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IEEE SMC International Conference on Distributed Human-Machine Systems 2008
Development of Haptic Device to Display
Frictional Moment
Haruhisa Kawasaki Yoshio Ohtuka Tetsuya Mouri
Department of Human and Department of Human and Department of Human and
Information Systems Information Systems Information Systems
Faculty of Engineering Faculty of Engineering Faculty of Engineering
Gifu University Gifu University Gifu University
1-1 Yanagido, Gifu 501-1193, Japan 1-1 Yanagido, Gifu 501-1193, Japan 1-1 Yanagido, Gifu 501-1193, Japan
h_kawasa@gifu-u.ac.jp mouri@gifu-u.ac.jp
Abstract— This paper presents a haptic device newly using a five-fingered haptic interface robot called HIRO II [8]
developed to display frictional moment, which is attached to the and also presented a method for computing the frictional
five-fingered haptic interface robot called HIRO II. The device is moment [9], which is based on soft-finger contact and
a new finger holder in which a small brushless motor and a disk calculates both static and/or dynamic states of the frictional
are mounted. Subjects’ perception of the frictional moment
moment. However, the effect of displaying frictional moment
while wearing the finger holder and operational feeling during
object manipulation in a virtual reality environment were
in a virtual realty environment is not verified experimentally
evaluated experimentally using our developed computational because there is not a suitable device to display frictional
method of frictional moment. moment. In order to enhance the reality of object manipulation
in a virtual reality environment, displays not only of frictional
I. INTRODUCTION force but also of frictional moment are required.
When an object is manipulated by the operator’s hand in This paper presents a developed compact haptic device,
virtual space, it is desirable that the object’s spatial movement which is attached to the HIRO II as a new finger holder to
be based on the laws of physics. Constraint force and friction, display frictional moment. A small brushless motor and a disk
which are generated at the contact points between the are built into the device. Subjects’ perception of the frictional
operator’s fingertips and the object surface, are important moment while wearing the finger holder and the operational
factors to enhance reality. In general, constraint force is feeling during object manipulation in a virtual reality
calculated in proportion to the penetration depth of the environment were evaluated experimentally to show the
fingertip touching the object, and frictional force on a effectiveness of the combination of the developed device and
tangential plane at the contact point is calculated in proportion the computational method of frictional moment.
to the constraint force. Physically, there are two friction states
at the contact point: namely, static (without sliding) and
II. COMPUTATIONAL METHOD OF FRICTIONAL MOMENT
dynamic (with sliding) friction states. Some research on
friction models for haptic rendering has already been carried Physical simulation in haptic environments requires that the
out [1]-[6]. For example, W. S. Harwin et al. [3] presented a manipulated objects have a number of the same physical
method based on so-called god-objects [2] and friction cones, properties as are present in the real world. For instance, an
which permits the computation of both static and dynamic object’s dynamic motion must be based on external forces
forces. In this method, the frictional force is calculated in such as grasping force, gravitational force, frictional force and
proportion to the penetration depth of the fingertip into the frictional moment. We have presented a computational
virtual object, and the haptic interface point moves to the edge method of frictional moment [9], which is proportional to the
of the friction cone if the haptic interface point lies outside the relative torsion angle and the constraint force between the
friction cone. However, the frictional moment, which is a vital fingertip and the object. An outline of the method is presented
aspect of modeling in multi-point haptic interactions, has not briefly for understanding of the experimental system.
yet been considered. Both frictional force and frictional
moment models are needed to simulate the dynamics of an The relative torsion angle is represented as a rotational angle
object. A method based on the contact volume of polygonal around ni, which is the unit normal vector of the object surface
objects by Hasegawa et. al., [7] computes frictional force and at the contact point Ci between the i-th fingertip and the object.
moment, but it needs more computational time than the single Then, let us establish the fingertip coordinate system
contact approach. Our group has presented the effect of
Σ i = { x i , y i , z i } at the contact point Ci of the i-th fingertip,
B B B B
displaying frictional force in a virtual reality environment
where z i B coincides with the normal direction of the object
surface at the contact point, and the xi B yi B plane coincides
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IEEE SMC International Conference on Distributed Human-Machine Systems 2008
with a tangential plane at the contact point. At the same time, where γ i ( = k d θ i ) is the coefficient of frictional moment at the
the object coordinate system Σ i = { x i , y i , z i } at the contact dynamic sate, ρ i is the damping coefficient, and k d (< k s ) is a
point Ci of the object is superposed on Σ i B . When the two parameter depending on the physical characteristics of the
coordinate systems move spatially, the rotation angle of the x i finger and the object in the dynamic state. These relations
axis about the x iB × x i axis is calculated as sin −1 (|| x iB − x i ||) . show that the frictional moment is proportional to the
constraint force and a relative torsion angle between finger
The relative torsion angle between the fingertip and the object
and object at the contact point. This computation method has
at the i-th contact point is proportional to the direction cosine
no effect on the contact point and the haptic interface point,
of the x iB × x i axis to the ni axis as given by
which means that computations of frictional force and friction
x iB × x i moment can be done separately. Object dynamics can be
θ i = sin −1 (|| x iB − x i ||) niT (1) simulated by taking the frictional force and frictional moment
|| x iB × x i ||
into account.
The static frictional moment is computed by
III. FIVE-FINGERED HAPTIC INTERFACE ROBOT HIRO II
m i = ζ i || f i n || ni , (2)
We developed a 5-fingered haptic interface consisting of the
where ς i is the coefficient of frictional moment, which is
arm and fingertips haptic display shown in Fig. 2, named
given by HIRO II. Details of the haptic interface can be seen in [8]. Its
ς i = k sθ i , (3)
mechanism is here outlined briefly for understanding of the
experimental system.
where ks is a parameter depending on the physical
characteristics of the fingertip. This satisfies The HIRO II can present force and tactile feeling at the five
0 ≤ ς i ≤ k sθ i where θ i max is the maximum relative torsion fingertips of the human hand. It is designed to be completely
max
angle at the static frictional moment. Now let us consider a safe and similar to the human upper limb both in shape and
frictional moment arc with vertex angle θ i max as shown in Fig. mobility. Its mechanism consists of a 6 DOF arm and a 15
DOF hand with 5 fingers. Each finger has 3 joints, allowing 3
1. When | θ i |≤ θ i , it is a static frictional moment state, and DOF. The first joint, relatively to the hand base, allows
max
when | θ i | > θ i , it is a dynamic frictional moment state. At abduction/adduction. The second joint and the third joint
max
the dynamic frictional moment state, the xi*-axis obtained by allow flexion/extension. The thumb is almost the same as the
rotating x i around ni with the rotation angle −θ i max can be above mentioned fingers except for a reduction gear ratio and
the movable ranges of its joint 1 and joint 2. In order to read
linearly approximated by
the finger loading, a 6-axis force sensor in the second link of
θ i max each finger is installed. To manipulate, the haptic interface
x i* = x i − ( x i − x iB )
θi (4) user has to wear a finger holder on his/her fingertips. The
finger holder has a ball attached to a permanent magnet at the
A new starting point of frictional moment is set by replacing force sensor tip and forms a passive spherical joint. We call
xi* with x iB such that x i lies on the edge of the frictional this a magnet type spherical joint. This passive spherical joint
moment arc. Then, the dynamic frictional moment is has two roles. The first is the adjustment of differences
computed by between the human and haptic finger orientations. Each
human finger has 6 DOF and each haptic finger has 3 DOF.
m i = (γ i || f i n || + ρ iθ i )ni , (5) Hence, an additional 3 passive DOF are needed. The second is
i max
i
i min
xi
x iB
x i*
Fig. 1 Movement of xiB
Fig. 2 Five-fingered haptic Interface robot: HIRO II
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IEEE SMC International Conference on Distributed Human-Machine Systems 2008
to ensure that the operator can remove his fingers from the human and haptic fingers orientations and the withdrawal of
haptic interface when it malfunctions. The suction force by the the operator’s fingers from the haptic interface at need is
permanent magnet is 5 N. By virtue of this mechanism, possible, which are the same functions of the magnet type
friction can be presented, but frictional moment cannot be spherical joint.
presented.
The suction force and frictional moment between the ball and
the support hole are shown in Table 1. The suction force of the
The architecture of the HIRO II system is a distributed
non-magnet type joint can be adjusted by changing the ratio of
multithreaded affair on separate PCs [10]. VR simulation and
the ball insertion into the support hole, which is given as the
the haptic controller are connected by a high-speed network.
ratio of the depth of the ball in the support hole to the diameter
HIRO II is controlled by a redundant force control method in
of the ball. Frictional moments of magnet- and non-magnet
which all the joints of the mechanism are force-controlled
type spherical joints, which arise from contact between the
simultaneously to present the virtual force. The sampling
cycle of the control is 1 ms.
IV. FINGER HOLDER TO DISPLAY FRICTIONAL MOMENT
A. Design concept
It is not desirable to make the haptic device to display
frictional moment too complicated. We designed a device
according to the following concepts.
1) In order to display frictional moment at the operator’s Fig. 3 Developed finger holder to display frictional moment
fingertip by rotational motion with one degree of freedom, a
small-sized motor and a disk are built in a finger holder.
2) Frictional moment that more than 80 % operators recognize
at constraint force 2 N can be displayed [9].
3) In order to simplify the control method and mechanism to Human’s
display frictional moment, not angle position control but finger
open loop torque control is adopted. Its output motor torque
is proportional to the frictional moment.
B. Developed device
Disk
We have developed a new finger holder to display frictional Rigid ball
Motor
moment with almost the same shape as the previous finger
holder [8], as shown in Fig. 3. A small-sized brushless motor
(Namiki Precision Jewry Co., SBL-06H1PG337) is built into Fig. 4 Structure of developed finger holder
a ball of 8 mm diameter attached to the finger holder as shown
in Fig. 4. Specifications of the motor are given as follows:
outside diameter 2.4 mm, overall length 10.8 mm, mass 0.245
g, gear ratio 337, and maximum torque 0.69 mNm at a rated
voltage of 3 volts. A disk 7 mm in diameter and 1 mm thick is
attached to the end of the motor axis so as to put the operator’s
fingertip in contact with the disk. Frictional moment can be
presented at the fingertip by rotational motion of the motor.
When the ball of the developed finger holder is connected to
the passive spherical joint of HIRO II, the motor does not
work because of the strong magnetic force of the permanent Fig. 5 Support hole of passive spherical joint without a
magnet in the spherical joint. Therefore, the development of a magnet
passive spherical joint in which a permanent magnet is not Table 1 Comparison with magnet and non-magnet type
used is required. Fig. 5 shows the newly designed support hole spherical joints
of the passive spherical joint without a permanent magnet. We
Joint Type Ratio of ball Suction force Frictional
call this a non-magnet type spherical joint. The support hole is insertion moment at joint
made of MC nylon. The developed finger holder is desorbed [mm] [Nm] [mNm]
from the spherical passive joint using the elastic behavior of Magnet Type 0.31 5.4 2.21
the MC nylon. This structure of the spherical joint realizes
Non-magnet type 0.60 3.5 0.45
functions such that the adjustment of differences between the
0.65 7.5 -------
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IEEE SMC International Conference on Distributed Human-Machine Systems 2008
ball and the support hole, are 2.21 mNm and 0.45 mNm, and unclear. Most subjects recognized frictional moment of
respectively. The frictional moment of the non-magnet type more than 0.45 mNm with 80% accuracy. This result is very
spherical joint is reduced to one fifth of that of the magnet type similar to those when a subject puts his index finger directly
spherical joint. Since the frictional moment at the spherical on a disk driven by DC motor which is fixed on the load
joint has a negative effect on the display of force sensing, its measurement instrument [9], shown in Fig. 7 as the case of no
reduction contributes to improving the accuracy of the force finger holder. This means that the existence or nonexistence of
display. However, the movable angle of the non-magnet type a finger holder does not have an effect on the recognition of
spherical joint becomes a little bit small because the support frictional moment.
hole should cover more than half of the ball to generate
B. Experiment in virtual reality environment
suction force. This point is an issue to be solved in the future.
First, we examined frictional moment states when subjects
V. EXPERIMENTS handled a virtual rectangular solid with size 0.06×0.012×0.03
m and mass 2 g using HIRO II as shown in Fig. 8. The subjects
A. Recognition of rotation direction of frictional moment wore the newly developed finger holder or the previous finger
Subjects’ perception of frictional moment was examined by holder. The small balls in the computer graphics are fingertips.
using a simple experimental system as shown in Fig. 6. The In the virtual reality simulation, not only the frictional moment
subject puts his index finger wearing the newly developed but also the frictional force were computed. The following
finger holder on a disk with specified pushing force 2 N. This numerical values were set to present natural motion of the
force could be observed by the subject through the load grasped object: ζ i = 0.3, γ i =0.2, θ i max = 0.02 rad, and ks =1.0
measurement instrument. The frictional moment was and 0.8 at static and dynamic states respectively. The subjects
controlled by a motor current input. The number of subjects executed the following actions sequentially as shown in Fig. 9:
(ages 21 to 24) was 10. The directional recognition rate of (1) grasp the object firmly at contact points by the thumb and
frictional moment at 2N pushing force (constraint force) is the index finger; (2) lift the object and rest with the static sate
shown in Fig. 7. For measurement of the directional where the orientation of object is not varied; (3) slide the
recognition rate, the frictional moments are displayed to the
subject’s fingertip as step inputs at random levels between 0.1
and 0.9 mNm, 13 times for each subject. The display time of
the force moment is 3 seconds. Before the experiment,
subjects trained four times to familiarize themselves with the
experimental apparatus. After displaying the frictional
moment, the subject answered whether he felt a frictional
moment and gave its rotational direction: that is, right, left,
Fig. 8 Object manipulation in virtual reality environment
Fig. 6 Measurement system of human’s perception of
frictional moment
100
(1) Grasp (2) Lift and rest
Recognition rate [%]
80
60
40
20 finger folder
0 no finger folder
0.0 0.2 0.4 0.6 0.8 1.0
Frictional moment [mNm]
Fig. 7 Recognition rate of rotation direction
(3) Slide and rest (4) Release
Fig. 9 Scene of manipulation of a rectangular solid
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IEEE SMC International Conference on Distributed Human-Machine Systems 2008
1.0 1.0
Status
Status
0.5 0.5
0.0 0.0
45 46 47 48 49 50 51 52 45 47 49 51 53 55
Time [s] Time [s]
0.5 0.5
Normal force [N]
Normal force [N]
0.4 0.4
0.3 0.3
y y
0.2 0.2
0.1
z 0.1 z
0.0 0.0
x x
-0.1 45 46 47 48 49 50 51 52 -0.1 45 47 49 51 53 55
Time [s] Time [s]
Frictional moment [Nm]
Frictional moment [Nm]
0.0015 0.0015
0.0010 0.0010
y y
0.0005 0.0005
z z
0.0000 0.0000
x x
45 46 47 48 49 50 51 52
-0.0005 -0.0005 45 47 49 51 53 55
Time [s] Time [s]
Frictional angle [rad] 0.000
Frictional angle [rad]
0.000
-0.005 45 46 47 48 49 50 51 52 -0.005 45 47 49 51 53 55
-0.010 -0.010
-0.015 -0.015
-0.020 -0.020
-0.025 -0.025
Time [s] Time [s]
1.5 1.5
ψ
Euler angle [rad]
Euler angle [rad]
1.0 1.0 ψ
0.5 θ 0.5 θ
0.0 0.0
-0.5 45 46 47 48 49 50 51 52 -0.5 45 47 49 φ 51 53 55
-1.0 φ -1.0
-1.5 -1.5
Time [s] Time [s]
Fig. 10 Experimental results of object manipulation in virtual reality environment
object around the axis connecting the contact points of the grades, with 1 being the worst and 7 the best. The number of
thumb and the index finger to create a dynamic frictional subjects (ages 21 to 24) was 10. Fig. 11 shows the results.
moment state and rest again; and (4) release the object. Fig. Subjects expressed the feeling that wearing the new finger
10 shows the status that indicates the frictional moment state holder is not comfortable by comparison to the case of the old
of the index finger, in which the static frictional moment state finger holder. This feeling of discomfort is caused by the
is indicated by level 1 and the dynamic state by level 0.5, as electric circuit of the brushless motor, which is mounted on the
well as the normal force, the frictional moment, the relative finger holder case as shown in Fig. 8. The feeling of the
torsion angle at the contact point of the index finger, and the frictional moment and the coincidence between the object
ZYZ-Euler angles that indicate orientation of the object. Fig. motion in computer graphics and the display of the frictional
10 (1) is the case of the old finger holder, that is, that without a moment when wearing the new finger holder were very good
built-in motor, and (2) is the case of the new finger holder. In in comparison to the old finger holder. Operationality and the
both cases, a non-magnet type spherical joint is used. immersive feeling when wearing the new finger holder were
Transition between static and dynamic frictional moment better than those of the old finger holder. According to the
occurs according to the physical phenomena, and the significant difference test of performances by t-test, the
frictional moment at the static state is nearly equal to a value improvement in operationality had a significance level of
calculated by the geometrical moment of inertia around the 10 % and that in the immersive feeling had a significance level
contact point. This means that the new finger holder does not of 1%. This means that the combination of the newly
disturb the object manipulation in the virtual reality developed finger holder and the computational method of the
environment and gives a physical simulation of reality. frictional moment greatly enhances the sense of reality in the
virtual environment.
Second, we evaluated subjects’ psychological experience
when wearing each finger holder, using a rating scale with 7
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IEEE SMC International Conference on Distributed Human-Machine Systems 2008
Old finger holder
New finger holder
(a)Comfort at wearing
the device
[9] H. Kawasaki, Y. Ohtuka, M. O. Alhalabi, T. Mouri, Haptic Rendering
(b) Feeling of moment
and Perception of Frictional Moment, Proc. of EuroHaptics 2006,
pp.201-206
(c) Consistency of CG and [10] O. Halabi, V. Daniulatis, H. Kawasaki, T. Mouri and Y. Ohtuka, Future
display of frictional moment Haptic Science Encyclopedia: Realistic Stable Haptic Interaction with
Highly Deformable Objects Using HIRO-II, Journal of Robotics and
(d) Operationality Mechatronics, Vol. 18, No.4, pp. 409-417, 2006
[11] H. Kawasaki and T. Mouri, Design and Control of Five-Fingered haptic
(e) Immersive feeling Interface Opposite to Human Hand, IEEE Transaction On Robotics,
Vol. 23, No.5, pp. 909-918, 2007
1 2 3 4 5 6 7
Fig. 11 Result of questionnaire
VI. CONCLUSION
We have developed a new finger holder to display frictional
moment as a part of a five-fingered haptic interface robot
HIRO II, in which a small brushless motor and a disk are built.
Experiments of subjects’ perception of frictional moment
using the new finger holder were presented. The combination
of the new finger holder and the computation method of
frictional moment, in which the friction moment is computed
in proportion to the constraint force and the relative torsion
angle between fingertip and the virtual object at the contact
point, have enhanced the reality of object manipulation in the
virtual reality environment.
ACKNOWLEDGMENT
The authors express gratitude for partial funding and support
from the Ministry of Education, Culture, Sports, Science and
Technology, and the Ministry of Internal Affairs and
Communications in Japan.
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