is measured, potentiallyrelated cues are preferably kept useless [20], [21], [22]. In
the case of our study, such a channel can be created using
uncorrelated noisy vibratory forces. However, such noise
signals to the proprioceptive sensations signiﬁcantly inﬂuence the skin sensations. Similarly, it is difﬁcult toapply a force to a ﬁnger pad without inﬂuencing theother skin parts. It is challenging to entirely segregate
the skin and the proprioceptive perceptions. Therefore,
in the present study, where cue isolation is difﬁcult, one
cue is ﬁxed whereas another cue is varied. For suchcases [20], the integrated percepts arefˆsp1 = ws2 (fˆs1 , fˆp1 )fˆs1 + wp2 (fˆs1 , fˆp1 )fˆp1
fˆsp2 = ws2 (fˆs2 , fˆp1 )fˆs2 + wp2 (fˆs2 , fˆp1 )fˆp1

σ̂sp = wp2 (fˆs1 , fˆp1 )σ̂p

(6)
(7)

(9)

holds. Let σ̂s and σ̂p be the respective deviations ofpercepts fs and fp when one cue is manipulated andthe other is ﬁxed. When the two cues are optimally
integrated, σ̂sp becomes equal to the deviation of fˆsp .
From (8), (9), and ws2 +wp2 = 1, the relative contribution
ratios of the two sensory channels are described by
ws2 (fˆs1 , fˆp1 ) =σ̂p,σ̂s + σ̂p

wp2 (fˆs1 , fˆp1 ) = 1 − ws2 (fˆs1 , fˆp1 ).

(10)
(11)

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3

E XPERIMENT

3.1 Method
3.1.1 Experimental System
The requirements for the force and tactile interfaces usedin the experiment are that the displays can separately
apply forces to the skin and the proprioceptive stimuli.
For the skin stimulus, the display applied a shear force
to the ﬁnger pad, fs . For the proprioceptive stimulus, thedisplay applied a force to the proximal interphalangeal
joint of the ﬁnger, fp .
Fig. 2 shows the tactile interface developed for theskin stimulus to the ﬁnger pad. The interface used anacrylic plate that was placed beneath the ﬁnger pad
and was driven by a DC motor (RE-10, Maxon motor,
Sachseln, Switzerland) to which a string was fastened.
The acrylic plate and the ﬁnger pad were bonded bya double-sided tape for preventing slippage. The ﬁnger
pad was ﬁxed in place by the antiskid sheath of theinterface, which precluded the force applied to the skinfrom being transferred to the ﬁnger joint. However, thisalso means that the reaction force was received by thenail part. The motor was torque-controlled using a motor
driver (ADS 50/5, Maxon motor) while compensating forthe preliminary identiﬁed gear friction.
Fig. 3 shows the interface for applying the proprioceptive force to the ﬁnger. By using a set of idlers andstring, the interface transferred the force to the fabricband twisted around the proximal interphalangeal jointof the ﬁnger. One of the idlers was linked to a spring
tensioner. The force was generated by a DC motor (RE280, Mabuchi Motor Co. Ltd., Japan) to which a string
was fastened. As well as the device for the ﬁnger pad,the torque of the motor was controlled by a motor
driver. The torque instruction was determined such thatthe preliminary identiﬁed friction caused by a gear andpulley mechanism was compensated for. The force ismainly perceived by the metacarpal phalangeal joint of
the ﬁnger and the wrist. It should be noted that when
the interface applied the force to the fabric band, a subtle
pressure stimulus was also applied to the lateral side of
the ﬁnger in contact with the fabric band. It is difﬁcult totransfer the force to the muscle and tendon without also
stimulating the skin unless we locally anesthetize a digit.
Such solutions were seen in some studies to test the roleof cutaneous sensations [23], [24], [25], [26]. For ethicalmatters to use anesthesia for non-medical purposes, weavoided this approach.
As shown in Fig. 4, participants wore both displays on
the right index ﬁnger with their forearms resting on anarmrest. Beneath the acrylic plate of the skin stimulator,
a low-friction linear slider was located so that the plate
beneath the ﬁnger pad could be moved without thefrictional constraint with the ﬂoor surface. Furthermore,
two load cells (Model 1004, Tedea-Huntleigh, Canada,
resolution: 1.0×10−4 N) measured the ﬁnger’s pressing
force along the Z-axis for controlling the experimental
conditions (see also sec. 3.1.2).

Encoder
Motor Fabric band

Encoder
Motor
Z

PulleyFingerZ

Acrylic String
X plateAntiskid
sheathY(i) Front view(ii) Side viewFig. 2. Interface for applying shear force to finger pad
X

Motor
Idler

Y

PulleyStringLinear slider

݂௣Fabric band
FingerFig. 3. Interface for applying proprioceptive force to finger

3.1.2 Task and participants
The experiment was conducted based on the methodof constant stimuli. First, the interface applied either
the reference or the test stimulus to the participants’ﬁnger for 2 s. Second, the other stimulus was appliedfor 2 s. Afterward, participants were asked to judge theforces with which the interfaces pulled the ﬁnger andanswer whether they perceived the force of the second

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Fig. 4. Experimental setup: Participant wearing skin andproprioceptive force displays
stimulus to be larger than that of the ﬁrst stimulus. They
were instructed to maintain a constant ﬁnger positionand pressing force at 1–2 N during each trial, andthey could see this force value displayed on a screen
before each trial. It is known that the impedance of
the ﬁnger pad varies with the pressing forces [27], [28].
They closed their eyes so as not to see their ﬁngers andaurally blocked the motor activation sound by listening
to pink noise through headphones. The participants (P1–
P8) were eight students recruited from Nagoya University. All of them were ignorant of the objective of theexperiment.
3.1.3 Stimuli
The skin sense display applied a shear force fs to the ﬁnger of the participant. Simultaneously, the proprioceptive
display applied force fp to the proximal interphalangeal
joint of the ﬁnger. The reference stimuli were (frs , frp )= (1.0 N, 1.0 N) and (0.3 N, 0.3 N). The following test
stimuli were presented.
Test stimuli for estimating PSE: The test stimuli for
1.0 N were (fts , ftp ) = (0.7 N, {0.7, 0.8, 0.9, 1.0, 1.1, 1.2,
1.3 N}) or (1.3 N, {0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3 N}). The
test stimuli for 0.3 N were (fts , ftp )=(0.2 N, {0.0, 0.1,
0.2, 0.3, 0.4, 0.5, 0.6 N}) or (0.4 N, {0.0, 0.1, 0.2, 0.3, 0.4,
0.5, 0.6 N}). We investigated the PSE of the reference
stimulus using these test stimuli.
Test stimuli for estimating DL: The test stimuli for
1.0 N were (fts , ftp ) = ({0.4, 0.6, 0.8, 1.2, 1.4, 1.6 N}, 1.0 N)or (fts , ftp ) = (1.0 N, {0.7, 0.8, 0.9, 1.1, 1.2, 1.3 N}). The
test stimuli for 0.3 N were (fts , ftp ) = ({0.0, 0.1, 0.2, 0.4,
0.5, 0.6 N}, 0.3 N) or (fts , ftp ) = (0.3 N, {0.0, 0.1, 0.2, 0.4,
0.5, 0.6 N}). The step size of the test stimuli was set sothat participants could easily distinguish the maximum
and the minimum stimuli from the reference stimuli. The
skin sensation has inferior discriminability around 1.0 N
compared to the proprioception. Hence, the step size for
fts was set to 0.2 N around 1.0 N.
The order of the test stimuli was determined bya pseudo-random generator in a single set consistingof 52 types of stimuli. Fourteen sets were conducted,
which means that each stimulus was presented 14 times

Fig. 5. Example data to obtain point of subjective equality
from a single participant (P7). Response rates and fitting
curves of “bigger” toward reference stimulus of (frs , frp )= (1.0 N, 1.0 N). Circles and triangles indicate response
rates of test stimuli at fs = 1.3 and fs = 0.7, and they are
fitted to solid and dashed curves, respectively.
through the experiment. Thus, in total, 728 (52 stimuli ×
14 repetition) trials were conducted for each individual.
Different orders were used for different participants.
The participants took a 5-min rest every 50 trials. The
entire procedure took 6–7 h per participant, including
the necessary explanations, practice, and documentation.
3.1.4 Fitting of normal distribution curve
The response variable was the proportion of responses
for which participants answered that the force of the test
stimulus was larger than that of the reference stimulus.
Using MLE ﬁtting [29], the response rates were ﬁtted
with a cumulative density function of the normal distribution. We deﬁned ftp or fts at which the rate of the
ﬁtted curve is 0.5 as the PSE. The 84% DL was deﬁned
as the difference of the forces between response rates of
0.84 and 0.50.
3.2 Results
3.2.1 Results of PSE-based approach
Fig. 5 shows the example data for 1.0 N from a single
participant (P7). For the test stimuli at fts = 0.7 and1.3 N, the PSEs were (fts , ftp ) = (0.7, 1.05) and (1.3,
0.88), respectively. The relative contribution ratios were
calculated using (2)–(5) for individuals. Table 1 showsΔfp , contribution ratios reported by the participants,
mean and standard deviation of these values, and χ2 forﬁtting. If these values had exceeded χ2 (0.95, 6) = 12.6,
the ﬁtting would not have been statistically valid. Δfp ,wp1 , and ws1 are the average values for the two PSEs
of fts = 0.7 N and fts = 1.3 N. The results for 1.0 N
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and 0.26±0.05 N, for the constant ftp and fts conditions,
respectively. These values were fairly close to the valueof the reference stimulus, i.e., 0.3 N.

4E XPERIMENT TO T EST VALIDITY OF DLBASED A PPROACH
When fˆs and fˆp are perceptually integrated following
the model described in sec. 2.2 with both cues being
taken into account by the observer and weighted in
an optimal fashion, the DL for the integrated skin andproprioceptive sensations is estimated byσ̂sp =σ̂s σ̂p.
σ̂s + σ̂p

(12)

The results of DL-based approaches can be experimentally validated by comparing the value of σ̂sp estimatedby (12) and that obtained directly from an experiment.
Fig. 6. Example data to obtain DL from a single participant (P7). Response rates and fitting curves of “bigger”
toward reference stimulus of (frs , frp ) = (1.0 N, 1.0 N).
Circles and triangles indicate response rates of test stimuli when fp and fs are variable, and they are fitted to solidand dashed curves, respectively.
two forces were 21% skin and 79% proprioception on
average. Similarly, Table 2 shows the results for 0.3 N.
Δfp , wp1 , and ws1 are the average values for the PSEs
of fts = 0.2 N and fts = 0.4 N. The results showed thatthe average contribution ratios were 46% skin and 54%
proprioception for the reference force of 0.3 N.
3.2.2 Results of DL-based approach
Fig. 6 shows the example data for 1.0 N from P7. When
ftp and fts of the test stimuli were variable values, the
84% DL values of this participant were 0.25 and 0.67 N
for proprioceptive and skin sensations, respectively. We
calculated the 84% DL for all participants, however, P3
was removed from the statistics owing to this large χ2
where the conﬁdence limit was χ2 (0.95, 5) = 11.1. We
then obtained the contribution ratios by using (10) and(11). Table 3 shows 84% DL, contribution ratios reportedby the participants, mean and standard deviation ofthese values, and χ2 for ﬁtting. The results showed thatthe average ratios of the weights used for combining thetwo forces were 23% skin and 77% proprioception. The
average PSEs of the reference stimuli were 1.01 ± 0.05 N
and 1.04 ± 0.11 N for the constant fts and ftp conditions,
respectively, and they indicated that the participants
were not signiﬁcantly biased.
We also calculated the 84% DL of skin and proprioceptive sensations for 0.3 N. For the same reason as
above, P1 was removed from the statistics. Table 4 shows
the statistic variables for individuals and their mean andstandard deviations. The results showed that the mean
weights were 51% skin and 49% proprioception. The
average PSEs of the reference stimuli were 0.27 ± 0.04 N

4.1 Stimuli and Task
We investigated the DL values for 1.0 N when the force
stimuli for the two sensations were consistently changed.
Five of the eight participants took part in this experiment
after participating in the experiments described in theprevious section. The other three participants could notparticipate in this experiment owing to the limitations
imposed by their work schedules. The employment ofanother group of participants might have led to morereliable conclusions, however, due to an economic reason, we asked the same participants to join this experiment. As in the previous tasks, they performed atask in which they compared the forces between thereference and the test stimuli. The reference stimulus
was (frs , frp ) = (1.0 N, 1.0 N), and the test stimuli were
fts = {0.7, 0.8, 0.9, 1.1, 1.2, 1.3} N, where ftp = fts .
These six types of stimuli were presented in a random
order with each one being repeated 10 times. In total,
60 trials were performed for individuals, and they tookapproximately 40–60 min.
4.2 Results
The results were analyzed as in the case of the previous experiments. All participants’ results were well
represented by cumulative Gaussian curves. The 84%
DL forces for integrated skin and proprioceptive sensations were 0.19, 0.17, 0.09, 0.16, and 0.21 N for theﬁve participants as summarized in Table 5. Their meanand standard deviations were 0.16 ± 0.04 N. The tablealso shows the DL values estimated by (12) from theseven participants. These values were calculated using
their σ̂p and σ̂s values, as listed in Table 3, that wereobtained through the experiments described in the previous section. The estimated and observed values are
consistent (t0 (10) = 0.14, p = 0.89, two-tailed unpaired
t-test, 1 − β = 0.99 with the possible effect of 0.1 N). This
indicates that the DL-based approach was potentiallyvalid for 1.0 N. Although we could not conduct the sameThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
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TABLE 1
Experimental results of PSE-based approach for 1.0 N. Δfp corresponding to change in forces applied to finger pad(Δfs = 0.30 N). Relative contribution ratios for skin (ws1 ) and proprioceptive sensations (wp1 ). χ2 of fitting to normal
cumulative density functions at fts = 1.3 N and fts = 0.7 N.
Participant
Δfp [N]
wp1
ws1
χ2 |fts =1.3
χ2 |fts =0.7

P1
0.08
0.79
0.21
6.57
10.3

P2
0.15
0.66
0.34
1.76
5.35

P3
0.03
0.90
0.10
1.26
1.99

P4
0.08
0.79
0.21
2.00
5.23

P5
0.09
0.77
0.23
3.93
2.77

P6
0.09
0.78
0.22
1.79
1.49

P7
0.09
0.78
0.22
0.46
4.17

P8
0.06
0.83
0.17
3.77
0.40

Ave. ± s.d.
0.08 ± 0.03
0.79 ± 0.07
0.21 ± 0.07-

TABLE 2
Experimental results of PSE-based approach for 0.3 N. χ2 at fts = 0.4 N and fts = 0.2 N. Δfp corresponding to Δfs
of 0.10 N.
Participant
Δfp [N]
wp1
ws1
χ2 |fts =0.4
χ2 |fts =0.2

P1
0.05
0.66
0.34
2.20
4.81

P2
0.16
0.39
0.61
0.25
2.22

P3
0.09
0.54
0.46
4.65
10.32

P4
0.09
0.52
0.48
2.34
0.71

P5
0.20
0.34
0.66
1.35
9.17

P6
0.06
0.64
0.36
1.92
0.93

P7
0.04
0.69
0.31
1.43
12.4

P8
0.08
0.55
0.45
4.89
3.14

Ave. ± s.d.
0.10 ± 0.05
0.54 ± 0.13
0.46 ± 0.13-

TABLE 3
Experimental results of DL-based approach for 1.0 N. χ2 and 84% DL (σ̂) for skin and proprioceptive sensations.
Participantsσ̂p [N]χ2pσ̂s [N]
χ2s
wp2
ws2

P1
0.27
1.51
0.69
1.97
0.72
0.28

P2
0.21
1.13
0.58
0.50
0.73
0.27

P3
0.18
0.52
16.0
-

P4
0.19
0.37
0.84
5.46
0.82
0.18

P5
0.26
2.87
0.59
0.20
0.69
0.31

P6
0.24
1.06
0.89
1.03
0.79
0.21

P7
0.25
0.49
0.67
0.94
0.73
0.27

P8
0.13
0.89
1.20
0.82
0.90
0.10

Ave. ± s.d.
0.22 ± 0.05
0.78 ± 0.22
0.77 ± 0.07
0.23 ± 0.07

TABLE 4
Experimental results of DL-based approach for 0.3 N.
Participantsσ̂p [N]χ2pσ̂s [N]
χ2s
wp2
ws2

P1
0.13
1.94
14.3
-

P2
0.17
4.57
0.19
0.28
0.53
0.47

P3
0.16
1.24
0.15
1.07
0.49
0.51

P4
0.20
0.84
0.18
4.00
0.47
0.53

P5
0.25
0.41
0.20
1.76
0.45
0.55

P6
0.16
4.13
0.17
0.75
0.52
0.48

P7
0.17
10.3
0.22
1.03
0.57
0.43

P8
0.23
0.55
0.16
3.27
0.41
0.59

Ave. ± s.d.
0.18 ± 0.04
0.18 ± 0.02
0.49 ± 0.05
0.51 ± 0.05

TABLE 5Integrated cues’ 84% DLs. Values estimated from the integration model and observed through experiments. χ2 offitting of the sampled data with normal cumulative density functions.
Participant
84%σ̂sp [N] (estimated)
84%σ̂sp [N] (observed)
χ2sp

P1
0.20
0.19
6.42

P2
0.16
0.17
1.13

P4
0.15
-

test for the reference force of 0.3 N, it seems that there isno speciﬁc reason to dispute the validity of the DL-based
approach for 0.3 N.

5G ENERAL D ISCUSSION

5.1 Review of DLs in related studies
The DL of skin sensations in this study is 2–7 times
larger than those in previous studies [3], [13], although
it was not directly comparable owing to differences in

P5
0.15
0.09
0.13

P6
0.16
0.16
2.32

P7
0.19
0.21
1.96

P8
0.11
-

Ave. ± s.d.
0.160 ± 0.03
0.163 ± 0.04-

conditions. In other words, the DL or contribution ratiosof sensory cues vary with tasks. The earlier studies dealt
with the weight perception of objects gripped by two
ﬁngers. In such cases, more skin cues are presumably
available for humans than in the one-ﬁnger conditionof the present study, whereas the wrist is commonly
involved for both one- and two-ﬁngered conditions.
Furthermore, during the grip, the normal force to theﬁnger pad varies with the shear force to it according to
the nature of automatic grip force adjustment [24], [30].

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Therefore, both the shear and the normal force cues applied to the ﬁngertip affected the skin sensations whereas
only the shear force was varied in the present study.
Under such conditions, the DLs of previous studies arenaturally lower than those of the present study becauseof the contributions of multiple cues [31].
The 84% DL of integrated cues in this study was
0.16 ± 0.04 N as reported in the previous section. Thisvalue corresponds to a 75% DL of 0.11 ± 0.02 N. Minamizawa et al. showed that the 75% DL for integratedskin and proprioceptive sensations under two-ﬁngered
grip was 9% for the standard stimulus of 1.0 N [13],which is close to our value of 11%. Furthermore, theWeber fraction of the perceived weight of a grasped
object is around 10% [2], which is also similar to ourvalue, although Giachritsis et al. reported a slightly
lower value of 6% [3]. As to the one-ﬁngered and active
touch condition, the Weber fraction of the friction coefﬁcients of smooth surfaces was reported to be 18% acrosswide range of friction coefﬁcients (0.2–1.0) [32]. This andour values are reasonably close despite the difference ofactive and passive touch. Interestingly, the discriminability of forces applied to the ﬁngertip worsens as the hand
movements become more active [33]. Overall, the DLs
estimated in the present study are likely to be consistent
with those reported in earlier studies when both skinand proprioceptive cues are available.

The values of these two approaches were in good agreement (t0 (13) = 0.97, p = 0.35, two-tailed unpaired t-test,
1 − β = 0.67 with the possible effect of 0.1). The data for
PSE- and DL-based approaches were based on eight andseven participants, respectively.

5.2 Contribution ratios of skin and proprioceptive
sensations

In this study, we investigated the relative contribution ratios of skin and proprioceptive sensations in the perception of forces of 1.0 N and 0.3 N applied to the ﬁngertip.
We calculated the ratios using PSE- and DL-based approaches. The results of these approaches showed good
agreement with each other. Moreover, the experimentaland literature-based inspection supported the validityof the results despite an imperfect experimental setup
in which the two sensations could not be completely
isolated. By superposing the 95% conﬁdence intervalof the contribution ratios from the two approaches, theratios are summarized as follows for the experiments
conducted in the present study. When humans perceivea force of 1.0 N, the relative contribution ratios of skinand proprioceptive sensations are 16–28% and 72–84%,
respectively. In contrast, when humans perceive a forceof 0.3 N, the respective ratios are 37–55% and 45–63%.
Because skin is more sensitive than proprioception forthe perception of relatively small forces applied to theﬁnger pad, the contribution of skin increases as theapplied force decreases.
Ideally, how these ratios vary with the applied forces
should be further determined, as we dealt with only
two force values. The roles of the two types of sensations can then be clariﬁed, and this should provide
design guidelines for haptic interfaces. Nonetheless, theﬁndings of this study are quite noteworthy. For haptic
interfaces with small force ranges, force feedback shouldbe imparted to the ﬁnger pads, whereas ﬁnger pads canalmost be neglected for large force ranges. For forces

5.2.1 Ratios for perception of 1.0 N
From the PSE-based approach, in the perception of aforce of 1.0 N to the human ﬁngertip, the means andstandard deviations of the contribution rates of the two
sensory channels were
ws1,1.0 : wp1,1.0 = 0.21 ± 0.07 : 0.79 ± 0.07.

(13)

From the DL-based approach, the contributions of thetwo sensory channels were
ws2,1.0 : wp2,1.0 = 0.23 ± 0.07 : 0.77 ± 0.07.

(14)

These contribution ratios of skin sensation showed nostatistically signiﬁcant difference between the two approaches (t0 (13) = 0.61, p = 0.60, two-tailed unpaired
t-test, 1 − β = 0.67 with the possible effect of 0.1). The
data for PSE- and DL-based approaches were based oneight and seven participants, respectively.
5.2.2 Ratios for perception of 0.3 N
From the PSE-based approach, in the perception of aforce of 0.3 N, the relative contribution ratios of skinand proprioceptive sensations were
ws1,0.3 : wp1,0.3 = 0.46 ± 0.13 : 0.54 ± 0.13.

(15)

From the DL-based approach, the contribution ratios
were
ws2,0.3 : wp2,0.3 = 0.51 ± 0.05 : 0.49 ± 0.05.

(16)

5.2.3 Contribution ratios estimated by two approaches
From the above analyses, the PSE and DL-based approaches show good agreement in terms of the estimatedcontribution ratios. Furthermore, the validity of the DLbased approach was conﬁrmed in that the DL calculated
from the model was not signiﬁcantly different fromthat measured by a post-hoc experiment. These facts
support the reliability of the experimental results despite
the partly insufﬁcient statistical powers of the abovedescribed analyses.
As a conservative estimation of the contribution ratios,
we calculated the 95% conﬁdence intervals from the results. For a 1.0 N force applied to a ﬁngertip, the intervalsof skin contribution ratios were 21% ± 5% and 23%± 5% for PSE and DL-based approaches, respectively.
Hence, the superposed intervals of the skin ratio become
16–28%. The proprioceptive sensation ratio becomes 72–
84%. Similarly, for a 0.3 N force, the skin ratios are 37–
55% and the proprioceptive ratios are 45-63%.

6

C ONCLUSION

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of around 0.3–1.0 N, both cues have to be considered.
For example, a weight of 200–300 g feels lighter when
proprioceptive cues are ﬁxed [12]. To prevent such underestimation, the force stimuli should be applied toboth cues. Otherwise, if force feedback to these two
types of sensations cannot be realized for some reasons,the remaining cue is adjusted such that the perceived
force would become equal to one with both cues intact,
considering the contribution ratios of the two sensory
channels.

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Kenya Matsui is a mechanical engineer who
received a M.S. degree in engineering from
Nagoya University, Japan in 2013. Currently, he
is a Ph.D. candidate of the Graduate School ofEngineering, Nagoya University. His study interests include human-computer interfaces.

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Shogo Okamoto received a B.S. degree inengineering from Kobe University in 2005, and
M.S. and Ph.D. degrees in information sciencesin 2007 and 2010, respectively, from the Graduate School of Information Sciences, Tohoku
University. Since 2010, he has been an assistantprofessor at the Graduate School of Engineering, Nagoya University. His research interests
include haptic interfaces and human-assistive
technology.

Yoji Yamada received a Ph.D. degree from theTokyo Institute of Technology, Japan, in 1990.
He has been an associate professor at the Toyota Technological Institute, Nagoya, Japan since1983. In 2004, he joined the National Instituteof Advanced Industrial and Science Technology (AIST), as a group leader of the Safety
Intelligence Research Group at the Intelligent
Systems Research Institute. In 2008, he moved
to the Graduate School of Engineering, Nagoya
University, as a professor.