A Bioinspired Stiffness Tunable Sucker for Passive Adaptation and Firm
Attachment to Angular Substrates

Arman Goshtasbi
Department of Biomechanical Engineering
University of Twente
Enschede, The Netherlands
<EMAIL_ADDRESS>|  Ali Sadeghi
Department of Biomechanical Engineering
University of Twente
Enschede, The Netherlands
<EMAIL_ADDRESS>
---|---

###### Abstract

The ability to adapt and conform to angular and uneven surfaces improves the
suction cup’s performance in grasping and manipulation. However, in most
cases, the adaptation costs lack of required stiffness for manipulation after
surface attachment; thus, the ideal scenario is to have compliance during
adaptation and stiffness after attachment to the surface. Nevertheless, most
stiffness modulation techniques in suction cups require additional actuation.
This article presents a new stiffness tunable suction cup that adapts to steep
angular surfaces. Using granular jamming as a vacuum driven stiffness
modulation provides a sensorless for activating the mechanism. Thus, the
design is composed of a conventional active suction pad connected to a
granular stalk, emulating a hinge behavior that is compliant during adaptation
and has high stiffness after attachment is ensured. During the experiment, the
suction cup can adapt to angles up to 85∘ with a force lower than 0.5 N. We
also investigated the effect of granular stalk’s length on the adaptation and
how this design performs compared to passive adaptation without stiffness
modulation.

##  1 Introduction

Adaptation plays a pivotal role in grasping, manipulating, and interacting
with unknown environments. Due to their low mechanical flexibility,
conventional robots require complex control and sensory and actuation systems
to achieve such adaptation [1]. In most cases, these robots lack adaptability
and are only suitable for a single task [2]. On the other hand, inspired by
animals’ inherent ability to adapt to unknown surroundings, studies suggest
that soft grippers, thanks to their compliance, can exceed rigid robots’
limitations and perform more adaptively in undefined conditions [3].

Many animals utilize astrictive prehension, also known as adhesive grippers,
to attach to surfaces or grab objects. Different techniques have been
suggested to achieve adhesion inspired by such animals. For instance,
different grippers have been developed using van der Waals force inspired by
microfibers on gecko’s toes [4], [5]. However, controlling the force in such
grippers is difficult [6]. Another technique, inspired by suction cups in
octopus tentacles [7], and suction disc on northern clingfish ventral side [8]
[9], is surface attachment using negative fluid pressure in a suction cup. Due
to their fast, controllable, and efficient way of attaching to surfaces [10],
vacuum suction grippers have shown great potential in various grasping
applications, such as surface grasping in wall-climbing robots [11], grasping
in surgical application [12], and haptic exploration [13]. The suction cups
are either passive, in which the change in the shape provides negative
pressure, or active, in which an external vacuum pump generates the pressure.
The active vacuum gripper produces more grasping force and is easier to detach
by connecting it to ambient pressure. At the same time, the latter provides a
tetherless solution and a more energy-efficient solution for grasping [10].

Despite the numerous advantages of suction cups, conventional suction cups
have some limitations in adaptation to various environments. For instance,
rough and porous surfaces prevent the vacuum suction cups from providing
negative pressure. Several studies have proposed designs to overcome these
shortcomings by looking at how animals overcome such problems. For example,
Inspired by sea urchins, combination of soft suction pad and chemical adhesive
material improve the grasping on very rough surfaces ([14]). [15]
microfabricated a thin elastomer with multiple micro-suction cups in an
octopus-like suction cup. Furthermore, [16], Developed a micro-bumps surface
for rough surface grasping. Aside from the bio-inspired designs, [17] designed
a filmed base suction cup that can attach to rough and porous surfaces.

Another challenge for vacuum suction cups is grasping objects with unknown-
shaped objects and angular surfaces. The suction cups require flexibility to
adapt to the object’s surface to overcome this issue. [18] suggest attaching a
thin elastomer membrane to the suction cup, enabling it to attach to round
objects. [19] proposed an origami-based design to adjust to the object’s shape
by actuating shape memory alloys. Finally, inspired by Octopus, [20] attached
the suction cups to a flexible stalk to emulate spherical joint behavior.

Although each design solves a critical problem, most of them pay the most
attention to grabbing an object rather than attaching it to an angular
surface, which can benefit applications such as manipulating unknown objects.
Furthermore, the flexibility in these designs that makes the adaptation
possible causes a lack of stiffness, which can be problematic for manipulation
applications. Several researchers have investigated methods to tackle this
paucity using stiffness modulation techniques, such as employing layer jamming
to increase and control the vertical stiffness, enabling lifting heavier
objects [21]. In addition, [22] designed a cloth-rubber beam to provide enough
stiffness for surgical applications. Also, in the origami design of [19], the
shape memory alloys endow the design with the possibility to lift 50 times
more of its weight. However, most studies do not discuss bending stiffness,
which plays a significant role in wall-climbing applications.

In nature, octopus suction cups provide the best solution for adaptation and
bending stiffness. Octopus, similar to other Cephalopod mollusks, such as
squids and cuttlefish, employ muscular hydrostats which make them capable of
active stiffening and force generation [23][24]. In the suction cup, the
octopus uses muscular hydrostats to not only adapt the surface and generate
the negative pressure required for grasping but also control the bending
stiffness and manipulate the grasped object using the extrinsic muscle of the
suction cup. The extrinsic muscle is the muscle that connects the sphincter to
the arm of the octopus.

In this study, we propose a new granular jamming base suction cup inspired by
the rotary behavior of octopus suction cups [20][24] and jamming designs [25]
[26]. This design adapts steep angular surfaces with the material’s compliance
and provides high bending stiffness after the attachment with the vacuum of
granular particles. The stiffness modulation in this design does not require
an additional actuator, which helps weight and energy efficiency. In addition,
the design is sensorless and simplifies the control in many applications. This
study investigated how changing parameters such as pressure, angle, and
material compliance affect the design performance.

##  2 Material and Methods

###  2.1 Design and Fabrication

Figure 1: (A) Schematic drawing of octopus suction cup and the connection to
arm via extrinsic muscle. The extrinsic muscle enable the octopus suction cup
to have rotary manipulation and also provide stiffness modulation. (B) Drawing
of the proposed suction cup. (C) The adaptation sequence of the suction cup to
a angular surface.

In the design shown in Fig 1, a soft stalk is attached to a conventional
suction pad to imitate wrist-like behavior for passive adaptation to angular
surfaces. Although in this design, the flexibility of compliant materials
renders the possibility of adaptation to steep angles, the low stiffness of
such materials reduces the bending tolerance which can be disadvantageous in
some applications such as wall-climbing and grasping object from lateral side.
Therefore, stiffness modulation techniques endow this design with high
flexibility of compliant materials for adaptation and high shear resistance
after surface attachment. We choose granular jamming as a stiffness modulation
method, since it can be activated by negative pressure. This creates the
possibility to use the same source of negative pressure for activation of both
suction cup and stiffness tunable stalk. This stalk design perform similar to
octopus extrinsic muscle which enables angular manipulation and adaptation for
the suction cup.

For fabrication of the suction pad, we degassed silicone rubber (1atm,
degassing time: 10min) and poured it into a 3D-printed mold. For the
experiments, series of suction cups were fabricated with different silicone
rubbers (Ecoflex 00-10 and Dragonskin 10, Smooth ON) to study how the suction
pad softness affects the adaptation. In the fabrication of the soft stalk, as
presented in Fig2, we cast a thin film of Ecoflex 00-10 with a thickness of
0.2 mm on a plate using the doctor blade casting method [27] and cured it in
the oven (60∘). Using such a thin film makes the design significantly
compliant during adaptation and stiff after attachment. After the silicon was
cured, we peeled off the film and rounded it on a cylinder with a diameter of
12mm to attach two sides of the film using the same silicone rubber. Finally,
the suction cup was cast on top of the cylindrical film. Based on [28], the
area in the thin film tube was filled with coffee grains as the granular
particle to enhance modulation. In addition to the granular stalk, we cast
silicon rubber arms (Ecoflex 00-10 and Dragonskin 10) with the exact
dimensions as the granular stalk (20mm) to compare the adaptation of the
proposed design with adaptation using only material flexibility and without
stiffness modulation. As shown in Fig1, a fine braided textile was used as
cylindrical filter and is placed in the middle of the suction cup to have an
air connection and prevent coffee grains from entering the pump. In addition
to preventing coffee from going into the pump, the filter also improves the
suction cup’s axial load capacity.

Figure 2: (A) Casting silicone rubber on a plate and use blade to make uniform
thin film. (B) The silicone rubber cast on plate and left to b cured. (C)
Peeling the film from plate (D) Wrapping the film around a cylinder and
sealing two sides of the film. (E) Attaching the suction pad to the stalk. (F)
Adding coffee and place filter in the suction cup.

###  2.2 Theory

Figure 3: The L-beam used to model the behavior of the suction cup during the
adaptation. (A) the initial shape of the beam and the suction cup. (B) The
deformed suction cup with the deformed L-shape beam. (C) the free body diagram
(FBD) of the stalk, here $F$ is the required force for adaptation, $\gamma$ is
the surface angle, $\theta$ is the tip deflection, $\phi$ is the angle between
the force and stalk which in this case is $180^{\circ}$, and also a moment
relative to the force and the radius of the suction pad is also applied to the
beam.

As shown later, the dynamic behavior of the suction cup during the adaptation
is complex, especially with granular particles moving during the deformation.
Therefore, we modeled the suction pad and the stalk as an L-shape beam to
simplify such complicated behavior, as presented in Fig3. Since the stalk
deforms significantly during the adaptation, the conventional static beam
load-deflection equations are invalid. Hence, the dynamic beam deflection
model presented in [29] is used. In this model, when a straight beam is under
load F with force angle $\phi$, and moment M, the beam bending differential
equation is

$\frac{d^{2}\theta(s)}{ds^{2}}=\frac{Fsin(\theta(s)-\phi)}{EI}\quad
with\quad\theta(0)=0\quad\theta(L)=\frac{M}{EI}$ (1)

Where E is Young’s modulus, I is the second moment of inertia, and S is the
length coordinate which is between 0 and the length of the beam (L). In our
case, as shown in the free body diagram (FBD) in Fig3-C, the moment depends on
the force applied to the stalk. In addition, Eq1 is dependent on geometry and
material properties. Therefore, to make the equation independent of the length
of the stalk and the stalk material, Eq1 is normalized as follows:

$\frac{d^{2}\theta(s)}{ds^{2}}=\alpha sin(\theta(\bar{s})-\phi)\quad
with\quad\theta(0)=0\quad\frac{d\;\theta(L)}{ds}=\frac{\alpha R}{L}\quad
Define:\alpha=\frac{FL^{2}}{EI}$ (2)

Where R is the radius of the suction pad. This equation is the second order
differential equation with two boundary condition. In order to solve Eq2, we
used a numerical approach presented in [30]. To find the $\alpha$ for each
angle, we numerically solve the equation until the tip angle ($\theta$) equals
the surface angle ($\gamma$). By solving this equation, the $\alpha$ required
for adaptation to various angles can be calculated, as shown in Table1 for
angles from $0^{\circ}$ to $90^{\circ}$ with $15^{\circ}$ increments. Later,
to convert the calculated $\alpha$ to the adaptation force, we used measured
data from the stiffness test to calculate the stiffness of each scenario.

Table 1: The required $\alpha$ for different angles from the theory presented in Eq2 Angle(∘) | Required $\alpha$
---|---
0 | 0
15 | 0.445
30 | 0.772
45 | 1.03
60 | 1.254
75 | 1.467

###  2.3 Experimental Setup

As mentioned, the design goal is high flexibility during adaptation and high
stiffness after attachment. We performed two experiments to characterize the
design behavior for both claims. A universal tensile test machine (Instron
3343, Instron, USA) with the shown setup (Fig 4) was used for all the tests.
In the first experiment, the adaptation force of the suction cup to the
angular surface was measured by vertically pushing the suction pad to the
surface with constant speed (1mm/sec) while a vacuum pump provided the
negative pressure. The applied force was measured until the suction pad was
attached to the surface, monitored by measuring the pressure sensor. Then, we
experimented with various surface angles (15∘ to 90∘ with 15∘ increments) to
measure adaptation force and ultimate adaptation angle. For each scenario, the
test was conducted 4 times to check the repeatability of the suction cup
behavior.

Figure 4: The setup used for adaptation and bending stiffness test. (A) the
adaptation test setup: (B) The bending stiffness test setup

Furthermore, we conducted the experiment with different lengths of the
granular stalk (5-10-20mm) and different stalk materials (Ecoflex 00-10 and
Dragonskin 10) but with the same diameter to exhibit how stiffness change
affects the adaptation force and ultimate adaptation angle, and also how the
granular joint performs compare to uniform soft material. Finally, to
investigate the effect of suction pad material on adaptation, an Ecoflex 00-10
suction pad was attached to the 20mm granular joint, and the adaptation test
was performed. In all adaptation tests, the surface was plexiglass, and the
pressure after grasping was -60KPa relative pressure.

We performed the bending stiffness experiment with the setup shown in Fig 4 to
assess the stiffness modulation impact on the bending stiffness of the stalk.
In this experiment, while the suction pad was attached to the surface with the
vacuum pump, the tensile test machine applied a force to the end of the soft
stalk with a constant speed of (1mm/sec). The applied force to the stalk end
and the respective deflection was measured until the deflection was 5mm. To
evaluate the effect of the length factor on the stalk stiffness, we carried
out the test with different joint lengths (same as the previous experiment).
Moreover, the bending stiffness of silicone rubber joints from earlier
experiments was measured to compare to granular joint performance. In this
test, the measured force demonstrates how much lateral force the suction cup
tolerates in the worst situation before deforming 5mm.

##  3 Result

###  3.1 Adaptation Test

In this test, we experimented with the adaptation of the proposed design to
various angles and measured the required force for such adaptation. We
performed this experiment with different lengths of the granular joint, joint
materials, and suction pad materials. As mentioned, each prototype was tested
four times to check the repeatability of the suction cup performance. In
general, as presented in Fig 5 and Table 2, the adaptation experiment
demonstrated that the proposed suction cup could adapt to very steep angles
with a small force. For instance, with a 20mm granular joint, the suction cup
was adapted to various angles with a force range of 0.33N at 85∘ to 0.48N at
30∘ and had ultimate adaptation angles of 85∘ (See Supplementary video 1). In
addition, we repeated the test with different granular stalk lengths. The
results show that a longer granular stalk would improve the ultimate
adaptation angle and force. For example, for 10mm, the force increased to a
range of 0.43N at 80∘ to 0.69N at 45∘, while for 5mm, the force was
0.51N-1.31N. During the test, the pressure of the suction cup was measured. As
presented in Fig 6, the pressure inside the granular stalk is -8KPa which is
due to small self jamming between granular particles, and -60KPa after
attachment to the surface. For all angles the response time for the suction
cup to reach vacuum pressure was around 0.4 second, and 3 seconds for vacuum
release during the detachment.

Figure 5: (A) Measured required force for adaptation to various angles. Since
at 60∘ and 75∘ 5mm granular, Dragonskin 10 and Ecoflex 10 pad suction cup
could not attach to surface, the values are not shown. (B) The measured value
of the adaptation force and the required force calculated from the theory. The
stiffness of different cases was calculated using the measurements shown in
Fig7. Similar to (A), the missing data are for the cases that suction cup
could not attach.

Furthermore, we changed the granular stalk to silicone rubber and repeated the
experiment to compare the adaptation of the proposed design with using only
material softness. For the Ecoflex 00-10 stalk, the suction cup adapted to
angles up to 65∘ with a force range of 0.51N at 15∘ to 1.15N at 45∘ (See
Supplementary Video 1). For Dragonskin 10, the adaptation force increased
significantly to almost 5N at a 45∘ angle which was also the ultimate
adaptation.

In order to investigate the effect of the suction pad stiffness on adaptation,
we changed the suction pad from Dragonskin 10 to Ecoflex 00-10 and attached
the pad to 20mm granular stalk. With this change, the measured force at 15∘
was 0.36N, lower than 20mm granular with Dragonskin pad. However, at 30∘, the
force rises to 0.73N which is higher than granular cases with Dragonskin pad.
Moreover, in this case, the ultimate adaptation angle was only 45∘, much lower
than 20mm coffee with stiffer pad.

Figure 6: (A) The recorded pressure during the adaptation test for various angles (I) the initial pressure due to the self jamming of the granular particle during the adaptation (II) The pressure after the surface attachment (III) the pressure after detachment. (B) The pressure against the adaptation force at 45∘ surface angle. The force is only recorded until the suction cup attached to the surface, since after the attachment the tensile tester record the surface weight. Table 2: Ultimate adaptation angle and the required force for adaptation at these angles for various scenarios Adaptation | Ultimate | Force at
---|---|---
Scenarios | adaptation angles (∘) | ultimate angle (N)
20mm Granular | 85 | 0.33
10mm Granular | 80 | 0.43
5mm Granular | 55 | 1.17
Ecoflex 00-10 | 70 | 1.09
Dragonskin 10 | 45 | 4.96
Ecoflex 00-10 suction pad | 45 | 0.69

###  3.2 Bending stiffness test

As mentioned in 2.3, we conducted the bending stiffness test to investigate
the granular jamming impact on the stalk’s bending stiffness and compare it to
silicone rubber stalks. Here, the force was applied to the stalk’s end and
measured until the stalk end deflected 5mm. Looking at Fig 7, it is apparent
that shorter granular joints improve the stalk’s shear force strength. For
instance, 1.02N deflected 20mm granular stalk 5mm, while the required for such
deflection for 10mm and 5mm were 2.74N and 2.91N, respectively.

Moreover, the obtained results show that using granular jamming instead of
uniformly soft stalk provides higher bending stiffness. For example, the
measured force at 5mm deflection for Ecoflex 00-10 stalk was 0.51N, lower than
all the granular scenarios. For Dragonskin 10 also, the maximum recorded shear
force was 1.64N, which means 10mm and 5mm granular stalks can resist higher
shear force than Dragonskin10.

Figure 7: The required force to deflect the stalk’s end in various scenarios
and the deflection values. The pressure for all scenarios except the last one
is -60KPa. In the last scenario the pressure was set to -8KPa to measure the
bending stiffness of the stalk due to granular particles self jamming before
surface attachment.

##  4 Discussion

In this letter, we describe a suction cup design capable of adapting angular
surfaces and assess how stiffness impacts the design in such adaptation. The
results from the conducted experiments indicate that granular stalks adapting
to angular surfaces required less force (max 0.48N) than silicone rubber
stalks with the same length (max 1.15N for Ecoflex and 4.96N for Dragonskin)
due to the lower stiffness of granular particles without jamming as. In
addition, the Ecoflex stalk adapted easier to higher angles than the
Dragonskin stalk. Therefore, these results agree with Eq 2, in which with
having same $\alpha$, more compliant stalk due to lower Young’s modulus
requires less adaptation force. Besides low stiffness, another reason for the
significant difference in the adaptation of the granular stalk is that the
granular particles reshape during adaptation. As shown in Fig 8, such
reshaping endows the granular stalk with a hinge-like behavior to adapt easier
to steep angles, unlike silicone rubber stalk, which requires uniform bending
to achieve adaptation. These results suggest that using granular stalks
perform better adaptation than silicone rubber stalks.

Figure 8: The suction cup shape while attached to a steep angle. (A) the
wrinkle and hinge-like behavior of the granular stalk (B) the uniform bending
curvature in silicone rubber stalk.

Furthermore, the adaptation force and the ultimate angle were compared for
various granular stalk lengths. The results reveal that a longer stalk
requires less force to adapt to angular surfaces and adapts to higher angles
because of higher compliance. In addition to compliance, another possible
explanation for this result is the suction cup geometry during adaptation to
steep angles. For instance, with a 20mm diameter suction pad, the 5mm granular
stalk was too short of providing enough bending motion required for adaptation
to angles higher than 60∘, and the force increased remarkably at 45∘.

Another point in the adaptation test is the trend that emerged in which for
granular stalks and Ecoflex stalk extremum occurs in the recorded forces.
Although from Eq2, we expect higher forces at higher angles, but during the
adaptation, the stalks would wrinkle and behave similar to a buckled beam
which result in lower forces at higher angles. As expected, the extremum angle
is higher for the stiffer stalk, since the stiffer stalk requires more force
to be wrinkled and behave as a buckled beam. For instance, the maximum for
20mm was recorded at 30∘, while for 10mm and 5mm, it was at 45∘.

By combining the adaptation and stiffness experiment results, the 20mm
granular suction cup not only adapts with less than 0.5N force to angles up to
85∘ but also had twice the bending stiffness of Ecoflex 00-10 stalk, which
required twice the force at some angles. In addition, 10mm and 5mm granular
stalks had higher bending stiffness than Dragonskin 10 stalk, which required
nearly seven times more force adapting to 45∘ surface than 10mm granular.
Hence, these findings suggest that granular stalks endow the suction cup with
more effortless passive adaptation to angular surfaces and provide higher
bending stiffness than passive adaptation with just material flexibility.

In another experiment, one unanticipated result occurred when we replaced the
Dragonskin suction pad with Ecoflex. We expected using more compliant
materials for the suction pad decreases the adaptation force, which also can
be seen in the result at 15∘. However, at 30∘ and 45∘, the suction cup with
Ecoflex pad required more adaptation force than the Dragonskin pad. This
unexpected result is because the softer suction pad deforms more and faster
than the stiffer pad which leads to moment arm of L-shape beam be smaller
Fig9. As a result, the moment on the stalk will be lower and makes the
adaptation harder at higher angles. In addition, shortening the moment arm
also leads to significant deformation in the stalk (Fig9) which also increase
the adaptation force.Moreover, the ultimate adaptation angle of this suction
cup was only 45∘, much lower than the Dragonskin pad. Therefore, although
Ecoflex suction pads can attach to rougher surfaces, using such pad impacts
the adaptation drastically. It is important to bear in mind that using a
material with more stiffness than Dragonskin does not necessarily improve the
adaptation result, since stiffer suction pad may require much higher force for
deformation and may not changing the moment arm considerably. Further studies
are needed to understand better how the suction pad design itself affects the
adaptation.

Figure 9:  (A) Deformation of suction cup with Dragonskin pad which keep the
moment arm ($R_{1}$) enough for bending the stalk. (B) Deformation of the
suction cup with Ecoflex 00-10 suction pad, with shorter moment arm ($R_{2}$)
due to flexibility of the pad. (C) The adaptation of suction cup with Ecoflex
suction pad which deformed irregularly compare to Dragonskin pad.

For final discussion, although in theory, we can calculate the required force
for adaptation at any angle, in reality, if the force overcomes the friction
between the suction pad and the surface, the suction cup slips on the surface.
In such situations, the applied force only moves the suction pad on the
surface and can not bend the stalk to achieve adaptation. With this point in
mind, it is also possible to calculate the ultimate adaptation angle, which is
beyond the scope of this study. Furthermore, despite the theory shows the
general trend of the suction cup behaviour, there is an error between the
actual measured force and the force obtained from the theory. The main reason
behind the difference is that the suction pad with the stalk is modelled as a
single L-shape beam while in reality there are deformation at the connection
point which is neglected in the model. In addition, we represent the stalk as
a beam with uniform young’s modulus. However, due to composite structure of
the granular stalk, and also particles movement during adaptation, this
assumption is not accurate as well.

##  5 Conclusion and Future Work

This study sets out to develop a suction cup design capable of adapting to
angular surfaces and having high lateral stiffness after adaptation. The
results of this study have identified that using granular jamming techniques
offers adaptation and lateral stiffness, which could not be matched with
adaptation with only material flexibility. Therefore, the proposed design
could be used to enhance the performance in unconstructed areas. For instance,
by having a 10mm granular suction cup as the adhesion to surface method, the
actuator or the robot can attach to all surfaces with less than 80∘ slope,
with less than 0.7N, which most soft actuators can provide. Furthermore, the
suction cup would tolerate 270gr weight with only 5mm deflection. Besides
adaptation to high angles and high lateral stiffness, one main strength of
this design is that the modulation is sensorless and without an additional
actuator, which reduces the complexity in both design and control. Therefore,
this design allows soft actuators to adapt and manipulate easily in undefined
environments.

Figure 10: (A)-(C) adaptation to the uneven surfaces of a bottle, (D) adding
lateral load by pouring water (E) holding 1028 grams of lateral load (F)-(G)
manipulation and releasing the object.

For future work, a more detailed and thorough model would help to optimize the
design further. As mentioned in the discussion, the results show that the
ratio between the suction pad stiffness and the stalk stiffness considerably
influences the suction cup performance. Therefore, the best material stiffness
for the suction pad can be selected with a better model. In addition,
depending on the actuators and the application, the length of the stalk can
accordingly be modified for specific cases. Another interesting future work
can be potential applications of this suction cup by adding it to spider
robots or manipulating irregular object such as Fig10 and supplementary video
2.

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