Proceedings of the 2005 IEEE
International Conference on Robotics and Automation
Barcelona, Spain, April 2005

An Encounter-Type Multi-Fingered Master Hand
Using Circuitous Joints
Shuhei Nakagawara, Hiroyuki Kajimoto,
Naoki Kawakami, and Susumu Tachi

Ichiro Kawabuchi

Graduate School of Information Science and Technology
The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan{nkgwr, kaji, kawakami, tachi}@star.t.u-tokyo.ac.jp
Abstract – We have developed a new type of master handto control a dexterous slave robot hand for telexistence. Our
master hand has two features. One is a compact exoskeleton
mechanism called “circuitous joint,” which covers wide
workspace of an operator’s finger. Another is the encountertype force feedback that enables unconstrained motion of theoperator’s finger and natural contact sensation. In this paper,the mechanism and control method of our master hand are
introduced and experimental master-slave finger control isconducted.
Index Terms – Master hand, Encounter-type haptic device,
Force feedback, Telexistence

I. INTRODUCTION
Recently some dexterous robot hands have beendeveloped. To control these hands (slave hands), an
operator must wear master hands. The master hands can bedivided into two categories. One is exoskeleton type such as
CyberGrasp [1]. However, most conventional exoskeleton
type master hands tend to be bulky and require an operator
wearing a glove to measure the state of an operator’s finger.
The other is endoskeleton type such as Rutgers Master II[2]. Although it is light-weight and compact and does notneed a glove, it does not allow complete fist closure, due tothe placement of the actuators in the palm.
We have developed a new type of master hand (Fig. 1)
to improve these disadvantages. Our master hand has two
features as follows.

TechExperts Incorporation
4-15-5 Omori Nishi, Ota-ku, Tokyo, Japanichiro_kawabuchi@post.pioneer.co.jp
One is the compact exoskeleton mechanism of themaster hand’s finger contrived to cover wide workspace ofan operator. Possible ways to place an exoskeleton
mechanism are to place it over (parallel joint) or beside(coaxial joint) an operator’s finger. To place it over theoperator’s finger, there is a problem that master finger
disturbs the motion of the operator’s finger when the finger
is bent as shown in Fig. 2. However, to place it beside anoperator’s finger is difficult, because there is little space toplace it. To solve this problem, we propose “circuitous
joint” that coincides joint axis of the master hand with thatof the operator by extending the link length in proportion to
the joint angular displacement (Fig. 3).

Fig. 2 Parallel joint disturbing operator’s motion when finger is bent

Fig. 3 Basic scheme of the circuitous joint

The other is the encounter-type force feedback.
Encounter-type haptic device was first proposed by
McNeely [3], and Tachi [4] proposed a similar idea
independently. Encounter-type device stays at the locationof the object in the remote world and waits for an operator
to encounter it. As shown in Fig. 4, our encounter-type
master hand’s finger usually follows the operator’s finger
without contact. It enables him to touch nothing when theslave hand contacts nothing. When slave hand touches anobject, master finger contacts the operator’s finger andprovides resistive force. Therefore, our master hand is able
to provide both perfect unconstrained motion and natural
touch sensation.

Fig. 1 Appearance of the master hand

0-7803-8914-X/05/$20.00 ©2005 IEEE.

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In this paper, we introduce our encounter-type force
feedback multi-fingered master hand. Section II details themechanism including “circuitous joint” of the master hand.
Section III describes encounter-type force feedback and thecontrol of the master hand. Experimental master-slave
control using our master hand is given in section IV.

shown in Fig. 6, we placed the rack on the upper side of thesector gear to enlarge the distance between the master handmechanism and an operator. In order to keep the reverse
gears in line with the rack and the sector gear, sliders areused (Fig. 7).

Fig. 6 The circuitous joint with upper side racks and reverse gears

Fig. 4 Concept of the encountered-type force feedback master hand

II. MECHANISM OF THE MASTER HAND
A. Circuitous Joint
The principle of the circuitous joint is shown in Fig. 5.
In order to extend the length of the link in proportion to
joint angular displacement, the mechanism that consists ofrack and sector gear is adopted from the viewpoint of thesimplicity of structure, the certainty of movement, and highrigidity. A sector gear rotates on a rack by relative rotationof two links, and movement of the gear center axis produces
flexible movement of the link with the rack. Since two links
have to make extension stroke together, two sets of a rackand a sector gear are used in the reverse direction.

Fig. 7 The circuitous joint mechanism with sliders

Our master finger consists of three circuitous joints inseries corresponding to human finger’s three joints (DIP,
PIP, MCP joint). The length of the finger is different fromeach other, so the length of the link is adjustable bychanging the position of connecting screws. Additionally, inorder to make the width short, a part of each link overlaps
alternately (Fig. 8). The width of the master finger is about
19[mm] which is the same as human. As shown in Fig. 9,
the length of the master finger in flexion becomes up to
about twice as long as it in extension.

Fig. 5 Disassembled view of the circuitous joint

To coincide the rotation axis of the master finger andthat of the operator in all rotation angles, the relation
between the rotation angular displacement and the extension
stroke of the link must be nonlinear. This means that therectilinear rack and the sector gear whose radius is constant
are not appropriate. However, it is possible to keep the error
to acceptable range. We obtained the radius that minimizes
the maximum value of the error between ideal position andreal one of fingertip position. Meanwhile, we contrived to
avoid the friction of the master finger and an operator. As

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Fig. 8 Adjustable serial connection of three joint units

TABLE I
Approximate maximum velocity and acceleration of the master finger
DIP

Maximum joint angular velocity[rad/s]Maximum joint angular acceleration[rad/s 2 ]Fig. 9 Bending motion of the practical mechanism with three joints

Maximum fingertip velocity [m/s]2

B. Driving Method
Driving motors must not be near the joints because
mechanism gets larger and heavier. Therefore, we used wire
mechanism as shown in Fig. 10. A wire is set between two
links via a pulley on the sector gear’s center axis, and a
motor pulls the wire to the extensional direction. Since thewire cannot produce a force in an opposite direction, acompression spring is used to produce a force in the
direction of flexion (Fig. 11).

Maximum fingertip acceleration [m/s ]Extension

Flexion

4.5

5.0

PIP

6.8

7.5

MCP

4.5

5.0

DIP

1500

1500

PIP

2300

2300

MCP

1500

1500

0.85

0.95

300

350

Fig. 12 Coupled driving method of the master finger
with pulling all ropes by one drum

Fig. 10 Driving method by pulling a wire rope

C. Sensing for Encounter-Type Force Feedback
For encounter-type force feedback, the distance
between tip of the master finger and that of the operator andthe force between them must be measured. As shown in Fig.
13, we set a photo reflector (Sanyo Electric Co., Ltd., SPI315-34), a reflecting plate (thin stainless plate with hinge
and spring), and a thin force sensor (Nitta Corporation,
FlexiForce) at the tip of the master finger.

Fig. 11 Built-in compression spring

As each joint is driven by one rope, three wires are used for
one finger which are driven by one motor (FaulHaber
GmbH&Co., 1724SR). Three circuitous joints are coupledand each rate of rotation is decided by the radius of thedrum (Fig. 12). The maximum resistive force applied isabout 8[N]. The approximate maximum velocity andacceleration of master fingertip are shown in Table I. Froma preliminary experiment the maximum velocity andacceleration of human fingertip are appropriately 1.0 [m/s]and 300 [m/s 2 ] respectively. Our master hand has enoughability to follow operator’s normal motion without contact.

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Fig. 13 Sensors put on the tip of master finger

III. CONTROL OF THE MASTER HAND
A. The Model to Calculate the TorqueFirst, we derived the relation between rope tension andjoint torque of a circuitous joint. Parameters were defined asshown in Fig. 14.

When some circuitous joints are connected in series
like our master hand, the sum of all rope tensions works as
the joint torque. Thus, the rope tension of the root joint thathas to generate a great force is divided into some ropes. In
the case of our master hand, as shown in Fig. 15, three ropes
are used. The relation between joint torque and three ropes
tension at the jth joint isτj =3∑ F (2r + r ) ( j = 1,2,3) .
m

j

p

(7)

m= j

Next, given the joint angular displacements θ1 , θ 2 , θ3
and contact force FT acted on T (at the tip of the finger),the rope tension is derived as follows. The relation between
jth joint torque and contact force is expressed asτ j = J j T × FT ( j = 1,2,3) . (8)⎛ j : Joint number⎞⎜⎟⎜θ j : Joint angular displacement⎟⎜ s : Joint stretching displacement⎟j⎜⎟⎜ rj : Radius of pitch circle of the sector gear
⎟
⎜
⎟
r
:
Radiusoftheropepulley⎜ p⎟⎜ k1 j : Spring constant of the compression spring 1⎟⎜⎟⎜ k2 j : Spring constant of the compression spring 2⎟⎜τ : Joint torque⎟j⎜⎟⎜ F j : Rope tension⎟⎜ w : Rope stretch⎟j⎜⎟⎜ Fs1 j : Spring force of the compression spring 1⎟⎜⎟:
Springforce
ofthecompressionspring1
F⎜ s2 j⎟⎜ Fs '1 j : Spring force of the compression spring 1 when θ j = 0 ⎟⎜⎟⎜ Fs '2j : Spring force of the compression spring 2 when θ j = 0 ⎟⎝⎠where J jT is a vector from joint J i to T.
By substituting (8) to (7), (7) is⎧( F + F + F )(2r + r ) = J T × F ,
1
2
3
1
p
1
T
⎪⎪
⎨( F2 + F3 )(2r2 + r p ) = J 2 T × FT ,⎪⎪⎩ F3 (2r3 + r p ) = J 3T × FT .

From (9), rope extension isFig. 14 Relation between rope tension and joint torque at a circuitous joint

The relation between rope stretch and joint angulardisplacement is
s j = rj ⋅ θ j , (1)w j = 2s j + rp ⋅ θ j .

(9)

(2)

When motor angular displacement changes from θ j to 0,
the work done by rope stretch is F j ⋅ w j , the work done by⎧
J T × FT J 2 T × FT J 3T × FT
⎪ F1 = 1−−,
2 r1 + r p
2 r2 + r p
2 r3 + r p⎪⎪
J 2 T × FT J 2 T × FT⎪−,
⎨ F2 =
2 r2 + r p
2 r2 + r p⎪⎪
J T × FT
⎪ F3 = 3.
2 r3 + r p
⎪⎩

(10)

Additionally, from (4), rope stretch is⎧w1 = (2r1 + r p )θ 1 ,⎪⎨w 2 = (2r1 + r p )θ 1 + (2r2 + r p )θ 2 ,⎪w = (2r + r )θ + (2r + r )θ + (2r + r )θ .
1
p 1
2
p
2
3
p
3
⎩ 3

(11)

joint torque is τ j ⋅ θ j , and the energy displacement ofcompression spring 1, 2 areFs '1 j ⋅s j − k1 j ⋅ s j 2 / 2

and2

Fs '2 j ⋅s j − k2 j ⋅ s j / 2 . Therefore, the relation between ropetension and joint torque is derived by the law ofconservation of energy as follows,
Fj ⋅ wj = τ j ⋅θ j + (Fs '1 j ⋅s j − k1 j ⋅ s j 2 / 2) + (Fs '2 j ⋅s j − k2 j ⋅ s j 2 / 2) . (3)From (1), (2) and (3), rope tension is
w j = (2rj + rp )θ j , (4)Fj =τj
2r j + r p+( Fs '1 j + Fs ' 2 j )r j
2r j + r p+( k1 j + k 2 j ) r j 2
2(2r j + r p )

θj.

(5)

The second and third term in the right-hand side of (5) is theeffect of the compression spring, so if we treat it withdisregard, (5) is written as
F j = τ j /(2rj + rp ) . (6)Equation (6) indicates that the relation between rope tension
and joint torque is linear, and joint angular displacement has
no effect. That is, the driving method using wire rope hasan advantage that the control of joint torque is easy. We
omit the effect of the compression spring hereafter for
simple expression of equation.

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Fig. 15 Force equilibrium on the master finger mechanism

As mentioned above, our master finger is driven with three
coupled joints whose ratio (constant) isθ1 : θ 2 : θ3 = 1 : u : v . (12)We assume the following three conditions; (i) no
friction of master hand mechanism, (ii) contact force acted
on T intersects perpendicularly with the direction of the link
length, (iii) point of application of the contact force isconsidered to be “Virtual T” in Fig. 16.
Then from (12), (11) is⎧w1 = (2r1 + r p )θ 1 ,⎪⎨w2 = (2r1 + r p ) + (2r2 + r p )u θ1 ,⎪ w = ( 2 r + r ) + ( 2r + r ) + ( 2r + r )v θ .
1
p
2
p
3
p
1
⎩ 3

(
(

)

the operator’s fingertip and its tip when the slave hand does
not contact an object, which is a simple position control.
When slave hand touches an object, master finger iscontrolled to produce a force that is equal to the force
applied on the slave finger (force control). At the same time,
the slave finger is always controlled to take the same
position as that of the master finger (position control). Thisbilateral control is so-called force-reflecting servo type. In
Fig. 17, X is position, F is force, d is the distance
between tip of the master finger and that of the operator,
measured by an optical sensor, and d d is its desired value.
Each suffix m, s represents master and slave respectively.

(13)

)

⎛ t : Offset between the master finger and an operator' s finger ⎞⎜⎟⎜ a j : Length of the link⎟
⎜ b : Center of mass of the link⎟j⎜⎟
⎜ m j : weight of the link⎟⎝⎠
Fig. 16 Specifications of the master finger mechanism

Since the radius of each drum is proportional to the rope
stretch given in (13), torque to rotate the drum is⎛ (2r1 +rp) +(2r2 +rp)u (2r1 +rp) +(2r2 +rp)u+(2r3 +rp)v ⎞F2 +τD =⎜F1 +F3⎟rD (14)⎜⎟
2r1 +rp2r1 +rp⎝⎠⎛ rD : Radius of the drum which reels the shotest rope ⎞⎟.
⎜⎟⎜τ D : Torque to rotate the drum⎟⎜θ : Rotation angular displacement of the drum⎠
⎝ D

Additionally, each vector is⎧⎛−sin(θ1 +uθ1 + vθ1)⎞⎟⎟,⎪FT = FT ⎜⎜⎝ cos(θ1 +uθ1 + vθ1) ⎠⎪⎪⎛cos(θ1 +uθ1)⎞⎛cosθ1 ⎞⎟⎟⎟⎟ +(a2 + r2 ⋅ uθ1 + r3 ⋅ vθ1)⎜⎜⎪J1T = (a1 + r1 ⋅θ1 + r2 ⋅ uθ1)⎜⎜⎝ sin(θ1 +uθ1) ⎠⎝ sinθ1 ⎠⎪⎪⎪⎛cos(θ1 +uθ1 + vθ1)⎞⎟⎟,+(a3 + r3 ⋅ vθ1)⎜⎜⎨⎝ sin(θ1 +uθ1 + vθ1) ⎠⎪⎪⎛cos(θ1 +uθ1 + vθ1)⎞⎛cos(θ1 +uθ1)⎞⎟⎟,⎟⎟ +(a3 + r3 ⋅ vθ1)⎜⎜⎪J2T = (a2 + r2 ⋅uθ1 + r3 ⋅ vθ1)⎜⎜⎝ sin(θ1 +uθ1 + vθ1) ⎠⎝ sin(θ1 +uθ1) ⎠⎪⎪⎛cos(θ1 +uθ1 + vθ1)⎞⎟⎟.
⎪J3T = (a3 + r3 ⋅ vθ1)⎜⎜⎪⎩⎝ sin(θ1 +uθ1 + vθ1) ⎠Fig. 17 Block diagram of control

IV. EXPERIMENT
A. Confirmation of the Model of the Master Hand
To confirm the control model of the master handmentioned in III-A, a control experiment is conducted. In
III-A, we disregarded the effect of compression springs andmass of the links above, but in fact we cannot ignore it.
When we regard the mass of the link, (8) isτ j = J jT × FT +=w3

( 2r1 + rP ) + (2r2 + rp )u + (2r3 + rP )v
rD rg θ m

( 2r1 + rP ) + (2r2 + rp )u + (2r3 + rP )v

j m

m

(17)

m= j

(15)
In (15), θ1 is decided from (13), motor angulardisplacement θ m and reduction gear ratio rg as
θ1 =3∑(J m × m G) ( j = 1,2,3) .

(16)r
G is the gravity direction. Considering the effect ofcompression springs and mass of links, using (5), (13), and(17), the relation between motor torque and resistive force iswritten as.

Finally, by substituting (10) and (15) to (14), the relation
between joint angular displacement θ1 , fingertip load FT ,and torque τ D is obtained.
B. Control Method
As shown in Fig.14, for encounter-type force feedback,the master finger is controlled to keep the distance between

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{

rD ⎡
J1T × FT + J1m1 × m1G + J1m2 × m2G + J1m3 × m3G
2r1 + rp ⎢⎣1⎫+ (Fs11'+Fs21')r1 − (k11 + k21)r12θ1⎬
2
⎭
1
⎧
⎫
+ u⎨J2T × FT + J2m2 × m2G + J2m3 × m3G + (Fs12'+Fs22')r2 − (k12 + k22)r22θ2 ⎬
2
⎩
⎭
1
⎧
2 ⎫⎤
+ v⎨J3T × FT + J3m3 × m3G + (Fs13'+Fs23')r3 − (k13 + k23)r3 θ3⎬⎥ .
2
⎩
⎭⎦

τD =

(18)

We compared motor torque generated by PID control andtheoretical one calculated by (18). The theoretical motor
torque is calculated by the following parameters,⎛ a1 = 0.050[m], a 2 = 0.0030[m], a 3 = 0.015[m],⎜⎜ r1 = 0.0063[m], r2 = 0.0072[m], r3 = 0.0063[m],⎜ r = 0.00225[m], r = 0.00325[m],D⎜ P⎜ t = 0.012[m],⎜⎜ m1 = 0.050[kg], m 2 = 0.030[kg], m3 = 0.020[kg],⎜ b1 = 0.020[m], b2 = 0.015[m], b3 = 0.010[m],⎜⎜ u = 1.5, v = 1.0, g r = 63 / 2300,⎜ k = 800[ N/m], k = k = k = k = k = 400[ N/m],
21
12
22
13
23
⎜⎜ 11
=
=
=
=
=
F
'
5
[
N
],
F
'
F
'
F
'
F
'
Fs ' 23 = 3[ N].
s
11
s
21
s
12
s
22
s
13
⎝

confirmed its accuracy by an experiment. Additionally, we
examined the precision of the encounter-type force feedbackby experimental master-slave control.
Index finger, middle finger, fourth finger, and fifth
finger can be controlled by the method mentioned above.
However, thumb of human hand has very complicatedstructure and our next step is to realize the non-contact
motion following of thumb.

The result is shown in Fig. 18. The vertical axis is motor
angular displacement and the horizontal axis is the ratio of motor
torque to contact force between the operator and master finger. An
obvious accordance of real and theoretical value can be
seen.

Fig. 18 Relation between real value and theoretical one

B. Experimental Master-Slave Control
Using our master hand and a slave hand [5],experimental master-slave control is conducted. The
extension and flexion motion of three joints of this slave
hand’s finger is coupled like our master hand. Therefore, weonly have to control the motor’s rotation angle of the slave
finger in accordance with that of the master finger. We used
only one finger because four fingers except thumb arecontrolled in the same way. In the first period (0~5seconds), slave finger is not in contact with an object, and in
the latter half (5~13 seconds), slave finger touches theobject.
Results are shown in Fig. 19. As shown in Fig. 19 (top),
the slave finger can follow the motion of the master finger.
As shown in Fig. 19 (middle), when the slave finger doesn’t
contact an object, the master finger mechanism can keep a
distance from an operator’s finger. As shown in Fig. 19(bottom), when the slave finger contacts the object, masterfinger can produce as much resistive force as the slave
finger’s.
V. CONCLUSION AND FUTURE WORKIn this paper, we introduced an encounter-type multifingered master hand focusing on its two features. One is its
compact exoskeleton mechanism called circuitous joint,
which can cover wide workspace of the operator. The otheris the encounter-type force feedback which enables anoperator to feel real free and real touch sensations. We
derived a torque calculation model of the master hand and

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Fig. 19 Motor’s rotation angle (top), distance between operator’s andmaster’s fingertip (middle), and contact force (bottom) of the master andslave.

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Mechatronics, Vol. 7, No. 2, pp. 256-263, 2002.
[3] W.A.McNeely: “Robotic Graphics, “A New Approach to ForceFeedback for Virtual Reality,” Proc. of 1993 IEEE Virtual Reality
Annual International Symposium (VRAIS ’93), pp. 336-341, 1993.
[4] S.Tachi, T.Maeda, R.Hirata, and H.Hoshino, “A Construction Methodof Virtual Haptic Space,” Proc. of the 4th International Conference on
Artificial Reality and Telexistence (ICAT ’94), pp. 131-138, 1994.
[5] K.Hoshino and I.Kawabuchi: “A humanoid robotic hand performing
the sign language motions,” Proc. of 2003 International Symposium on
Micromechatronics and Human Science (MHS2003), pp.89-94, 2003.