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Design of a Variable Stiffness Flexible Manipulator with Composite
Granular Jamming and Membrane Coupling
Allen Jiang, Georgios Xynogalas, Prokar Dasgupta, Kaspar Althoefer, and Thrishantha Nanayakkara
Abstract— Robotic manipulators for minimally invasive surg-
eries have traditionally been rigid, with a steerable end effector.
While the rigidity of manipulators improve precision and
controllability, it limits reachability and dexterity in constrained
environments. Soft manipulators with controllable stiffness on
the other hand, can be deployed in single port or natural orifice
surgical applications to reach a wide range of areas inside
the body, while being able to passively adapt to uncertain
external forces, adapt the stiffness distribution to suit the
kinematic and dynamic requirements of the task, and provide
flexibility for configuration control. Here, we present the design
of a snake-like laboratory made soft robot manipulator of
20 mm in average diameter, which can actuate, soften, or
stiffen joints independently along the length of the manipulator
by combining granular jamming with McKibben actuators. It
presents a comprehensive study on the relative contributions of
the granule size, material type, and membrane coupling on the
range, profile, and variability of stiffness.
I. INTRODUCTION
Medical robotics today is making use of a variety of
robotic types, from the rigid robotic arms for minimally
invasive surgeries (MIS) to flexible endoscopes for natural
orifice transluminal endoscopic surgery (NOTES). While
the success rate between traditional laparoscopic surgery
and robot assisted laparoscopic surgery is similar, patients
who have undergone robotic surgery recover significantly
faster and incur lower costs [1], [2]. However, while these
systems are good for MIS, they still have several drawbacks
in surgeries designed to be even less invasive such as
NOTES and laparo-endoscopic single-site surgery (LESS).
Rigid robotics, such as the da Vinci robot, are difficult to
use in these surgeries because the instruments clash with
each other [3]. On the other hand, while flexible endoscopes
provide increased maneuverability and require fewer trocar
ports, they have lower platform stability than their rigid
counterparts and visualization which is not independent of
the instruments [4], [5].
Thus, to take advantage of the stability and performance
of rigid robotics as well as the maneuverability and access
This work was supported by the Guy’s and St. Thomas’ Hospital Charity
and by the Engineering and Physical Sciences Research Council, UK, under
grant agreement EP/I028773/1.
Allen Jiang, Georgios Xynogalas, Kaspar Althoefer, and Thris-
hantha Nanayakkara are with the Centre for Robotics Research,
Division of Engineering, King’s College London, Strand, London,
WC2R 2LS, UK allen.jiang, georgios.xynogalas,
k.althoefer, thrish.antha@kcl.ac.uk
Prokar Dasgupta is with the Robotic Surgery and Urological Innovation
group, King’s College London, St Thomas Street, London, SE1 9RT, UK
prokar.dasgupta@kcl.ac.uk
requirements of a flexible system, a variable stiffness robot
is a clear contender. There are currently several systems
which are dexterous manipulators, but most lack the aspect
of variable stiffness [6], [7], [8]. The most common type of
flexible manipulator, tendon driven systems, generally suffer
from backlash and large external footprints [9], [10], [11],
[12]. Tendon driven robots can achieve variable stiffness by
pulling or slacking wires, but the stiffness of the tip cannot be
greater than the stiffness at the base. Snake-like robots that
use micro-motors within the joints suffer from low torque,
rendering them unable to manipulate tissue [13], [14]. So,
while they can have the middle section of the snake-like
robot be at a relatively lower stiffness, the absolute stiffness
attainable is insufficient for surgical manipulation.
In the field of variable stiffness, flexible manipulators,
there are a wide range of designs. A group in this field
developed a soft robot based on thermally activated joints, in
which a solder-based mechanism is used to lock and release
joints [15]. This technique has a limited ability to vary level
the stiffness. Ie, the solder is either fully rigid or completely
soft, as opposed to partially rigid. Another group created
a manipulator consisted of pre-curved concentric tubes [8].
This design uses curved, plastic tubes of varying stiffness to
extend the distal tip of the robot. However, like tendon driven
systems, the segments near the tip of the manipulator must be
less stiff than the preceding segments. While the concentric
tubes do benefit from small diameters, the inherent design
of the robot cannot quickly adapt and requires a good map
of its environment.
This paper aims to address these problems with granular
jamming, a phenomenon where many solid grains can act as
’fragile matter’ [16]. An externally applied stress can change
a granule system from being fluid-like to solid-like. There
are several examples of granular jamming being used as a
universal joint and actuator [17], [18], [19]. When in its
fluid-like state, a granular system can encompass arbitrary
shapes and then, most importantly, change stiffness when
the external stress is applied. This phenomena has lead a
variety of applications to use jamming, such as the haptic
system in [20] and elephant trunk in [21]. Additionally,
unlike technologies such as concentric tubes or tendon driven
systems, a manipulator with granular jammed joints can vary
its stiffness at different points of the arm. For example, a
three joint system can be configured to be rigid-soft-rigid
with granular jamming, whereas the former two types of
manipulators cannot have a soft middle. However, there
2012 IEEE/RSJ International Conference on
Intelligent Robots and Systems
October 7-12, 2012. Vilamoura, Algarve, Portugal
978-1-4673-1736-8/12/S31.00 ©2012 IEEE 2922
Fig. 1. Diagram of the joint segment as a cantilever. The left diagram is
the system in its normal state, and the right diagram is it in its deflected
state. Region 1 undergoes tension and granules lose contact with each other,
whereas region 2 experiences compression. Region 3 is where particles
remain in their normal configuration.
are problems with granular jamming, specifically with the
limit of rigidity. For a robot, granular jamming is used
by encompassing the grains in a membrane. The internal
pressure of the system is pulled under vacuum, causing
the, typically atmospheric, external pressure to squeeze the
granules together. Because of this, there is a limit to the
amount of external pressure which can be applied, as we
cannot increase the pressure differential by pulling more
than an absolute vacuum. The purpose of this comprehensive
study is to optimize the variable stiffness structure of a
granular jamming joint by aiming to understand the dominant
factors that underpin the way to increase the spectrum of
stiffness we can achieve with minimum hysteresis.
While the effects of granule shapes and sizes have been
studied by several groups before, to the best of the authors’
knowledge, no experimental studies have been done on soft
granules or the coupling between the membrane and the
granules.
II. JAMMING FROM THE POINT OF VIEW OF
RIGID CANTILEVER MODELING
To understand the behavior of granular jamming joint, we
modeled it as an one end fixed cantilever beam undergoing
a force at the tip, as seen in Fig. 1. The purpose of these
simulations is to study the effect of Young’s modulus Ein
the context of granular jamming. The total bending moment
Mis the following:
|M|=|L|| Fext |(1)
where Mis the total moment, Lis the length of the
beam, and Fext is the externally applied force. For our
experiments, Lwas 40 mm, and will be likewise used for
our simulations. The moment of at single point along the
beam is characterized by the following:
M=Fext (L−d)(2)
where dis the distance from the fixed end. From (2) we
can see that the change in moment decreases linearly, as d
approaches the tip. Thus, with the fixed end undergoing the
largest moment, the jammed system will bend the most at
that point, as seen in Fig. 3.
To calculate the bending of a beam, approximating our
beams have a rectangular cross section, the follow equation
can be used:
Fig. 2. Calculated beam bending to find the equivalent Young’s modulus
E, given a tip force Fext and tip displacement y(L).
Fig. 3. Diagram of our experimental setup, where the granular jammed
joint is treated as a cantilever beam.
y(d) = 12Fext
Ewt 3(Ld2
2−d3
6)(3)
where wand tare the width and thickness of the beam,
and y(d)is the perpendicular displacement of the beam along
distance d. Fig. 2 shows the calculated beam bending shape
and corresponding Evalue from (3), where the tip deflection
distance y(L)is kept constant at 10 mm and Fext is from
experimental data.
Comparing the images generated by our simulations and
experiments, such as Fig. 2 and Fig. 3, we find that our joints
can be approximated as cantilever beams, as the bending
profiles are the same.
III. EXPERIMENTAL PROCEDURE
Our set up consisted of horizontally deflecting a cylin-
drical, latex membrane packed with granules by pushing an
ATI Mini40 Force/Torque sensor to 10 mm, holding for 5
seconds, and returning the sensor to its initial position. The
sensor was mounted on a linear module programmed to move
the sensor in 0.77 mm steps, pausing for 1 second between
steps to allow the granular material and membrane, to relax
and approach a steady state.
The pressure was measured by a Honeywell 0-30 PSI
Absolute pressure sensor, where 0 PSI is full vacuum and
15 PSI is atmospheric pressure. A Mastercool 90066-2V-220
Vacuum Pump was connected to the granular joint with a
filter used to prevent granules from traveling into the pump.
An air tank was not used, because the pump was large
enough to keep the pressure at a constant level. If more joints
2923
Fig. 4. For our prototype, we used a 10 mm diameter by 40 mm long
cylindrical membrane, and tested several commercially available, round,
plastic beads. Because of the fixed size of the membrane, the 4 mm beads
were found to have the highest stiffness and least variability.
are used, it may become necessary to add an air tank to better
regulate the pressure. An intermediate vacuum chamber may
also be required to achieve lower pressures, as our pump was
only able to reach a pressure of 1.5 PSI absolute. A Labview
program was used to control the motor position and log the
pressure and force data.
IV. EX PER IME NTAL RE SULTS
Table I summarizes the experimental results. The peak
force range compares the max force exhibited between 15
PSI and 1.5 PSI. The hysteresis column is the average loss
of force between the pushing and returning measurements
of the 1.5 PSI state. The variability column lists the average
standard deviation of the 1.5 PSI pressure level and the total
average standard deviation across all four pressures.
A. The effect of granular size and shape
1) Granular size test: The smaller the granule, the larger
the surface area to volume ratio there is. Thus, we can expect
smaller granules to have more traction between each other
and the membrane, and consequently have a larger stiffness
range. Five sizes were tested: 8 mm, 6 mm, 4 mm, 2 mm, and
1.5 mm. For these granules, 4 mm beads were the smallest
commercially available size we could find at a price range
similar to that of the 6 and 8 mm beads. Thus, the decision
was made to continue the size comparison from the sphere
beads in Fig. 4 with cube beads in Fig. 5.
Fig. 5. Tests on cube, plastic beads show that the is no significant
improvement in stiffness or variance in sizes below 4 mm.
2) Shape: The geometry of the individual granules is
significant as well. The shape of cube granules yielded
results with much less variability than the sphere beads. The
repeatability and linearity of the 4 mm cube beads made
them a more ideal candidate for a robotic system, despite
the sacrifice in maximum stiffness.
3) Volume fraction: Affected by both size and shape, the
volume fraction is an important factor to maximize, with the
granular system achieving better stiffness ranges at higher
packing rates. The volume fraction φcan be found with the
following equation:
φ=Vgranules
Vtotal
(4)
Vtotal is the volume of the cylindrical membrane, which is
3141.59 mm3. The volume fraction for the 8 mm diameter,
round beads is φ8mm = 0.682. Comparatively, for the 4
mm round beads φ4mm = 0.864, and 4 mm cube beads
φ4mmcube = 0.703. Despite being a good indicator of granular
performance, however, there are other contributing factors
for picking an ideal granule type, since a high φvalue does
not correspond to a low variance or hysteresis.
B. The effect of soft granule deformation
1) Solid rubber granules: Based on the work in [22],
deformable granules were tested to verify their simulations.
They postulated that deformable granules, with their over-
lapping stiffness, would improve the total tangential force
between granules. [22] notes that this total tangential force is
limited by the Coulomb frictional limit, as past this value the
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Fig. 6. Tests on solid rubber cube beads show that while the standard
deviation is low at 0.05, the peak force is also low at 1.8 N. However,
unlike the solid, plastic beads, these granules exhibit a much more linear
profile for both pushing and returning.
Fig. 7. The cube, hollow, rubber beads had similar profiles, despite varying
the pressure. There was only a 0.35 N improvement from atmospheric
pressure to near vacuum.
grains begin to slide across each other. For our tests, we used
polyurethane rubber with a hardness of shore 70A. However,
Fig. 6 shows that despite the added traction between indi-
vidual granules to adjacent neighbors, the deformability of
the granules themselves decreased the upper bound of the
stiffness range.
For comparison, a solid block (10x10x40 mm) of the same
polyurethane had a peak force of 5.47 N. So, rubber granules
are significantly softer than a solid structure of the same
material.
2) Hollow rubber granules: To investigate the behavior
of granules with a spring coefficient and negligible damping,
hollow rubber grains were made and tested, as seen in Fig. 7.
The same polyurethane rubber was used. Plastic molds were
printed with a rapid prototyping machine, and sheets of half
of the hollow cubes were pressed together to create airtight,
hollow rubber granules that held an internal pressure at an
atmospheric 15 PSI.
3) Composite granules: Fig. 8 shows the behavior of
solid, hard granules with high traction. Plastic granules were
individually covered in a 0.5 mm layer of the polyurethane
rubber. Our results show that the composite cubes improved
the force range over purely rubber granules, and improved
both the hysteresis and variability over purely plastic gran-
ules.
C. The effect of membrane coupling
The stiffness of the granular jammed joint no longer sig-
nificantly improves after a certain deflection point, possibly
as the granules shift or no are longer able to maintain good
contact with each other. We see that at these instances the
membrane is effectively the only thing resisting the external
Fig. 8. Results for a composite, cube granule type, where the center of
each particle is solid plastic surrounded by a layer of rubber. The force only
peaked at 2.16 N, but had a very low level of hysteresis.
Fig. 9. Measured data of 4 mm plastic spheres in a latex membrane with
4 mm half spheres lining the inside. The force peaked at 2.27 N.
force. To remedy this, we coupled the membrane to the
granules by embedding 4 mm half-spheres along the inside
of the membrane itself, so that it would lock the granules
into place.
Fig. 10. A sheet of latex rubber used to create a “bumpy” membrane to
couple the granules to the membrane.
V. THE ROLE OF GRANU LAR JAMMING IN
VARIABLE STIFFN ESS ACTUATIO N
We have shown that by reducing the pressure inside
the membrane, the joint elements become stiff without a
significant volume change. As a proof of concept that these
granular systems can also exhibit actuation, we wrapped
a mesh around each membrane, and inflated the elements
with positive pressure. The elements acted like a pneumatic
muscles and contracted. By placing three or more elements
at each joint, actuation can be achieved with two degrees of
freedom. This is similar to the design used by [23]. Their
design consists of a McKibben actuator wrapped in several
jamming modules. They achieve actuation by stiffening se-
lected modules and contracting the single pneumatic muscle.
2925
Fig. 11. A set variable stiffness actuators shown with one actuator activated
at 55 PSI absolute (40 PSI gauge). The change in angle is low at 15 degrees.
Though all of the actuators were filled with granules, the two other elements
were neither actuated or stiffened.
However, by integrating the granular jamming element into a
McKibben actuator itself and using several in parallel, we can
increase the manipulator force. This is because the direction
of actuation is not dependent the stiffness of the jammed el-
ements, but rather on the actuators themselves. Additionally,
this design reduces the number of tubing required per joint
by at least one. This is due to the fact that the actuation
and stiffening mechanisms can share the same line, whereas
[23]’s design requires an additional, independent line for the
center actuator. Future designs of manipulator can reduce the
number of required pneumatic lines even further. Two main
lines, one for compressed air and another for vacuum, can
run down the length of the robot, and each joint will have
their own lines branching off of the two mains.
Our actuators respectively achieved 10% strain 15% strain
at gauge pressures of 10 and 40 PSI. This is about 2-4
times higher than unwounded shape memory alloy (SMA)
wire, which achieve about 4% strain, not to mention that a
pneumatic muscle can achieve much larger forces. Another
advantage over SMAs or conventional push/pull rods is that
this design, without metal components, could be compatible
for magnetic resonance imaging (MRI). One issue with
this design, however, is that when actuated, the increase in
internal volume can rearrange the granules in an undesirable
manner. While on its side, the problem is minimal, but
when held vertically, the granules in an contracted actuator
will collect at the bottom. This problem could be reduced
by compartmentalizing the membrane’s internal structure or
futher coupling each granule to the membrane with strings.
Future work can be done on the bending profiles when one
of the three segments at a joint is actuated, while the other
two are unactuated, stiffened, semi-stiffened, and actuated.
These profiles and the muscle control schemes are, however,
beyond the scope of this paper.
VI. DI SCU SSI ON
From Table I, we find that at atmospheric pressure, the
peak forces are similar for all granule types. The medium
sized granules, chiefly the 2-4 mm sizes, achieved higher
peak forces under vacuum than granules of a larger or smaller
size. This indicates that there could be an optimum size for
granules. However, the 2-4 mm size may only be a local
optimum, since very small grains may experience other sig-
nificant factors such as electrostatic forces or intermolecular
bonding. Studies of these effects are outside the scope of this
paper.
The force-deflection profile of many of the tests display a
plateau effect, where the measured force no longer increases
as the system is further deflected, most notably seen in Fig. 4
and 5. This is possibly a result of granules shifting and losing
contact with adjacent particles, particularly in the tensioned
side of the system, as demonstrated in Fig. 1. At that point,
the main resisting force could be the membrane itself, which
has a maximum value.
While the rubber granules in Fig. 6 and 7 proved to be
insufficiently stiff, the linearity and low hysteresis of their
profiles could be attributed to the decreased probability of
shear between individual granules. As shown in Fig. 8, a
new, composite bead type did achieve better linearity, albeit
little improvement for stiffness. Nonetheless, the linearity of
the stiffness and lower hysteresis will simplify the control
scheme for the manipulator.
The “bumpy” membrane, seen in Fig. 10 and 9, proved
to less effective than the composite granules, but did signif-
icantly improve the hysteresis and linearity over both the 4
mm plastic spheres and cubes with decoupled membranes.
While the variability was not improved, membrane coupling
TABLE I
SUM MA RY OF G RA NU LA R EX PE RI ME NTA L RE SU LTS
Bead Type Membrane Type Force Range (N) 1.5 PSI Hysteresis 1.5 PSI Variability (Total Mean) # of Trials
8mm Plastic Spheres Decoupled Latex 0.48 - 2.47 1.25 0.53 (0.32) 10
6mm Plastic Spheres Decoupled Latex 0.61 - 2.27 1.25 0.57 (0.35) 10
4mm Plastic Spheres Decoupled Latex 0.61 - 3.16 1.60 0.31 (0.16) 10
4mm Plastic Cubes Decoupled Latex 0.45 - 2.38 0.94 0.20 (0.09) 5
2mm Plastic Cubes Decoupled Latex 0.50 - 2.70 1.16 0.10 (0.07) 6
1.5mm Plastic Cubes Decoupled Latex 0.51 - 2.49 1.65 0.19 (0.11) 6
4mm Solid Rubber Cubes Decoupled Latex 0.75 - 1.82 0.34 0.05 (0.04) 6
4mm Hollow Rubber Cubes Decoupled Latex 0.65 - 1.00 0.29 0.02 (0.03) 5
10mm Solid Rubber Block N/A 5.47 - 5.47 0.30 1.17 8
4mm Composite Cubes Decoupled Latex 0.53 - 2.16 0.13 0.24 (0.22) 5
4mm Plastic Spheres Coupled Latex 0.30 - 2.27 0.58 0.67 (0.29) 5
2926
remains to be an interesting area to be explored in the field
of jamming.
Many further improvements can be made to increase the
overall stiffness, increase the linearity of the stiffness, and
decrease the variance, possibly with interlocking granules
or internal sub-membranes. Our tests suggest the following:
volume fraction affects the overall stiffness of the jammed
matter; membrane coupling affects the hysteresis and lin-
earity of the system; and inter-particle traction affects the
variability, hysteresis, and linearity of the stiffness. We would
also like to note that the membrane coupling and inter-
particle traction seem to be tackling the same phenomena, the
shifting of granules. However, for membrane coupling, only
the outer layer of granules are kept in their relative positions
during and after deformation. Whereas for the composite
granules, the inter-particle traction keeps the granules from
sliding between each other, as well as from sliding against
the latex membrane.
While the actuation work done for the granular jammed
joint is still preliminary, granule filled air muscles in Fig.
11 were able to successfully actuate. Paving the road for a
viable variable stiffness flexible manipulator.
There were several experimental limitations for our in-
vestigations. The granules tested in each category were not
uniformly sized, with a measurement difference of about 5-
10% between “identical” sets of granules. Also, the volume
fraction differed between certain trials, as different packing
configurations yielded more or fewer granules inside the
membrane. This could have increased the size of some of
the error bars, as well as the limited number of trials. While
still just a proof of concept, the braided sleeves used for the
pneumatic muscles had a neutral state (uncontracted form)
which was stronger than the stiffness of the internal granular
jammed system. However, we do plan to resolve this issue
with a different type of braid.
The identification of the factors affecting the stiffness
range, hysteresis, linearity, and variability in granular jam-
ming and the utilization of new material types, such as the
composite granules and membrane coupling, in this paper
opens opportunities for further research in granular jamming
and soft robotics.
VII. ACKNOWL EDGMENTS
The authors gratefully acknowledge the contribution of the
Guy’s and St Thomas’ Hospital Trust Foundation, the Engi-
neering and Physical Sciences Research Council (EPSRC),
UK, and reviewers’ comments.
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