Composable Flexible Small ActuatorsBuilt from Thin Shape Memory Alloy Sheets

E. Torres-Jara†∗, K. Gilpin∗, J. Karges∗, R. J. Wood† and D. Rus∗∗Computer Science and Artificial Intelligence Lab.

Massachusetts Institute of TechnologyCambridge, MA 02139

Email: etorresj@csail.mit.edu†Microrobotics Laboratory

School of Engineering and Applied SciencesHarvard University

Cambridge, MA 02139

Abstract— Alternatives to traditional actuators such as elec-tromagnetic motors are needed in applications where space andweight are limited, for example, laparoscopic medical probes,miniature robotics, and micro-lens positioning systems. Wepresent a family of small light-weight actuators that can becomposed out of a basic unit-cell to yield linear, rotational, andsurface actuation. The unit-cell actuator is built using ShapeMemory Alloy (SMA) sheets. It is activated by electrical currentand the resultant heating. Depending on the combination of theseunit-cells, the designer can control the direction of actuation, theamount of force generated, and the expansion (stroke) of theactuator. The unit-cell design overcomes limitations of actuatorsbuilt with SMA wires. For example, the heat needed to activatethe SMA is localized in a specific area by controlling thegeometry of the electrical conduction path. This geometry is easilyconstructed by laser-cutting the desired pattern. Additionally, theSMA can be mounted by its non-heating areas.

In this paper, we characterize the new actuator, compare itsperformance with that of a traditional electromagnetic motor,and report on results of endurance tests. We also demonstrate arobotic system driven by these actuators.

I. I NTRODUCTION

We wish to develop printable robots constructed out of smartmaterials that embed actuation, computation, communication,and sensing. Printable robots will revolutionize the way webuild and use robots, opening the way to applications thatrequire small, soft machines. An important challenge forprintable robots is the actuation system. Actuators shouldbesmall, light, flexible, simple to fabricate, easy to integratewith surrounding materials, and capable of exerting high force.This paper describes our work developing actuators that satisfythese properties and can be used as alternatives to traditionalactuators such as electromagnetic motors. In general, motorsrequire heavy magnetics, gear heads to exert high torque,rigidity to maintain internal alignment, and ample time todesign and manufacture(e.g. skeletal muscle). In contrast, ahuman muscle is light, flexible, and able to exert high forcesdirectly.

Overcoming the differences between traditional electromag-netic motors and muscles requires approaching the problemwith a different perspective. Biological systems present small

Time

Fig. 1. Sequence of an linear actuator expanding.

actuators that are robust and flexible but produce small forces.The output forces from many actuators are combined togenerate larger forces. In contrast, electromagnetic motors areenlarged or attached to a gearhead to increase their torquegenerated.

We describe an approach to designing composable actuatorsmade out of small unit-cells that is inspired by the heirarchyof biological systems. Managing the fabrication and assemblyof many small parts and mechanisms could be a daunting task.However, with current technology that enables the 3D-printingof small structural designs, laser-cutting of thin metallic sheets,deposition of metals onto a variety of surfaces, and the preci-sion etching of flexible circuits, we are able to overcome thesemanufacturing challenges with a relatively simple productionprocess. Hopefully, this will lead to the creation of fully

printable actuators in the future.More specifically, we have developed a family of small

composable flexible actuators using thin Shape Memory Alloy(SMA) sheets. SMA is a material that in general can exist intwo states: martensite and austenite. In the martensite statethis material can be readily deformed. When heat is appliedSMA transitions to the austenite state recovering its originalshape. The force exerted by the material during this transitionis the principle used in SMA actuators. SMA is advantageousfor actuation because of its light weight, silent operation, andflexibility. However, it is not easily scalable and its powerconsumption is high. Our actuators overcome these limitations.Each unit-cell of the actuator is small and light. It is activatedby electrical current. Unit-cell actuators can be composedintolinear, rotational, and surface actuators. The geometry ofanassembly of unit-cells determines the direction of actuation,the force generated, and the expansion (stroke) of the actuator.The actuators are capable of exerting high forces and can bepowered from a battery [1]. For example, a prototype linearactuator (Figure 1) composed of 24 unit-cells weights0.5grequires1.5A and consumes6W power. The actuator can lift80g, which is 160 times its weight.

FF

F

a

b

heat

c d

time

FF

FF

martensiticmartensitic austenitic austenitic

Trajectory

Trajectory

Fig. 2. (a) From left to right we can observe the response of a folded SMAsheet as it is heated. The heat causes a transition from the martensitic toaustenitic phase which in turn causes the SMA to exert force as it returnsto its programmed shape (flat). As shown in the second frame, the forceis greatest when the bend radius is the smallest. (b) Sectional view of aheated SMA folded sheet transmitting force to the blue structure. The creasegenerates the force while the unbent part transmits the force to the structure.The length of the latter part is minimized to prevent bendingunder the actionof the force from the crease and the reaction force from the structure.(c) Thefolded SMA sheet is connected to a structure to transmit the generated force.Connecting the sides to the structure directly is preferredfor circular motion.(d) This configuration is preferred for linear motion. The two additional bendscontribute to the generated force.

Our work builds on several novel actuation systems thatuse SMAs (both wires and sheets) as soft actuators. Forexample, SMA springs wires were developed to increase theperformance of SMA wire actuators [6]. The spring config-uration was programmed by annealing the SMA wire. Thesespring actuators have been used to build robotic worms [6],micro-robotic fish [5], and circular robots for crawling and

jumping [7]. Control methods for wire SMA actuators havealso been developed. For instance, SMA wires of differentlength were combined to control a robotic hand [2]. The strokeof the actuator was controlled by the activation pattern ofthe wires. The energy consumption of these actuators wasimproved by using thermoelectric modules. The effect of theSMA response time in the control has also been addressed ina biped robot [4]. Pulse Width Modulation (PWM) has beenused to reduce the energy consumption [8] [9]. Thin sheetactuators have been developed for small devices such as microgrippers [3]. A major advantage of SMA sheets is that theycan be cut using a laser which simplifies fabrication.

Our work introduces a class of modular composable SMAactuation systems based on a flat SMA unit-cell. In thispaper we describe the unit-cell at the basis of our actuationsystem (Section II). We then show how many unit-cells canbe composed to form linear actuators, rotational actuators,and surface actuators (Section III). We proceed to showthat our actuators have performance comparable to that of asmall electromagnetic motor and characterize the lifetimeofthe actuator (Section IV). Finally, we demonstrate that ouractuators can be used to control the movement of a soft robotthat rolls by deforming it geometry (Section VI).

b

c

a

I

Fig. 3. (a)The SMA cell is heated up by passing a electrical current throughit. The cell is built with a pattern that increases the electrical resistance inthe regions where the sheet is bent. Due to their increased resistance, onlythe bent areas will heat up when current is applied. The remainder of thestructure has less resistance and therefore heats up significantly less. Thesecooler regions can be used when mounting the cell. (b) The SMApatternof (a) is bent to form the basic actuation cell. (c) The cell ismounted in asupport structure so that it can exert force.

II. T HE UNIT-CELL

The unit cell is designed around a patterned SMA sheet. Ingeneral, SMA can exist in two states: martensite and austenite.In the martensitic phase, SMA is relatively easy to bend andstretch. The application of heat triggers a phase transition tothe austenitic phase causing the material to exert force asit attempts to return to a pre-programmed shape. This pre-programmed shape can be set by annealing the SMA whilefixing its shape as desired.

Our actuators are based on SMA sheets that naturallyflatten when transitioning to the austenitic phase. Therefore,as illustrated in Figure 2a, heat will cause any bent regionsto exert force as they attempt to reflatten. This force increasewith curvature. As shown in Figure 2b, we can mount a foldedSMA sheet on the points between which we wish to applyforce. Since the force generated by the unit-cell is at the crease,we want to minimize the amount of material that is not foldedbecause this part of SMA is not doing useful work and, due toits limited thickness, is not rigid enough to effectively transmitforce.

Two alternatives for mounting the unit-cell are shown inFigure 2. The simplest method attaches the sides of the creaseto a rigid structure (see Figure 2c). This configuration workswell for generating circular trajectories. The attachmentshownin Figure 2d has two additional bends in the SMA thatalso contribute to the force generated. This configuration ismore effective for generating linear trajectories. We use thisconfiguration for the unit-cell (Figure 3c).

The unit-cell activation is achieved by applying heat tothe SMA to reach the transition temperature (Af ) of 95◦C.The SMA used is theAlloy H from Memory-Metalle GmbH.Instead of relying on an external heat source, our actuatorsare heated by the current passing through them. Because thecreases are the regions that exert force, we increase theirelectrical resistance relative to the rest of the structuresothat current heats the creases much more quickly than theremainder of the structure. Figure 3a shows the pattern usedto increase the electrical resistance of the creases. By foldingthis SMA sheet, we built the basic cell shown in Figure 3b.The central crease bends180◦, and two side creases each bend90◦. Consequently, when the cell is fully expanded, it will beabout57% longer than its compressed configuration (assumingthat there is no distance between the creases).

This unit-cell design presents several advantages. The powerneeded to actuate the cell is reduced because only specificregions of the SMA material are heated. Additionally, thewider sections of SMA provide good structural mountingpoints because they are stronger and do not deviate noticeablyfrom room temperature. Finally, the non-heating sections ofSMA provide heat sinking that allows the higher resistanceareas to cool quickly once current is removed. This increasesthe effective bandwidth of the actuator.

It is important to note that the resting configuration ofthe SMA that we use to fabricate the cell is flat. When afolded unit-cell is heated, it will try to become flat. However,it is also possible to “program” [6] the material so that itsresting configuration is bent. In this case, when a flat cell isheated, it will try to reach the its bent configuration, whichwill cause cell compression instead of expansion. This can bedone by annealing the SMA while in the bent configuration.The remainder of this paper focuses on actuation systemsusing expanding cells built from an SMA sheet whose restingposition is flat.

F

dd/2

a b

d/2

e

h

w

c

r

Fig. 4. (a) The pattern of one cell that is bent and mounted in astructure. The thickness of the sheet is0.063mm and its dimensions are:h = 0.25mm, w = 1.75mm, e = 0.25mm. Table I has the dimensiond for each actuator. Each of the three bends has a radiusr = d/π. Thedisplacementx and the forceF are measured when the cell is locked. (b)The actuators used for characterization have 6 unit-cells connected electricallyin series and mechanically in parallel. (c) Actuators assembled in the extendedconfiguration.

TABLE I

CELL SIZE OF EACH ACTUATOR

Actuator 1 2 3 4 5d (mm) 0.6 0.9 1.2 1.5 1.8

A. The Effect of Unit-cell Dimensions

We characterized the response of a given size actuator bymeasuring its force and displacement. The geometric patternused to build a unit-cell is shown in Figure 4a, where thesections of lengthd and d/2 are bent180◦ and90◦, respec-tively. Accounting for these bends, the initial length of thebent region isx0 = 4r = 4d/π. Upon the application of heat,this cell expands to reach a sizex1 = 2d + 2e. Consequently,its theoretical expansion is about57% assuming thee can bedisregarded. In practice, this expansion is smaller because theSMA performance degrades until is reaches a stable state.

The size of the unit-cell has direct effect on its characteris-tics. To determine this relation we built 5 actuators (Figure 4c)whose unit-cells differ in size. Each actuator has 6 cells that areelectrically connected in series (Figure 4b). The dimensions ofthe cells are shown in Figure 4a and in Table I.

Each of the 5 actuators was tested as follows. Each testbegan with the actuator in its fully expanded position. Oneside was mounted in a motion stage whose position wasprecisely controlled using a stepper motor. The motion stagewas moved so that the other side of the initially expandedactuator just barely came in contact with a load cell capableof measuring compressive force (see Figure 4a). Then, weperformed a series of three steps. First, the force exerted by theunheated actuator was measured. Second, we applied currentto the actuator, (1.8A for 2.0s), and measured the force again.Third, the actuator was allowed to cool for20.0s. After eachiteration of this three-step measurement loop, we moved themotion stage closer to the load cell to further compress theactuator and repeated the same set of three steps for the newdisplacement. We continued this process until the actuatorwasfully compressed. By measuring the response of the actuatorwhen the SMA was inactive we could discount the actuator’s

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Normalized displacement

For

ce (

N)

Force−displacement

PassiveTotalActive

Fig. 5. Force-displacement response of actuator number 3 (d=1.2mm). Thedisplacement is normalized with respect to the assumed initial position whenthe three bends measure90◦, 180◦, and90

◦, respectively. The active forceis obtained by removing the passive force from the total force measured. Weobserve that for displacements smaller than one the force remains roughlyconstant. For displacements greater than one, the forces reduces rapidly.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.5

0

0.5

1

1.5

2

2.5

Normalized displacement

For

ce (

N)

Active Force−Displacement. 5 Actuators

d=0.6mmd=0.9mmd=1.2mmd=1.5mmd=1.8mm

Fig. 6. The active force-displacement response of the five actuators showsthat for d <= 1.2mm the peak and average exerted force increases quicklywith increasingd. For d > 1.2mm the force begins to slowly drop off asdbecomes progressively larger. The active force is obtainedby discounting thepassive force from the total force measured.

natural spring effect.The response of the actuator withd = 1.2mm is shown in

Figure 5. In this plot, the normalized displacement is definedas the expansion divided byx0, the ideal initial configurationof the unit-cell in which all three bends are multiplies of90◦(Figure 4a). In the upper plot of Figure 5, we observethe total force generated by the actuator and its passiveresponse. The passive response of the actuator is similar toa linear spring. This passive response is due to the naturalspringiness of the bent SMA metal. The active force generatedby the SMA is shown in the lower plot of Figure 5 where

the passive component has been discounted. We observe thatthe force generated by the actuator decreases rapidly as itexpands past a normalized displacement of1.0. In contrast, forrelative displacements less than1.0, the force remains roughlyconstant. For system design purposes, we consider the unit-cell an on/off actuator, that operates in the expansion region,and whose force depends on its maximum displacement.

Discounting the passive force, the active force generated atnormalized displacementxnorm. = 1 is 2.25N . The maximumnormalized displacement achieved isxnorm. = 1.436.

In Figure 6, we can observe the active force response ofdifferent sized actuators. As we increase the size of the cells,the generated force increases. This behavior reaches a peakaround d = 1.2mm and as the size of the cell increasesfurther, each generates less force. This can be attributed tothe structural effects as explained in Figure 2b. This showsthat continuing to increase the amount of SMA in a unit-celldoes not continue to generate more force. Instead, the forceexerted by an actuator can be increased by combining multiplecells.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.51.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

Time[s]

SM

A R

esis

tanc

e [O

hm]

SMA Resistance vs. Time vs. Driving Current

2.0A1.8A1.6A1.4A1.2A1.0A

Fig. 7. Current applied to the SMA was swept from 1.0A to 2.0A in order todetermine the response time of the SMA actuator as indicatedby a change inits resistance. Higher currents produced quicker responses (less than 0.5sec).

B. Electrical Resistance Response

The response of the cell to different values of electricalcurrent was also tested. The response is shown in Figure 7where we can observe the resistance change at least15% ofits initial value when the transition temperature is reached. Thevalue of the resistance correspond to 24 cells (d = 1.2mm) inseries. The intensity of the electrical current affects thetimetaken to reach the transition temperature. In the case of 0.9Athe transition temperature was not reached in the time windowconsidered for the experiment.

III. C OMPOSINGACTUATORS

In general, actuation mechanisms that work effectively insmall dimensions but do not scale up well can be combined to

24 cells array

unit-cella

bb

Linear Rotational Surface

Fig. 8. (a) SMA pattern that contains 24 unit-cells electrically in series. (b)An unit-cell array can be mounted in different support structures to producedifferent trajectories.

obtain larger forces or displacements. Consider human musclewhere the output force is generated by a combination ofcontractile proteins (myofilaments) connected in parallelandin series. We can do the same with the unit-cells of our SMAactuators. The force exerted by a single unit-cell does not scaleup well because the current required to heat thicker pieces ofSMA becomes prohibitive. As shown in Section II-A above,increasing the length of the SMA beyond a certain point doesnot continue to produce larger forces either.

The alternative is to combine the output effects of multipleunit-cells by mounting them in parallel and/or series to obtaindifferent expansions, trajectories, and forces. The complexityof fabricating such actuators increases because many unit-cells need to be mounted and controlled, but this additionalcomplexity is more than offset by the flexibility offered inreturn. In many cases, the control of the unit-cells can besimplified by separating them in groups. These groups of cellscan be placed in a common electrical circuit for simultaneousactivation.

Figure 8 shows different configurations of unit-cells tocreate linear, rotational, and surface actuators. All the actuatorsin this figure use 24 unit-cells electrically connected in series.These unit cells are organized in 6× 4 or 4× 6 arrays that aremounted in different support structures to produce the desiredtrajectory. The array of unit-cells was patterned with a laseron a SMA sheet (0.05mm thickness) whose default positionis flat. These actuators were built to operate in one direction.Bidirectional actuators can be achieved by using two or moreactuators antagonistically.

A. Linear Actuator

Figure 9b shows the idea used to built a linear actuator. 6cells are mounted on plastic hexagons that serve as supportstructures. Figure 9a illustrates the working principle; the 6cells expand simultaneously on a linear trajectory. By mount-

a

F

s

b ca b c

Fig. 9. (a) 6 unit-cells expand simultaneously to generate alinear trajectorys. The forceF is the summation of forces generated by each unit-cell. (b)Perspective of a 6 unit-cell actuator built on two hexagonalstructures. (c)

ing 24 unit-cells on 5 hexagons (3D printed), we built a 4 stagelinear actuator that is shown in Figure 9c. This linear actuatorwas operated with1.5A and4V (6W ). The maximum outputforce measured is80gf = 0.784N . The actuator weights0.5g,consequently its force to weight ratio is1568N/Kg. This isequivalent to lifting80g with a weight of0.5g (160 times itsweight disregarding the weight of the power supply).

One important feature of this actuator is its ability to followtrajectories that are not perfectly straight because its operationdoes not require perfect alignment.

B. Rotational actuator

F

s

a

b c

Fig. 10. (a)The unit-cells, mounted on a radial structure, describe a circulartrajectory s when expanding. (b) Perspective of a rotational actuator. (c) Arotational actuator and one of the elements used for the support structure.

A rotational version of the actuator can be realized bymounting the unit-cell on a radial support structure as shown inFigure 10. Using this configuration, we have built a rotationalactuator composed of 24 unit-cells mounted on 5 radial supportelements (Figure 10c). This actuator was designed so that theangle formed by the first and last support elements changesfrom 90◦ to 180◦ upon activation. The support elementsseparate the center of rotation from the SMA attachment pointsby 6.5mm. The SMA pattern used is identical to the one inthe linear actuator described in Section III-A. The featuresof this actuator are shown in Table II. In this table, we havealso included data from two electromagnetic motors of similardiameter (16mm) for comparison purposes. In particular, therotational actuator weighs approximately 1/40th and 1/25th

of the weight of the Micromo 1624006S and Maxon A2516motors respectively. It produces 3.4 and 6.7 times their torque,and consumes 4.5 and 7.5 times as much as power. Theratio Torque/Power is comparable to the electromagnetic motorwhereas the ratio Torque/Weight is notoriously higher.

TABLE II

ELECTROMAGNETICMOTORS/SMA ACTUATOR

Micromo Maxon SMAUnits 1624006S A2516 Actuator

Dia. mm 16.00 16.00 13.00Length mm 23.80 17.40 18.25Torque mNm 1.50 0.76 5.10Power W 1.31 0.80 6.00Weight g 21.00 12.40 0.50Torq/Power mNm/W 1.15 0.95 0.85Torq/Weight mNm/g 0.07 0.06 10.20

C. Surface actuator

F

sa

b c

Fig. 11. (a) Sectional view of a surface composed of flexible and rigid parts.Unit-cells are mounted on the rigid parts and upon activation, they bend theflexible parts changing the surface curvature following thetrajectory s. (b)Perspective of a surface actuator partially bent.(c) A surface actuator with 24unit-cells arranged in 6 columns of 4 actuator each.

An array of unit-cells can also be used to bend a flexiblesurface. This surface is shown in cross-section in Figure 11awhere the two different colors represent the rigid and flexibleparts. The light color represents the flexible surface that isconnected at several points to rigid elements. The unit-cellsare anchored on the rigid parts, and when they expand theybend the flexible elements changing the surface curvature.We built a surface actuator using a 24 unit-cell array. Thesupport structure was printed on a 3D printer that can produceflexible and rigid section within the same part (see Section Vfor details). This structure has 7 rigid columns that supportthe 6 columns of 4 unit-cells each. The actuator is shown inFigure 11c and is capable of generating a maximum torque of3.0mNm when is flat.

IV. ENDURANCE

The lifetime of an actuator depends of several factors. Forinstance, the lifetime of the support structure, the heat profile

applied to the SMA, the range of motion of the SMA, and thetype of mounting mechanism used. In our case, we have testedthe endurance of a 24 unit-cell linear actuator mounted in ahexagonal structure as shown in Figure 9c. This actuator wasbuilt 6 months ago and it has been in operation sporadicallysince then.

To test the actuator endurance, we placed a weight ontop of the linear actuator. We used a video camera and apotentiometer (which adds a frictional resistance of13.5gf )to measure displacement. We conducted three experiments onthree separate days. In the first experiment, the actuator wascommanded to perform 300 extension operations with a16.5gweight. In the second experiment the actuator was commandedto perform 1,000 operations and its motion was videotapedevery 100 iterations. In the third experiment the actuator wascommanded to do 10,000 lifting operations with a weight of16.5g . During this experiment we used the potentiometer tomeasure displacement with higher resolution which added aresistance of13.5gf . The actuator was opposing a force of30.35gf . After the three experiments the actuator continuesto be operational.

Figure 12 shows the behavior of the actuator with the twodifferent loads. We observe that there is an initial period wherethere is not motion. In this period the SMA is heating up.While it reaches its transition temperature, its generatedforceincreases. Because of this, the motion of the different loadsstarts at different points.60ms and83ms for the 16.85g and30.35g. The load is lifted until the current is removed, attime 2s, then the load compresses the actuator to its initialposition. The load also limits the maximum displacement ofthe actuator.

This displacement decreases as the number of repetitionsincrease as shown in Figure 13. We can observe the averagevalue and the standard deviation every 500 repetitions. Thefa-tigue of the material is expected because we are not controllingthe SMA temperature and with repeated activation the heatbuilds up in the creases and potentially alter the crystallinestructure. After 10,000 repetitions with the30.35g load wesee that the actuator changed its maximum displacement fromabout 4.28mm to about 1.17mm. For reference, we alsoplotted the data for 1,000 repetitions with the16.85g load.We observe that the standard deviation is quite similar andthat we can expect a change of about0.5mm in the first1, 000

repetitions.

V. FABRICATION

The fabrication of the actuator consists of three parts:patterning of the SMA sheet, building of the support structure,and mounting.

A. SMA pattern

The SMA sheet is patterned using a Diode-Pumped SolidState (DPSS) laser that has a resolution of10µm. The thick-ness of the SMA used has been either0.05mm or 0.065mm.The pattern cut has been designed to electrically connect inseries a number of unit-cells and to provide anchor points

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6

7

Time [s]

Dis

plac

emen

t [m

m]

Displacement−Time

mass=16.85gmass=30.35g

Fig. 12. Displacement of the linear actuator with differentloads. The actuatoris lifting 16.85g (blue curve) and30.35g (red curve). The displacements weremeasured with a video camera and with a linear potentiometerrespectively.A 1.5A current is applied to the actuator for 2s. We can observe that asthe temperature increases because of the current applied, the force generatedincreases as well. Because of this the different load start their motion atdifferent times:60ms andt83ms respectively.

for mounting the cells to a support structure. The dimensionsof one unit-cell and a pattern of 24 unit-cells are shown inFigures 4 and 8, respectively.

In order to electrically connect the ends of the SMA patternwe typically use one of two methods. In one, we crimp copperfoil around the SMA sheet and later solder a copper cableon it. In the other, we used screws and nuts to clamp theSMA against a copper terminal. Both methods work well butcrimping the terminal is time consuming. We did not use directsoldering to the SMA because the chemical treatment neededmakes it impractical.

B. Support structure

The hexagons used for the linear actuators (Figure 9) were3D printed with either one or two holes in each face dependingon weather the SMA was anchored with bolts or wire. Theprinters used were a Stratasys Prodigy Plus FDM 3D or aObjet Connex 500. The hexagons sides were each4mm long.The hexagons have a opening in their center to mount theactuator on a guide rod if required. This guide can have somecurvature because the actuation mechanism does not rely onalignment.

The rotational actuator uses16mm×6.5mm rectangles as asupport structures (Figure 10). These rectangles are all boundtogether at the center of rotation. These elements were builtby gluing together three layer of card board (0.54mm thick)that were patterned on a laser cutter (VersaLASER).

The structure used for the surface actuator (Figure 11) was3D printed on a Objet Connex 500 that can create parts usingtwo types of materials. The rigid material wasVeroWhiteandthe rubber material wasTango+ shore 50. The height of thestructure (2.74mm) is small and can be considered a thick

−2000 0 2000 4000 6000 8000 100001

2

3

4

5

6

7

Repetitions

Dis

plac

emen

t [m

m]

Displacement−Repetitions

mass=30.35gmass=16.85g

Fig. 13. The figure shows the displacement of the actuator for10,000repetitions with a load of20.35g and for 1,000 repetitions with a loadof 16.85g. The average displacement and the standard deviation every500repetitions are shown. The configuration used is the same as the one describedin Figure 12.

plane. As in the linear actuator case, the rigid parts have eitherone or two holes for SMA mounting purposes.

C. Mounting

Mounting the SMA on the support structure was the mosttime consuming step in the actuator manufacturing process.Our first method to attach the SMA to a structure was stitchingthe two together with 34 gauge copper wire. The wire wasthreaded through two holes in both the SMA and the supportstructure and then tied with a square knot on top. This processwas very time consuming as each stitch took at least 4minutes to complete. A few failure modes include the wiresnapping due to axial tension during activation or fabrication;the knot becoming untied due to inconsistent stitching; andthewire cutting completely through the plastic support structurecreating a slot instead of two holes. We have improved themounting by using0.5mm, hexagonal head bolts that self tapinto the plastic support structures. Because the bolts are sosmall, it is easy to strip the hex head with the hex driver,rendering the bolt unable to be tightened without the use ofmini-pliers. The threads in the plastic that the bolt creates foritself can also be subject to stripping since the threads aresosmall and so close together. To date, we have had few problemswith either the head or the threads stripping. Our only recordedfailure occurred when we applied too much current and meltedthe plastic support material surrounding the bolt.

VI. A CTUATORS IN PRACTICE: THE HEXROLLER

In order to show that our actuators can be easily and reliablyused in practical systems, we built the six-module autonomouschain robot shown in Figure 14 that we call the HexRoller.The rigid links of the robot are printed circuit boards (PCBs)containing the circuitry necessary to control the joints–eachof which is a surface type SMA actuator. For reference, the

total weight of the HexRoller is85g; it is 9cm in diameterand4cm wide.

ba

Fig. 14. (a) The HexRoller is an autonomous chain-type robotconsisting ofsix PCBs. Each one controls an actuator and is powered by on-board batteries.These modules communicate via a flexible circuit . (b) The actuator has arubber and plastic base with 24 SMA unit-cells.

Using a closed-loop distributed controller running at10Hzon each of the six modules, we performed experiments tocharacterize both the HexRoller’s speed and reliability. At anygiven time, there are always two actuators that are activated–the actuator resting on the ground nearest the direction ofmotion and the actuator directly opposite it. For example, if theactuators are numbered sequentially, the actuation sequencegoes 1 and 4, followed by 2 and 5, followed by 3 and 6,followed by 4 and 1, etc. In the speed test, the HexRollermoved27.94cm in 9s for a speed of3.1cm/s. During this timeit executed 6 steps or one step every1.5s. Select frames fromthis rolling sequence are shown in Figure 15 wheret = 0.000swas chosen arbitrarily.

t=0.000s t=0.367s t=1.133s

t=1.200s t=1.267s t=1.333s

Fig. 15. This sequence of frames shows the most significant events as theHexRoller takes onestepfrom left to right.

We tested the reliability of the actuators by allowing theHexRoller to step until it stopped on its own. In five tests, therobot was able to take 32, 12, 16, 16, and 48 steps respectivelybefore it was unable to keep moving. In three of these cases,(the first, fourth, and fifth), a software bug causing one of themodules to lock up was responsible for the robot’s ultimatehalting. Also, it should be noted that the robot performedthe 32- and 48-step sequences when its batteries were fully

charged. The 12- and 16-step sequences were all performedin quick succession after the 32-step sequence. The HexRollerdemonstrates several important features of our new actuators.First, the actuators can be powered by batteries. A3.7Vlithium-polymer battery rated for130mAh is attached to eachmodule in the chain. Using a flex circuit, these six batteriesare wired into three parallel groups, each group containingtwobatteries in series. This results in a combined output of7.4Vrated for 390mAh. While these batteries cannot power theHexRoller indefinitely, the 48-step sequence mentioned abovedemonstrates that a single charge can supply current for atleast 96 actuations. It is worth noting that the HexRoller driveseach of SMA pieces with a linear regulator that dissipatesa significant amount of energy as heat. With a switchedcontroller, we would expect to see a noticeable increase inbattery life.

Second, the HexRoller demonstrates that the SMA actuatorsexhibit relatively fast relaxation times. The speed test showedthat the robot moving at 1.5 steps per second. Given that theactuators are always used in tandem to make each step, eachactuator only had three seconds to cool down before it wasenergized again. Moreover, in the (1.5s long) step immediatelyafter each actuator is activated, the geometry of the HexRollerforces it to morph from its energized flat shape back to itsnatural curved configuration. In other words, the actuatorsareable to transition from relaxed, to activated, back to relaxedin less than three seconds.

Finally, our experiments with the HexRoller show that theSMA actuators are robust. During the reliability test, eachof the six SMA pieces was actuated over 40 times. Fromthe first experiment to the last, the HexRoller showed nodegradation in performance. These 40 cycles are in additionto many more that were performed while refining the low-level software and high-level control algorithm. Unlike linearSMA actuators based on single strands of SMA wire whichmay degrade in performance when subject to even moderatestrains, our surface actuators are able to withstand near360◦

bending over many cycles.

VII. C ONCLUSION

We have presented a simple but effective method to designflexible actuators. This process relies on the understanding thebehavior of a simple unit-cell element built out of SMA sheet.The unit-cell effectively uses the properties of flat SMA sheets:it operates in the bent region where more force is generated;it minimizes the non-bent SMA; and it heats up only the bentregions. However, the force generated by this unit-cell doesnot scale up well, and an array of them is needed to increasethe force generated. Building an actuator out of an array ofunit-cells increases its complexity but provides advantagesincluding the control of expansion length, trajectory, andgenerated force. Given the current technologies including3Dprinting and laser cutting, a variety of support structurescanbe built to create an actuator with a given behavior. We haveshown three types of configurations: linear, rotational, andsurface. The linear actuator has been tested for endurance

and can easily perform over 10,000 repetitions under loadwithout breaking. These actuators have been tested in actualsystems such as the battery-operated HexRoller robot that usessix actuators connected in a chain. The robot demonstratesthat this SMA actuator is power efficient compared to otherSMA designs that cannot operate with batteries. We have alsoshowed that a rotational version of this type of actuator iscomparable to an electromagnetic motor.

These actuators are light and small because of their con-stituent materials. Their support structure can be built withflexible materials for applications that requires deformability.They can be designed to follow complex trajectories that aredifficult to achieve with traditional technologies. The actuatorsfabrication process is simple and could be fully automated tohave printable actuators. These features make these actuatorsa promising alternative to traditional technologies in currentand new robotics applications.

ACKNOWLEDGMENT

This work is supported in part by Defense Advanced Re-search Projects Agency (DARPA) grants W911Nf-08-1-0228(Programmable Matter) and W911NF-08-C-0060 (ChemicalRobots). The authors would like to thank Ara Knaian forfacilitating the test rig used to determine the force response ofthe actuators.

REFERENCES

[1] Torres-Jara, E.; Rus, D.,“Flexible Actuator Based on Shape Memory AlloySheet,”US Patent No.: 61/248,838, 5 October 2009.

[2] Kyu-Jin Cho; Rosemarin, J.; Asada, H.; , ”Design of vast DOF artificialmuscle actuators with a cellular array structure and its application to afive-fingered robotic hand,” Robotics and Automation, 2006.ICRA 2006.Proceedings 2006 IEEE International Conference on , vol., pp.2214-2219,15-19 May 2006

[3] Leester-Schadel, M.; Hoxhold, B.; Lesche, C.; Demming, S.;Buttgenbach, S.,“Micro actuators on the basis of thin SMA foils,”Microsystem Technologies, 2008. Springer Berlin/Heidelberg, pp.697-704, 27 February 2008.

[4] Esfahani, E.T.; Elahinia, M.H.,“Stable Walking Pattern for an SMA-Actuated Biped,”Mechatronics, IEEE/ASME Transactions on , vol.12,no.5, pp.534-541, Oct. 2007

[5] Kyu-Jin Cho; Hawkes, E.; Quinn, C.; Wood, R.J.,“Design, fabricationand analysis of a body-caudal fin propulsion system for a microroboticfish,” Robotics and Automation, 2008. ICRA 2008. IEEE InternationalConference on, pp.706-711, 19-23 May 2008

[6] Sangbae Kim; Hawkes, E.; Kyujin Choy; Joldaz, M.; Foley,J.; Wood,R., “Micro artificial muscle fiber using NiTi spring for soft robotics,” In-telligent Robots and Systems, 2009. IROS 2009. IEEE/RSJ InternationalConference on, pp.2228-2234, 10-15 Oct. 2009

[7] Sugiyama, Y.; Shiotsu, A.; Yamanaka, M.; Hirai, S.,“Circular/SphericalRobots for Crawling and Jumping,”Robotics and Automation, 2005.ICRA 2005. Proceedings of the 2005 IEEE International Conference on,pp. 3595-3600, 18-22 April 2005.

[8] Chee Siong Loh; Hiroshi Yokoi; Tamio Arai; , ”New Shape MemoryAlloy Actuator: Design and Application in the Prosthetic Hand,” Engi-neering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27thAnnual International Conference of the, pp.6900-6903, 17-18 Jan. 2006

[9] Ma, M.; Song, G.,“Control of shape memory alloy actuator using pulsewidth modulation,”Smart Materials and Structures, vol. 12, no. 5, pp.712,2003.