Development of a Multi-fingered Robot Hand with Softnesschangeable Skin Mechanism

Hiroki Takeuchi1 and Tetsuyou Watanabe1
1 Graduate School of Natural Science & Technology, Kanazawa University, Kakuma-machi, Kanazawa-shi, 920-1192, JAPANThis paper develops a multi-fingered robot hand with skin mechanism enabling
softness change. We show how the softness of the skin affects grasping and manipulation. Elastic skin provides stable grasping while precise manipulation islost. Hard skin provides precise manipulation while stability of grasp is lost. We
will try to change the softness of the skin according to situation, object, and so on.
In this paper, we develop a novel human like robot hand with softnesschangeable skin mechanism.
1

Introduction

Recently there are many attentions to develop a robot
which can work in human society. One of the most important functions is to (grasp and) manipulate/move an object.
Without the function, the robot can not work and help human. Robot hand is one of the devices which have possibility to equip such a function. Our vision of this study is
to develop such a robot hand which can work inside human society.
In a daily life, there are many kinds of tools which humanbeing uses. Therefore, Robot hand which resembles human
hand is considered to have advantage to work in humansociety.
Next, for the dexterity, it is also important that thumb opposes the other finger. Without this function, the angle between the tip surface normals for thumb and for the otherfinger becomes large. Then, robot hand needs large frictional forces to keep grasping.
From the other viewpoint, human lives in an environment
which is variously changeable. Therefore, robot hand isrequired to grasp and manipulate many kinds of unknown
objects in the environment. Then, to have dexterity is a key
issue for such a robot hand [1] [2] [3] [4] [5] [6]. To improve the dexterity of robot hand, we consider to add a
special function which human hand does not have. It issoftness changeable skin. Recently, some robot hands havesoft surface of the hands like human hand [7]. As withhuman skin, moderate softness is considered to be advantages to grasp and manipulate objects [8]. Soft skin increases contact area between hand and object and increase
frictional force. Since we grasp and manipulate an object
through friction, frictional force is essential. However, finger with soft skin sometimes disturbs precise manipulation.
Softness might absorb the motion. For example, if moving
the fingertip with soft skin which contacts with the object,whole fingertip motion is not directly transmitted to object
motion.On the other side, hard skin can transmit. Summarizing, softness and hardness of skin have both advantage
and disadvantage. Therefore, skin whose softness/stiffness
is changeable has large advantage to improve the dexterity.

Concerning the above, we develop a robot hand named
Kanazawa Hand which has following characters.
(1) The shape of the hand resembles human hand.
(2) Thumb opposes every other finger.
(3) Softness-changeable mechanism is attached to skin.
This Kanazawa Hand can attain not only dexterous manipulation with hard skin, but also stable grasping with soft
skin, and then appropriately adjust many kinds of situations, objects, and environment.
This paper is organized as follows. First, design of thehand is described. Then the effect of the skin softness on
stable grasping and precise manipulation is described, andproposed softness changeable mechanism.

2

Skeletal structure

In this chapter we present the brief structure of the Kanazawa Hand and describe the detail mechanism of its finger
module.

2.1

Structure of the hand

Figure 1 shows an overview of the developed hand which
has four fingers: thumb, index, middle, and ring fingers.
As shown in Figure 2, we chose the kinematic structure
like human hand so that the robot hand can use many kindsof tools for humans. Table 1 shows the basic design specification for the hand.
The thumb has 4 DOF for 3 joints: 2 DOF for CM joint, 1
DOF for MP joint, and 1 DOF for IP joint. The CM joint islocated at the center with respect to the width direction of
the hand (See Figure 3(a)). There is rotation axis at the
CM joint to be able to twist the thumb (See Figure 3(b)).
The normal direction of the surface for the thumb finger
tip can coincide with that for the other finger tips as shownin Figure 4(a). In contrast, human cannot always makesuch postures as shown in Figure 4(b). Then, it can be said
that the developed thumb has much better mechanism thanhuman from the viewpoint of opposability (thumb ability
to oppose the other fingers.)
The index finger has 3 DOF for 3 joints: 2 DOF for MP
joint and 1 DOF for PIP joint. DIP joint is coupled with the
PIP joint like a human finger. The MP joint with 2 DOF

works to adduct/abduct and flex/extend. This kinematic
structure of 3 DOF is completely the same as human index
finger.
The mechanism of the middle finger is the same as that of
the index finger except for the MP joint mechanism. The
middle finger lacks one DOF (adduction/abduction of the
MP joint) compared to the index finger. The posture resulted from the adduction/abduction of the MP joint canalso be formed by the other finger motion (without the adduction/abduction of the MP joint). Therefore the hand candexterously manipulate objects even if the one DOF isomitted. That leads advantages of the reduction in size,
weight, and the cost of the robot hand.
The ring finger is the same finger structure as the index
finger.

2.2

Mechanism of a finger module

The hand can be separated into every finger module because the four fingers are mechanically identical. Since
each finger module uses almost the same mechanism, we
present the only mechanism of the index finger. A finger
module has 3 joints (MP, PIP, and DIP) and 3 links(proximal, middle, and distal link) as defined in Figure 5.
It has 3 DOF: 2 DOF for the MP joint and 1 DOF for the
Table 1
Dimensions

Specification of the Kanazaawa hand

handfingerLength

290

[mm]

Width

160

[mm]

Length

170

[mm]

Width

25

[mm]

4

[fingers]

Total

12

[joints]Thumb3[joints]

Index

3[joints]

Middle3[joints]

Fingers
JointsD.O.F.

Figure 1

Overview of the Kanazawa hand
WeightFingertip force

Figure 2

Ring

3[joints]

Total

12

[D.O.F.]

Thumb

4[D.O.F.]

Index

3[D.O.F.]

Middle2[D.O.F.]Ring

3[D.O.F.]

1.5

[kg]

7

[N]

Joint structure(a)The Kanazawa Hand(b)Human hand
Figure 4
Thumb opposes the other fingers

Figure 3 (a)Position of CM joint(b)Twisting mechanism

Figure 5

Finger module without finger tip

PIP joint. The DIP joint is coupled with the PIP joint. Two
motors (motor 1 and 2) for driving the MP joint are placedin the palm, and one motor (motor 3) for driving the PIP
joint is placed in the proximal link. The motor 1 and 2 are
DC motors (3.5[W], provided by Maxon motor) with epicyclic gear (gear-ratio 128:1) and encoder (256 pulse/rev).
In contrast compact DC motor of motor 3 (0.5[W], provided by Maxon motor) with epicyclic gear (gear-ratio
256:1) and encoder (16 pulse/rev) is used for the PIP joint.
This finger module has two core mechanisms: first one is
MP joint mechanism providing two rotations whose axes
are orthogonal to each other, second one is DIP-PIP joint
mechanism where the DIP and the PIP joints move together. We descried their detail in the following subsections.

2.2.1

MP joint mechanism

The MP joint with 2 DOF works to adduct/abduct andflex/extend. Figure 6 shows the mechanism of the MP
joint in detail. Gears 1 to 4 consist of differential bevel
gears mechanism. The gears 1 and 2, driven by the motor 1
and 2 respectively, rotate only about flexion/extension axis.
The gear3 is fixed to the proximal link so that the proximal
link can adduct/abduct by the gear3. The gear4 isconnected to the proximal link and freely rotates in
adducent/abducent directon, irrespective of the proximal
link motion (rotation). The adduction/abduction axis θad-ab
and the flexion/extension axis θfl-ex are given by:⎡ θ fl −ex ⎤ ⎡1 2 1 2 ⎤ ⎡θ1 ⎤
(1)
⎢θ
⎥=⎢
⎥⎢ ⎥
⎣ ad − ab ⎦ ⎣1 2 − 1 2⎦ ⎣θ 2 ⎦2.2.2

PIP-DIP joint mechanism

Figure 7 shows the mechanism that the PIP joint is coupled with the DIP joint. To couple the PIP joint with the
DIP joint, the specially designed shaft mechanism is developed. Figure 8 shows the mechanism of the PIP shaft.
The PIP shaft consists of two short shaft, a hollow shaft,and two bearings. The shaft 1 drives with the PIP joint bydriving the motor, but the shaft 2 does not directly drives
with the motor. If the gear 2 connected to the shaft 1 isdriven by the motor through the gear 1, PIP joint rotates.
Then, the shaft 2 and the gear 3 connected to the shaft are
driven, and then the gear 4 rotates about the middle shaft.
The rotation of the gear 4 drives the DIP joint through the
middle shaft, the gear 5 and the gear 6. Since the gear 1 to
6 are the same gear ratio, the PIP and the DIP joint
flex/extend with the same angle.

3

Skin mechanism

Here, we describe softness-changeable mechanism. First,
we present why softness-changeable mechanism is needed
for grasping and manipulation of the object. Second, we
present the novel softness changeable skin mechanism.
Lastly, we present fundamental experimental results toshow the effectiveness.

3.1

Effect of softness on grasping and manipulation

3.1.1

Frictional effectwhere θ1 and θ2 are the angles driven by the motor 1 and 2. Figure 9 shows that a hand grasps a rigid object when using soft contact area and hard contact area. We define stable grasping as a hand being able to continue to hold an
object even when gravity or external force is exerted on
the object. To balance large external forces, we need large
contact forces. Since contact forces are constructed by

Figure 6

Figure 7

Mechanism of MP joint

Mechanism of PIP and DIP joint

Figure 9

Figure 8

Design of PIP shaft(a) Hard skin(b) Soft skinGrasping an object with hard skin and soft skin

normal force and frictional (tangent) forces, friction has animportant role to enlarge contact forces. To increase contact force, there are two methods: one is to increase normal
force, the other is to increase friction. However, it is notpractical to increase normal force. Frictional forces increase with the increase of normal force. However, its increasing amount is low if friction is small. Then, we canincrease contact forces in only limited directions. Additionally, large force per unit area, namely, large pleasuremight cause destruction of a fragile object. Therefore,
large friction is important for stable grasping. If considering the softness of skin, soft skin provides large contact
area comparing with hard skin. In case of using soft skin,
the contact area can deform its shape along the shape ofthe object shown in Figure 9. It means we can get larger
contact area, and then can get larger friction forces withoutchanging the magnitude of normal force. Hence it can besaid that finger with soft contact area is superior to finger
with hard contact area for stable grasping.

3.1.2

Quasi-static analysis from the viewpointof manipulability

Here, we discuss manipulability [9] to understand how easily the hand can manipulate the object. Figure 10 shows
the model of the fingertip and the object. For the convenient, we discuss only fingertip motion, and assume that we
can move the fingertip in arbitrary directions. Every fingertip has a shape of deformable hemisphere. The object
has flat surface at the contact point and is rigid body. We
consider to grasp the object with n fingertips. Let Σο and Σibe the coordinates located at the gravity center of the object and at the center of hemisphere of ith fingertip. Let bepi and po are the positions of the origin of Σο and Σi, and pci
be the position of the center of the contact surface between
the fingertip and the object. ωι and ωo are angular velocities of Σο and Σi. ni is unit contact normal directing insideof the object. t1i and t2i are unit contact tangential vectors.
ri is the hemisphere radius of the fingertip and Δri is thedeformation amount by contact. Δri can be a parameter expressing skin softness. If Δri is large, it means the skin is
soft and vice versa.
The relationship between pci and pi is given by(2)
pci = pi + ( ri − Δri )ni
If differentiating this relationship with respect to time, weget(3)
p& ci = p& i + (ri − Δri )(ωi × ni + v i ) − Δr&i ni
where
v i = Ri i n& i(4)where Ri denotes rotational matrix of Σi .
On the other side, the relationship between pci and po isgiven by(5)
pci = po + ai ni + b1i t1i + b2i t 2i
where ai , b1i and b2i denote the distances between Σo andpci along the directions of ni, t1i and t2i, respectively. Notethat ai is constant since it represents the distance between
Σo and the side of the object.
If differentiating this relationship with respect to time, we
get
p& ci = p& o + ωo × (ai ni + b1i t1i + b2i t 2i i )(6)+ a& n + b& t + b& t
i

i

1i 1i

2i 2i

From eq.(3) and (6), the following equation is obtained.

p& i + (ri − Δri )(ωi × ni ) − Δr&i ni= p& o + ωo × (ai ni + b1i t1i + b2i t 2i )(7)Here we use the following relationships: a& = 0 andb&1i t1i + b&2i t 2 i = (ri − Δri )vi

which expresses there is no slippage between the fingertip
and the object. Eq.(7) can be rewritten by&&
T ⎡ Pi ⎤T ⎡ Po ⎤(8)G= n Δr& + G⎢ ⎥⎣ ωi ⎦

fi

where

i

oi

⎢ ⎥
⎣ ωo ⎦

T= [I 3− ri [n i × ]]T

= [I 3− [( a i n i + b1i t 1i + b 2 i t 2 i ) × ]]

G fri
G oi

i

G fdi

T

= [O 3T(9)[n i × ]]T

G fi = G fri + Δ ri G fdi

T

If aggregating Eq.(8) for all n contact points, we getTT(10)
G f x& f = NΔr& + Go x& o
where
⎡ x& 1 ⎤⎢ x& ⎥⎡ p& i ⎤⎡ p& o ⎤x& i = ⎢ ⎥ x& o = ⎢ ⎥ x& f = ⎢ 2 ⎥⎢ M ⎥⎣ωi ⎦ ,⎣ωo ⎦ ,
⎢ ⎥⎣ x& n ⎦⎡G f 1T⎢T
Gf = ⎢
⎢
⎢
⎣⎢ 0
⎡ n1
⎢
N =⎢
⎢
⎢
⎣0

Gf2

T

O

n2
O

0 ⎤
⎥
⎥
⎥
T ⎥
G fn ⎦⎥

0 ⎤
⎥
⎥
⎥
⎥
nn ⎦

⎡ G o1T ⎤⎢T ⎥GT
Go = ⎢ o2 ⎥
⎢ M ⎥
⎢
T ⎥
⎣⎢ G on ⎦⎥Here we consider the generable object velocity with thecontact velocity whose magnitude is equal to or less than 1.
The set of the generable object velocity is expressed byT(11)| NΔr& + Go x& o |≤ 1
Figure 10

Model of the fingertip and the object

This means that the magnitude of generable object velocity
decreases with the icrease of the deformation velocity Δr& .
It means deformation might decrease manipulability (howeasily we can generate object velocity x& o ).
Now, we discuss the case when Δr& → 0 to simplify the
analysis. In this case, Eq.(10) becomesTT(12)
G f x& f = Go x& o = p&ˆ c
Since GoT x& o does not include any parameters related withthe deformation, there is no effect of the deformation about
how much large object velocity can be generated with contact velocity whose magnitude is equal to or less than 1.
Then, we consider how much large contact velocity we cangenerate with the fingertip velociy whose magnitude isequal to or less than 1. It direcly coressponds to how muchlarge object velocity we can generate with the fingertip
velociy whose magnitude is equal to or less than 1. Fromeq.(12), we get
T + &
+
(13)
x& f = G fpˆ c + I − G f G f k

( )

(

)

where (G f ) denotes the psedo-inverse matrix of G f T and k
T +denotes an arbitrary vector. Then, we obtainT
1 ≥ x& f x& f( ) pˆ& + k (I − G G ) k≥ pˆ& G (G ) pˆ& = pˆ& (G G ) pˆ&= pˆ& (diag (G G )) p&ˆ= pˆ& c G f G f
+

T

f

f

f

T

c

T

T

c

+ 2

T

c

T +

+

T

c

T +

fi

c

T

+

f

f

c

+

fi

c

where diag denotes block diagonal matrix constructed by
the following elements. This set expresses the set of generable contact velocity with the fingertip velocity whose
magnitude is equal to or less than 1. Then, the magnitudeof the generable contact velocity depends onT(diag (G fi G fi )) + , namely G fiT G fi . The larger G fiT G fi is, Thelarger p&ˆ c we can generate.
From eq.(14), we get
TTT
T
G fi G fi = G fri G fri + Δri G fdi G fri + G fri G fdi

(

)

(15)

T

2

+ Δri G fdi G fdi

Here, we define the following two matrices expressing theterm which does not include the Δri and the term includingΔri, resectively.
T
G fi G fi = G1i + G 2i
T(16)
G =G G
1i

fri

(

fri

T

T

)

2

T

G 2i = Δri G fdi G fri + G fri G fdi + Δri G fdi G fdi
2T

Here, we discuss softness effects from the viewpoint ofdynamics. In order to consider dynamic behavior of thedeformation, we utilize a four-element viscoelastic model:
two springs and two dampers (See Figure 11). This model
can express both hard skin and soft skin. If spring constantk and viscosity coefficient c are large, it means hard skin.
In contrast, soft skin can be expressed by small spring constant k and viscosity coefficient c. For the convenient, weconsider only fingertip motion. Let be fri the force exerted
on the contact surface of the fingertip in the normal direction. Then, relationship between fri and Δri is given byΔri = Δri1 + Δri 2 + Δri 3
ki1Δri1 = f ri

(19)
ki 2 Δri 2 + ci 2 Δr&i 2 = f ri
ci 3Δr&i 3 = f ri
From eq.(10) and the principle of virtual work, we get
w fi = G fi f

(20)

fr = N T f

where f is contact force vector, wfi is the force and moment
corresponding to the contact force f, and wo is the resultant
force and moment applied to the object.
The motion equation of the ith fingertip and the object are
respectively given by
1 &(21-a)&
M i &x&i + ( M
i + S i ) xi + w fi = ui
2

1 &&M o &x&o + ( Mo + S o ) xo = w o2(21-b)

where Mi and Mo are inertia matrixes of ith fingertip andthe object, Si and So are the skew-symmetric matrixes toexpress nonlinear forces such as Coriolis forces for ith fingertip and the object, and ui is the input force and moment
vector for the fingertip.
Here, we consider the following input force (and moment)&:
U and output velocity Λ⎡ u1 ⎤⎢u ⎥⎢ 2⎥
U =⎢ M ⎥,⎢ ⎥⎢ un ⎥⎢⎣ w o ⎥⎦⎡ x& 1 ⎤⎢ x& ⎥⎢ 2⎥
Λ& = ⎢ M ⎥⎢ ⎥⎢ x& n ⎥⎢⎣ x& o ⎥⎦The sum of kinetic energies for the fingertip and the object
is represented by

From eq.(16), G2i is expressed by

G 2i = (Δri − 2ri Δri )G fdi G fdi =p 0

Dynamical analysis

w o = Go f

(14)

f

3.1.3

(17)

because Δri ≤ ri . Here 0 =p A means the matrix A is semidenfinite. From this relationship and eq.(16), we can get
the following relationship(18)
G1i + G 2i =p G1i
This means the magnitude of generable contact velocity
decreases with the icrease of deformation Δr . Namely,
the magnitude of generable object velocity decreases with
the icrease of deformation Δr .

Figure 11

Model of contact deformable area

K = K f + Ko
1 T
1 T
= ∑ x& i M i x& i + x& o M o x& o
2
i 2

(22)

The potential energy of the deformation part is expressedby2

E p = ∑∑ kij Δrij
i

(23)

2

Figure 12

j =1

Then, from eq.(19) to eq.(23) , the total power is represented by
dK f+ ∑ w fi x& i
T

dt
i
3
d (K + E p )2=+ ∑∑ cij Δr&ij
dt
i j =2(24)

Here, we consider the case when the input is zero. Then,eq.(24) becomes3
d (K + E P )2(25)= −∑∑ cij Δr&ij
dt
i j =2
From this relationship, it can be said that even if the input
is zero, the system will approach to its equilibrium state if
the skin is soft and corresponding cij is large. On the otherside, if the skin is hard and corresponding cij is small, it ishard to expect that the system will converge, and kinetic
and potential energies tend to preserve. Therefore, we canget more stability with soft skin. From the viewpoint of
convergence to the desired position, we need to use control
law to compensate the potential energies. If the skin is soft,the corresponding potential energies are large and viceversa. Then, we can easily control the system with hardskin and can not with soft skin. Summarizing, hard skinhas advantage for manipulation and disadvantage forgrasping while soft skin has advantage for grasping anddisadvantage for manipulation.

3.2

Mechanism to change softness of skin

Figure 12 shows the structure of softness-changeable
mechanism for a fingertip. We developed the fundamental
structure shown by gray colour. Its shape is crosswisely
cut circular cylinder, and it is made of duralumin. We fit apeltier device in the inside of its side surface, and fill agar
impression material in the cylinder. The end of fingertip iscovered with elasticized rubber made from latex. Agar impression material is a special material which can turn softby heating and hard by cooling, and has reversibility. On
the other hand, the temperature of peltier device can becontrolled by electric current. Then, this skin can turn softand hard by controlling electric current.
Figure 13 shows the relationship between the intensity ofthe electric current for the peltier device and the elastic
modulus of the skin mechanism. It can be seen that theelastic modulus of the skin mechanism changes from1.5[kPa] to 20[kPa] by controlling the electric current from
1.4 [A] to 1.8[A]. The range of the changeable elastic
modulus is considered to be enough large.

elastic modulus [Pa]U T Λ& =Structure of softness changiable skin

20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
1.3

1.4

1.5

1.6

1.7

1.8

intensity of an electric current [A]Figure 13 Relation between intensity of an electric current for
peltier device and elastic modulus of skin mechanism

3.3

Fundamental experiment

In order to see the effectiveness of our developed system,
we conducted the experiment how an object reacts during
manipulation. Figure 14 shows the overview of the experiment. The object is rigid, circular flat plate in shape,and 0.3[kg]. It is pinched by two fingertips disposed antipodally. The horizontal line on the object and red triangular marker on the fingertips is in the same straight line at
the start. Now, we try to observe the positional relationshipbetween the horizontal line and the marker after rotating
the object with 45 degrees by moving the two fingertips.
Figure 15 shows the experimental results when the hardskin with elastic modulus of 15[kPa] is used and the soft
skin with elastic modulus of 2[kPa] is used. Note that theelastic modulus for hard skin is over the range shown in
Figure 13 due to the variation of the used Agar impression
material. In case when using the hard fingertip shown in
Figure 15(a), the line on the object and the two red markers could keep to be on the same line during the manipulation. On the other side, when using soft skin shown in Figure 15(b), they could not. If the fingertip moves, the object
rotates with a little delay. The delay causes the declination(the line on the object and the two red markers are not on
the same line). Therefore, in order to complete the 45 degree rotation with soft skin, we need to move the fingertips
more comparing to the case when using hard skin. Then, it
can be said that the finger with hard skin has advantage formanipulation comparing to soft skin.

Figure 14

Overview of the experiment

Figure 15

4

Experimental results

Conclusion

We proposed the four-fingered robot hand with skinmechanism which is able to change the softness of the surface at the finger tip. The hand has 12 DOF and shape likehuman hand. Thumb is designed to be able to oppose every
other finger. We proposed a softness changeable mechanism with agar impression material and peltier device,
which can be controlled by electric current.
We analyzed how the softness of contact area affects on
the object grasping and manipulation from the viewpointof friction, quasi-statics, and dynamics. The analyses
showed that fingers with soft skin have advantages forgrasping but disadvantage for manipulation. In contrast,
fingers with hard skin have advantages for manipulation
but disadvantage for grasping. This is also shown by fundamental experiments.
Future work will be developments of the systems in which
the hand is able to automatically change its skin to appropriate softness according to the given objects, task, situation, and so on.

5

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