Method to Use Low-priced Data-glove Effectively
Based on Medical Knowledge for Hand Motion Pattern

Kenji Funahashi
Department of Computer Science
Nagoya Institute of Technology
Nagoya 466–8555 Japan
Email: kenji@nitech.ac.jp

Yutaro Mori1

Hiromasa Takahashi2

Yuji Iwahori

Nagoya Institute of Technology
Department of Computer Science(1 present: NEC Solution Innovators, Ltd.)
Chubu University(2 present: Chubu Electric Power Co.,Inc.)
Kasugai, Aichi 487-8501 Japan
1
Email: moriyu@center.nitech.ac.jp Email: iwahori@cs.chubu.ac.jp
2
Email: hiromasa@center.nitech.ac.jp

Abstract—A data glove is one of the major interfaces used in thefield of virtual reality. In order to get detailed data about thefinger joint angles, we must use a data glove with many sensors.
However, a data glove with many sensors is expensive and a lowpriced data glove does not have enough sensors to capture all thehand data correctly. We propose a method to obtain all finger
joint angles by estimating the pattern of hand motion from thelow-priced data glove sensor values. In our experiment system, we
assumed some representative hand motion patterns as grasping
behavior based on medical knowledge. We also assumed that
other hand motions can be represented by synthetic motion of
the representative patterns. In this paper, we used the data glove
with sensors covering two joints of each finger. And we also
estimate the finger joint angles when using the data glove that
sensors cover only the middle angle of each finger.

Figure 1. 5DT Data Glove 5 Ultra

Keywords–Data-glove; Hand motion estimation; Finger joint
angles estimation; Medical knowledge.

I.

I NTRODUCTION

Virtual Reality (VR) is a rapidly growing research fieldin recent years. VR technologies give us various advantages.
There are simulators to practice an operation and to fly a plane
as examples of VR technologies. These simulators enable us to
avoid the risk and to save on cost. VR researches that targets
to households also have been attracted. A data glove is oneof the major interfaces, which are used in the field of VR.
It measures curvatures of fingers using bend sensors. In ourlaboratory, we propose a method to get plausible user handmotion pattern from the low-cost glove [1]. In our first work,
we use 5DT Data Glove (see Figure 1) whose sensors cover
two joints of each finger. Then, we estimate finger joint angles
when using the data glove DG5 VHand (see Figure 2) whose
sensors cover only the middle angle of each finger.
The rest of the paper is structured as follows. In Section
II, we present a state of the art of data gloves. In Section
III, we describe a method how to estimate finger joint angels.
In Section IV, we describe about representative hand motion
patterns based on medical knowledge. In Section V, we apply
this method to the data-glove whose sensor positons arelimited. In Section VI, the experimental results are shown. In
Section VII, we consider the difference between users’ handshapes. In Section VIII, the experimental results for hand shapeare shown. Finally, we conclude in Section IX.

Figure 2. DG5 VHand

II. S TATE OF THE A RT
In order to obtain accurate hand motions, it is necessary to
use a data glove, i.e. Immersion CyberGlove, which has many
sensors, but it is expensive. It is preferable that an interface issmall scale and low cost. Various types of researches about data
glove have been conducted [2][3][4][5]. On the other hand,
there is a low cost data glove, which measures an angle foreach finger through one sensor. But it cannot get detailed data
directly. For example, the 5DT Data Glove 5 Ultra and DG5VHand have a single sensor on each finger, so they have fivesensors in the whole hand (see Figures 1 and 2). However,there are three finger joints for each finger, a single sensor can
not measure all of these three angles directly.
Our proposed novel method estimates the kind of handmotion patterns using each relation among angles of fingers

-(/#5/#"#'2-%.#(5-6#/'(p!"""!"""!"""###"""!"""###$$(((=("#'"&/(.-43#(((78(!"""!"""!"""""""""!""""$(((>((S(!S1, S2, ... S5) $$4&"#!"""!"""!"""""""""!""""$
97(-'04#"(((((>($(((((((&1((:&;'2"(θpij((((>(%"""""""""""""""""%$(((>(!"#$%&'())*+,!
$&5#'(µpn, Σpn(((((977 !"""!"""!"""""""""!""$(((>($3//#'2("#'"&/($(((.((((((.-43#(S!"""!"""!"""###"""!"""###$$?-'@(A&%&'(!/-%&,(

Epij, Fpij,
Gpij, Hpij

Figure 3. Overview of method-.#/-0#(&1(2/3#(-'04#!

$3//#'2(-'04#"<(#-$?("#2(&1("-A54#!

!"#$%"#&"#$"#'#()%*+#&,%(-&./*/(&$%0#"('&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!"#$%"%*/(&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&1'#2*/(&33456&&
7#28-#&$%"%.#)#"'&)/&2%92:9%)#&;(<#"&=/8()&%(<9#'&&&&&>/"&#%2,&"#$"#'#()%*+#&,%(-&./*/(&$%0#"(!
&&3($:)&7%)%&?9/+#&@#('/"&+%9:#'!
&&A'*.%)#&),#&,%(-&./*/(B&&&&"%*/&>/"&"#$"#'#()%*+#&,%(-&./*/(&$%0#"('&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!"/2#''&8(&"#%9&*.#&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&1'#2*/(&334C6&
D%92:9%)#&&&%99&%(<9#'&&&&&:'8(<&),#&$%"%.#)#"'&/>&$%0#"('&%(-&),#&"%*/&!

Figure 4. Detail of method

during operation. Then, it estimates all finger joint angles by
estimating the types of hand motion patterns from the correlation between each finger angle in the hand motion pattern.
We assume some representative hand motion patterns based on
medical knowledge [6], and consider that other hand motions
can be represented as a synthetic motion of the representative
hand motion patterns. In addition, we calculate the ratio of each
representative motion pattern. Moreover, estimating each finger
angle using the result, we express any hand motion patterns
other than the representative hand motions.
III.

E STIMATION OF F INGER J OINT A NGLESIn Section III, we describe an estimation method of finger
joint angles using 5DT data glove, which is developed in ourlaboratory (see Figure 3).
A. Representative Hand Motion Patterns
To estimate finger joint angles, this method limits user’s
hand motion to grasping motion. First of all, we had set thethree representative hand motions as grip, pinch and nip.
Furthermore, we assume that a human’s grasping motion
can be represented as a synthetic motion of representative
hand motion patterns. To derive three finger joint angles froma single sensor value, we use the following method (seeFigure 4). We sample many sets of the sensor values with the
low-priced data glove when some subjects open their hand first
and then close it to each representative hand motion patterns.
Also, we sample the sets of the true angles of finger joints
for the same representative patterns, provided that we use true
angles obtained from a data glove, which has a lot of sensors.
We use Immersion CyberGlove as data glove with a 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 Figure 5.
We derive the following numerical formulas using thiscorrespondence.
θpi1
θpi2
θpi3

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

=

(1)
(2)
(3)

where pattern p is one of representative hand motion patterns.
Angles θpi1 , θpi2 and θpi3 express the DIP, PIP, and MP joint
angle of the finger i for the pattern p. The DIP, PIP, andMP joint mean the first, second and third joint of a finger
respectively. The Si is sensor value of finger i. And Epij , Fpij ,Gpij and Hpij are constant parameters for the pattern p, finger
i and joint j. These parameters, Epij to Hpij , are calculated
by pre-experiment. Besides, DIP joint angle is obtained byproportional connection with PIP joint angle (equation (1)) [7].
Joint angles of finger i of pattern p are obtained by thesenumerical formulas.
B. Hand Motion Estimation and Angles Estimation
To represent user’s hand motion as synthetic motion ofrepresentative hand motion patterns, we need to know how
similar the user’s hand motion is and to which representative
hand motion patterns. Then, we set the following formulabased on the probability density function of the multivariate
normal distribution for n points in the five dimensional feature
amount space.
1
Lpn = exp{− (S − µpn )T Σ −1
(4)
pn (S − µpn )}2where S is the sensor value vector. And µpn and Σ pn
represent mean vector of sensor sample values, and variancecovariance matrix of sample point n (an integer satisfying
1≤n≤a number of samples) in representative hand motion pattern p. Besides, µpn and Σ pn are obtained by pre-experiment
for an average user. If the sensor values are obtained actually

Figure 5. Example of correspondence
Figure 7. Example of MP and PIP Joint Angle of Index Finger!"#$%#&%

5**67,(6-8$%-0./0";#"-&#,.1*$"#2"'&()*%+#&#,,-,./0"'().1*$"#2"+9#&#$:-#, /0"+#&#,,-,.4,-0

1(&23,#&.4,-0

Figure 6. Candidates of representative motions

Figure 8. Dendrogram of the Candidata 1

from the glove, we select the maximum value according to thefollowing formula.
Lp = max{Lpn (S : µpn , Σ pn )}n(5)Thus, we get the likelihood on representative hand motion
pattern p in current sensor values. After that, we decide theratio rp of hand motion pattern p according to the following
formula.
rp =LpPΣp=1 Lp(6)

where P is the total number of representative hand motions,which takes the value of four. As stated above, we can obtainθpij and rp . At last, each angle θij of current hand posture isderived by the following formula.
θij =

P
∑
p=1

rp ·θpij(7)

Figure 9. Average Hand Motions (left: MC2 , right: MC3 )TABLE I. JOINT ANGLE ERROR (INPUT: REPRESENTATIVE ONE)[DEGREE]

Candidate 1
Candidate 2
Candidate 3

thumb
8.3
5.9
7.2

index
5.7
2.5
4.2

middle
3.9
3.2
3.2

ring
3.4
4.9
4.5

little
6.5
3.0
4.2

average
5.6
3.9
4.7

TABLE II. JOINT ANGLE ERROR (INPUT: EXCEPT REPRESENTATIVEONE) [DEGREE]

Candidate 1
Candidate 2
Candidate 3

thumb
8.5
9.4
8.2

index
9.4
9.6
8.7

middle
9.1
9.6
8.7

ring
6.5
6.5
7.4

little
18.5
17.55
12.22

average
10.4
10.5
9.0

we can remove the redundant computation. So, we sampled
the sensor values for the candidate 1 and standardize them(mean 0 and variance 1). Then we performed hierarchicalcluster analysis for them using the ward method to createa dendrogram about the candidate 1 (Figure 8). The handmotions were classified into 4 classes based on the cutting
point 2.5 as a middle distance. The classes are defined asfollowing; C1 : Standard, C2 : Hook-like, Lateral Contact, Index
Ext, C3 : Tripod, Tip Contact, and C4 : Parallel Ext. Thereby
Standard, Lateral Contact, Tripod and Parallel Ext were selected as candidate No.2 according to the score. Furthermore
we constructed average hand motions MC2 and MC3 forthe classes C2 and C3 respectively (Figure 9), and obtained
candidate No.3.

Figure 10. Representative hand motion patterns

IV. R ECONSIDER R EPRESENTATIVE H AND M OTIONSIn Section IV, we reconsider the representative hand motion
patterns based on medical knowledge.
A. Candidate Selection
We reconsider them through the research on the grasping
behavior of human hand [8]. They had observed daily grasping
forms in experimental condition and classified them into 14
types to help reference in clinical. We select 10 candidates
as representative hand motion from these 14 types, because
they change enough sensor values of a data-glove respectively(Figure 6). And we obtained the transitions of each finger
joint angle of the 10 motions from open hand to each form
using data-glove, which has many sensor (CyberGlove). It wasalso confirmed that Parallel Flex and Circular Flex can be
represented in a part of Standard (Figure 7), and Phalangeal
Ext can be represented in a part of Lateral Contact. Therefore,
we selected 7 motions as representative ones of candidate No.1.
B. Candidate Reduction
If one of the representative hand motions is similar toanother one, it may not occur good estimation. If the number ofthe motions of candidate 1 can be reduced with enough result,

C. Confirmation Experiment
We had experiment for the three candidates using the
5DT Data Glove 5 Ultra, which has a bend sensor for eachfinger. When the input data are the representative motionsin this experiment, the averages of estimated ratio rp are;candidate 1: 0.83, candidate 2: 0.86, and candidate 3: 0.95. We
can also confirm the average of candidate 3 is higher than the
average 0.92 of conventional system with first representative
hand motions as grip, pinch and nip. Table I shows the averageof the errors of DIP, PIP and MP between estimated finger joint
angles and obtained angles by CyberGlove. The input data is
Tripod motion for candidate 1 and 2, and MC2 for candidate 3.
Table II shows the error when the input motion data is not
representative one for each candidate, that is, the input data is
MC2 motion for candidate 1 and 2, and Tripod for candidate 3.
We confirmed that the error of candidate 3 is smallest for the
average of both results, and it can deal with any hand motions
other than the representative ones. Therefore, we found thatcandidate No.3 is the most suitable for representative handmotions, and candidate No.2 is the second suitable one.
V.

DATA - GLOVE WHOSE S ENSOR P OSITIONS ARE
L IMITED
In Section V, we describe an estimation method of finger
joint angles using DG5 data glove whose sensor positions arelimited only to PIP joints.
A. MP Angle for Representative Hand Motion Pattern
Although we mentioned above a set of representative handmotion patterns is selected as candidate No.3, the pattern Par-

allel Ext is almost the motion related only to MP joints. When
doing the Parallel Ext pattern, the sensor values hardly change.
We tentatively use three other patterns as representative handmotion patterns except Parallel Ext from the candidate No.2
(Figure 10) for now.
For the 5DT data glove whose sensors cover PIP and MP
joints, the DIP angle is related to PIP directly, as mentioned in
the Section III. It means the sensor values contain all of theirinformation. However, using DG5 whose sensors are only on
PIP, the motion of MP does not change the sensor value. Of
course, we assume that the hand motion is a grasping one, so
the MP angle of a finger is related to the PIP angle of thesame finger. Then we can assume that the MP of a finger isrelated to the PIPs of all fingers.
We consider a new estimation model to obtain angles forrepresentative hand motion patterns using multiple regression
analysis. First, we make a estimation equation with explanatory
variable is a set of sensor values, and response variable is each
MP joint angle, as follows.
θpi3 =

5∑

Cpif 3 Sf + Ipi3

(8)

f =1

where θpi3 is MP joint angle of finger i of representative
pattern p, Sf is sensor value of finger f , and Cpif 3 and Ipi3
are constant.
Now, a subject opens his hand first and then closes it
to each representative pattern with DG5 data glove, the setof sensor value Sf (time) of finger f at time is sampled.
Then, the subject moves his hand as each same pattern with
CyberGlove, which has many sensors, the set of angle value
θpi3 (time) is sampled as true one.
Here, we should get the constant Cpif 3 and Ipi3 . The
residual sum of squares Q is represented as in (9).


2
5

∑
∑
Q=
θpi3 (time) − 
Cpif 3 Sf (time) + Ipi3  (9)


time

f =1

Focusing on coefficient Cpi13 where f = 1;

∑ (
)2
Q=
S1 (time)Cpi13

time


5
∑
+ 2S1 (time)Cpi13 Cpif 3 Sf (time) + Ipi3 
f =2− 2θpi3 (time)S1 (time)Cpi13

2
5
∑
+
Cpif 3 Sf (time) + Ipi3 
f =2

− 2θpi3 (time) 

5
∑
f =2


(
)2 
+ θpi3 (time)Using the partial differentiations with Cpi13 ;

5
∑
∑
∂Q
=2
S1 (time)
Cpif 3 Sf (time)∂Cpi13
time
f =1


+Ipi3 − θpi3 (time)(11)

Using the partial differentiations also with Cpif 3 and Ipi3 ;

5
∑
∑
∂Q
Cpif 0 3 Sf 0 (time)=2
Sf (time)
 0∂Cpif 3
time
f =1

(12)

+Ipi3 − θpi3 (time)


5
∑
∑
∂Q
=2
Ipi3 +
Cpif 3 Sf (time)

∂Ipi3
time
f =1


−θpi3 (time)(13)

The constant Cpif 3 and Ipi3 to be obtained make Q represented
as the minimum of the equation from (9). And the Cpif 3 andIpi3 that make Q minimum satisfy following equation.
∂Q
∂Q
=
=0
∂Cpif 3
∂Ipi3

(14)

Solving this, coefficient Cpif 3 and constant Ipi3 are obtained
to estimate MP joint angle for representative pattern with (8).
The angles of PIP are obtained directly from the sensor value
with (2), and the angles of DIP are also obtained only from
PIP with (1).
B. Hand Motion Estimation with Pseudo-Inverse Matrix
When the variance of sensor values is zero at the sample
point n of representative hand motion pattern, the variancecovariance matrix will be abnormal at the sample point n.
It means the inverse matrix of variance-covariance matrix of
sensor values Σ−1
pn can not be obtained, and the likelihood forthe sample data of representative pattern p can not be obtainedwith (4).
So, we use Moore-Penrose pseudo-inverse matrix to solve
it. The variance-covariance 5 × 5 matrix of sensor values Σ−1pn ,which is abnormal at the sample point n is represented as next
equation with 5 × r matrix Apn and r × 5 matrix B pn where
rank (Σpn ) = r;

(10)Σpn = Apn B pn

(15)

Here the Moore-Penrose pseudo-inverse matrix Σ+
pn for ΣpnCpif 3 Sf (time) + Ipi3 

is described as:

(
)−1
T
T
T
Σ+
=
B
A
Σ
B
ATpn
pn
pn
pn pn pn
(
)−1 (
)−1
= B Tpn B pn B Tpn
ATpn Apn
ATpn

(16)

Using this Moore-Penrose pseudo-inverse matrix Σ+
pn for (4)instead of the inverse matrix of variance-covariance matrix of

(1) Power grasp(2) Precision grasp(3) Lateral grasp

Figure 12. Result CG for Power grasp(4) Extension grasp(6) Index pointing(5) Tripod grasp

Figure 13. Result CG for Precision grasp(7) Basic gestures

Figure 11. Hand motions needed for ADL

sensor values Σ−1
pn at the sample point n where inverse matrix
can not be defined, the likelihood is obtained and the ratioof each hand motion pattern is determined with (5) and (6),respectively. Now, we can use a low-priced data glove whose
sensors cover only the middle angle of each finger to estimate
all finger joint angles of current hand posture with (7).
VI.

E XPERIMENT AND R ESULTWe performed an experiment to confirm the effectivenessof the method described above. The experiment system wasconstructed using the DG5 Data Glove whose sensor positions
are limited only on middle joints. Other hand motions thatwere different from representative patterns were tested. The
minimum of Activities of Daily Living (ADL) needs thefollowing hand motions (see Figure 11) [9].
1)
2)
3)
4)
5)
6)
7)

Power grasps (used in 35% ADLs)
Precision grasps (30% ADLs)
Lateral grasps (20% ADLs)
Extension grasps (10% ADLs),
Tripod grasps,
Index pointing, andBasic gestures.

We tested five motions; 1)–5).

The subjects opened their hands and then closed them toeach test pattern 1)–5) with DG5 data glove. The average of
estimated joint angles were compared with the true angles
obtained from CyberGlove, which had many bend sensors.
Table III shows the average error of finger joint angles.
Each error is around 10 degrees. The result using the 5DT data
glove whose sensors cover two joints of each finger also had
about 10 degrees error [6]. This means that the lower-priced
data glove can obtain joint angles accurately enough.
Actual hand posture images and the CG images generated
from estimated joint angles are shown in Figures 12 and 13.
The MP joints that were not covered with bend sensors are
estimated from the sensors on PIP joints.
VII. D IFFERENCE OF H AND S HAPE
In the method stated in previous sections, parameters areneeded to be precomposed for each user. However, using an

TABLE III. ERROR OF FINGER JOINT ANGLES [DEGREE]

Power G.
Precision G.
Lateral G.
Extension G.
Tripod G.
average

thumb
7.3
8.1
9.4
9.8
8.5
8.6

index
12.0
9.2
6.0
8.1
8.5
8.7

middle
10.5
7.2
8.8
11.0
7.2
8.9

ring
12.5
7.0
7.5
11.3
11.6
10.0

little
10.0
6.8
10.5
9.0
10.9
9.4

average
10.5
7.7
8.4
9.9
9.3
9.2

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 each participant to grasp a plastic bottle (500ml) with equipped data glove.
The reason to choose this grasping motion was user’s handmotion is little by little different every time even if user thinksthat one performs the same hand motion. And we defined thehand size of user as Hsize , which is decided by the distancefrom the wrist to the top of the middle finger (Figure 14). The
Hsize of each participant is shown in Table IV. 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
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
CyberClove. Table V 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 V.
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.
|X̄ − Ȳ |t0 = √
1
Ue ( m+ n1 )TABLE IV. Hsize OF EACH PARTICIPANT [cm]participant 1
participant 2
participant 3
sample person
average of Japanese male [10]average of Japanese female [10]

Hsize
17.0
18.1
20.5
17.7
18.3
16.9

standard deviation
0.8
0.7

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 Figure 15.
Then we conclude the following formula.
Hsize = aStotal + b(17)where X̄ and Ȳ are the average of joint angle errors, m and n
represent the sample size of two groups. And Ue is obtained
from the following formula.
(m − 1)Ux + (n − 1)Uy
Ue =
m+n−2

Figure 14. Definition of hand size

(18)

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 VI.
The P (T ≤t) represents 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 VI, the P (T ≤t) in all categories are smaller than 0.05.
They indicate that there are statistical significance in estimation
accuracy between the sample person and other participants. We
confirmed necessity of determining parameters for each user.

(19)

where a, b are constant parameters. Using this formula,user’s Hsize can be obtained by performing the simple handmotion.

TABLE V. JOINT ANGLE ERROR OF GRASPING PLASTIC BOTTLE[DEGREE]

sampleparticipant 1
participant 2
participant 3

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

TABLE VI. P-VALUES OF STUDENT’S T-TESTP (T ≤t)participant 1
participant 2
participant 3

6.8 × 10−6
1.0 × 10−2
9.6 × 10−4

avg.
13.6
17.1
12.3
20.7

TABLE VII. EXAMPLE OF SENSOR VALUE FOR MOTION p AT THE
TIME t
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

the sensor values si for finger i is obtained by the following
formula.
1∑
sij
n j=1
n

si =
Figure 15. Relation between Hsize and Stotal

At this time, covariance of finger x and y, represented as
Vxy , is obtained by (27). And variance-covariance matrix V
is defined as (28).

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 (19).
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

V

(21)

1∑
(sxk − sx )(syk − sy )
n
k=1


V11 V12 . . . V15
 V21 V22 . . . V25 
= 
..
.. 
..
 ...
.
.
. 
n

Vxy

(20)

=

V51

V0
(23)

(24)

ν1
ν2

where µupn , µApn , and µBpn represent vector of sensor sample values of user, A, and B. The µupn is used when using (4).
Using a weighted average of hand size, each parameter for
estimation can be determined.
D. Equivalency of Variance-Covariance Matrix
When using (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 VII shows an example of thesensor values at the time t in motion p. Next, the average of

(28)

V55

ln

(29)
(30)
(31)

where V A and V B represent mean variance-covariance matrixof participant A and B. The number of times n of participant
A is different from B generally, each number is defined as nA
and nB respectively. In this paper, each participant performs
hand motion 10 times. And V AB is the matrix obtained fromthe following formula.
V AB =(25)...

|V AB |ν1 +ν2|V A |ν1 |V B |ν2= nA − 1= nB − 1=

Also, we decide the µupn according to the following formula.
(hu − hB )µApn + (hA − hu )µBpnµupn =hA − hB

V52(27)

Then we decide V 0 according to the following natural logarithm (29).

(22)

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 follows.
θupij = Eupij Si3 + Fupij Si2 + Gupij Si + Hupij(26)

ν1 V A + ν2 V B
ν1 + ν2(32)

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)(33)

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

(34)

The χ20 follows chi-squared distribution. We describe the χ20
of each motion/user in Table VIII. We decide significancelevel α as 0.001. The χ2 (α = 0.001) is 37.70. So, if theχ20 is smaller than 37.70, there is not significantly different invariance-covariance matripants as Σ pn . Finally we can obtainthe finger joint angles of new user.

TABLE VIII. 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

TABLE X. JOINT 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

TABLE IX. ESTIMATED Hsize OF PARTICIPANTS [cm]Participant 4
Participant 5

True Hsize
17.6
19.1

Estimated Hsize
18.0
19.9

Error
0.4
0.8

VIII. E XPERIMENT AND R ESULT FOR H AND S HAPE
We had an experiment to confirm the effectiveness of themethod for hand shape.
A. Experiment Environment
We used 5DT data glove with representative hand motion
set No.2 for two experiment systems, system A and system B.
And two research participants 4 and 5 performed several handmotions.
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 .
B. Estimation Results
Table IX 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 VII-B.
Tables X to XIII show the average of the errors of the finger
joint angles between estimated finger joint angles and obtained
angles by CyberGlove. Besides, “Plastic bottle” represents thehand motion as same as in Section VII-A.
These results indicate that the estimation accuracy of thesystem B is better than the system A. We had Student’s ttest to these averages of the errors of each finger joint angles.
Tables XIV and XV 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 statistical significance 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 handsize estimation is needed.
IX. C ONCLUSION
In this paper, we described a useful method using a lowpriced data-glove based on hand motion patterns. It estimates
all finger joint angles using the data glove that sensors cover
two joints of each finger, and also only the middle angle

TABLE XI. JOINT ANGLE ERROR OF PARTICIPANT 4 IN SYSTEM B[DEGREE]

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

of each finger. A data glove is one of the major interfaces,
which are used in the field of VR. It measures curvaturesof fingers using bend sensor. However, in order to obtainaccurate hand motions, it is necessary to use an expensive
data glove, which has many sensors. On the other hand,
there is a low cost data glove, which measures an angle foreach finger through one sensor. It cannot get detailed data
directly. Our method estimates plausible user hand motion
patterns using each relation among angles of fingers during
the operation of the low-cost glove first. Then, it estimates
all finger joint angles by estimating the types of hand motion
patterns from the correlation between each finger angle in thehand motion pattern. We assumed some representative handmotion patterns, and considered that other hand motions could
be represented as synthetic motion of these. In the method
for the glove whose sensors cover only the middle angle, theratio of each representative motion pattern is calculated using
Moore-Penrose pseudo-inverse matrix, and all finger angles are
estimated using multiple regression analysis. The difference
between users’ hand shape was considered and confirmed
using the glove whose sensors cover two joint angles. With
the low priced data-glove being useful, it is expected thatVR systems that target households will become more popular.
In the future, we should reconsider the representative handmotion patterns because we removed Parallel Ext from our

TABLE XII. JOINT 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 XIII. JOINT 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 XIV. DIFFERENCE 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 XV. DIFFERENCE 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-

first research based on medical knowledge. We should also
expand the target hand motion patterns to various ones thatare not only grasping patterns.
ACKNOWLEDGMENT
The authors would like to thank our colleagues in ourlaboratory for useful discussions.
R EFERENCES[1] K. Funahashi, Y. Mori, H. Takahashi, and Y. Iwahori, “A Data Adjustment Method of Low-priced Data-glove based on Hand Motion Pattern,”in Proceedings of the PATTERNS 2017 (ComputationWorld), 2017, pp.
97–102.
[2] P. Temoche, E. Ramirez, and O. Rodrigues., “A Low-cost Data Glovefor Virtual Reality,” in Proceedings of the XI International Congress of
Numerical Methods in Engineering and Applied Sciences (CIMENICS),
2012, pp. TCG31–36.
[3] F. Camastra and D. Felice, “LVQ-based Hand Gesture Recognition usinga Data Glove,” in Proceedings of the Neural Nets and Surroundings Smart
Innovation, Systems and Technologies, vol. 19, 2013, pp. 159–168.
[4] N. Tongrod, T. Kerdcharoen, N. Watthanawisuth, and A. Tuantranont,“A Low-Cost Data-Glove for Human Computer Interaction Based on
Ink-Jet Printed Sensors and ZigBee Networks,” in Proceedings of theInternational Symposium on Wearable Computers (ISWC), 2010, pp. 1–
2.
[5] Y. Mori, K. Kawashima, Y. Yoshida, and K. Funahashi, “A Study for
Vision Based Data Glove with Back Image of Hand,” in Proceedings ofthe ICAT2015, 2015, (USB Flash Drive, no page number).
[6] H. Takahashi and K. Funahashi, “A Data Adjustment Method of Lowpriced Data-glove based on Representative Hand Motion Using Medical
Knowledge,” in Proceedings of the ICAT2013, 2013, (USB Flash Drive,no page number).
[7] G. Elkoura, “Handrix: Animating the Human hand,” in Proceedings of
the ACM SIGGRAPH/Eurographics Symposium on Computer Animation,
2003, pp. 110–119.
[8] N. Kamakura, H. Matsuo, M. Ishii, and Y. Mitsuboshi, F. Miura, “Patternsof Static Prehension in Normal Hands,” Am J Occup Ther 34, pp. 437–
445, 1980.
[9] C. Capriani, “Objectives, criteria and methods for the design of theSmartHand transradial prosthesis,” in Proceedings of the Robotica 2010,
vol. 28, 2010, pp. 919–927.
[10] M. Kawauchi, “AIST Measurements Hand Data of Japanese,” in
https://www.dh.aist.go.jp/database/hand/ 2012. (in Japanese, last access:5/Nov/2017)