IEEE Robotics & Automation Magazine - December 2020 - 58

(a)

The position of the joint and
The stiffness of the finger the stiffness of the finger
can be varied by applying change the amount of exerted
pressure inside the soft
force at the tipping point.
link.
(b)
Figure 2. A comparison between the configurations of the
proposed finger (left) and a conventional FEA-based finger (right)
when (a) reaching a particular point and (b) exerting a different
amount of force to a tipping point.

Ball Screw
(Changing Rotation to Translation)

Coupling

Translation Displacement
Soft Link Actuator Joint

Rotational
Movement
Connector Rod

Design Optimization

One Stepper Motor
for Rotation
One Stepper Motor for Translation
Figure 3. The assembly structure of the proposed finger and motors.

L1
L2

H1
D3
D2
H2

θ
D1

D1: Joint Diameter
D2: Hole Diameter
H2: Hole to Wall Thickness
D3: Chamber Diameter
L1: Joint Length
H1: Chamber-to-Wall Thickness L2: Chamber Length
Figure 4. The geometrical optimization parameters.

IEEE ROBOTICS & AUTOMATION MAGAZINE

In Figure 2(a), a conventional FEA finger (on the right)
and the proposed finger (on the left) are compared in terms of
dexterity and the strategies used to reach a particular point in
the workspace. Due to the uniform structure of conventional
FEA fingers and their limited DoF, it is not possible for them
to attain each point in their workspace with various configurations. On the contrary, the design of the proposed finger
suggests an array of possible configurations in which the finger can reach each point. This not only results in more flexibility of the finger in dealing with obstacles that limit the
workspace but also enhances the possible configurations in
which it can exert a different amount of force to a particular
point [Figure 2(b)]. The workspaces of these two fingers are
compared in the " Results and Discussion " section.
The mechanism used for changing the bending point of
the finger consists mainly of two stepper motors connected to
the joint (Figure 3). The first is linked directly to the joint and
is responsible for its rotational displacement. The connection
includes two rigid rods: one for transmitting the rotational
movement of the motor to the joint and the other, with a
tubular shape passing through the center of the link, for
enhancing the stiffness of its region between the vertical support and the joint, which facilitates deformation downstream
and improves controllability. As for the linear longitudinal
movement of the joint, its assembly and that of the first motor
are entirely displaced by the second stepper motor using a ball
screw mechanism. We chose to use a stepper motor solution
for the movable joint due to its position accuracy and fast
reactivity. Two air streams with different pressures are supplied to the finger: P1 deforms the joint, and P2 regulates the
stiffness of the link. These two air streams are applied via the
two rods between the joint and the stepper motor for rotation.

DECEMBER 2020

Finite Element Modeling
In this section, we describe the optimization procedure
for a finger with the approximate dimensions of a human
finger (diameter = 10 mm and length = 150 mm). The
goal of the optimization is to find the best values of the
parameters to meet the design objectives-as in maximizing the bending angle of the finger (i) and minimizing
the joint dimensions (length and diameter) under an
approximate value of applied pressure to the joint (P1).
This value is numerically determined based on the 80% of
pressure that causes the joint to burst with a 1-mm-thick
chamber wall (H 1), which is equal to 14 kPa. Figure 4
summarizes the design parameters under investigation,
including the main geometrical ones of the joint. The
range of variation for each design parameter is tabulated
in Table 1. The lower and upper bounds are specified
based on fabrication considerations and also the dimensions of the finger, which is expected to be equivalent to
the human finger. The pressure inside the link (P2) is
taken into account as another design parameter, and the
range of variation is selected in a way such that a sensible

IEEE Robotics & Automation Magazine - December 2020

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