Proceedings of IDECT/CIE 2005:
ASME Mechanism and Robotics Conference
24-28 September 2005 Long Beach, California, USA
DETC2005-85576
1Copyright © 2005 by ASME
Compliant Bistable Dielectric Elastomer Actuators for binary Mechatronic Systems
Jean-Sébastien Plante, MIT77 Massachusetts Ave. Room 3-469
Cambridge, MA, 02139
/ Matthew Santer, University of Cambridge
Deployable Structures Laboratory,
Trumpington St. Cambridge, CB2 1PZ, UK
Steven Dubowsky, MIT
/ Sergio Pellegrino, University of Cambridge
1Copyright © 2005 by ASME
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.
1Introduction
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 [[i],[ii]].
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 [ii,[iii],[iv],vi]. 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 [[v]].
Fig. 1: DE actuator operating principle [[vi]].
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 [[vii]]. Systems can be simple since low-level feedback control is virtually eliminated, along with the associated sensors, wiring, and electronics [[viii],[ix]]. 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 [ix]. 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.
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 asymmetrically-bistable [[x]]. 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.
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.
Fig. 3: Flip-flop bistable actuator concept [[xi]].
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 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.
2Compliant 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 [[xii]].
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.
Fig. 4: Exploded view of a 3 layers multi-layered DE actuator.
Fig. 5: Multi-layer DE actuator in OFF (left) and ON (right) positions.
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 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% [[xiii]]. 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 / ValuesNumber of Active Layers / 3
Operating Voltage (each layer) / 10 kV
Strain / 100%
Force / 3 N
Weight / 20 grams
Size (closed) / 110×30×15 mm
2.2 Bistable Mechanism
The bistable elements were designed to be symmetrically-bistable as neither direction of switching is preferred. The snap-through truss shown in Fig. 6 (a) was chosen as the basis for the design [[xiv]]. It was modified to become an all-polymer compliant mechanism by replacing the hinges shown with living hinges [[xv]].
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 snap-through 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 to the snap-through truss used in the compliant bistable actuator, Fig. 6 (b).
A first approach to analyzing the critical force 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:
(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 . It is necessary to relate 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.
Fig. 7: Definition of variables.
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 to the structure giving:
(2)
Fichter and Pinson have shown that Eqn. 2 may be solved to produce
(3)
(4)
in which , , and .
These equations may in turn be simultaneously solved numerically to relate 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 [[xvi],[xvii]].
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 quasi-static 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.
Fig. 8: Quasi-static displacement-controlled truss response curves.
2.3Actuator/ 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.
2.4Integrated 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 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.
Fig. 9: Predicted CBA performance.
Fig. 10: Exploded view of a CBA.
3Results 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 multi-layering. 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 [iv].