Self-Folding Miniature Elastic Electric Devices

Shuhei Miyashita1,∗, Laura Meeker1, Michael T. Tolley2,Robert J. Wood2, and Daniela Rus1

1 Computer Science and Artificial Intelligence Laboratory,Massachusetts Institute of Technology

2 School of Engineering and Applied Sciencesand the Wyss Institute for Biologically Inspired Engineering,

Harvard University

* corresponding author32 Vassar Street, Cambridge, MA, 02139, USA

shuheim@csail.mit.edu+1 412-228-8008

1

Abstract

Printing functional materials represents a considerable impact on the access to manufacturingtechnology. In this paper we present a methodology and validation of print-and-self-fold miniatureelectric devices. Polyvinyl chloride laminated sheets based on metalized polyester film (MPF) showreliable self-folding processes under a heat application, and it configures 3D electric devices. Weexemplify this technique by fabricating fundamental electric devices, namely a resistor, capacitor,and inductor. Namely, we show the development of a self-folded stretchable resistor, variableresistor, capacitive strain sensor, and an actuation mechanism consisting of a folded contractiblesolenoid coil. Because of their pre-defined kinematic design, these devices feature elasticity, makingthem suitable as sensors and actuators in flexible circuits. Finally, an RLC circuit obtained fromthe integration of developed devices is demonstrated, in which the coil based actuator is controlledby reading a capacitive strain sensor.

2

1 Introduction

The realization of “printing” functional robotshas the potential to bring unprecedented wide-scale access to rapid and versatile fabrication ofrobotic artifacts. Recent progress in techniquesfor printing 3D structures has provided engi-neers with rapid prototyping of robotic struc-tural components and consequently to robotsdevelopment. The challenge now shifts towardprinting entire robots - from sensing and actu-ation to controller to fully integrated and func-tional artifacts - with minimal human interven-tion. Toward this end, we develop a method andtechnique for self-assembling conductive materi-als to desired functional formations.

Recently, folding processes, inspired byOrigami art work and protein folding, have beenexploited for the construction of various types ofrobots. RoACH is a 2.4 g autonomous hexapodrobot with a body shape made through foldingand assembling processes [1]. Onal et al. de-veloped inchworm robots by patterning a singlePolyester sheet and manually folding [2]. Hawkeset al. achieved the self-folding of an origamistructure using a shape memory alloy for actua-tion [3]. Yasu and Inami demonstrated the self-folding of a robot-like structure in a microwaveoven, using a heat-sensitive sheet coupled witha microwave-sensitive aluminum sheet [4]. Fel-ton et al. achieved the self-folding using Shapememory polymer powered by Joule heating, andshowed an inchworm robot [5, 6]. Tolley et al.investigated various types of self-folding meth-ods for robotic applications [7, 8], and Miyashitaet al. achieved accurate self-folding of a robot’sstructure based on Angle folds using global heat-ing [9].

Whitney et al. developed μm-scale robotsbased on pop-up methods [10], and Abel et al.presented a theoretical framework for designingpop-up parallel folds [11]. Techniques for MEMSfolding was shown in [12]. DNA origami was re-alized through one-dimensional structure foldingin [13], and it was inspired by protein foldings in[14, 15, 16]. Elastomer-based folding techniquesare presented in [17].

A different line of research focused on develop-

ing soft electronics providing versatile capabili-ties to stretch, compress, twist, bend, and de-form [18, 19, 20, 21].

Toward the realization of “printable” robots,this paper investigates a method of print-and-fold that unifies structure and functionality forrobot development. As such we present basicprintable electric components and devices. Thecontribution of this study is developed basedon [22], with additional exemplifications thatthe developed self-folding method is capable ofproducing miniature scale devices whose featuresizes scale down to the millimeter. The contri-butions of this paper are (1) a method for resis-tance, capacitance, and inductance through theuse of a metalized polyester sheet, (2) a tech-nique for self-folding and self-assembly of con-ductive material, (3) miniature devices (stretch-able resistor, variable resistor, and capacitivestrain sensor) as examples of self-folded func-tional electric devices and attained an origami-coil actuation mechanism, and (4) combined in-tegration of these units in the form of a sensor-actuator system.

2 General Principles & Meth-

ods

Our technical approach for realizing resistors, ca-pacitors, and inductors exploits the conductiv-ity and resistivity using the structure or geom-etry of material sheets. In particular, we use50.1μm thick isotropic aluminum coating (oneside) polyester film (Metalized Polyester Film,MPF).

A specific resistance can be attained by vary-ing the material’s geometry. Thus, a 3 × 3 cmsquare cut of MPF has about ≈ 4.4Ω. The re-sistance can be linearly increased by lengthen-ing the MPF, and inversely, can be decreased bywidening the width of the sheet. By translatingthis cutting-and-regulating approach to foldingmethods, we can realize elastic resistors of vari-ous resistances (the limit is given by the geome-try).

Since the resistance of the MPF is relativelylow (the sheet resistance ≈ 1Ω), it can be used as

3

a conductive cable in short-length circuitry. Theconductivity is not as high as that of copper, sucha conductive cable is more suitable for digitalcircuits.

Capacitors can be obtained using two electri-cally isolated MPF. Capacitance of two parallelMPF is proportional to the surface area and in-verse proportional to the distance between theplates. Thus, the capacitance magnitude can beregulated by the arrangement and the geometryof the paired surfaces. With folding, we real-ized a capacitor by pairing angled MPF surfaces,where a shared edge forms the hinge between thetiles. This way, for example, two square MPF of2× 2 cm2 spanning an angle of 45 ◦ with a 2mmgap from the shared edge exhibits a capacitanceof ≈ 0.4 pF. Due to the fact that the capaci-tance increases roughly proportional to the sur-face area, the size of the device influences thecapacitance magnitude.

Inductance is the resistivity of a structureagainst the current change, and is commonlyseen in the form of a solenoid coil. To showthe capability of self-assembly in realizing folded3D structures that satisfy the topology of an in-ductor, we designed a self-folding solenoid coil.The coil can create a magnetic field within acertain volume, which can subsequently be usedfor actuation mechanisms, as introduced in Sec-tion 6.3. The inductance is determined by thenumber of turns as well as the geometry (size).For instance, an MPF solenoid coil with radius16mm, height 6mm, and 5 turns theoreticallyhas an inductance of 2.10μH.

Tests with an MPF-based inductor showedthat it can sustain up to an ≈ 300mA currentbefore an instant loss of conductivity occurs dueto changes in the characteristic of the polyesterlayer produced by heat. MPF maintains conduc-tivity as well as resistivity given the non-harsh it-erative foldings. The sheet can withstand a tem-perature range of −45◦C to 148◦C, making thematerial a poor candidate for soldered connec-tions. Therefore, conductive connections in thecircuit were made using conductive tape, con-ductive epoxy glue, and mechanical clippings.

3 Self-folding Method of MPF

3.1 Global Heating Application andThree Layer Structure

Among the various existing self-folding tech-niques, we have developed a simultaneous multi-crease self-folding technique based on globalheating with a heat sensitive sheet (Poly-VinylChloride; PVC, Shrink Bag, shrinking temper-ature: 65 ◦C ∼ 75 ◦C, thickness 0.025mm) [9].The key insight is to transform the internal stressof a contraction sheet into a folding torque.Our goal is to globally heat the structure toinduce simultaneous foldings. Fig. 1 showsthe designed mechanism for self-folding. The

(b)

contraction layer (inserted in middle)structural

layer

(a)

bend (mountain)

bend (valley)

bend (valley)

bend (mountain)

2

1

hinge 1 hinge 2

heat

contraction layer (PVC)

bridge

Wh

contract

bridge

structural layerstructural layer

Figure 1: Proposed self-folding method usingglobal heating.

PVC contraction layer is sandwiched by non-deformable structural layers with different gapwidths. When the structure is heated, the shearforce disproportionates to one side and gener-ates a bending torque (Fig. 1 (a),(b)). The gapwidth difference between the front and back ofthe sheet at the same position enables the dif-ferentiation of the bending direction: the planesbend toward wider gaps. The approach is capa-ble of folding mountain and valley folds simul-taneously. Furthermore, the folding angle (θ1and θ2 in Fig. 1) can be approximately encodedwith the gap widths as well as the bridge width.Namely, the wider Wh, the steeper the foldingangle becomes. The designs presented in thiswork feature Angle folds, which enables precise

4

targeted folding angles by indirectly actuatingother folding angles that are kinematically cou-pled (see [9]).

PVC has two ideal features: the capability oflow temperature contraction (less than 100 ◦C),and a relatively robust physical structure withtransparent visibility. PVC also has some disad-vantages: the material may deform at high roomtemperature, and it cannot be cut with a lasermachining system due to the emission of toxicgases.

3.2 Fabrication

Fig. 2 shows the design and fabrication process.After determining the desired variable proper-ties, such as the folded sheet structure, kinemat-ics, and circuit topology, we derived the creasepattern for self-folding considering all conditions(Fig. 2 (a)→(b)). The unique characteristics ofthis approach are: (1) alignment of the lami-nated three layers is achieved with a single foldduring fabrication (Fig. 2 (d)); (2) the geome-try of the target 3D structure (Fig. 2 (a)) canbe encoded in the folding pattern (Fig. 2 (b))to be realized after self-folding (Fig. 2 (f)); (3)there are driving (or input) angles and driven(output) angles, and the accurate driven anglesare roughly controlled by the driving angles bybalancing out the torsion by bridges with gener-ated torque (Fig. 2 (f)); (4) with the exceptionof the laser machining during fabrication, the en-tire process is completed without the assistanceof equipment; (5) the conductive surface in theself-folded 3D structure can be exposed or hid-den depending on which side of the MPF facesup in the lamination phase (Fig. 2 (c)); (6) fur-ther lamination of layers is possible to provideadditional functionalities.

Conductivity is maintained via “bridges” thatlink the conductive tiles (Fig. 2 (c)), which alsomaintain a constant separation between tilesduring self-folding and enforce the direction offolds. (Due to the torque required, bridges canonly be placed over mountain folds). The totalthickness of the self-folding sheet is 0.3mm.

4 Resistance

4.1 Model

This section models the MPF resistor. For 3Dresistance, R = ρ

ltlhlw

:= Rslhlw, where ρ is the

resistivity intrinsic to the material, lt is the un-known thickness of coated aluminum, lh is theheight, lw is the width of the material, and Rs

is the sheet resistance. We measured the resis-tivity of the material using the Van der Pauwmethod (the sample thickness is much less thanthe width and length of the sample [23]), andobtained the sheet resistance of Rs = 0.933Ω.

Fig. 3 shows the plot of experimentally mea-sured resistances depending on the differentwidth (lw) to height (lh) ratios of the rectan-gular MPF. By fitting the curve, we obtain R =

0 5 10 15 20

5

10

15

20

height (lh) / width (lw)

Res

ista

nce

[ohm

s]

Measured data pointsFit to measured dataModel (0.93x)Model with additonal constant term (0.93x + 1.8)

Figure 3: Resistance of MPF with different ge-ometries.

0.93 lhlw+1.8, which shows a similar value to what

we obtained from the Van der Pauw method, andwe will use this model for rectangular resistors.

To embed resistance within a (self-)foldedstructure, we wish to estimate the resistancewhen bridges are included in a pattern (seeFig. 2). Fig. 4 illustrates various resistancesmade by cutting 3 × 3 cm2 pieces of MPF andvarying the width (lw) and height (lh) of thebridges. By comparing (b) and (h), it can be de-rived that the position of a bridge does not affectthe resistance. The resistance of a sheet, Rtotal

5

5. Peel off MPF4. Laser cut MPF

8. Remove

9. Apply heat

7. Sandwich and adhere with adhesive tape

bridges

will becomefront face will becomeback face

θin

θout

10. Self-fold by Angle folds

3. Laminate

Angle folds(driving angle)

(driven angle)

(b)

(d)(e) (f)

(a) (c)2. Derive crease and laser cutting patterns

1. Detect aimed 3D structure, kinematics, and circuit topology

MPF

complete

backing layer

6. Insert PVC

targeted angle θheigh

twidth

heigh

t

width

thickness

thickness

Figure 2: Design, fabrication, and self-folding processes.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

no bridges,R=4.4 Ω

centered,lw: 1mm, lh: 2mmR=10.7 Ω

centered,lw: 2mm, lh: 2mmR=6.2 Ω

centered,lw: 1mm, lh: 0mmR=6.4 Ω

centered,lw: 1mm, lh: 4mmR=11.4 Ω

centered,lw: 2mm, lh: 4mmR=6.8 Ω

zigzag,R=64.8 Ω

off center,lw: 1mm, lh: 2mmR=10.7 Ω

two symmetric bridges,lw: 1mm, lh: 2mmR=6.2 Ω

measure R

3cm

3cm

Figure 4: Various resistances realized by cutting3× 3 cm2 MPF.

can be modeled as connections of the i-th (i ∈ N)surfacial geometric portion that attributes theresistance Ri connected in parallel and in series.For example, the resistance i serial resistances,each composed of one surfacial portion, can becalculated as Rtotal =

∑iRi where Ri is the re-

sistance of the i-th surface. For example, thetotal resistance of the structure in Fig. 4 (b) canbe approximately calculated as the sum of theresistance of Fig. 4 (d) and the 1× 2mm2 bridgeportion. With this model, our calculation es-timates that the Rtotal of Fig. 4 (b) is 10.18Ω,while the measured value was 10.7Ω (≈ 5.1%error). In the same way, the model estimatesthe Rtotal of Fig. 4 (e) as 12.0Ω, where the mea-sured value was 11.4Ω (≈ 5.0% error). Consid-ering that the measured resistances are relativelysmall and are not stable when measured with amultimeter, the derived model can be consideredto reasonably estimate the model. In practice,with a surface area 3 × 3 cm2, our estimation ofthe achievable resistance range is ≈ 4Ω−3.2 kΩ,with the assumption that the thinnest width ob-tainable with our laser cutter is lw = 0.5mm.This resolution and the layer alignment accuracy

6

mainly limit the attainable smallest feature sizeto be at the mm-scale.

4.2 Stretchable resistor

Fig. 5 shows one of the images of self-folded re-sistor (MPF resistor). In order for the resistor toattain physical compressibility and stretchabilityin one direction, we combined slit traces [24] andAngle folds (Fig. 5(a)). The result is a structurewith reversible extension ratios of up to 118 withthe large scale model, and 5 with the small scalemodel (the difference is due to the fact that thethickness of the material is constant).

Fig. 5(b) shows the self-folding process. 68creases are simultaneously folded in about 2 min-utes after the initiation of deformation. Defor-mation occurs at temperatures over 50 ◦C (theoven requires approximately 2 minutes to reachthis temperature). In general, the duration de-pends on the characteristic of the oven used,though a steady increase in temperature is re-quired to keep spatial uniformity in self-folding.

The structure is floated on water during theprocess in order to avoid direct heat applicationand to reduce the frictional influence of groundwhen deformation occurs. We note that self-folding can be attained also on a low-frictionalsurface such as Teflon sheet. With gradual heat-ing, the temperature of the water to be approx-imately the same as the air temperature in theoven during self-folding experiments.

We show the self-folded MPF resistor inFig. 5(c), with a 5 : 1 scale model fabricatedwith the same process in Fig. 5(d).

4.3 Variable resistor

This section demonstrates self-folding of a vari-able resistor as a demonstration of the capabili-ties of our system. The idea was to connect theelectrical tiles that make up a folded structure inan electrical circuit, and to manually short thecircuit, thereby changing (reducing) the resis-tance in steps (four steps in this case). The tilingpattern and the path of electrical conductivity(depicted with blue lines) are shown in Fig. 6 (a).This figure shows tiles from the front surface in

measure Rtotal

stretchablecompressible

5mm

(d)

valley fold, cut throughmountain foldoutline

crease pattern

(c)

(a)

(b) 0s

32s

64s

139s

Figure 5: Designed stretchable/compressibleMPF resistor. (a) The crease pattern. (b)Self-folding process. (c) Self-folded MPF re-sistor at normal length with compressed andstretched images besides (US dollar coin in-cluded for scale). (d) Large scale self-foldedMPF using the same fabrication process. High-lighted with square is magnified in (c). See theself-folding process in the supplemental video.

7

red and from the back surface in blue. This cir-cuit topology allows for adjacent faces to be elec-trically connected in series, and the self-folded3D geometry forms a scaling zigzag pattern foreasy pinching to vary the measured resistance.Fig. 6 (b) shows images from self-folding experi-

electrically connected

front faceback face

(b)

(c)

(a)

5mm

Rtotal (d)

Rtotal

compressible

Figure 6: Self-folded MPF variable resistor. (a)Designed crease pattern with front and backsides overlaid. (b) Self-folding process in anoven. (c) The outlook of the self-folded vari-able resistor and the compressed amd stretchedstates in the insets. (d) Two-shot image withlarger scale variable resistor generated with thesame technique. See the self-folding process inthe supplemental video.

ments. The repeatable self-folding process tookabout one and a half minutes after the defor-mation initiated. Fig. 6 (c) shows the self-foldedMPF variable resistor. Due to the kinematicsof the structure, linearly aligned tiles on the top

surface can be shorted by hand, as shown in theinset. The structure possesses elasticity, and itrecovers its original posture when the externalforce is removed.

For reliable output values, we tested the largescale variable resistor. The measured resis-tances are 83.56 ± 1.44Ω (with no pinches),74.48 ± 2.20Ω (with 1 of 4 sections pinched),62.49± 1.86Ω (2 pinches), and 49.94± 0.94Ω (3pinches) (in each case, n = 8). By approximat-ing triangular shapes to the similar geometricratios’ rectangles, our model roughly estimatesthe resistance with no pinches as ≈ 90.4Ω. Dueto limitations of our CO2 laser machining systemwe used, the actual dimensions of the bridges donot reliably reproduce the intended designs.

5 Capacitance

5.1 Model

In order to fabricate capacitors by self-folding,we explored designs composed of electrically iso-lated conductive faces, mechanically connectedalong fold edges. Here we develop an analyti-cal model for the fundamental case of identicallyshaped paired angled MPF tiles (see Fig. 7 forthe schematic representation of a side view in(a) and an angled view in (b)). Each capacitoris made up of two conductive isosceles triangu-lar tiles (colored in red). Here, r is the length ofthe non-conducting parts of the upper and lowertiles measured from their common hinge, respec-tively, and l is the height of the aluminum coatedconductive part of respective conductive surfaces(∴ r + l ≤ height of tile).

The thickness of the tiles, 0.05mm, is denotedas T

2 , and the angle of the outward facing tip ofeach tile is given by φ. The capacitance of the tilepair varies in accordance with the relative anglebetween them, which is given by θ. Defining thex-axis as parallel to the bottom face, the capac-

8

(a) (b)

θ

φ

d(θ,x)

w(θ,x)

x

T/2

lr

l

rl

r

Figure 7: Capacitor for a folding structure.Schematics in a side view (a) and in an angledview (b). Conductive portions are shown in red.

itance C as a function of angle θ is:

C(θ) = ε0εr

(r+l)∫r

w(θ, x)

d(θ, x)dx

=ε0εr tan

φ2

tan θ·(

(r + l) ln((r + l) cos θ

r− (r + l) +

r

cos θ)

),

(1)

where ε0 = 8.85×10−12 Fm−1 and εr = 1.00059are the absolute permittivity and relative per-mittivity of air, respectively, w(θ, x) is the widthof the conductive plate, and d(θ, x) is the dis-tance between the two plates at position x.

5.2 Capacitive strain sensor

Based on the folded capacitor model describedin the previous section, we produced a self-folding capacitive strain sensor. The crease pat-tern, shown in Fig. 8 (a), was developed basedon the X-form spans folding pattern [25]. Thetiling pattern with connections between tiles viabridges formed a compressible five parallel ca-pacitors when self-folded, and thus could be usedas a capacitive strain sensor. Using global heat-ing in an oven, the sheet reliably activated 100creases simultaneously and self-folded into theintended 3D strain sensor (Fig. 8 (b)). Note thatall the necessary circuitry was defined duringlaser machining, thus the structure was readyto use after self-folding. Due to the kinematics

electrically connected

front faceback face

0s 19s

39s 52s

5mm

(b)

(c)

Ctotal

(a)

Ctotal

(d)

Figure 8: Self-folding of a capacitive strain sen-sor made in an oven. See the self-folding processin the supplemental video.

of the structure, it can be compressed, and whenthe force was released, the structure expandedback to its original length.

We measured the capacitance of our strainsensor as a function of the applied strain (Fig. 9).Within the marked region of 30−60◦, the sensorshowed approximately linear behavior accordingto the equation Ctotal = 11.67 · strain + 12.01.Within this region, the measured resistance in-creased by 15% with respect to its original value,making it a functioning capacitive strain sensor.

9

0 10 20 30 40 50 60 70 8030

35

40

45

50

55

60

Strain [%]

Cap

acita

nce

[pF]

Figure 9: Capacitance of self-folded strain sen-sor.

6 Inductance

6.1 Model

To generate an accurate model for folded induc-tive coils, we employed Harold Wheeler’s formula[26] for calculating the inductance, L, of a single-layer coil since this formula smoothly connectsthe “short coil” and “long coil” approximations:

L = μ0n2lR

[ln

(1 +

πlRlH

)

+

(2.3 + 1.6

(lHlR

)+ 0.44

(lHlR

)2)−1 ]

,

(2)

where μ0 is the permeability of free space, n isthe number of turns, lR is the radius of the coil,and lH is the height of the coil.

First, we determined the crease pattern forself-folding (Fig. 10 (a)). The folding patternwas designed to (1) generate a spiral structureof six folds per coil turn, (2) attribute a determi-nate thickness to the wire for stable overlap, and(3) electrically connect all the tiles for currentflow along the spiral structure. The entire pat-tern was designed to configure into a hexagonalcoil of 5 turns, 16.0mm radius, and a height of6.0mm. Note that the helix radius of this design(and thus the density of turns and coil height)

5mm

(a)

(b)

(c)

electrically connectedfront face

80s

100s

10s

40s

Figure 10: Self-folding MPF coil: (a) creasepattern, (b) self-folding process, and (c) MPFsolenoid coil. See the self-folding process in thesupplemental video.

can be adjusted by regulating the gap widths ofthe valley. As the folding angle approaches 180◦,the turn density reaches its maximum value andthe magnetic field increases for a given current.

6.2 Solenoid coil

Fig. 10 (b) shows the self-folding process of theMPF solenoid coil. The folding, from begin-ning to end, only took about a minute and ahalf. Fig. 10 (c) shows the self-folded solenoid

10

coil. Note that due to the kinematics, the coilcould be compressed. Wheeler’s formula pre-dicted L = 0.52μH, though the actual value wastoo small to measure with an LCR meter.

6.3 Application to Actuation Mecha-nism

In order to demonstrate the effect of the mag-netic field generated by a folded solenoid coil,we investigated the possibility of an actuationmechanism. The basic design was based on avoice coil, in which an electrical coil generates aforce that acts on a permanent magnet, vibratinga membrane to generate sound. Our approachwas to have a compressible origami coil with twoferrous cylindrical cores suspended inside bothends. When the current was run through thecoil, the ferrous cores within become magne-tized in the same direction and attracted eachother (Fig. 11 (a)). The coil would then contractdue to the attractive force between the ferrouscores. A similar concept is used in microroboticsto achieve locomotion in a microrobot equippedwith two magnets, the separation of which aremanipulated using an externally applied reso-nant magnetic field [27].

In practice, our conductive material (MPF),was unable to conduct sufficient current for actu-ation at this scale. We therefore utilized a manu-ally folded 24-winding copper-based origami coilwith the same folding geometry pattern shownin Fig. 10. In this case we insulated the copperlayers using polyimide tape. For the cores, we

(a) (b)top and bottom ends of cylindersare suspended to the coil

coil contractioncompressibleorigami coil

coil power off

coil

leng

ths

28.06.6

22.4

25.4 29.6

17.2

2.4

11.0

1.4

magnetization

coil power on

attractioniron cylinders(bolts)

Figure 11: Concept and schematics of origami-coil actuation mechanism. Units are in mm.

used a 6.3mm diameter ferrous cylinder (bolt)

for the upper end and an 11.1mm diameter fer-rous cylinder for the lower end. Using an LCRmeter, we measured the inductance of this foldedcoil to be L = 4.6μH, which was 8% smallerthan the value predicted by Wheeler’s formula(L = 5.0μH).

Fig. 12 shows the magnetic flux density gen-erated by the origami coil, which increased as alinear function of the applied current.

1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

8

9

10

Current [A]

Mag

netic

fiux

den

sity

[T]

no core11mm diameter ferrous core

x10-3

Figure 12: Magnetic field density generated bymanually folded copper origami coil.

We tested the origami voice coil actuator byapplying current and measuring the resultingcontraction caused by attraction of the magne-tized cores (Fig. 12). At 5A of applied current,a ≈ 0.8mm contraction (≈ 3.57% compression)was observed in the structure. Presumably, theamount of contraction could be improved usinga thinner insulation layer, a larger number ofcoil windings, or a higher application of current.The non-linear increase of contraction with ap-plied current results from the nonlinear strengthof the magnetic force between the cores, whichis inversely proportional to their relative sepa-ration to the power of four. While predictingthe compression rate to obtain a precise modelof the spring constant of our origami coil is re-quired for further development of this actuator,we leave this characterization for future work.

11

contraction

current ON

1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Current [A]

Con

tract

ion

[mm

]

measurementsfit

current OFF

Figure 13: Contraction measured with differentcurrent amounts.

7 Integration of Devices

This section demonstrates the integrated useof the three electric devices presented above;namely, the self-folded MPSF resistor, the self-folded MPF capacitive strain sensor, and themanually folded origami-coil actuator. We read

PWMcurrent

power supply circuitry and motor driver(back)

MPF resistor

handle

MPF capacitive strain sensor

Charging/dischargingcircuitry includingMPF resistor (220 Ω)

MPF capacitive strain sensor Arduino Dicimila

controller boardOrigami-coil actuatior

Motor driver(TA7267BBP)3 in parallel

coil actuator

Figure 14: Experimental setup and control dia-gram. The demonstration is shown in the sup-plemental video.

the (large scale) MPF capacitive strain sensordata with an Arduino controller board with thesupport of two resistors (10MΩ and 220Ω), andwe controlled the magnetic field strength gener-ated by the folded-coil actuator as the linear out-put of the strain value of the (large scale) MPFcapacitive strain sensor. We incorporated theMPF resistor into the circuit as the 220Ω resis-

tor. A range of 10 to 50 pF of optimized capaci-tance, regulated manually through compression,is linearly mapped to a 0 to 5A current range inorder to power the origami-coil actuator. Fig. 14shows the experimental setup and the control di-agram. With the compression of the capacitivestrain sensor, we observed the compression of theorigami-coil actuator resulting from the genera-tion of a magnetic field from the origami-coil.The demonstration, which is shown in the sup-plemental video, demonstrates the combined us-age of the devices presented in this paper.

8 Discussion & Conclusion

In this paper, we presented the method, develop-ment, and usage of self-folding electric devices.We combined MPF and a heat-sensitive shrink-ing film to fabricate self-folding structures acti-vated by applying global heating. The resultingfolded structures are characterized by both con-ductivity and elasticity, making this approachappropriate for the fabrication of elastic electricdevices, such as a variable resistor, a strain sen-sor, and a voice-coil based actuator. The resultindicates that the required circuit topology canco-exist with the capability of self-folding whilesatisfying the required kinematics for the sensor.We further integrated these devices and demon-strated basic sensor-motor control by reading thestrain of the capacitive sensor and regulating thefolded coil-based actuator.

The novel electric devices have unique prop-erties due to the underlying material and thefabrication process. The MPF resistors havelimitations in terms of the maximum resistanceoutput when compared to conventional resistors.Nonetheless, the structure features elasticity andtangibility in fabrication. The maximum value ofthe MPF capacitor is in the pF range. This im-plies that an appropriate use for these capacitorsis as sensors, as they showed reliable and repeat-able outputs. The limited current capacity thatthe MPF coil supports is not a negligible issue,but it will be addressed in future work in orderto create actuation mechanisms with higher out-put.

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In summary, the methodology showed the po-tential of using a conductive polyester sheet forelectric devices by means of a simple and cheapprinting-based fabrication and a reliable self-folding process. In addition to pursuing the cre-ation of a wide functional platform based onthe presented methodology, future work will con-tinue to improve the automation of the entireprocess.

Acknowledgment

Support for this work has been provided par-tially by NSF grants 1240383 and 1138967, andthe Swiss National Science Foundation Fellow-ship Grant PBZHP2-133472.

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