Design and Optimization of a Five-Finger Haptic Glove Mechanism

Abstract

This paper describes the design and optimization of a novel five-finger haptic glove mechanism, which uses a worm-geared motor and an antagonistically routed cable mechanism at each finger as both active and passive force display actuators. Existing haptic gloves either restrict the natural motion and maximum output force of the hand or are bulky and heavy. In order to tackle these challenges, the five-finger haptic glove is designed to minimize the size and weight and maximize the workspace and force output range of the glove. The glove is a wireless and self-contained mechatronic system that mounts over the dorsum of a bare hand and provides haptic force feedback to each finger. This paper describes the mechatronic design of the glove and the method to optimize the link length with the purpose of enhancing workspace and the force transmission ratio. Simulation and experimental results are reported, showing the future potential of the proposed system in haptic applications and rehabilitation therapy.

Full text

Zhou Ma
Robotics and Mechatronics Lab,
Department of Mechanical and
Aerospace Engineering,
The George Washington University,
801 22nd Street, North West,
Washington, DC 20052
Pinhas Ben-Tzvi
Robotics and Mechatronics Lab,
Department of Mechanical and
Aerospace Engineering,
The George Washington University,
801 22nd Street, North West,
Washington, DC 20052
e-mail: bentzvi@gwu.edu
Design and Optimization
of a Five-Finger Haptic Glove
Mechanism
This paper describes the design and optimization of a novel five-finger haptic glove mech-
anism, which uses a worm-geared motor and an antagonistically routed cable mechanism
at each finger as both active and passive force display actuators. Existing haptic gloves
either restrict the natural motion and maximum output force of the hand or are bulky and
heavy. In order to tackle these challenges, the five-finger haptic glove is designed to mini-
mize the size and weight and maximize the workspace and force output range of the glove.
The glove is a wireless and self-contained mechatronic system that mounts over the dor-
sum of a bare hand and provides haptic force feedback to each finger. This paper
describes the mechatronic design of the glove and the method to optimize the link length
with the purpose of enhancing workspace and the force transmission ratio. Simulation
and experimental results are reported, showing the future potential of the proposed sys-
tem in haptic applications and rehabilitation therapy. [DOI: 10.1115/1.4029437]
1 Introduction
Haptic interfaces have greatly augmented immersive reality
sensing beyond the senses of sight and hearing [1]. Using three
stimuli—visual, auditory, and haptic—it is possible to generate
many desired environments in a believable and immersive manner
[2]. For tasks requiring more dexterity, such as telemanipulation, it
may be necessary to control applied forces on independent fingers
rather than at the wrist, as joysticks and master arms do [3]. One
kind of haptic device, the haptic glove, is worn on the user’s hand
and provides force feedback to the fingers. This type of mechanism
improves force feedback by allowing the user to “feel” virtual
objects in a more natural way. This ability is required in many
applications such as virtual reality [4], tele-operation [5], human-
assistive devices [6], and medical applications [7]. The high dex-
terity of haptic gloves also makes them applicable to the control of
complex movements of remote robots, as opposed to other haptic
devices such as joysticks and PHANTOM [8].
A haptic glove should have two basic functions: (1) to measure
the kinematic configuration (position, velocity, acceleration) and
contact forces of the user’s hand and (2) to display contact forces
and positions to the user [9]. However, due to the human hand’s
dexterity and complex anatomy, physiology and sensory struc-
tures [10,11], designing a haptic glove to match the hand’s dexter-
ity and to provide force feedback for grasping and manipulating
objects of varying sizes and weights is not an easy task.
As a force feedback user interface, the haptic glove should be
user-friendly and effectively apply force to the fingers. A “user-
friendly” glove is ergonomic and lightweight with a compact
design that does not harm fingers. An “effective” glove provides
controllable contact forces ranging from a gentle touch to full
opposition to finger movement without kinematic constraints on
the finger movement.
However, existing haptic gloves do not fully meet these criteria
(i.e., user-friendly and effective) without shortcomings. Although
significant research has been performed into haptic glove design
[4–7,9–15], they either restrict the natural motion and maximum
output force of the hand or are bulky and heavy.
Turner et al. [12] evaluated the CyberGrasp, a commercial hap-
tic glove. The CyberGrasp is a haptic device with one-direction
(extension only) active force feedback on each finger [13]. The
glove joints are actuated by a cable-driven mechanism that trans-
mits the force loading from an actuation unit to each finger. The
heavy actuation unit is located on the table or worn as a backpack.
The maximum output force at each finger is 12 N and the entire
device’s workspace is a sphere of 1 m radius due to the limit of
the cable length. The mass of the mechanism which must be
worn on the hand is 539 g, and this can lead to user fatigue. Two
key drawbacks of this system are its complexity and its cost
(approximately $39,000). In addition, the one-direction actuation
mechanism only allows forces to be applied to the fingertips in the
direction of extension, which limits its utility in force assistance
grasp or rehabilitation application.
Some other haptic gloves utilize internal grasp structures
[14–16]. Bouzit et al. [15] presented the Rutgers Master II, an
active glove for dexterous virtual interactions and rehabilitation.
The system is actuated by four pneumatic actuators arranged
inside the palm of the hand. Hall effect sensors and infrared
sensors are integrated with the actuation cylinders to reduce the
necessity of a separate sensing glove. The objective of the mecha-
nism is to deliver a compact and lightweight structure on the
hand. The Rutgers Master II weights 185 g including the wires
and pneumatic tubing (excluding the pneumatic pump, power
source, etc.), and provided forces up to 16 N on each of the four
fingers. However, the Rutgers Master II limits the hand’s work-
space and prevents complete fist closure due to the placement of
the actuators in the palm.
Based on the above analysis, the primary performance require-
ments of a new haptic glove design are detailed below:
•Size – The glove should easily fit on a human hand.
•Weight – The glove should be as light as possible for port-
ability on a hand. To help achieve this goal, each finger
should require only one dedicated actuator.
•Flexibility of Mechanism – The glove should match the
hand’s dexterity without limiting the hand’s range of motion.
•Dynamic Range – The glove should be sufficiently versatile
to be used in both highly sensitive and large force tasks.
•Safety – The user should be protected from any type of harm
from the mechanism including protections built into the soft-
ware and mechanical limits in the mechanism.
The glove mechanism presented in this work was designed to
address these challenges. Figure 1shows different configurations
of one left hand wearing the glove in different views. This
Contributed by the Mechanisms and Robotics Committee of ASME for
publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received
November 24, 2013; final manuscript received December 12, 2014; published online
March 23, 2015. Assoc. Editor: Pierre M. Larochelle.
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five-finger haptic interface represents a follow-up to the two-
finger glove developed earlier [17]. The new glove is wireless,
lightweight, easy, and comfortable to wear and operate. In addi-
tion to the extension to a five-finger design, with the optimization
analysis, the new glove’s workspace is increased by over 30%,
and thus could adapt to larger range of different hand sizes and
improved the transmission efficiency.
The main contributions of this paper are the mechatronic design
and the optimization of a haptic glove mechanism. The paper is
organized as follows: Section 2describes the mechanical design
of the system. Section 3describes the numerical model of the
mechanism and the optimization of the glove’s finger segment
lengths. Section 4provides the simulation results and experimen-
tal validation of the mechanics model and control system, and
Sec. 5summarizes the paper and describes future work.
2 Glove Mechanism Design
2.1 Mechanical Design. The glove mechanism is composed
of three basic elements: a support pad, five actuation units and
five-finger mechanisms, as shown in Fig. 2. Table 1lists the mass
of each component of the glove (total mass is 310 g).
The support pad is custom-made of thermoplastic material in a
curved shape to match the shape of the user’s hand and rest on it
comfortably. Two adjustable elastic bands are routed around the
thumb and attach to the sides of the support pad, making the pad
sit on the back of the user’s hand tightly (Fig. 1(d)). The
adjustable elastic band allows the support pad to fit on different
hand sizes easily. The support pad is used as the “ground” link of
the finger mechanisms, and the actuators and electronics, includ-
ing the battery, are all attached to the support pad.
Each finger mechanism is attached to the support pad through a
passive pin joint which enables the finger to move in adduction and
abduction directions freely. This mechanism has a mechanical limit
which prevents the finger from rotating until it reaches a certain
controlled position (approximately 5 deg in adduction/abduction
direction. This 5 deg angle works fine for the four fingers, but it
limits the thumb function due to the flexibility of the thumb, and
this is one slight weakness of the current design). Each finger con-
sists of three phalanges with interconnecting rotation joints, as
shown in Fig. 2. This configuration follows the model of human
physiology and imitates basic human hand characteristics. The
fingertip pad, which is attached to link 3, attaches directly to the fin-
gertip using an adjustable length Velcro wrap and applies both flex-
ion and extension tendon forces (measured by strain gauge attached
to the fingertip pad) directly to the finger. Because of this band, the
glove can be put on quickly and is easily adjustable to different fin-
ger sizes. A thin, soft layer of fabric is wrapped around the inside
of the Velcro band to make the glove comfortable to wear. As
shown in Figs. 1and 2, printed circuit board (PCB) is used to con-
struct the mechanical links (link 1 and link 3) and to carry the elec-
trical components (Hall Effect sensors to measure joint angles).
This dual use allows the glove to be both lighter and stronger [17].
Based on the performance requirements in Sec. 1, the force
feedback for each finger will be driven by a distinct actuation
module. This requires the movements of the three joints of each
finger—namely, the distal interphalangeal (DIP), the metacarpo-
phalangeal (MCP), and the proximal interphalangeal (PIP)
joints—to be accounted for in mapping the applied actuation com-
mand to the applied force at the fingertip. Each finger is controlled
by an antagonistic pair of tendons which are routed along the fin-
ger exoskeleton to the fingertip through primary and secondary
pulleys. These pulleys allow the motor to generate torques in each
of the mechanism’s joints. One end of each tendon is wound about
the active pulley attached to the actuation module, while the other
end is attached to the tip of Link 3. Figure 2provides a side view
of the active tendon assembly routed along to a glove finger. The
pair of tendons is wound in opposite directions around the actuator
spool to enable the tendons to transmit forces for both pulley rota-
tion directions. These forces along the exoskeleton drive the links
to follow or resist finger movement. In this antagonistic configura-
tion, the actuator controls the relative length of the tendon pair,
shortening one of the tendons while simultaneously lengthening
the other. As shown in Fig. 2, when the actuator rotates the active
pulley counterclockwise, the grasp tendon (red) is tensioned, and
the mechanism/finger closes. When the active pulley rotates
clockwise, the release tendon (blue) is tensioned and the mecha-
nism/finger opens. The glove links allow full flexion and exten-
sion of all joints, and this tendon-driven mechanism does not have
any limits in the adduction or abduction directions since this
motion will not change the cable length. The material Dyneema
was chosen for the tendon cabling because of its high strength and
flexibility with minimal stretching and weight.
With a single motor driving three joints, each finger mechanism
is under actuated. However, the motion of the glove is not directly
Fig. 1 Glove prototype: (a) and (b) side view in open/closed
configuration, (c)and(d) top/bottom view in open configuration
Fig. 2 CAD model of the index finger mechanism of the glove
Table 1 The glove component mass
Component Mass (g)
Support pad 15
Finger actuator 5355
Finger mechanism 5155
Control unit 25
9 V rechargeable battery 20
Total mass 310
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controlled by the motor; rather, the mechanism’s motion is driven
by the user’s finger movement. The contact force between the
user’s fingers and the glove is what is regulated by the actuator.
2.2 Worm Drive Mechanism. In haptics applications, the
contact force Fis typically calculated as a linear function of
the slave’s virtual penetration distance xinto the object and the
slave’s velocity ( _x)[1]. This results in a virtual spring-damper
model for F, defined in Eq. (1), where kis the virtual object’s
stiffness and bis the object’s damping coefficient
F¼b_
xþkx (1)
A key challenge in haptics that has been repeatedly highlighted
in the literature [12,16–19] is the difficulty in virtually represent-
ing very rigid or hard objects due to the limited stiffness of the
haptic device. Even a solid block will seem to have some compli-
ance to the touch. However, if kand bare set too high, undesirable
oscillations often occur, and the touch sensation is unnatural to
the operator [20].
In general, a haptic glove with force-feedback should be capa-
ble of delivering a maximum force that matches the human hand
output force. According to Ref. [21], the maximum thumb/finger
strength is 35 N (male sustained hold). The glove mechanism is
able to provide this force due to the nonback drivable worm drive
incorporated into the actuation module. Each actuator unit con-
sists of a brushed DC-motor (Mabuchi FA-130, with a Tamiya
70103 universal gearbox at 101:1 gear ratio). The last stage of the
gearing is a nonback drivable metal worm drive, with the active
pulley (which actuates the finger mechanism) attached to the
worm-gear shaft. This actuator is self-locking without power con-
sumption, making the passive force as high as 35 N. The maxi-
mum active output force that the glove mechanism can provide
on the fingertip is 10 N, which is slightly smaller than the 12 N
maximum dynamic output force provided by CyberGrasp [13].
However, the 10 N is sufficient to provide realistic active force
feedback and will not harm the operator’s finger.
The benefit of the nonback drivable mechanism is seen when
the haptic device is used to touch or feel some hard object (e.g., a
concrete wall). In this situation, back drivable motor-actuated hap-
tic devices would run the motor while stalled to generate the high
force. Due to the current and power limits of haptic devices, the
force resulting from this stall torque is still insufficient [22] com-
pared to the human finger output force (35 N). However, for the
glove mechanism in this situation, the motor current is zero by
virtue of the self-locking characteristic of the worm-gear mecha-
nism. Because such high force feedback only occurs in passive
force output mode, it will not hurt the user’s finger. With closed-
loop force-feedback control, the glove can provide a realistic
feeling of both hard and soft materials ranging from a concrete
wall to soft cotton.
When the glove is powered on, with proper speed command to
each actuator unit, it can provide force feedback proportional to
the velocity difference between the finger’s motion and that of the
worm-gear mechanism. When the glove is powered off, each
worm-gear mechanism becomes nonback drivable. Another bene-
fit of the worm drive mechanism is that the power consumption of
the actuators is very low. The 9 V battery can last as long as
40 min for continuous use of the entire glove.
3 Optimization of Link Length
In order to optimize the glove mechanism design presented in
Sec. 2, a 4-bar finger mechanism with bidirectional tendon actua-
tion is modeled and optimized relative to several composite
design indexes simultaneously, including workspace size, force
transmission ratio, and mechanical design parameters. Con-
strained optimality theory is applied to obtain the optimal sets of
link lengths. Glove-link-configurations optimized for special per-
formance indices are also illustrated.
3.1 Introduction. For each finger, the haptic mechanism and
the finger itself can be modeled as a single six-bar mechanism, as
shown in Fig. 3, where the hand/support pad represents the
ground. Each finger has three links, and the haptic mechanism for
each finger has three links, too. However, the terminal link of
each finger is assumed to be rigidly connected to the terminal link
of the haptic mechanism through the Velcro strap discussed in
Sec. 2. Therefore, there are 6 links in total (1 ground link, 3 finger
links, 2 haptic mechanism links) and 6 revolute pin connections
(ignoring the adduction/abduction due to its relative small range).
According to Grubler’s formula, the mobility of the system can be
calculated using Eq. (2), where DF is the system’s degrees of free-
dom (DOF), n¼6 is the number of links, f
1
¼6 is the number of
lower-pair (1DOF) joints, and f
2
¼0 is the number of higher-pair
(2DOF) joints. Therefore, there are 3DOF in the system.
DF ¼3n1ðÞ2f1f2¼3(2)
Based on Fig. 3, equations for the fingertip position ðxA3;yA3Þand
angle /are derived in Eqs. (3)–(5) in terms of the finger joint
angles ðh1;h2;h3Þand the mechanism joint angles ða1;a2;a3Þ,
where l
i
is the length of the ith mechanism link Bi1Bi,piis the
length of the ith finger link Ai1Ai,lpis the length of B3A3.In
addition, sand crepresent sine and cosine, functions such that
c
a,12
is cos a1þa2
ðÞ
xA3¼xB0þl1ca;1þl2ca;12 þl3ca;123 þlpc90þa;123ðÞ
¼p1ch;1þp2ch;12 þp3ch;123 (3)
yA3¼yB0þl1sa;1þl2sa;12 þl3sa;123 þlps90þa;123ðÞ
¼p1sh;1þp2sh;12 þp3sh;123 (4)
/¼a1þa2þa3¼h1þh2þh3(5)
After solving Eqs. (3)–(5) according to Ref. [23], the mecha-
nism joint angles a1,a2, and a3may be calculated using Eqs.
Fig. 3 Kinematic diagram of the finger/glove system
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(6)–(8). Since the glove linkage is longer than the human finger,
two solutions can be found: elbow up and elbow down configura-
tions. In order to avoid the collision between the finger and the
glove linkage, the elbow up solution is chosen. The finger angles
h1,h2, and h3are prescribed by the user
a1¼Atan 2 N
M

þarccos p2
1þp2
2þN2M2
2p1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
M2þN2
p

(6)
a2¼arccos M2þN2p2
1p2
2
2p1p2

(7)
a3¼h1þh2þh3a1a2(8)
where
M¼xB0þl1ch;1þl2ch;12 þl3p3
ðÞch;123 þlpsh;123
N¼yB0þl1sh;1þl2sh;12 þl3p3
ðÞsh;123 þlpch;123
Next, the Jacobians of the mechanism are calculated. For this
model, there will be two Jacobians Ju
qto relate the joint angular
rates _
q¼f_
hi;_
aigto the fingertip velocities _
u, as shown in Eq. (9):
finger Jacobian Ju
hand mechanism Jacobian Ju
a
_
u¼_
xA3;_
yA3;_
/

T¼Jq_
q(9)
Here, Ju
q¼@u=@q1;@u=@q2;@u=@q3
½is the Jacobian relating
the task space coordinates uto the joint space coordinates, q.
Based on this definition, the two Jacobians—finger Ju
hand mecha-
nism Ju
a—are defined by
Ju
h¼
b11 b12 b13
b21 b22 b23
111
2
43
5and Ju
a¼
a11 a12 a13
a21 a22 a23
111
2
43
5
where b11 ¼p1sh;1p2sh;12 p3sh;123,b12 ¼p2sh;12p3sh;123 ;
b13 ¼p3sh;123,b21 ¼p1ch;1þp2ch;12 þp3ch;123;b22 ¼p2ch;12
þp3ch;123,b23 ¼p3ch;123 ;a11 ¼l1sa;1l2sa;12 l3sa;123 lpca;123;
a12 ¼l2sa;12l3sa;123 lpca;123,a13 ¼l3sa;123 lpca;123;a21
¼l1ca;1þl2ca;12 þl3ca;123 lpsa;123; and a22 ¼l2ca;12 þl3ca;123
lpsa;123,a23 ¼l3ca;123 lpsa;123 .
Since this finger–glove system has 3DOF, three joint angles
must be specified to define the configuration. If the three human
finger joints (MCP, DIP, and PIP) are selected as input angles, the
finger–glove mechanism can be considered dependent, or vice
versa. Therefore, the internal kinematic relationship between de-
pendent joints and independent joints is required to deal with the
problem mentioned above.
The equivalent velocity relation is given by
_
u¼Ju
h
_
h¼Ju
a_
a(10)
where _
h¼_
h1;_
h2;_
h3

Tand _
a¼_
a1;_
a2;_
a3
½
T.
Premultiplying the inverse of the matrix Ju
hto the second and
third terms in Eq. (10) results in the following equation:
_
h¼Ju
h

1Ju
a_
a¼Jh
a_
a(11)
where Jh
adenotes the first order kinematic matrix relating hto a.
According to the velocity/force duality [23], the force relation
between the independent joints and the dependent joints can be
defined using the following equation:
sa¼Jh
a

Tsh(12)
3.2 Geometric Optimization. In haptics, a key requirement
is that the human operator’s movement should not be restricted by
the haptic device when there is no contact with a remote or virtual
object. Thus, adequate DOF and sufficient workspace are required
for the haptic device, especially for the haptic glove worn on the
operator’s hand, the most dexterous part of the human body.
The finger–glove’s geometric parameters, particularly link
length, determine the properties of the linkage such as its
workspace and force transmission ratio. In this research, the link
lengths are optimized to be able to enhance the glove’s work-
space, and maximize the force transmission ratio and avoid
collision between each finger and the glove mechanism. Thus, the
problem is formulated as a multi-objective optimization function
that optimizes over the force transmission ratio and contact
force magnitude subject to geometric, and collision avoidance
constraints. The design variables to be optimized are the link
lengths l
1
,l
2
, and l
3,
as shown in Fig. 3.
Furthermore, in order to increase the collision free workspace,
the first link of the glove is composed of two perpendicular
segments, resulting in an Lshape as illustrated in Fig. 2.
3.3 Force Transmission Ratio Objective Function. The val-
ues of the link lengths are a function of the size of a human finger
and the finger joint angular motion ranges. However, these proper-
ties vary across the human population quite significantly. To avoid
the need to customize a glove for each unique user, it is desirable
to accommodate a large number of different users with a given
design. From Eqs. (3)–(5), the conclusion can be drawn that the
solutions always exist if the finger length is much shorter than the
total length of the mechanism (about 140 mm), thus the glove
mechanism design can accommodate variations in finger length.
Figure 1demonstrates that the same mechanism can easily adapt
to different finger sizes because each articulated linkage mecha-
nism remains extendable when each finger is fully stretched.
In order to accommodate a wide variety of users, the “stochastic
reachable workspace” method was adopted into the design of the
glove interface mechanisms [24]. The workspace and average
dimensions of a male index finger are shown in Table 2[25].
According to the inverse kinematic analysis in Sec. 3.1, given a
set of link lengths l
i
, the mechanism joint angles a
i
can be calcu-
lated given the finger joint angles h
i
if solutions exist according to
Eqs. (3)–(5). Thus, Eq. (13) summarizes the relation mentioned
above
ai¼fhi;lj
 (13)
Joint range is defined as
ai;var ¼ai;max ai;min;i21;2;3
fg (14)
Each finger of the glove mechanism is actuated by a motor rota-
tion that generates tension in a pair of tendons. The tendons are
routed from the actuator through pulleys to the fingertip. How-
ever, friction between the tendons and the pulleys reduces the
amount of force available to the finger tip. To compensate this,
the actuator must generate more tension, which may result in low
efficiency, high current, and, eventually, damage to the motor or
the mechanism. Therefore, the efficiency issues in cable and
pulley systems must be thoroughly understood. Some relevant
research on friction efficiency has been described in Refs. [26]
and [27]. However, understanding the tendon friction
Table 2 Normal values for range of motion of joints
Finger joint Angular motion range (deg) Finger link length (mm)
MCP [90, 30] 48.3
PIP [120, 0] 28.2
DIP [80, 0] 19.1
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characteristics in our particular application is not common and is
therefore discussed and experimentally tested herein.
Nonlinear complex friction phenomena are the main reasons for
the inefficiencies and loss of tendon transmission. Coulomb
friction, viscous friction, and static friction can all be present in
tendon transmission systems [28]. To actuate the glove mecha-
nism, the tendon needs to slide within the groove of the pulley.
Therefore, only kinetic friction is considered in this paper.
If the tendon wraps around the pulley at a given angle c, the
ratio between tendon tension force before F
1
and after F
2
routing
may be modeled using Eq. (15), where lis the coefficient of fric-
tion caused by sliding motion between the tendon and pulley [26].
F1=F2¼elc (15)
It is important to note that the pulley radius, magnitude of the
cable tension, and sliding velocity do not influence the tendon
friction. Because the glove mechanism tendon material (dyneema)
is very soft, even a very small pulley radius will not accelerate
cable wear, and the friction coefficient will not be affected over
time. Therefore, the secondary pulleys are made of a 2 mm screw
and a steel ring, as shown in Fig. 4, and the secondary pulley is
modeled as a stationary cylinder.
As Eq. (15) indicates, the main parameters influencing cable
transmission efficiency are cand l. While lis dictated by the
tendon and cylinder materials, cdepends on the mechanism geom-
etry. As shown in Eq. (16),cmay be broken down into two com-
ponents: a constant component c
c
corresponding to the minimum
wrap angle configuration and a variable component Dcthat
depends on the geometric configuration of the mechanism. The
maximum value of Dcfor each joint is the joint range ai;var,
defined in Eq. (14)
c¼ccþDc(16)
In order to maximize the tendon force transmission ratio, the
wrap angle for each joint should be minimized. This corresponds
to minimizing the joint range ai;var at each joint. The norm of these
angles is chosen to formulate the scalar force transmission ratio
objective function z
1
, as shown in the following equation:
z1¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a2
1;var þa2
2;var þa2
3;var
q(17)
3.4 Contact Force Objective Function. The primary force
that will be sensed by each finger in the glove mechanism will be
the normal force applied to the surface of the fingertip [29,30].
The accuracy of the magnitude of this normal force f
y
, as shown
in Fig. 3, is a key factor in haptic glove and precision tele-
operation grasping tasks applications. Thus, the contact force
components in other directions (f
x
and f
z
) are ignored.
The joint torques (s
1
,s
2
, and s
3
) are calculable from the
fingertip contact force F¼fx;fy;fz
½
Tand the mechanism Ja-
cobian, Ju
aaccording to the following equation:
s1;s2;s3
½
T¼Ju
a

Tfx;fy;fz
½
T(18)
After substituting for Ju
aand setting f
x
and f
z
to zero, the joint
torques become s1¼a21fy,s2¼a22 fy, and s3¼a23fy.To
maximize the contact forces for a given set of joint torques, these
coefficients should be minimized. As before, the norm of these
coefficients is chosen to formulate the scalar contact force objec-
tive function z2as shown in the following equation:
z2¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a2
21 þa2
22 þa2
23
q(19)
3.5 Constraints. The multi-objective optimization problem is
subject to constraints related to limitations in mechanical design,
kinematic configurations and the collision-free operational requirement.
In order to fit on a human hand, the total length of each of the
glove’s fingers should be greater than the length of an average
human finger. Therefore, kinematic constraint g
1
ensures the total
length of the mechanism is greater than the total length of the
average finger segments, as defined in the following equation:
g1:l1þl2þl3>p1þp2þp3(20)
In addition, the glove mechanism link 1 should exceed the fin-
ger segment 1 length to prevent the intersection between the finger
and glove mechanism. Therefore, kinematic constraint g
2
ensures
link 1 length is greater than the length of the finger’s first segment,
as shown in the following equation:
g2:l1>p1(21)
Due to mechanical design constraints, each joint of the glove
finger cannot continuously rotate and its working range is limited
to a maximum of 150 deg. This joint angle limit also protects the
user’s fingers from rotating beyond normal range of motion and
causing injury. Therefore, kinematic constraint g
3
will restrict the
joint range ai;var at each joint ito less than 150 deg, as shown in
the following equation:
g3:ai;var <150 deg;i21;2;3fg (22)
3.6 Collision-Avoidance Constraint. If the glove link
lengths are not properly designed, intersection between the finger
and glove mechanism will occur. In order to avoid this intersec-
tion, collision detection algorithms are incorporated into the
optimization procedure. From Fig. 3, each pair of segments,
Bi1Biand Ai1Aifor i¼1;2;3 are examined. When collision is
detected, the associated mechanism joint angles are excluded
from the optimal result, as shown in Fig. 5, where the solutions at
which intersections occurred are marked in red.
3.7 Optimization Formulation and Results. Based on Eqs.
(17) and (19), the multi-objective optimization function may be
defined by Eq. (23), where w
1
and w
2
are the weighting coeffi-
cients, and is subject to the constraints defined in Eqs. (20)–(22)
Z¼w1z1þw2z2(23)
In order to solve this constrained nonlinear optimization, two
methods are used. The second derivatives of the Lagrangian
method using the brute-force global search (BFGS) formula at
each iteration (implemented with MATLAB optimization toolbox
using the fmincon function) was obtained to find the local mini-
mum value of the penalty function. The BFGS method was also
used to verify that the result was correct.
For the numerical optimization, a set of initial guesses (the
lengths of human hand fingers from Table 2multiplied by 1.5)
and the lower (human fingers lengths from Table 2) and upper
(fingers lengths from Table 2multiplied by 2) boundaries were
chosen and all of the weight coefficients were set to 1 (implying
equal importance for all two objective functions).
The optimal length of link 3 quickly converges to 19.1 mm, so
only link 1 and link 2 are shown in Fig. 5. The optimized solution
Fig. 4 Fixed secondary pulley prototype and model
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set, with minimum objective functions that satisfy all the con-
straints, was summarized in Table 3.
In order to find the singular points of the glove mechanism, the
determinant of its Jacobian should be set equal to zero, as shown
in Eq. (24). A singularity will occur when a
2
equals zero or 180
deg. However, for the glove mechanism, the working range of a
2
is [130,50], which will avoid all calculated singularities
det Ju
a

¼l1l2sin a2¼0(24)
4 Simulation and Experiments
4.1 Index Finger Workspace Simulation. Two methods are
used to calculate the workspace of the human finger and the glove
mechanism: joint angle sweep and the recursive swept boundary
method. For the joint angle sweep, large numbers of points are
generated in the workspace based on varying the joint angles
through their known ranges, and the workspace boundary is com-
puted based on these points. Whereas this method is computation-
ally inefficient, it is relatively simple to implement and highly
accurate. Alternatively, the recursive swept boundary method [31]
is very computationally efficient. However, it is significantly more
difficult to implement.
Based on the mechanism model defined in Sec. 2, the finger
joint ranges of motion defined in Table 2, and the optimal link
lengths calculated in Sec. 3.7, the 2D workspace for a finger and
the glove mechanism can be obtained, as shown in Fig. 6. As the
figure illustrates, the finger workspace is a subset of the mecha-
nism’s workspace, ensuring the glove allows unimpeded finger
motion. Similar results are seen for the workspaces of the other
fingers and mechanisms.
4.2 Friction Model Validation. Figure 7shows the apparatus
used to measure the friction coefficient between the tendon and
stationary pulley. A custom manufactured plate was designed to
ensure that the wrap angles were at specific desired values. To
experimentally simulate the tension over the stationary pulley, a
weight was suspended from one end of the tendon. In addition, to
prevent static friction effects, a 50 W brushless motor with a 23:1
planetary gearbox (Maxon Gear 166936, Maxon Motor 251601)
was attached to the tendon spool, lifting and lowering the weight
at various constant speeds. A load cell (MLP-10, Transducer
Techniques, Inc.) was connected in series with the tendon between
the active tendon spool (connected to the motor) and the station-
ary pulley to measure the tension of the tendon. In addition, differ-
ent lubrication conditions were tested to evaluate the lubricant’s
effect on the friction coefficient.
The wrap angle was varied from 45 to 315 deg in 45 deg incre-
ments to evaluate its effect on the friction coefficient, and the
mass at the end of the tendon was varied from 100 g to 1000 g in
100 g increments. When the actuator lifts the weight, the load cell
measures the active pulling force F
1
in Eq. (15), and the hanging
weight corresponds to F
2
. Conversely, when the actuator lowers
the weight, the load cell measures F
2
and the weight is F
1
.
The linear behavior of the experimental results shown in Fig. 8
and the close friction coefficient values when the wrap angles
vary as shown in Fig. 9suggest that Eq. (15) is an acceptable
model of the tension system when the wrap angle is above 90 deg,
which will always be satisfied for the glove mechanism. The
effective friction coefficient can be found by applying a least-
squares fitting to the data for 90 deg wrap and above. The average
friction coefficients for lubricated lLand nonlubricated lNL con-
ditions are 0.0530 and 0.0631, respectively.
4.3 Free Movement Test. The capability of free motion is a
basic evaluation criterion of haptic devices [32,33]. In the free
Fig. 5 Optimal result (local minimum, variance (19,
18) 5543.6889)
Table 3 Optimization results of the glove link
Glove link/joint Joint angle range (deg) Link length (mm)
1[79.86, 59.98] 73.88
2[127.8, 58.3] 47.23
3[82.3, 81.6] 19.1
Fig. 6 2D workspace comparison between index finger and
the glove mechanism when l 5[73.88; 47.23; 19.1],
a1¼½80;60,a2¼½130;50,a3¼½80;60
Fig. 7 Friction model validation experimental test platform
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motion mode (i.e., the state with zero force input), the haptic
glove’s user should be able to move his/her fingers freely without
feeling resistance or inertia from the glove. The resistance and
inertia should be compensated for via a real-time control algo-
rithm based on the force and position sensors input. It is assumed
that the force between the glove and the human finger should be
as small as possible in free motion. If we control the device and
set the force to be zero, the glove will follow the movement of the
user’s fingers. Thus, the user cannot feel the resistance force.
In this experiment, 4 male and 1 female subjects were asked to
wear the glove prototype and to move all fingers in close/open
maneuvers, in two different modes: without cabling and with
cabling. In the “without cabling” mode, all the actuation cables
were removed. Without the worm-gear locking function, the fin-
ger mechanisms move easily even under a small external force.
To test whether the glove is comfortable to wear, 25 people were
asked to perform the wear test (repeat fully open/close maneuvers
three times) in this mode. None has reported any hand movement
constraint issues. The “with cabling” mode is the normal glove
mechanism system with the cable installed and force feedback
enabled. In this second mode, the control algorithm actively posi-
tions the actuators to ensure the glove mechanism tracks the
finger’s movement.
The glove does not require calibration for different users. How-
ever, before the test, the finger length of each user was measured
by a ruler. During the test, each user was asked to repeat two
close–open hand maneuvers five times in approximately 3 s in
both modes. The 15 joint angle sensors of the glove measured the
joints angles at a sampling frequency of 300 Hz. Before recording
the data, each user spent several minutes to get used to the system.
The graphical results for two close/open maneuvers acquired by
the first user’s index finger in test no. 1 are reported in this paper
as a representative example of the total test results. Five parame-
ters are displayed for the two modes in Figs. 10 and 11: the three
measured joint angle trajectories, the contact force and the actua-
tor current (note that the actuator current is not applicable to the
“without cabling” mode because the motor is not used). In each
test, the user took about 1 s for one full close/open maneuver. The
glove can be actuated faster, but for safety considerations the
maximum speed was limited to 1 s for one full close/open maneu-
ver. At this speed, the maximum contact forces were approxi-
mately 200 mN in the “without cable” mode and 100 mN in the
“with cable” mode. This result shows that the mechanism’s inter-
nal resistance can be effectively compensated by a proportional
integral derivative (PID) force controller. Since the main focus of
this paper is the five-finger glove design and optimization, details
on the control algorithm can be found in Ref. [17].
Pearson product moment correlation (rP)[34] was adopted to
assess the level of similarity of joint trajectories between two dif-
ferent modes. Table 4records the values of rPand the standard
deviation (s.d.) averaged over the five repetitions. As shown in
Table 4, the slight differences between two different modes
demonstrate the effectiveness of the haptic glove in following the
movement of the user’s fingers.
Fig. 8 Least-squares fitting plots for load cell output when lift-
ing objects with lubrication
Fig. 9 Friction coefficient with and without lubrication
Fig. 10 Human index finger trajectories for two close\open
maneuvers acquired by user 1 in test #1
Fig. 11 Contact force (a) and actuator current (b) measured in
free movement
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5 Conclusions and Future Work
The main contributions of this paper are: (1) the mechatronic
design of a haptic glove mechanism, (2) the optimization of the
mechanism’s geometry based on geometric and force transmission
characteristics. Primarily, we proposed a method to optimize the
link length in a haptic glove design for the purpose of enhancing
the workspace of the mechanism and maximizing the force trans-
mission ratio of the link mechanism. Free motion experiments
were established to demonstrate the effectiveness of resistance
compensation. The research has shown that a lightweight compact
actuation package can provide excellent motion and force control
potential in a complex, dexterous manipulator.
Future work will be devoted to the redesign of the thumb mech-
anism in order to add one more DOF to adopt the flexibility of the
thumb joint. Furthermore, dynamic constraints optimization, such
as the unintended force between the finger and the glove due to
the non-back drivable actuator, will be addressed. For virtual real-
ity applications, object recognition experiments will be conducted.
For rehabilitation application, this system will be exploited to
record and analyze the common movements of hand function
including grip and release patterns, thus the glove could generate
these movement patterns in playback fashion to assist a weakened
hand to accomplish these movements, or to modulate the assistive
level based on the user’s intent for the purpose of hand rehabilita-
tion therapy. For virtual reality applications, “Digital Clay”, a
three-dimensional haptic computer interface [35] will be used to
interact with the five-finger glove to evaluate the glove design and
functionality. For tele-operation applications, the glove mecha-
nism will be adapted for hand gesture-based remote control of
mobile robots [36–38].
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Table 4 Product moment correlation
User 1 User 2 User 3 User 4 User 5 All uses
rPða1Þ6s:d:0.9907 60.0022 0.9923 60.0037 0. 8671 60.0542 0.9722 60.0144 0.8864 60.0842 0.9417 60.0602
rPða2Þ6s:d:0.9135 60.0227 0.7635 60.0314 0. 7163 60.1012 0.8702 60.0867 0.8034 60.0770 0.7981 60.0814
rPða3Þ6s:d:0.8992 60.0471 0.9018 60.0126 0. 8134 60.0261 0.9139 60.0408 0.7413 60.0865 0.8692 60.0558
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