2021 IEEE 4th International Conference on Soft Robotics (RoboSoft)
April 12-16, 2021, Yale University, USA

Design Parameters for Stacked-Ribbon Shape-Memory Alloy
Bending Actuators*
2021 IEEE 4th International Conference on Soft Robotics (RoboSoft) | 978-1-7281-7713-7/20/$31.00 ©2021 IEEE | DOI: 10.1109/RoboSoft51838.2021.9479427

Trevor L. Buckner, Rebecca Kramer-Bottiglio
Abstract— Soft robots continue to suffer from a lack of
powerful actuator options that do not rely upon bulky external
power supplies or fluid pumps. This is especially true ofbending-type actuators that often require immersion in an ionicor aqueous fluid, or fail to provide adequate forces for morethan trivial tasks. Shape memory alloys (SMA) have recently
seen use as a bending actuator that occupies little space,provides large forces, and can be powered from a small onboard battery. In this work, we investigate design parametersof bending SMA actuators made from flattened Nitinol wires—referred to as SMA ribbons—which possess a geometry
favorable to repeatable bending actuation. We then present a
novel “stacked” SMA ribbon actuator that provides increased
bending forces while reducing overall system stiffness,compared to a single thick SMA ribbon.

Figure 1. SMA ribbon actuator manufacture. (A) SMA wire is softened
via annealing (1) and then flattened in a rolling mill (2), repeating thesesteps until desired thickness is reached; the flattened ribbon is wrappedaround a steel rod (3), and clamped in place (4); the rod is heated andquenched (5), repeated three times; the ribbon is removed from the rod andunwrapped (6). (B) SMA ribbons prepared for programming by wrapping
around steel rods of varying diameter and clamping in place.

I. INTRODUCTION
In addition to flexible components, soft robots often
require parts that are small, lightweight, and self-contained.
In the case of actuators, a large percentage of soft robots
utilize vacuum or pressure-based systems, requiring a heavy
external pump or fluidic storage to which the robot remains
tethered. In the move toward untethered operation[1], there
have been numerous approaches toward the concept of“artificial muscles”[2], generally implying a thin, possibly
fiber-like form factor that can provide motion intrinsically,rather than via external volume displacement from a pump or
an off-camera cable drive. Normally, these artificial muscles
exhibit strictly contractile or extensile motions, as in thecases of super-coiled nylon muscles[3], conductive polymers
such as polypyrrole[4], dielectric Peano-HASEL actuators[5],shape memory polymers[6], shape memory alloy springs[7],or electromechanical spun carbon nanotubes[8]. On the other
hand, some pure-bending actuators have also been developed,
including electroactive polymer composites[9] andhydrogels[10], although both of these tend to suffer fromextremely slow actuation times and low forces. Recently,
research has begun to utilize Shape Memory Alloys (SMA)
in flattened sheets or ribbons as an electrically-controlled
bending actuator, which provides higher output forces anddisplacements in applications where the profile of the robot
must remain extremely thin [11]–[13]. Herein, we offer
characterizations of a Nitinol SMA bending ribbon actuator,
and its performance as influenced by programming shape andcross-sectional geometry. We further introduce a novel“stacked” SMA ribbon actuator that offers greater net force

for antagonistic actuation while also reducing overall systemrigidity for soft applications.
II. MATERIALS AND METHODS
A. Preparing SMA Ribbons
Shape Memory Alloy ribbons are formed from round
Nitinol wire (Memry), with the initial wire diameter selected
depending on the desired cross-section of the resulting
ribbon. Building from the process first described in [13], theround wire is first softened by annealing in an oven for 20
minutes at 500 °C. After air-cooling, the softened wire ispassed through a simple manual rolling mill machine,
reducing the thickness in incremental steps of approximately
10 μm. Ribbons are annealed between steps as needed torelieve any work hardening and prevent damage to theequipment. Note that the total cross-sectional area is reduced
somewhat as the ribbon is elongated during this process.
In this work, specimens are flattened into two sizes: 410 ×
1,070 μm from the initial round diameter of 762 μm (0.03 in),and 140 × 1,070 μm from an initial round diameter of 508 μm(0.02 in), hereafter referred to as “thick” and “thin” ribbons.
Note that the total cross-sectional area of the thin ribbon isalmost exactly 1/3 that of the thick ribbon.
B. Programming SMA Ribbons for Bending Motion
Prepared SMA ribbons are tightly wrapped, flush arounda 316 stainless steel rod and clamped in place via a split-shaft
collars (McMaster-Carr) at both ends of the wrapped coil.
The rod is then placed in an oven at 390 °C for 20 minutes,
after which the rod is removed and quickly quenched inroom-temperature water for 30 seconds until fully cooled.
This heating and quenching step is repeated three times.
Then, the SMA ribbon is unclamped and straightened, readyto actuate back into a curled configuration (Fig. 1A). All
specimens in this work were programmed in the same batch.

*Research supported by NASA.
R. Kramer-Bottiglio is with the School of Engineering and Applied
Science, Yale University of New Haven, Connecticut, CT 06520 USA,(phone: 203-432-9662; e-mail: rebecca.kramer@yale.edu).
T. L. Buckner is with the School of Engineering and Applied Science,
Yale University of New Haven, Connecticut, CT 06520 USA, (e-mail:trevor.buckner@yale.edu).
978-1-7281-7713-7/21/$31.00 ©2021 IEEE

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III. RESULTS
Flattening an SMA wire into a thin ribbon provides ageometry favorable to repeatable bending actuation. We haveshown in a previous work that while a round wire may twistout of plane or roll around, thin ribbons with greater crosssectional aspect ratios are able to more efficiently direct theirforces along the programmed trajectory[13]. That is, a flat
ribbon will provide larger bending forces than a round wireof similar area moment of inertia. In this work, we focus on
further characterization of ribbon actuators.
A. Effect of Coil Programming Diameter
It is well-known that the performance of a contracting
spring actuator made from SMA wire will vary greatly
depending on the chosen coil diameter and pitch angle during
the programming step[14]. However, the analogous
properties for bending actuators are understudied. Here, wecharacterize the impact of programmed curvature bymeasuring the performance of a set of bending actuators,
programmed by wrapping SMA ribbons about stainless steelrods of varying diameter: 1.59, 3.18, 6.35, and 12.7 mm(1/16, 1/8, 1/4, and 1/2 inches, Fig. 1B). In each case,unwrapping and then heating the ribbons to 100 °C under freedeflection caused the actuator to return to its fully coiled state
without any discernible loss to the overall stroke curvature.

Figure 2. SMA bending actuator performance dependent on initialprogrammed diameter. (A) Force-displacement curve for specimens in a 3point bending test, bent opposite the actuation direction. (B) Flexural
rigidity calculated from (A). (C) Blocked bending tip force over atemperature ramp. 100 °C is the maximum safe operating temperature. (D)Mean blocked tip force at 100 °C.

Using a universal testing machine (Instron 3345) toperform a 3-point bending test with a support span of 3 mm,
we measured the bending rigidity of the SMA ribbons,bending each specimen (5 per program diameter) opposite its
normal actuation direction (Fig. 2A). The flexural rigidity(EI) becomes noticeably higher as the coils are wrapped more
tightly, approximately following a power series curve withchanging programmed diameter (Fig. 2B).

rigidity, although we expect that the optimal point will varydepending on the particular alloy and specimen cross-section.
This further suggests that SMA ribbons designed to perform
more complex bending motions, such as moving into analternating “ripple” pattern, or forming a radiallycompressive “clover” could be optimized by programmingeach curve along the entire ribbon with a specified, andperhaps varying radius of curvature, to meet localized force
and rigidity targets (Fig. 3A).

Similar specimens for each programmed diameter werealso measured for blocked bending tip force generation usinga Dynamic Mechanical Analyzer (TA Instruments, DMA
Q850). Specimens were placed in a single-cantilever fixture
with a constraining plate on one face to prevent the ribbon
from popping up. The free end of the specimen was placed
precisely on the force probe and then subjected to atemperature ramp from 20 °C to 120 °C at a rate of 3 °C/min(Fig. 2C). Interestingly, the smallest programming diameter
appeared to cause a delay of about 10 °C in the onset of force
generation. This delay may be a result of over-straining
during the wrapping stage, resulting in small dislocations that
inhibit the austenite-martensite transition that governs
actuation until reaching a higher temperature[15]. It is
important to note that for the particular alloy used, the safe
activation temperature is 100 °C, and moving beyond thatpoint for extended periods risks “burning out” the actuator by
inadvertently annealing the material and reverting the
programmed state. Knowing this, it is apparent that theactuators programmed at the tightest diameter (1.59 mm) areunable to fully activate within the safe temperature region(Fig. 2C), while the loosest diameter (12.7 mm) is unable togenerate a large amount of force even beyond 120 °C, simply
because its programmed bend angle is so shallow (Fig. 2D).

B. Stacked Actuator Performance
We developed a “stacked” SMA actuator, composed ofseveral thin ribbons layered, but not adhered, on top of eachother. This stacked configuration essentially multiplies theoutput force of the actuator while mitigating much of therigidity that would be present in a single thicker ribbon,
following classical beam theory. In evaluating this novel
stacked SMA actuator, we performed the same tests again as
described in Section A to characterize the effective flexural
rigidity and the blocked tip force for each actuatorconfiguration. In this case, we compared a single thin ribbon,
a single thick ribbon (Fig. 3B), a stack of 3 thin ribbons (“3stack”, equivalent cross-sectional area as the thick ribbon),and a stack of 6 thin ribbons (“6-stack”, Fig. 3C). Each ofthese configurations was programmed using the 6.35 mm
diameter steel rods.
Observing the results, we note that the thick actuator has
a drastically (19.4×) higher flexural rigidity than the thinactuator (Fig 3D, E), while only providing 3.2× the force(Fig. 3F, G). On the other hand, the 6-stack has a flexural
rigidity of 4.6× the thin ribbon but provides 3.0× the force.
Ideally, the 3- and 6-stack would provide 3- and 6× the force

Observing the above results, it becomes clear that for therange of programmed diameters tested in this work, the 6.35mm size has the highest ratio of output force to flexural
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of the thin actuator, respectively, but we suspect that
performance is reduced due to interfacial losses between the
many layers, and the tendency for the ribbons to slide apart if
not bundled together with crimps or tightly wrapped thread.
Stacked SMA ribbon actuators may be useful for
antagonistic actuation. Previous work has confirmed thatbending SMA actuators are indeed capable of delivering therequired forces to bend an opposing actuator, although doing
so consumes energy, reducing the total force available for
performing work toward a chosen task[13]. By using thinner
wires in a stacked configuration, the ratio of flexural rigidity
to actuation force can be decreased, resulting in higher net
forces in an antagonistic setting (Fig. 3H). Given the force F
at 100 °C, and flexural modulus K of two different SMA
actuators, the formula (F6-stack/Fthick)∙(Kthick/K6-stack) compares
the rigidity/force ratio between two actuator types, andindicates that simply exchanging a thick actuator for a
6-stack would provide a 3.9× increase in the percentage of
input force remaining as net force, while a 3-stack would
provide an increase of 5.2×.
C. Stacked Actuator Cooling Time
A known bottleneck in SMA actuation is cooling time,
which can require several seconds between actuation
strokes[16], particularly because an SMA becomes 2-3 times
more rigid when active[17], which prevents antagonistic
motion until the opposing actuator has cooled. The coolingtime can be severely impacted by proximity to insulating
materials in the host robotic structure, as well as the volume
and thickness of the SMA component. We investigated thischaracteristic for each of the different actuator configurationsin free convection. Every specimen (5 of each) was lightly
coated in a high-emissivity ink, and then suspended between
two non-conducting supports. Specimens were then Jouleheated above 100 °C. The power was then disconnected, andthe temperatures were recorded over time using a thermal
camera (Fluke TiX 580). The thin actuators cooled to room
temperature (22 °C) within 20 seconds, while both the 3-stackand thick actuators took approximately twice as long due totheir increased mass (Fig. 3I). Interestingly, the increased
surface-area-to-volume ratio of the 3-stack compared to thethick ribbon did not seem to provide any reduction in coolingtime, which may have been a result of each layer in the stack
being pressed tightly together, concealing the interfacialsurfaces during the test.

Figure 3. SMA bending actuator performance of thin, thick, 3-stack, and6-stack configurations. (A) Example sketches of potential complex ribbons
using varied programmed diameters, including a circular curve, a serpentine
ripple, a right-angled polygon, and a compressive clover. (B) Microscopecross-sections of thin and thick ribbons. (C) 6-stack actuator in the actuated,curved position, and in the unactuated straight position. (D) Forcedisplacement curve for specimens in a 3-point bending test, bent opposite
the actuation direction. (E) Flexural rigidity calculated from (D). (F)Blocked bending tip force over a temperature ramp. 100 °C is the maximum
safe operating temperature. (G) Mean blocked tip force at 100 °C. (H)Relative performace of each actuator configuration, normalized against the“thin” ribbon. (I) The thin actuator takes approximately 20 s to cool to 22°C, while the thick and 3-stack actuators take 35 and 40 s respectively.

IV. CONCLUSION
The technique of using SMA ribbons as a bending-type
actuator is relatively young, but also holds significant
promise for the field of soft robotics, among others. By
intelligently selecting the design parameters of the ribbon,
including thickness, programming angle, and even stackingof multiple ribbons, the net force and overall system rigidity
can be tuned to better suit the desired application
performance, including localized regions of increased or
reduced forces. We expect that the stacked actuator design
can be further improved by using greater numbers of thinner
ribbons. Further, we suspect that by including a thin,
conductive bonding layer between ribbons, such as a liquidmetal/elastomer composite[18], cooling time could be further
reduced[19], taking advantage of the increased surface areafor heat dissipation while keeping ribbons attached to eachother in a way that still allows independent flexure.
ACKNOWLEDGMENT
This work was supported by The National Aeronautics
and Space Administration (grant no. 80NSSC17K0553).

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REFERENCES[14] J. Koh, “Design of Shape Memory Alloy Coil Spring
Actuator for Improving Performance in Cyclic
Actuation,” Materials, vol. 11, no. 11, Art. no. 11, Nov.
2018, doi: 10.3390/ma11112324.
[15] E. Alarcon et al., “Fatigue performance of superelastic
NiTi near stress-induced martensitic transformation,”International Journal of Fatigue, vol. 95, pp. 76–89,
Feb. 2017, doi: 10.1016/j.ijfatigue.2016.10.005.
[16] Y. Tadesse, N. Thayer, and S. Priya, “Tailoring the
Response Time of Shape Memory Alloy Wires throughActive Cooling and Pre-stress,” Journal of Intelligent
Material Systems and Structures, vol. 21, no. 1, pp. 19–
40, Jan. 2010, doi: 10.1177/1045389X09352814.
[17] K. Otsuka and C. M. Wayman, Shape Memory
Materials. Cambridge University Press, 1999.
[18] S. Rich, S.-H. Jang, Y.-L. Park, and C. Majidi, “Liquid
Metal-Conductive Thermoplastic Elastomer Integration
for Low-Voltage Stiffness Tuning,” Advanced
Materials Technologies, vol. 2, no. 12, p. 1700179,
Dec. 2017, doi: 10.1002/admt.201700179.
[19] M. Leary, F. Schiavone, and A. Subic, “Lagging forcontrol of shape memory alloy actuator response time,”
Materials & Design, vol. 31, no. 4, pp. 2124–2128,
Apr. 2010, doi: 10.1016/j.matdes.2009.10.010.

[1] S. I. Rich, R. J. Wood, and C. Majidi, “Untethered soft
robotics,” Nature Electronics, vol. 1, no. 2, Art. no. 2,
Feb. 2018, doi: 10.1038/s41928-018-0024-1.
[2] S. M. Mirvakili and I. W. Hunter, “Artificial Muscles:
Mechanisms, Applications, and Challenges,” Adv.
Mater., vol. 30, no. 6, p. 1704407, Feb. 2018, doi:
10.1002/adma.201704407.
[3] S. M. Mirvakili et al., “Simple and strong: twisted
silver painted nylon artificial muscle actuated by Joule
heating,” San Diego, California, USA, Mar. 2014, vol.
9056, p. 90560I, doi: 10.1117/12.2046411.
[4] J. Foroughi, G. M. Spinks, and G. G. Wallace, “Highstrain electromechanical actuators based onelectrodeposited polypyrrole doped with di-(2ethylhexyl)sulfosuccinate,” Sensors and Actuators B:
Chemical, vol. 155, no. 1, pp. 278–284, Jul. 2011, doi:
10.1016/j.snb.2010.12.035.
[5] N. Kellaris, V. G. Venkata, G. M. Smith, S. K.
Mitchell, and C. Keplinger, “Peano-HASEL actuators:
Muscle-mimetic, electrohydraulic transducers thatlinearly contract on activation,” Science Robotics, vol.
3, no. 14, Jan. 2018, doi: 10.1126/scirobotics.aar3276.
[6] Y. Meng, J. Jiang, and M. Anthamatten, “Bodytemperature triggered shape-memory polymers withhigh elastic energy storage capacity,” J. Polym. Sci.
Part B: Polym. Phys., vol. 54, no. 14, pp. 1397–1404,
Jul. 2016, doi: 10.1002/polb.23990.
[7] S. Kim, E. Hawkes, K. Choy, M. Joldaz, J. Foleyz, andR. Wood, “Micro artificial muscle fiber using NiTi
spring for soft robotics,” in 2009 IEEE/RSJ
International Conference on Intelligent Robots andSystems, St. Louis, MO, USA, Oct. 2009, pp. 2228–
2234, doi: 10.1109/IROS.2009.5354178.
[8] W. Guo et al., “A Novel Electromechanical Actuation
Mechanism of a Carbon Nanotube Fiber,” Adv. Mater.,vol. 24, no. 39, pp. 5379–5384, Oct. 2012, doi:
10.1002/adma.201201845.
[9] A. Punning, M. Kruusmaa, and A. Aabloo, “A selfsensing ion conducting polymer metal composite(IPMC) actuator,” Sensors and Actuators A: Physical,
vol. 136, no. 2, pp. 656–664, May 2007, doi:
10.1016/j.sna.2006.12.008.
[10] Z. Han et al., “Dual pH-Responsive Hydrogel Actuatorfor Lipophilic Drug Delivery,” ACS Appl. Mater.
Interfaces, vol. 12, no. 10, pp. 12010–12017, Mar.
2020, doi: 10.1021/acsami.9b21713.
[11] H. F. M. Ali, A. M. Khan, H. Baek, B. Shin, and Y.
Kim, “Modeling and control of a finger-like mechanism
using bending shape memory alloys,” Microsyst
Technol, Jan. 2021, doi: 10.1007/s00542-020-05166-0.
[12] J. K. Paik and R. J. Wood, “A bidirectional shapememory alloy folding actuator,” Smart Mater. Struct.,vol. 21, no. 6, p. 065013, May 2012, doi: 10.1088/09641726/21/6/065013.
[13] T. L. Buckner, R. A. Bilodeau, S. Y. Kim, and R.
Kramer-Bottiglio, “Roboticizing fabric by integrating
functional fibers,” PNAS, vol. 117, no. 41, pp. 25360–
25369, Oct. 2020, doi: 10.1073/pnas.2006211117.
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