IEEE Robotics & Automation Magazine - December 2020 - 62

tipping point workspace of previous traditional FEAs is
assumed to be a constant arc [20].

Table 2. The FEM optimized parameters.
Design Parameters

Optimized Value

Joint length: L 1 (mm)

44.6

Chamber length: L 2 (mm)

42.5

Joint diameter: D 1 (mm)

22.3

Chamber diameter: D 3 (mm)

9.14

Chamber-to-wall thickness: H 1 (mm)

1.68

Results and Discussions
Workspace Analysis
For a better understanding of the finger mechanism, the
workspace analysis is evaluated (Figure 8). The kinematic
model of the finger is considered as one joint and two
links. The first link (red) is fixed, and the second one
(blue) can bend up to 90° in the xy-plane. The whole finger can rotate around the x-axis about 300°. By changing
the position of the joint, the bending point and the length
of the two links are changed. As noted in the " Design
Optimization " section, the length of the finger and joint
were presumed to be within the range of 4.46 and 15 cm.
The bending point (center of joint) can be moved along
the x-axis from 2.5 to 12.5 cm, and the resulting workspace
of every point touched by a fingertip in 2D [Figure  8(a)]
and 3D [Figure 8(b)] is calculated. The 2D workspace
comparison between the proposed finger and a traditional
design shows that changing the position of bending
increases the number of accessible points, while the

Experimental Results
Validating the numerical model introduced in the previous
sections, the fabricated finger undergoes two sets of experiments, as in bending and force tests. Figure 9(a) shows the
prototype assembled to conduct the tests.
An Arduino Uno board controls the whole process,
including reading sensors, switches, and electric motors, and
it is connected to the computer via a USB wire. A 12-V, 350-kPa
air pump is used for supplying the pressurized air for the system.
Regulating the pressures P1 and P2 independently, one solenoid
valve and one silicon piezoresistive pressure sensor are embedded in each air stream. The feedback signals that transfer from
each pressure sensor to the Arduino are used to switch the air
pump and the relevant solenoid valve on and off. Two test
benches are developed to characterize the bending angle as well
as the blocking force of the fingertip. The bending angle of the
finger is checked using a printed protractor, placed at the joint's
center of bending [Figure 9(b)]. As for measuring the force
applied by the fingertip, a sensor is situated below the tipping
point of the finger and directly transfers the force data to the
computer [Figure 9(c)]. Due to the weight of the link, at the initial state, a deflection of 10° at the tipping point can be
observed; this will be resolved by applying the pressure P2
inside the link. Different pressures P1 are applied to the joint,
and the consequent bending angles are measured. These angles
are compared with the numerical results in Figure 10(a). It can
be noticed that there is an acceptable agreement between the
experimental and numerical data, which can be taken as
the validity of the model and thus the optimization results. As
the second test with the assembled prototype, the force at the

2D Workspace of Proposed Finger
2D Workspace of Conventional FEA

3D Workspace of Proposed Finger
3D Workspace of Conventional FEA

15

20
15

10

10
5

Range of
Bending Point
2.5 < d < 12.5

-5

-10

-10
0

-15
-10
-15
-5

-20
20
0

5
10
x (cm)
(a)

15

20

10
10

5
y (cm)

-10

-20

m)

-5

-20

0

x (c

0

z (cm)

y (cm)

5

20

(b)

Figure 8. A workspace evaluation of the proposed finger compared to conventional FEAs with 12.5-cm length in (a) 2D space and
(b) 3D space (the finger can rotate around its axis about 300° ).

62

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

DECEMBER 2020
IEEE Robotics & Automation Magazine - December 2020

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2020
