Proceedings of IDECT/CIE 2005:
ASME Mechanism and Robotics Conference
24-28 September 2005 Long Beach, California, USA
DETC2005-85576
COMPLIANT BISTABLE DIELECTRIC ELASTOMER ACTUATORS FOR BINARY MECHATRONIC
SYSTEMS
Jean-Sébastien Plante, MIT
77 Massachusetts Ave. Room 3-469
Cambridge, MA, 02139
jsplante@mit.edu
Matthew Santer, University of Cambridge
Deployable Structures Laboratory,
Trumpington St. Cambridge, CB2 1PZ, UK
mjs204@eng.cam.ac.uk
Steven Dubowsky, MIT
dubowsky@mit.edu
Sergio Pellegrino, University of Cambridge
sp28@eng.cam.ac.uk
ABSTRACT
In this paper, a new all-polymer actuation approach for
binary mechatronic systems is demonstrated. The technology
consists of using Dielectric Elastomer actuators in a binary
fashion by coupling them with a properly designed compliant
structure. Here, a bistable actuator based around the “flip-flop”
concept is implemented in which two antagonistic actuators
switch a compliant truss between two stable positions. This
prototype shows promising performance with output forces
ranging from 1 to 3.5 N and displacements of 30% of the
actuator dimension.
1 Introduction
Future mechatronic applications, ranging from space
exploration to industrial systems, will require devices that are
simple, robust, lightweight and inexpensive. Current systems
using conventional actuators such as electric motors with gears
are complex, expensive, heavy, and have high power
consumption. Polymer actuators and, in particular, Dielectric
Elastomer (DE) actuators, have been proposed for future
mechatronic systems because they are lightweight, simple,
inexpensive, and have potentially large displacements and
specific work output [1,2].
Dielectric elastomer actuators consist of an elastomeric
film coated with compliant electrodes on both sides as shown in
Fig. 1 (a). Motion occurs when there is a high voltage
differential between the two electrodes, as shown in Fig. 1 (b).
While a number of potential uses have been proposed, few
successful practical applications of DE actuators to mechatronic
systems have been demonstrated [2,3,4,6]. In our experience,
DE actuators have low reliability, short lifetimes and
experience adverse viscous effects when powered for extended
periods of time and with significant displacements. Analytical
models of the actuator failure mechanisms suggest that these
problems are fundamental problems of DE actuators based on
viscoelastic elastomers such as VHB 4905/4910 and that
attempting to use such DE actuators in a continuous fashion
imposes significant performance limitations making them
impractical for many applications [5].
V
Elastomer film
Compliant
electrodes
(a)
(b)
Fig. 1: DE actuator operating principle [6].
Recent research at MIT has led to DE actuators with
improved performance, robustness and reliability when used in
an intermittent fashion. Intermittent use of DE actuators
matches well with binary or bistable actuation. Binary
actuation can be thought of as the mechanical equivalent to
digital electronics, where each actuator “flips” between one of
two possible states [7]. Systems can be simple since low-level
feedback control is virtually eliminated, along with the
associated sensors, wiring, and electronics [8,9]. These devices
are fundamentally simple, robust, lightweight, inexpensive, and
easy to control. A number of applications of binary actuation
such as space walking robots and manipulators have been
proposed [9]. These applications typically require a high
number of actuators to obtain sufficient levels of accuracy.
However, few practical applications of binary actuation
technology have yet been developed because of the previously
stated disadvantages of conventional actuators.
Hence, DE actuators and binary actuation are well
matched. The intermittent nature of binary actuation does not
limit DE actuator performance and at the same time, the
excellent performance, simplicity and low cost of DE allows it
to be used in large quantity in binary systems.
1
Copyright © 2005 by ASME
In order to design a bistable element to be used in
conjunction with a DE actuator, it is useful to classify bistable
structures into two types: symmetrically- and asymmetricallybistable [10]. A symmetrically-bistable structure, as indicated
by the rollercoaster analogy in Fig. 2 (a), is one in which the
two stable states store equal amounts of strain energy. An
actuator must supply the energy required to switch the state of
the bistable structure and to perform external work. An
asymmetrically-bistable structure, as indicated in Fig. 2 (b), has
one stable state which has a greater amount of strain energy, i.e.
is less energetically preferential than the other stable state. This
means that in the transition between the high- to the low-energy
stable state, the excess stored strain energy may be released by
the structure as useful work output. Asymmetrically-bistable
structures are useful when high speed, one-way switching is
required. This is not the case for the actuators described in this
paper, in which no importance is attached to switching in either
direction, so a symmetrically-bistable mechanism is the logical
choice for integration with DE actuators.
Energy
Energy
Displacement
(a) Symmetric-Bistability
Displacement
(b) Asymmetric-Bistability
Fig. 2: Definition of symmetry of bistability
The combination of DE actuators and bistable mechanisms
first considered was a flip-flop configuration, where two
antagonistic actuators move a bistable element back and forth,
see Fig. 3. In the figure, when actuator DE 2 extends, the
bistable element is pushed through to a second stable
configuration represented by the dotted line. At this point, the
bistable element then comes into contact with actuator DE 1,
which may then extend to return the bistable element to its
original stable configuration.
the compliant bistable actuator compare well with analytical
predictions. The compliant bistable actuator is shown to be
capable of providing more than 1 N over a 25 mm range in
about 10 seconds with a non-optimized mass of 220 grams.
2 Compliant Bistable Actuator Design
The design objectives were to have an all-polymer bistable
actuator with dimensions of ~100×50×50 mm, output
displacements of ~25 mm and forces of ~1 N. The selected
strategy was to build on the flip-flop concept (see Fig. 3).
2.1 DE Actuator
Many robotics applications require their actuators to have
high specific work outputs. The specific work output is defined
by the ratio of the actuator output work over a complete cycle
divided by its mass. Increasing this ratio in DE actuators is
most effectively done by maximizing the fraction of active to
passive material. Here, the selected strategy used to increase
the active mass fraction is the multi-layering of planar polymer
films. The details of multi-layered DE actuator design are
extensive and are provided elsewhere [12].
The multi-layered DE actuator presented in this study used
three individual active film layers stacked between two rigid
frames, see Fig. 4. Each film layer has a diamond shape which
expands upon voltage application to provide useful motion
along the diamond short axis direction, see Fig. 5.
The
diamond shape is selected because it deforms uniformly over its
entire surface which maximizes the mechanical energy transfer
of each layer.
Rigid
frames
Assembled
actuator
Film layers
DE 2
Fig. 4: Exploded view of a 3 layers multi-layered DE
actuator.
Bistable
Element
Elastic
bands
DE 1
Fig. 5: Multi-layer DE actuator in OFF (left) and ON
(right) positions.
Fig. 3: Flip-flop bistable actuator concept [11].
In this paper, a second generation of compliant bistable
actuator (CBA) powered by DE actuators is presented along
with its performance. This design has been jointly developed
by MIT and Cambridge University. MIT developed a new
reliable multi-layered DE actuator with high specific work
output with respect to traditional DE actuators. The approach
used to match the bistable element to the DE actuators is also
presented. Experimental results (force versus displacement) of
To keep the number of layers to practical levels while
increasing the actuator force capabilities, few thick layers were
preferred over many thin ones. The trade-off of this selection is
to ease the assembly process by lowering the number of parts at
the expense of using higher voltages.
The layers are
manufactured from a 1.5 mm thick film made by laminating
together three 0.5 mm layers of VHB 4905. The layers are then
assembled inside the rigid frames and a pair of elastic bands are
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Copyright © 2005 by ASME
installed to provide a non-linear restoring force canceling the
film stiffness, see Fig. 5.
This DE actuator design has shown excellent performance
characterized by large extensions that can exceed 100%,1 see
Fig. 5. The specifications of the three layer actuator used in
this study are given in Table 1. A force/displacement curve is
also presented later in Fig. 9. It should be noted that such DE
actuators with 100s of layers are currently feasible and this
design has yet to be optimized to reduce actuator voltage and
weight and improve efficiency.
The diamond frame actuator has also shown good
reliability. A prototype of the diamond frame actuator concept
using a single active layer achieved 15,000 actuation cycles at
60% strains. In comparison, rolled actuators have been
reported to show no signs of damage after 1.1 million cycles at
5% strains and to fail at about 36,000 cycles when the strains
are increased to 12% [13]. Their performance at higher strains
has not been documented but extrapolating from those numbers
suggests that CBAs using diamond frame DE actuators are
capable of maintaining robust, reliable performance at much
higher strains than rolled actuators.
Table 1: DE actuator properties (3 layers).
Performance Metrics
Values
Number of Active Layers
3
Operating Voltage (each layer)
10 kV
Strain
100%
Force
3N
Weight
20 grams
Size (closed)
110×30×15 mm
to the snap-through truss used in the compliant bistable
actuator, Fig. 6 (b).
A first approach to analyzing the critical force PEULER of a
straight-membered snap-through truss, as illustrated in Fig. 6
(a) is to resolve the actuation force axially to the buckling
member, and then apply the standard Euler buckling formula
for a pin-ended strut:
PEULER   2
EI
L2
(1)
in which E is the Young's modulus, and I and L are the second
moment of area and the length respectively of the buckling
member. This permits an initial sizing estimate to be
performed, and provides a method for assessing different
materials for suitability. In the preferred snap-through truss
design shown in Fig. 6 (b), the curvature of the buckling
member, material non-linearity and small load eccentricity
caused by the construction of the living hinges must be taken
into account. This is done by solving a modified elastica
formulation. We assume that the hinges have negligibly small
physical dimensions and exert zero moment under rotation. As
the snap-through truss transitions between the stable states, the
buckling members are subject to a change in the end-to-end
distance L . It is necessary to relate L to the resolved force
P to determine the snap-through properties of the truss. We
analyze the pin-ended curved members of the compliant
bistable actuator by decomposing each member into two
cantilevered beams joined in the middle. This is illustrated in
Fig. 7.
2.2 Bistable Mechanism
The bistable elements were designed to be symmetricallybistable as neither direction of switching is preferred. The snapthrough truss shown in Fig. 6 (a) was chosen as the basis for the
design [14]. It was modified to become an all-polymer
compliant mechanism by replacing the hinges shown with
living hinges [15].
Fig. 7: Definition of variables.
(a)
(b)
Fig. 6: Progression from (a) a simple snap-through
truss to (b) the truss used in the CBA.
To provide lateral restraint to the central element,
resistance to side-sway, and structural rigidity, two snapthrough trusses each consisting of two buckling members are
combined. The snap-through truss is a highly scalable design
which enables its size to be matched to the actuators both with
their current geometry and also for future miniaturized
versions. The buckling members are made initially curved to
reduce the maximum force that they will carry and to smooth
the snap-through response of the truss. These modifications led
1
Referring to this figure, in which  is the curvature of the
member,  the member's end rotation, resolved force P is
applied at an eccentricity a normal to the end of the member,
and the subscript 0 refers to the initial configuration, we may
apply the standard moment-curvature relationship EI  M to
the structure giving:
 EI    0   P y  a cos 
(2)
Fichter and Pinson have shown that Eqn. 2 may be solved to
produce
2 2
 sin 

4r 1 1  p u


0
(3)
L  S 0 1 

du 
2
2
0



 q
0
1

r
u



1
p

1
du
0
1  p 2u 2 1  r 2u 2
q
(4)
Referring to the film strain in the short axis direction
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Copyright © 2005 by ASME
in which p  sin( / 2) , q  P / PEULER , pu  sin( / 2) and
r
 2 p 2q
.
2
2


  0   aq cos     2 p 2 q


2L


These equations may in turn be simultaneously solved
numerically to relate L to the axially resolved force P which
is then related to the total actuation force by resolving parallel
to the central column and summing the contribution from all
the buckling members [16,17].
The above analysis was used to determine the truss design
that was used in the CBA. This truss requires a peak resisting
force of 3N, corresponding to the maximum force the DE
actuator can achieve. The final design consists of four HDPE
buckling members, each having a rectangular cross section of
depth 6.35 mm and thickness 2.3 mm, a distance between
hinges of 60.6 mm and a uniform initial curvature of 0.0145
mm-1. A general property of the force/displacement response of
an unconstrained snap-through truss is the presence of low
stiffness at each extreme deformation. To overcome this, it was
decided to constrain the truss by means of mechanical stops to
ensure that the truss is in a higher-stiffness configuration at the
start of the actuation.
The truss actuation force response was verified
experimentally by means of displacement controlled quasistatic tests. In Fig. 8 (a), a full cycle is shown for an
unconstrained truss (the mechanical stops shown by dotted
lines in the figure were not present, but facilitate comparison
with Fig. 8 (b). It can be seen that the peak resisting force of the
truss is 3.5 N (slightly higher than analytically predicted) which
is greater than the DE actuator can achieve. However, it turns
out that due to the relaxation properties of HDPE, this peak
resisting force becomes lower and the truss may be successfully
incorporated into the CBA. It can be seen that over the
transition, which was slow due to the quasi-static nature of the
test, the profile (originally anti-symmetric about the zero
displacement point) is foreshortened. When the truss is held at
zero load, however, it recovers to the expected displacement. In
a faster cycle, the amount of creep-recovery required would be
smaller. This means that for this particular truss fabricated from
HDPE, sufficient time must be left between transitions to
ensure that the expected force is being achieved.
The truss was then held by a mechanical stop at the
displacement shown in the figure for 12 hours before a second
quasi-static response test was carried out. This led to the
response labeled ‘A’ in Fig. 8 (b). It can be seen that the peak
resisting force has reduced from 3.5 N to 1.7 N. Only half of
the cycle is shown for clarity. Following a number of additional
cycles, and a period of 4 months being held at load, the
response labeled ‘B’ was measured. It can be seen that these
curves represent a steady state response – there is minimal
difference between the two response curves. It can also be seen
that the effect of the truss being constrained over a period of
time is not only to reduce the peak resisting force but also to
foreshorten the sinusoidal profile further. This may be
overcome in future designs by using a low-creep plastic or by
using composite material. The steady-state response shown in
Fig. 8 (b) is used to predict the compliant bistable actuator
performance as the effects of creep are not accounted for by the
analysis.
a) Truss quasi-static response immediately after assembly
b) Truss response after being held by mechanical stops
for 12 hours (A) and 4 months (B).
Fig. 8: Quasi-static displacement-controlled truss
response curves.
2.3 Actuator/ Truss Combination
The compliant bistable actuator performance is obtained by
adding the experimentally-determined truss response to the
measured actuator force/displacement response, see Fig. 9. In
order to add the truss response, it is necessary to switch the sign
of the response shown in Fig. 8 (b). The result is the predicted
force output of the complete compliant bistable actuator
system.
2.4 Integrated Compliant Bistable Actuator
The packaging of the bistable truss and DE actuators must
satisfy a number of functions, mainly: provide lateral restraint
to the truss, provide a rigid base for the actuators and, most
importantly, be compact. The design must also be easy to
construct and assemble. The assembly of the complete unit is
shown in Fig. 10. As shown in the figure, the volume is
minimized by placing the DE actuators on each side of the
bistable truss, where the two actuator motions will not conflict.
Parts were minimized, e.g. the actuators were given secondary
roles as mechanical stops. The casing pieces were CNC-milled
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Copyright © 2005 by ASME
from Plexiglass sheet and glued with cyano-acrylate adhesive
to form two pieces, simulating a possible molding, which, like
the truss, can be easily scaled in the future.
The compliant bistable actuator weight can be reduced in
at least three ways. First, a packaging concept using a single
DE actuator is currently under development, which will reduce
the mass by almost 50%. Second, the DE actuators’ specific
work output can further be increased, for example by adding
more active layers. Third, all components such as the bistable
truss can be optimized to reduce weight.
Bistable Truss
25 mm
DE 2
Fig. 9: Predicted CBA performance.
DE 1
Casing
Bistable Truss
Casing
Fig. 11: CBA during extension.
DE Actuators
Fig. 10: Exploded view of a CBA.
3 Results and discussion
3.1 Prototype Performance
The resulting compliant bistable actuator prototype is
shown in Fig. 11 (along with a US quarter for size comparison).
Here, the compliant bistable actuator is at the end of the
extension stroke where the bottom DE actuator is seen pushing
against the bistable truss. The performance specifications of the
prototype were measured experimentally and are summarized
in Table 2.
The forces reported in Table 2 are relatively low because
the DE actuators only consisted of three active layers. The
forces could be significantly increased (×10) through multilayering. Such a device could already be used in applications
not dependent on actuator weight such as locking mechanisms
e.g. automotive door locks.
However, Table 2 indicates that the parameters involving
weight (such as specific work output and force-to-weight ratio)
must be improved before the prototype can be used in
applications where weight is critical, i.e. when the device must
lift itself. Fortunately, there is much room for improvement
because the specific work output of the prototype is four orders
of magnitude lower than the specific energy of the elastomer
film which is around 3 J/g [4].
Table 2: CBA specifications.
Performance Metrics
Displacement
Strain (based on 81mm length)
Force (min/max)
Weight
Force-to-weight
Specific work output
Switching time
Size (closed)
Values
25 mm
30%
1 – 3.5 N
220 grams
0.46
1.14×10-4 J/g
10 s
135×81×48 mm
3.2 Predictions vs. Experiments
The quasi-static experimental response of the compliant
bistable actuator assembly is compared against analytical
predictions, in which the response is assumed to be the
superposition of the quasi-static responses of the bistable truss
and the DE actuator, in Fig. 12. The experimental data was
obtained by attaching the CBA prototype to the platens of a
tensile testing machine. With the CBA in one stable state, the
tensile machine moved to the other state at a constant velocity
of 2.5 mm/s as soon as the driving actuator was turned on. The
force applied by the CBA was recorded during the motion. The
voltage was turned on a few seconds before the start of the test
so the initial force spike is not visible on the experimental data.
The quasi-static prediction is in good agreement with the
experimental results. In particular, the first and second turning
points of the analytical and experimental curves are in close
correlation. Discrepancies occur principally at the transition
where the actuator stops and all the work is carried out by the
bistable truss itself. This is a consequence of the manual
actuator control that was used in the test. The actuator was kept
turned on beyond the transition point set at 18 mm until the end
of the motion at about 25 mm. The transition at 18 mm was set
as a conservative design value and is not an actuator limit.
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Copyright © 2005 by ASME
4 Conclusion
Fig. 12: CBA performance versus prediction.
There is a good match between prediction and experiment
because the velocity (or strain rate) was kept identical during
the acquisition of actuator design data (Fig. 9), and the
measurement of the compliant bistable actuator performance
(Fig. 12). DE actuators have a strongly viscoelastic nature and
are significantly affected by test velocity. For example, if the
DE actuators are displaced more slowly than they would if
unconstrained, viscoelastic relaxation causes the output force to
become higher.
Vogan, J., Wingert, et al., “Manipulation in MRI Devices Using
Electrostrictive Polymer Actuators: with an application to
Reconfigurable Imaging Coils” 2004 IEEE International Conference
on Robotics and Automation (ICRA 2004), New Orleans, Louisiana,
2004
1
Kornbluh R., Pelrine R., et al., “Electroelastomers: Applications of
Dielectric Elastomer Transducers for Actuation, Generation and Smart
Structures,” Smart Structures and Materials 2002: EAPAD, Yoseph
Bar-Cohen, Editor, Proceedings of SPIE, 4695, 2002
2
Hanson, D., White, V., “Converging the Capabilities of EAP
Artificial Muscles and the Requirements of Bio-Inspired Robotics,”
Smart Structures and Materials 2004: EAPAD, Yoseph Bar-Cohen,
Editor, Proceedings of SPIE, 5385, pp. 29-40, 2004
3
Kornbluh R., Pelrine R., et al., “Electroactive Polymers: An
Emerging Technology for MEMS,” MEMS/MOEMS Components and
Their Applications 2004, Siegfried W. Janson, Editor, Proceedings of
SPIE, 5344, 2004
4
Plante, J.S., Vogan, J., et al., “An Analytical and Experimental Study
of Failure Modes of Dielectric Elastomer Actuators,” Submitted to
ASME Journal of Applied Mechanics, 2005
5
Wingert A., “Development of a Polymer-Actuated Binary
Manipulator,” M.S. Thesis, Department of Mechanical Engineering,
Massachusetts Institute of Technology, Cambridge, MA, 2002
6
Chirikjian, G., J. Burdick, J., “Hyper-Redundant Robotic
Mechanisms and Their Applications,” IEEE/RSJ International
Workshop on Intelligent Robots and Systems, Osaka, Japan, 1991
7
Sujan, V., Lichter, M., Dubowsky, S., “Lightweight Hyper-redundant
Binary Elements for Planetary Exploration Robots,” Proc. 2001
IEEE/ASME International Conference on Advanced Intelligent
Mechatronics (AIM '01) 811, Como, Italy, July 2001
8
This paper reports on the development of a second
generation of all-polymer compliant bistable actuator using
dielectric elastomer actuators. The device uses the flip-flop
concept in which two antagonistic actuators move a bistable
element. The DE actuators used three active elastomer layers
to demonstrate the feasibility of the multi-layering approach. A
bistable truss was optimized to work with newly developed,
high specific work output, actuators.
The physical result of this study is a functional prototype
capable of deploying at least 1 N over 25 mm in both directions
in about 10 seconds with a non-optimized mass of 220 grams.
This first generation of compliant bistable actuators is already
appropriate for applications where weight is not critical. More
work is required to further improve the specific work output
and force-to-weight ratio for weight critical applications. Also,
bistable trusses that do not creep still need to be developed.
ACKNOWLEDGMENTS
The authors would like to acknowledge the contribution of
T. Schioler to the work presented in this paper, particularly in
the analysis of snap-through trusses. This research was funded
by the Cambridge-MIT Institute (CMI).
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