One of our goals with Robotic Muscles Kit was to demonstrate that these actuators can be built on a low-cost budget. Although the construction of the DEA itself can be done under $100, powering it is another matter. Low-cost DEA construction has been similarly demonstrated by the team behind Soft Robotics Toolkit, but their power supply was a hefty high-voltage amplifier box capable of outputting multiple thousands of kilovolts, and costing much more than the $100 budget we had set for ourselves.
We didn't know whether it was possible to move heavy loads with a DEA powered by a few hundred volts, so we decided to aim for a lower target -- generate any actuation visible to the naked eye. The challenge was thus posed: was it possible to produce a visible actuation on the DEA, using a low-cost power supply that could still generate multiple hundreds of volts?
We investigated multiple power supply solutions, including low-cost power transformers and regulators. However, the solution we settled with was a relatively simple booster circuit, courtesy of ElectroBOOM, that could generate 340 V from a standard US wall outlet.
2-stage capacitor/diode booster circuit, credit to ElectroBOOM
Standard US wall outlets output a 120 V AC supply (left of the diagram), which can be fed through two capacitors and two diodes as pictured in order to generate a 340 V DC supply on the output capacitor C2.
The specifics of how this works are best left explained by ElectroBOOM, but a surface level explanation is that AC voltage consists of rapidly-alternating positive and negative voltages. When the AC goes negative, the capacitors would ordinarily discharge, but diodes can prevent the movement of charge in one direction while permitting them in another. As a result, this configuration of diodes and capacitors allows the capacitors to charge when AC is positive, while diodes prevent the capacitors from discharging when AC is negative. The resulting capacitors reach much greater voltages, in exchange for forcing our voltage to be direct (non-alternating).
We do not detail instructions on how to build this circuit yourself, but we did procure all parts from Sparkfun. In general, make sure the parts you use have a voltage rating that meets the expected voltages on each part listed above, or else they will be damaged, or even explode. Our capacitors were rated to about 500 VDC, and diodes at around 450 VDC.
With our budget constraints and power supply strategy in mind, we were ready to determine how thick the DEA dielectric had to be in order to produce a visible movement.
A quick Google search shows that, from a distance of 16 inches, the smallest perceivable object resolution is 0.116 mm. We round this off to a target value of 0.120 mm.
Additional constants we required were derived from reference sheets as follows:
Young's Modulus: 220 KPa (source)
Dielectric Constant: 3.21 (source)
VHB4910 Unstretched Thickness: 1.02 mm (source)
Using the strain-voltage equation derived in the Design Principles section, we modify it to account for the ratio between prestretched and unstretched thicknesses.
S = (1/Y)x(KxZ)x((V/(D/R))^2)
where R is the prestretching ratio, or how thin the prestretched dielectric is relative to the unstretched one.
A way to calculate this ratio, for a simple material like VHB4910, is to consider it the product of the stretch in width and length directions.
Consider a dielectric shaped as a rectangular prism. Its volume V and base area A will be:
V = X x Y x Z
A = X x Y
therefore: V = A x Z
where: X is the prism length
Y is the prism width
Z is the prism thickness
If we stretch the dielectric by 2x, in the length and width directions, then we will generate new dimensions, X' and Y':
X' = 2X
Y' = 2Y
A' = X' x Y'
therefore: A' = 2X x 2Y = 4(XY)
Finally, we assume our VHB4910 is incompressible. This is a fancy term for saying "the volume of the material will never change, no matter how we stretch it". The details of this term can be found in college-level mechanics courses, but we merely need the simple definition for now.
V' = V
V' = A' x Z'
V' = 4(XY) x Z'
To maintain equality of volume: Z' = (1/4)Z
This tells us that, if we stretch our dielectric to 2x its original width and length, it must diminish to a quarter of its original thickness. Hence, a prestretching ratio of 4! If we stretched our dielectric to 3x width and length, our prestretching ratio would be 9, and so on.
Derivation aside, we assumed our prestretching ratio to be 9, and determined that the resulting strain for a 340 V input would be 0.12%. The total displacement would then be about 0.00122 mm, which is far below our target value. Hands-on testing, with the physical booster circuit built, confirmed this.
(Side note 1: A miscalculation during our target calculations resulted in deriving a displaement of 0.122 mm -- which made us believe we could achieve our target value. As it turns out, the miscalculation was converting strain into a percentage by multiplying it by 100. Expectedly, this yielded a displacement 100x the actual value.)
(Side note 2: During said hands-on testing, Kevin accidentally zapped himself with the full 340 V on the output capacitor. While thankfully nonlethal, he describes the sharp, brief pain as a gut punch, spread throughout your entire chest and both arms. Lingering chest pain, centered on the heart, continued for around 2-3 hours afterwards. It is definitely an experience you shouldn't be eager to repeat for yourself!)
By the time our hands-on prototype was complete, we were approaching December 2020 (for reference, prototyping began around September 2020). Moving on to the next phase of our project was going to be essential towards completion, so in the interest of time, we decided to abandon the DEA altogether.
All the more reason to abandon the DEA were safety concerns. While troubleshooting our DEA, we consulted with Dr. Dae-young Lee, an expert in DEA's and other soft actuator research at Harvard University. He pointed out that our voltage simply wasn't enough, and that we would have to aim for at least 5 kV in order to see reliable actuation. This wasn't something we could afford relatively easily -- in fact, it was what we were trying to avoid altogether! In addition, given how painful a shock at 340 V felt, we did not feel comfortable trying to create a home-built solution that could output 5 kV, nor would we feel comfortable being responsible for instructing others how to do so as well.
In the end, we decided to retain all of our work on the DEA's on this website, as a notable example of how great ideas can fall through during execution. It is a common occurrence in engineering, and one that engineers can encounter throughout their lifetimes. In retrospect, we should definitely have done our target calculations much sooner, and figured out early that it was going to be impractical to create a low-voltage DEA.