A Data Adjustment Method of Low-priced
Data-glove Corresponding with each User Hand
Yutaro Mori

Kenji Funahashi

Nagoya Institute of Technology
Gokiso-cho, Showa-ku,
Nagoya, Japanemail: moriyu@center.nitech.ac.jp

Nagoya Institute of Technology
Gokiso-cho, Showa-ku,
Nagoya, Japanemail: kenji@nitech.ac.jp

Abstract—A data glove is one of the major interfaces which areused in the field of virtual reality. An expensive data glove witha lot of sensors can get detailed data about finger joint angles.
However it is too expensive to use in ordinary home. There is a
low-priced data glove, but it does not have enough sensors to get
detailed data. We have proposed the method to obtain all finger
joint angles from low-priced data glove by estimating the typesof hand motions from sensor values. In this method, we assume
some representative hand motions and consider that other handmotions can be represented as synthetic motion of them. Howeverparameters to calculate angles are gotten from pre-experiment
for specific user, and they are not appropriate for other users.
In this paper, we suggest the method to determine parameters
for each user hand automatically.

Fig. 1. 5 DT Data Glove 5 Ultra

I. INTRODUCTION
Virtual Reality (VR) is the rapidly growing research field inrecently years. VR technologies give us various merits. There
are simulators to practice an operation and fly a plane as
examples of VR technologies[1]. These simulators can enable
us to avoid the risk and save the cost. A data glove is one of
the major interfaces which are used in the field of VR. Until
today, various types of researches about data glove have been
conducted[2][3][4]. Data gloves measure curvatures of fingers
using bend sensor. A data glove with a lot of sensors canget detailed data about finger joint angles, and it enables toobtain finger joint angles accurately. However, this data glove
is too expensive to use in ordinary home. There is a lowpriced data glove but it can not get detailed data because it
does not have enough sensors. For example, the 5DT Data
Glove 5 Ultra and Essential Realty P5 Data Glove have asingle sensor on each finger, so they have five sensors in thewhole hand (Fig. 1, 2, 3). However there are three finger
joints for each finger, a single sensor can not measure all ofthese three angles directly. In our laboratory, we have proposeda data adjustment method of low-priced data gloves[5]. Thismethod enables to obtain all finger joint angles by estimating
the types of hand motions from a low-priced data glove. We
assume some representative hand motions, and consider that
other hand motions can be represented as synthetic motion ofthem. The pilot system was specified for specific user, andit could not be applied for any users. Even if another user
moves his/her hand same as the specific user, the sensor values
obtained from data glove are different from the specific user’s

Fig. 2. P5 Data Glove

Fig. 3. Finger and bend sensor

one. It means that the pilot system can not estimate any user’s
angles exactly, and we need to give calibrated parametersFig. 5. Example of correspondence

We derive the following numerical formulas using these
correspondence.
θpi1

Fig. 4. Representative hand motions

for estimation equations to each user. The parameters haveto be given through pre-experiment for each user, and it has
much trouble. In order to solve this problem, we focus on thesize of hand[6]. We assume that the differences of the sensor
values are caused mainly by hand size. We investigated thecorrespondence of hand size to difference of the sensor values
in advance. Also we propose a method to determine parametersfrom only user’s hand size.
II. ESTIMATION OF FINGER JOINT ANGLES
In this section, we describe a estimation method of finger
joint angles which have been proposed in our laboratory untilnow.
A. Representative Hand Motions
To estimate finger joint angles, this method limits user’s
hand motion to grasping motion. First of all, we choose several
representative hand motions from human’s grasping motion(Fig. 4)[7][8].
Furthermore, we assume that human’s grasping motion canbe represented as synthetic motion of them. To derive threefinger joint angles from a single sensor value, we use thefollowing method. We get the sensor values with the lowpriced data glove when doing each grasping motion. Also, we
get true angles of finger joints at that time. Provided that we
use true angles obtained from a data glove which has a lotof sensors. We use Immersion CyberTouch as data glove witha lot of sensors. Then, the sensor values and the true angles
of finger joints at the same time are associated. We show an
example of correspondence in Fig. 5.

θpi2
θpi3

2
θpi2
3
= Epi2 Si3 + Fpi2 Si2 + Gpi2 Si + Hpi2
= Epi3 Si3 + Fpi3 Si2 + Gpi3 Si + Hpi3
=

(1)
(2)
(3)

Where motion p is one of representative hand motions. Angles
θpi1 , θpi2 and θpi3 express the DIP, PIP, and MP joint angleof the finger i for the motion p. The DIP, PIP, and MP joint
mean the first, second and third joint of a finger respectively.
The Si is sensor value of finger i. And Epij , Fpij , Gpijand Hpij are constant parameters for the motion p, finger iand joint j. These parameters, Epij to Hpij , are calculated
by pre-experiment. Besides, DIP joint angle is obtained byproportional connection with PIP joint angle (eq. 1)[9]. Joint
angles of finger i of motion p are obtained by these numericalformulas.
B. Hand Motion Estimation and Angles Estimation
To represent user’s hand motion as synthetic motion ofrepresentative hand motions, we need to know how similaruser’s hand motion to which representative hand motions[10].
Then, we set the following formula based on the probability
density function of the multivariate normal distribution for npoints in the five dimensional feature amount space.
1
Lpn = exp{− (S − µpn )T Σ −1
pn (S − µpn )}2(4)

Where S is the sensor value vectors. And µpn and Σ pn
represent mean vector of sensor sample values, variancecovariance matrix of point n (an integer satisfying 1≤n≤25)
in representative hand motion p. Besides, µpn and Σ pn are
obtained by pre-experiment for specific user. If the sensor
values are obtained actually from the glove, we select the
maximum value according to the following formula.
Lp = max{Lpn (S : µpn , Σ pn )}n(5)TABLE I
Hsize OF EACH PARTICIPANT [cm]participant 1
participant 2
participant 3
sample person
average of Japanese male[11]average of Japanese female[11]

Hsize
17.0
18.1
20.5
17.7
18.3
16.9

standard deviation
0.8
0.7

TABLE IIJ OINT ANGLE ERROR OF GRASPING PLASTIC BOTTLE [ DEGREE ]sampleparticipant 1
participant 2
participant 3

Fig. 6. Definition of hand size

Thus, we get the likelihood on representative hand motion p
in current sensor values. After that, we decide the ratio rp ofhand motion p according to the following formula.
rp =

Lp
P
Σp=1 Lp(6)

Where P is the total number of representative hand motions.
As stated above, we can obtain θpij and rp . At last, θij isderived by following formula.
θij =

P
∑

rp ·θpij(7)

p=1

III. DIFFERENCE OF HAND SHAPE
In the method stated in previous section, parameters areneeded to be precomposed for each user. However, using an
expensive glove to obtain the true angles of finger joints is
not suitable from perspective of utilization in ordinary home.
Furthermore, parameters to calculate angles are obtained bya lot of trials of hand motions. They are troublesome forgeneral user. In this section, we try to determine the parameters
automatically for motion and angles estimation.
A. Estimation Accuracy between Different Users
We investigated estimation accuracy between different
users. With the cooperation of three research participants,
we had an experiment. In this experiment we asked eachparticipant to grasp a plastic bottle (500ml) with equipped data
glove. The reason to choose this grasping motion was user’s
hand motion is little by little different every time even if user
thinks that he/she performs the same hand motion. And we
defined the hand size of user as Hsize , which is decided by the
distance from the wrist to the top of the middle finger (Fig. 6).
The Hsize of each participant is shown in Table I. The sample
person is who provided each parameter for estimation in preexperiment. And the parameters for estimation were obtainedby the sample person’s hand. When each participant grasped
the plastic bottle, their finger joint angles were estimated bythese parameters of sample person. We measured finger joint

Thumb
7.6
31.1
15.3
30.2

Index
17.9
17.7
17.7
10.5

Middle
11.2
26.4
11.6
27.2

Ring
16.2
5.0
11.7
17.7

Little
14.8
5.1
5.0
17.7

avg.
13.6
17.1
12.3
20.7

angles when their hand was touching completely with theplastic bottle. And we investigated the average of the errors
between estimated finger joint angles and obtained angles by
CyberTouch. Table II shows the results. These results indicatethat estimation accuracy using parameters of the person whose
hand size is different becomes worse. We expected that joint
angle errors of the sample person was minimum because
sample person’s parameters were used for estimation. However
the average error of participant 2 was minimum in Table II.
We concluded that the reason was the sensor values were
not uniform but also scattering when user moved one’s hand.
However, only because of these numerical values, the results
can not be judged whether they are significant or not. Then
we had statistical hypothesis testing to confirm these results
are significant. At this time, we adopted Student’s t-test. We
had Student’s t-test to the average of joint angle errors of
the sample person and other participants. Test statistic t0 is
obtained from the following formula.
t0 = √|X̄ − Ȳ |(8)1
Ue ( m+ n1 )

Where X̄ and Ȳ are the average of joint angle errors, m andn represent the sample size of two groups. And Ue is obtained
from the following formula.
(m − 1)Ux + (n − 1)Uy
(9)
m+n−2
Where Ux and Uy are unbiased variance. As stated above, test
statistic t0 can be obtained and t0 follows t distribution. Pvalues obtained from Student’s t-test are shown in Table III.
The P (T ≤t) represent significance probability. In this paper,
we decide that significance level α is 0.05. So it is statisticalsignificance if P (T ≤t) is smaller than 0.05. Looking at
Table III, the P (T ≤t) in all categories are smaller than
0.05. They indicate that there are statistical significance inestimation accuracy between the sample person and other participants. We confirmed necessity of determining parameters
for each user.
Ue =TABLE IV
E XAMPLE OF SENSOR VALUE FOR MOTION p AT THE TIME t

TABLE IIIP- VALUES OF STUDENT ’ S T- TEST

participant 1
participant 2
participant 3

P (T ≤t)
6.8 × 10−6
1.0 × 10−2
9.6 × 10−4

trial
1
2
3
..
.
n

Thumb
s11
s12
s13
..
.
s1n

Index
s21
s22
s23
..
.
s2n

Middle
s31
s32
s33
..
.
s3n

Ring
s41
s42
s43
..
.
s4n

Little
s51
s52
s53
..
.
s5n

Of course the parameters EApij to HApij and EBpij to HBpij
for hA and hB participants are calculated previously using
expensive data glove (parameters for another participant arealso calculated). Then numerical formula for estimation of
finger joint angles of the user is decided as following.
θupij = Eupij Si3 + Fupij Si2 + Gupij Si + Hupij(15)

Also, we decide the µupn according to the following formula.
(hu − hB )µApn + (hA − hu )µBpn(16)hA − hB
Where µupn , µApn , and µBpn represent vector of sensor
sample values of user, A, and B. The µupn is used when usingeq. 4. Using a weighted average of hand size, each parameterfor estimation can be determined.
µupn =

Fig. 7. Relation between Hsize and Stotal

B. Hand Size Estimation
We assume that parameters to calculate finger joint angles
are determined by knowledge of user’s Hsize . To evaluateuser’s Hsize , we try to use the sensor values when user
performs one hand motion. When deciding hand motion for
estimation of hand size, it is important that a hand motion
is simple. If it is obscurity motion, there is difficulty inperforming hand motion. Then, we consider the total valueof five sensors when user closes hand (=Stotal ). We obtained
Stotal and each Hsize from each research participant. The
correspondence between Hsize and Stotal is shown in Fig. 7.
Then we conclude the following formula.
Hsize = aStotal + b(10)Where a, b are constant parameters. Using this formula,user’s Hsize can be obtained by performing the simple handmotion.
C. Determination of Estimation Parameters
We would like to determine the estimation parameters of
new user whose Hsize is hu . The size hu is obtained by eq. 10.
If two of the three participants are A and B, each hand size
is hA and hB respectively (hA > hB ), the parameters for hu
user are defined as below.
Eupij

=

Fupij

=

Gupij

=

Hupij

=

(hu − hB )EApij + (hA − hu )EBpij
hA − hB(hu − hB )FApij + (hA − hu )FBpij
hA − hB(hu − hB )GApij + (hA − hu )GBpij
hA − hB(hu − hB )HApij + (hA − hu )HBpij
hA − hB

(11)
(12)
(13)
(14)

D. Equivalency of Variance-Covariance Matrix
When using eq. 4 to estimate hand motion, it is difficult
to calculate the all parameters Σ −1
pn directly for each user.
So we investigated equivalency of variance-covariance matrix
between different users by using Box’s M Test. First of all,we got the sensor values when each participant performed
representative hand motions. Each representative hand motion
is performed n times. Table IV shows an example of the sensor
values at the time t in motion p. Next, the average of the sensor
values si for finger i is obtained by the following formula.
n
1∑
si =
sij
(17)
n j=1
At this time, covariance of finger x and y, represented as Vxy ,is obtained by eq. 18. And variance-covariance matrix V isdefined as eq. 19.
n
1∑
Vxy =
(sxk − sx )(syk − sy )
(18)
n
k=1


V11 V12 . . . V15
 V21 V22 . . . V25 
V =  .
(19)
..
.. 
.
.
.
 .
.
.
. 
V51 V52 . . . V55
Then we decide V 0 according to the following natural logarithm (eq. 20).
V0

=

ν1
ν2

=
=

|V AB |ν1 +ν2|V A |ν1 |V B |ν2nA − 1nB − 1

ln

(20)
(21)
(22)

TABLE V
χ20 OF EACH RESEARCH PARTICIPANT

Standard
Lateral Contact
TripodParallel Ext

participant 1, 2
22.44
29.34
31.60
33.69

participant 2, 3
28.64
36.22
35.51
35.54

pariticpant 1, 3
28.84
20.87
29.89
32.41

Where V A and V B represent mean variance-covariance matrix of participant A and B. The number of times n ofparticipant A is different from B generally, each number
is defined as nA and nB respectively. In this paper, eachparticipant performs hand motion 10 times. And V AB is thematrix obtained from the following formula.
V AB =

ν1 V A + ν2 V B
ν1 + ν2(23)

Also, we decide k according to the following formula.
k

= 1−(

1
1
1
2q 2 + 3q − 1
+
−
)·
ν1
ν2
ν1 + ν2
6(q + 1)

(24)

Where q represents the number of explanatory variables.
Now q is number of Thumb, Index, Middle, Ring, and Little
finger, 5. Finally, we obtain test statistic χ20 from the following
formula.
χ20 = kV 0

Fig. 8. Appearance of experiment
TABLE VI
E STIMATED Hsize OF PARTICIPANTS [cm](25)

The χ20 follows chi-squared distribution. We describe the χ20 ofeach motion/user in Table V. We decide significance level α
as 0.001. The χ2 (α = 0.001) is 37.70. So if the χ20 is smaller
than 37.70, there is not significantly different in variancecovariance matrix. As Table V indicates, the χ20 is smaller
than 37.70 in all categories. We confirmed that there isnot significantly different with regard to variance-covariancematrix. Thus we use the average matrix in variance-covariancematrix of all participants as Σ pn . Finally we can obtain thefinger joint angles of new user.

Participant 4
Participant 5

True Hsize
17.6
19.1

Estimated Hsize
18.0
19.9

Error
0.4
0.8

TABLE VIIJ OINT ANGLE ERROR OF PARTICIPANT 4 IN SYSTEM A [ DEGREE ]Standard
Lateral Contact
TripodParallel Ext
Plastic bottle

Thumb
8.8
10.8
18.6
10.4
15.2

Index
11.2
13.1
10.6
13.4
10.7

Middle
11.1
13.6
13.5
8.8
15.3

Ring
11.5
15.1
11.5
9.0
20.2

Little
10.1
7.3
17.5
10.3
9.9

avg.
10.5
12.0
14.4
10.4
14.3

IV. EXPERIMENTAL RESULT
We had an experiment to confirm the effectiveness of themethod described above.

finger joint angles (Fig. 8). With the cooperation of two
research participants 4 and 5, several hand motions were
performed.

A. Experiment Environment
We had constructed two experiment systems, system A andsystem B.
1) System A: The system A estimates user’s finger joint angles
using same parameters for all users. These parameters wereobtained by the hand of participant 2 because his hand size ismostly the same as average Japanese male’s one.
2) System B: The system B estimates user’s finger joint angles
using parameters obtained by the user’s own hand. User closes
hand first, then each parameter is determined using Hsize .
Both systems were used with the 5DT Data Glove 5 Ultra.
They were implemented with C language, and the specificationof PC is the following; CPU: Pentium (R) Dual-Core CPU
E5200 2.50GHz. They draw CG image based on the obtained

B. Estimation Results
Table VI shows estimated Hsize of two participants. An
estimation error of participant 4 is 0.37, and the error ofparticipant 5 is 0.79. The method can estimate user’s Hsize
almost correctly. We confirmed the effectiveness of the Hsize
estimation method described in section III-B.
Table VII to X show the average of the errors of the finger
joint angles between estimated finger joint angles and obtained
angles by CyberTouch. Besides, “Plastic bottle” represents thehand motion as same as in section III-A.
These results indicate that the estimation accuracy of thesystem B is better than the system A. We had Student’s t-test
to these averages of the errors of each finger joint angles.

TABLE VIIIJ OINT ANGLE ERROR OF PARTICIPANT 4 IN SYSTEM B [ DEGREE ]size estimation is needed.
V. CONCLUSION

Standard
Lateral Contact
TripodParallel Ext
Plastic bottle

Thumb
6.5
12.0
18.3
13.8
15.8

Index
6.3
11.7
7.5
11.4
3.6

Middle
3.6
11.4
12.7
9.6
14.0

Ring
15.0
11.4
8.4
9.2
14.2

Little
18.4
8.7
15.8
9.8
8.9

avg.
10.0
11.0
12.5
10.8
11.3

TABLE IXJ OINT ANGLE ERROR OF PARTICIPANT 5 IN SYSTEM A [ DEGREE ]Standard
Lateral Contact
TripodParallel Ext
Plastic bottle

Thumb
12.3
11.5
10.2
24.0
23.2

Index
12.8
21.5
8.2
9.2
13.6

Middle
12.7
16.4
12.8
4.3
16.2

Ring
14.2
21.2
22.9
7.6
31.0

Little
13.8
19.2
17.6
13.6
20.8

avg.
13.2
18.0
14.3
11.7
21.0

TABLE XJ OINT ANGLE ERROR OF PARTICIPANT 5 IN SYSTEM B [ DEGREE ]Standard
Lateral Contact
TripodParallel Ext
Plastic bottle

Thumb
13.1
9.3
9.4
13.0
26.1

Index
8.5
14.1
7.7
8.8
10.3

Middle
6.9
13.1
18.8
16.0
20.8

Ring
8.8
11.4
19.0
10.8
13.4

Little
12.5
16.8
17.5
13.5
11.0

avg.
10.0
12.9
14.5
12.4
16.3

TABLE XI
D IFFERENCE BETWEEN SYSTEM A AND B OF PARTICIPANT 4

Standard
Lateral Contact
TripodParallel Ext
Plastic bottle
averageparticipant 4
difference
P (T ≤t)-0.6
3.3 × 10−2
-1.0
2.7 × 10−2
-1.8
3.9 × 10−2
+0.4
1.6 × 10−1
-3.0
6.7 × 10−3
-1.2-

TABLE XIID IFFERENCE BETWEEN SYSTEM A AND B OF PARTICIPANT 5

Standard
Lateral Contact
TripodParallel Ext
Plastic bottle
averageparticipant 5
difference
P (T ≤t)-3.2
3.4 × 10−2
-5.0
1.7 × 10−2
+0.2
4.0 × 10−2
+0.7
8.1 × 10−1
-4.6
1.0 × 10−2
-2.4-

Table XI and XII show the differences of the estimation
accuracy between the system A and B, and p-values obtained
from Student’s t-test. It is statistical significance if the P (T ≤t)
is smaller than 0.05. They show that there is statisticalsignificance about the hand motion of which estimation accuracy were improved. There is not statistical significance about
Parallel Ext, but the estimation accuracy was not improved.
Totally the system B is better than the system A, it means
calibrated parameters for each user is effectiveness, and hand

In this paper, we proposed a method of hand size estimationand parameters calibration for finger joint angles estimationof low-priced data glove. The pilot system had been specified
for specific user, and it could not been applied for any users.
Our new system obtains user’s hand size only from simple
and easy task first, and parameters of estimation equations
can be obtained automatically. Then a low-priced data glove
can recognize the user hand motion, actually all finger joint
angles. When a data glove becomes commercial popular,
and VR applications will become commercial popular. VR
technologies can provide extra work space.
The information about a hand is not only length from wrist
to middle finger tip, however. In the future we would like to try
to consider more detailed information of hand, for example,
length of each finger, thickness, size of palm, and so on. We
should also examine the effect for the angles estimation. And
our system assumes grasping motion, so we would like toconsider other hand motions like hand and finger signs.
ACKNOWLEDGMENT
We thank our colleagues in our laboratory for useful discussions. This work was supported in part by JSPS KAKENHI
Grant Number 24501186.
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