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Shape Memory Alloy (SMA) materials are widely used as an actuating source for bending actuators due to their high power density. However, due to the slow actuation speed of SMAs, there are limitations in their range of possible applications. This paper proposes a smart soft composite (SSC) actuator capable of fast bending actuation with large deformations. To increase the actuation speed of SMA actuator, multiple thin SMA wires are used to increase the heat dissipation for faster cooling. The actuation characteristics of the actuator at different frequencies are measured with different actuator lengths and results show that resonance can be used to realize large deformations up to 35 Hz. The actuation characteristics of the actuator can be modified by changing the design of the layered reinforcement structure embedded in the actuator, thus the natural frequency and length of an actuator can be optimized for a specific actuation speed. A model is used to compare with the experimental results of actuators with different layered reinforcement structure designs. Also, a bend-twist coupled motion using an anisotropic layered reinforcement structure at a speed of 10 Hz is also realized. By increasing their range of actuation characteristics, the proposed actuator extends the range of application of SMA bending actuators.
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Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
35 Hz shape memory alloy actuator 
with bending-twisting mode
Sung-Hyuk Song1, Jang-Yeob Lee1, Hugo Rodrigue1, Ik-Seong Choi1, Yeon June Kang1 & 
Sung-Hoon Ahn1,2
Shape Memory Alloy (SMA) materials are widely used as an actuating source for bending actuators due 
to their high power density. However, due to the slow actuation speed of SMAs, there are limitations in 
their range of possible applications. This paper proposes a smart soft composite (SSC) actuator capable 
of fast bending actuation with large deformations. To increase the actuation speed of SMA actuator, 
multiple thin SMA wires are used to increase the heat dissipation for faster cooling. The actuation 
characteristics of the actuator at dierent frequencies are measured with dierent actuator lengths 
and results show that resonance can be used to realize large deformations up to 35 Hz. The actuation 
characteristics of the actuator can be modied by changing the design of the layered reinforcement 
structure embedded in the actuator, thus the natural frequency and length of an actuator can be 
optimized for a specic actuation speed. A model is used to compare with the experimental results of 
actuators with dierent layered reinforcement structure designs. Also, a bend-twist coupled motion 
using an anisotropic layered reinforcement structure at a speed of 10 Hz is also realized. By increasing 
their range of actuation characteristics, the proposed actuator extends the range of application of SMA 
bending actuators.
e selection of an actuator for a specic application is generally made by comparing the implementation require-
ments and the performance of dierent actuators. e performance of the actuator includes the mode of deforma-
tion, the scale of the deformation, its output force, and its actuation frequency. In the case of a bending actuator,
it is generally mainly characterized by its dimensions, bending deformation and actuation frequency. Although
mechanical actuators have good performance, their implementation requirements and the use of multiple joints
to produce smooth biomimetic motions disqualify them from a number of applications. On the other hand,
bending actuators making use of smart materials suer from a trade-o between their actuation frequency and
their bending performance with faster actuators having increasingly smaller bending performance.
Piezoelectric materials rely on a coupling between the electric eld and mechanical stress to produce deforma-
tions and bending actuators can be formed by bonding a piezoelectric plate together with a metal-ceramic layer
forming a unimorph or two piezoelectric plates forming a bimorph1,2. is type of actuator have the highest actu-
ating frequency of all smart material-based actuators, but they are limited by their small deformation as shown
in Fig.1 3–7. is is because the ceramic materials used in this type of actuator are very brittle and susceptible to
fracture8,9 such that large strains in the structure can degrade their actuating performance. Although there is no
information about their actuation speed, piezoelectric actuators showed up to deections of 1.48 mm10,11.
Ionic polymer-metal composite (IPMC) actuators, which is a type of ionic electroactive polymers (EAP) actu-
ator, rely on an ionic polymer whose surface is plated with a conductor where ions migrate towards one surface
with an imposed voltage12,13. is ion migration causes bending of the polymer in one direction, and actuators
capable of large bending deformations in the range of 26 mm maximum tip deformation have been reported as in
Fig.1 14–28. Brunetto et al. found that the actuator’s deformation is increased when the actuating speed is matched
to the natural frequency of the structure, resulting in an actuator capable of bending deections of 7.2 mm at
9.5 Hz18. Shahinpoor et al. performed experiments for frequencies ranging from 0.1 to 35 Hz and found that
there was an increase in maximum tip deformation around both the rst and the second natural frequencies23.
Although IPMC actuators have been reported to be capable of large deformations29, most of the IPMC actuators
exhibit relatively small maximum tip deformation at higher frequencies due the need to use a thinner matrix to
reduce the traveling distance of the ions within the matrix, but this also reduces the maximum deformation of the
actuator since the actuation force is proportional to the thickness of the actuator23,30,31.
1Department of Mechanical & Aerospace Engineering, Seoul National University, Seoul, 151-742, Korea. 2Institute
of Advanced Machines and Design, Seoul National University, Seoul, 151-742, Korea. Correspondence and requests
for materials should be addressed to S.-H.A. (email:
received: 28 October 2015
accepted: 18 January 2016
Published: 19 February 2016
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
Electronic EAPs are another category of EAPs that can be categorized according to their actuation mechanism
as either electrostrictive (ferroelectric polymers) or electrostatic (dielectric elastomers)32.
In ferroelectric polymers, the strain is generated by reversible alignment of polar groups due to the applied
electric elds, and Poly(vinylidene uoride) (PVDF) based polymers is the most widely used due to large bending
deformations33,34. Lee et al.35, Tzou et al.36 developed bending actuators using PVDF-based polymers. In the case
of dielectric elastomers, the electrostatic attraction between conductive layers generate a compression in thickness
and stretching in the area of the polymer lm33. To generate a bending motion, multiple at dielectric lms are
stacked and bending deformations up to 56 mm maximum have been reported37. Multiple materials have been
used to make these actuator such as Maleki et al. using PDMS38 and Mutlu et al. using stretched dielectric lm39.
However, none of the literature surveyed by the authors report both the actuation frequency as well as the bend-
ing deformation for either of these actuators.
Shape memory alloy (SMA) elements with an applied pre-strain undergo a strain recovery in the range of
4–8% when undergoing heating by transforming from a martensite phase at low temperatures to an austenite
phase at high temperature, and backwards during cooling. SMA has such advantages compared to other types
of smart materials as a high power density, but it has also been oen described as having a slow actuation speed,
which is seen as a major hindrance for its adaptation in a wider range of applications40. e main limiting factor
for its slow actuating speed is the heating and cooling speed of the SMA41, so various techniques have been inves-
tigated for improving the cooling speed of the SMA itself such as forced air convection42, the use of a heat sink40,
cooling using a water channel43 and a heat pump44. Other types of systems have also been proposed to increase
their actuation speed such as optimization of the applied current45, improved controller design46 and segmented
SMA control47.
In order to produce a bending motion using SMA, SMA wires are embedded or installed at an eccentric posi-
tion with regards to an elastic beam structure which converts the linear contraction of the SMA wire into a large
bending deformation of the structure. e actuation speed of this type structure and its actuating performance is
shown in Fig.1 48–56. ese SMA based bending actuators are advantageous since they have relatively larger max-
imum tip deformations than other types of bending actuator, but they are limited by their slow actuation speed
(~0.33 Hz) in comparison to both PZT and IPMC actuators. is is because most of the studies done on SMA
actuators have focused on the properties of the SMA itself, and were rarely focused on realizing the fast actuation
of a bending actuator. Similar principles have been used to produce diverse types of motions such as bending,
twisting, and coupled bending-twisting motions57–59.
is paper introduces a SMA-based bending actuator that is capable of both fast and large deformations can
be realized in either the pure-bending or coupled bending-twisting modes of actuation. To do so, smart so
composite (SSC) actuator consisting of a so matrix, multiple embedded SMA wires and an anisotropic layered
reinforcement structure were fabricated.
Figure1 shows the previous limits in terms of maximum tip deformation versus actuating frequency of
bending actuators using SMA and how the current work pushes the limits of SMA bending actuators up to
35 Hz such that the actuators presented in this work are those with the largest deformations amongst the smart
materials-based bending actuators within their range of actuation speed in the surveyed literature. Results for
the actuating length versus the actuation frequency as well as results related to the behavior of the actuator are
shown, and the resonance characteristics of the actuator are measured. A layered reinforcement structure design
strategy to target a specic actuation frequency is presented with a model to predict the length of the actuator
required to obtain a resonant frequency corresponding to this actuation speed. en, a layered reinforcement
structure design strategy is presented that allows the actuator to produce large bend-twisting coupled motions
Figure 1. Comparison of the actuation speed and maximum tip deformation of bending actuators. e
gure shows that the actuators in this paper extend the range of performance of this type of actuator such that
they have the largest maximum tip deformation for larger actuation speeds than previously realized.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
at fast frequencies is presented. Also, the method of control deformation of the actuator is presented to control
the amplitude of the motion and to produce asymmetric bending deformations. Finally, the performance of the
actuator with a tip payload mass is presented.
Actuator Design
e proposed actuator is a structure comprised of multiple SMA wires embedded in a polydimethylsiloxane
(PDMS) matrix along the length of the actuator at positive and negative eccentricity with an acrylonitrile buta-
diene styrene (ABS) layered reinforcement structure embedded at the center. PDMS is thermally stable through-
out the entire range of temperature during actuation of the SMA wires and presents good thermomechanical
properties that make it suitable for use in so actuators even though it, and many other polymers, is not the best
choice of material to optimize cooling conditions. e SMA wires on one side of the matrix are actuated to bend
the matrix towards that side, and the SMA wires on the other side of the matrix are actuated to bend the matrix
towards the other side. Other types of bending actuators, such as IPMC or PZT actuators have made use of res-
onant amplication to realize large deformations at high speeds, but this type of strategy has not been tested on
SMA-based bending actuators. e present work uses an SMA-based bending actuator where the actuation fre-
quency corresponds to the resonant frequency of the actuator. However, since SMA wires actuate by phase trans-
formation between the martensite and austenite states through changes in temperature, the actuator’s actuation
speed is limited by the time required for changing temperature. Since SMA wires can be heated rapidly by Joule
heating but cooling has to be done through convection or conduction, the cooling time is the main limiting factor.
In order to increase the cooling speed of SMA wire to make use of resonant amplication of the actuator, the actu-
ator is designed using multiple SMA wires with a small diameter rather than a single thick SMA wire (Fig.2a) and
its fabrication process is shown in Fig.2b and Supplementary Fig. S1. is is due to the total force generated by
SMA wires being proportional to the cross-sectional area of the wires but cooling rate being proportional to the
surface area of the wires. erefore, using multiple smaller wires with the same total cross-sectional area results
in the same actuation force with an increased rate of cooling.
Furthermore, this actuator design facilitates the use of multiple small diameter SMA wires versus external
actuation since all SMA wires have to be aligned precisely to facilitate the transfer of the contracting force to the
structure and also, since SMA wires break easily at small diameters, the SMA wires within the matrix are pro-
tected from external forces that could damage them or lower their durability. eir alignment can also be set at a
xed distance between each SMA wires to optimize the cooling rate.
In order to be able to vary the actuating characteristics of the actuator, a layered reinforcement structure is
embedded in the matrix whose conguration can be changed without making any other changes in the congu-
ration of the actuator. e layered reinforcement structure is fabricated using a 3D printer for ease of design and
manufacturing. Two layered reinforcement structure design strategies are presented in this work: the rst allows
changing of the natural frequency of the actuator, and the second allows the actuator to realize a bend-twist
motion. To change the natural frequency of the actuator, the spacing of the elements in the layered reinforce-
ment structure can be modied, two congurations are tested in this work where one has a large lament gap
between layered reinforcement structure elements and the other a small lament gap, as shown in Fig.3a,b. ese
two congurations have the same ply angle combination of [0/90/0] and the distance between each lament is
Figure 2. Design of the actuator. (a) Comparison of designs with one large SMA wire or multiple small SMA
wires, (b) fabrication by 3D printing and casting process, (c) complete actuator.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
only changed in the rst and third layers to change only the longitudinal stiness of the actuator. To realize a
bend-twist coupled motion, anisotropic properties are added to the layered reinforcement structure by varying
the angle of the layers of the layered reinforcement structure. To realize a symmetric bend-twist motion, where
the motion is the same whether the upper or lower set of SMA wires are actuated, a symmetric angle ply combi-
nation such as [θ
1] is used. In this work, an actuator with θ
1 and θ
2 equal to 30° and 45°, respectively, is built
and tested, as shown in Fig.3c.
Result and Discussion
Actuating length and actuating frequency.  e actuator’s length and its deformation magnitude are
closely related since the deformation of the actuator is larger at a xed radius of curvature for a longer actuator
length. However, for high speed actuation, this might not be the case due to interaction with its environment and
due to the decreased natural frequency associated with a longer length of the actuator. Furthermore, since the
temperature and the deformation are coupled rather than the voltage and the deformation, the cooling time might
have an eect on the maximum actuation angle. To verify these relations, experiments are conducted to measure
the relation between the actuator’s length and its actuation frequency as in Fig.4.
e length of the actuator where the embedded layered reinforcement structure has a large lament gap was
varied in increments of 2 mm for actuation frequencies of 10, 15 and 20 Hz, and the maximum tip deformation
and maximum apping angle at each lengths were measured (Fig.5a) and the shape of the actuator for actuation
speeds of 10 and 20 Hz are shown in Fig.6. For each frequency, there are noticeable peaks in both the maximum
tip deformation and apping angle at specic actuator lengths. is shows that dierent actuation frequencies
require dierent actuator lengths to obtain the largest deformation and that since the deformation is increased
signicantly at specic lengths, it can be assumed that the resonance is the main inuence behind this behavior.
It can also be seen that as the actuator length gets closer to the actuator length with a resonant frequency
corresponding to the actuation speed, which is where the largest deformation can be observed, the error in data
Figure 3. Design of the layered reinforcement structure. (a) Orthogonal layered reinforcement structure with
large lament gap, (b) orthogonal layered reinforcement structure with small lament gap and (c) anisotropic
layered reinforcement structure.
Figure 4. Setup and methods for observing the performance of the actuator. (a) Experimental setup,
(b) Measurement of the tip deformation and (c) apping angle.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
increases signicantly and then diminishes nearly entirely at this actuator length. ese characteristics corre-
spond to those observed in the beating phenomenon and are another evidence that the actuating characteristics
are inuenced signicantly by the resonance. is is shown more clearly in Fig.5b–d where the maximum tip
deformation and apping angles for multiple cycles at 15 Hz are shown for lengths of 26 mm, which shows the
highest deformation, and 28 mm which shows the largest error. In the actuator with actuator with a length of
26 mm, it can be seen that the actuator has a steady actuating performance. However, although it has a longer
length, the actuator with a length of 28 mm shows a smaller average and maximum deformation, and also dis-
played large uctuations corresponding to the beating phenomenon.
Since the resonance appears to be one of the main factors to determine the performance of the actuator, its
motion can be described as a forced vibration system. Furthermore, since the deformation of the actuator shows a
steady bending performance instead of increasing continuously to larger values, it can be described as a damped
system. To check this assumption, the behavior of actuator in the transient region at 20 Hz is measured from the
start of the actuation as shown in Supplementary Fig. S3. e behavior shown by the actuator is similar to that
of a 1-DOF damped harmonic oscillator where the actuator starts with a small deformation and increases until
Figure 5. Actuating performance of actuator according to the actuator length. (a) Actuator maximum tip
deformation and apping angle for dierent actuation frequencies and actuation lengths. (b) Tip deformation
and (c) apping angle of the actuator with a length of 26 mm at 15 Hz. (d) Tip deformation and (e) apping
angle with a length of 28 mm at 15 Hz.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
the amplitude is limited by the damping force of the actuator. is actuation behavior is dierent from other
SMA-based bending actuators where current is applied until the maximum actuation deformation at each cycle.
Modal Analysis of Actuator.  For verication of the previously obtained results, the natural frequency of
the actuator can also be measured directly from experimental modal analysis using an electromagnetic shaker.
Experiments were conducted for actuators with lengths of 20, 26 and 38 mm where the layered reinforcement
structure has a large lament gap, which corresponds to the actuator lengths with the highest maximum defor-
mations for actuation speeds of 10, 15 and 20 Hz as found previously. e tip displacements for the three dierent
lengths of the actuators are measured by varying the input frequencies. Modal analysis is done only for the rst
mode since the intended actuating motion of the actuator is that corresponding to this mode. Supplementary Fig.
S4 shows that natural frequencies of the actuators with lengths of 20, 26 and 38 mm are resulted in 8.5, 12 and
16.5 Hz, respectively. is diers slightly from the resonant frequencies found through actuation of the actuator,
which can be explained by the dierence in phase of SMA wires. During actuation, the SMA wires are heated and
cooled repeatedly, such that the SMA wires can either be fully or partially in the austenite state which has a higher
stiness than the stiness of the martensite state. However, the SMA wires should not be activated during the
modal analysis since actuating the SMA wires would results in movements of the actuator not related to vibration
from the exciter, such that the SMA has to be in the fully martensite state resulting in a slightly lower stiness than
during actuation. Although the resonant frequency of actuator during actuation is slightly higher than the natural
frequency measured in the modal analysis, this experiment gives a good approximation of the natural frequency
of the actuator during actuation.
Layered Reinforcement Structure Design for Tailoring of Actuation Characteristics.  One of the
principal advantage of SSC actuators is that it is possible to change the actuation characteristics of the actuator
by changing the layered reinforcement structure. Without making any changes to the conguration of the SMA
wires, the material of the matrix or in the manufacturing method, it is possible to change the overall properties
of the actuator by changing only the ply combination of layered reinforcement structure and therefore change
its actuation characteristics. is section will show how the design of the layered reinforcement structure can be
modied to change the actuation characteristics of the actuator.
Actuator Natural Frequency Design. Previous experiments showed that, with a xed layered reinforcement
structure design, the actuating length of the actuator can inuence to the deformation magnitude and the actu-
ator shows its highest deformation when it matches to the natural frequency of the actuator with that of the
intended actuating speed. In this experiment, the stiness of actuator is changed by changing the design of the
Figure 6. Deformation of the actuator with large lament gap in the layered reinforcement structure.
Actuators actuation of a speed of (a) 10 Hz and (b) 20 Hz.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
layered reinforcement structure of the actuator and comparing the actuating characteristics of dierent layered
reinforcement structure designs. Two dierent layered reinforcement structures congurations are tested in this
work, which are those shown previously in Fig.3a,b where one has a large lament gap of 400% the width of the
layered reinforcement structure lament between laments in the rst and third layers and the other a small
lament gap of 200%. e actuator with a large lament gap thus contains less ABS and has a lower stiness than
the actuator with a small lament gap, which should be helpful in realizing large deformation at small sizes for a
specic actuation frequency range. However, as the actuation frequency is increased, the actuator length required
to match the natural frequency becomes shorter, which reduces the active length of the SMA wire in the actuator
available to produce deformations. Due to this conict, it can be assumed that there is a specic frequency range
for the stiness of each layered reinforcement structure to realize large deformation for small size actuators.
erefore, to compare the actuating characteristics of the two layered reinforcement structure designs, the
length of each actuator where the resonant frequency of the actuator corresponds to actuating speeds of 10, 15,
20, 25, 30 and 35 Hz are obtained as previously done. e results of this experiment are shown in Fig.7a. e
maximum tested actuation frequency of the actuator with a large lament gap is 25 Hz because the tip deforma-
tion became very small at actuation frequencies above 25 Hz. As predicted, the actuator with a small lament gap
shows a longer length of the actuator to match the resonant frequency of the actuator with the actuation speed
across all tested frequencies, which results in larger maximum tip deformations.
However, in certain applications there is a need for maximum performance over a specic length, in which
case the maximum tip deformation per length becomes a critical parameter. e measured data is shown in
Fig.7b in terms of the maximum tip deformation per actuator length. ese results show that the actuator with
a large lament gap has a higher deformation per length at frequencies at or below 20 Hz while above 20 Hz the
actuator with a small lament gap actuator performs better. ese results show that dierent layered reinforce-
ment structure designs perform better for dierent parameters, and that there is no single best design. erefore,
the selection of the lament gap of the layered reinforcement structure will depend on multiple parameters
depending on the target application and its requirements.
Next, modeling of the actuation frequency based on lament gap is presented. Predicting the actuator’s
required actuator length for a specic layered reinforcement structure design is important in order to match the
target actuator length and the required deformation for the intended application.
As shown in Fig.3, the natural frequency of the actuator can be controlled through the design of the con-
guration of the lament gap, so there is a need to calculate the required actuator length at a specic actuation
frequency. In this paper, classical laminate theory and the beam vibration model are used to predict the resonant
frequency for dierent actuators lengths and for each lament gap designs.
e actuator has a clamping section for the wiring which is attached at the end of the actuator with a mass m of
1.3 g. e mass of the clamping section is concentrated at the tip of the SMA wires, so it can be simplied as a point
mass. erefore, the actuator can be described as a cantilever beam with an end mass m, an actuator length ,
actuator mass density ρ , actuator width b, actuator thickness t, area moment of inertia of actuator I and a natural
frequency f with the following relations60:
bt m
Ee is eective bending modulus of actuator, and its calculation is shown in the Supporting Information. e
results are then compared with the previously obtained results as shown in Fig.7c. e measured value is the
actuator length which shows the highest maximum tip deformation at a given actuation frequency and applying
the formula for a range of values allows to obtain the relationship between the actuator length and the natural
frequency of the actuator. Although the model will need to be improved in order to predict the length and natural
frequency of the actuator, the trends of the numerical model and of the experimental results are in agreement.
Bend-Twist Coupled Mode Design. In addition to being able to adjust the natural frequencies through the la-
ment gap design in the orthotropic ply conguration, the conguration of the layered reinforcement structure of
the actuator can be modied to give it anisotropic properties, and thus produce a combined bending and twist-
ing deformation. e layered reinforcement structures used in this work have three layers and their orientation
were previously in the [0/90/0] orientation, which does not give any bend-twist coupling. In this experiment the
layered reinforcement structure conguration was changed to [30/45/30], which gives the actuator bend-twist
coupling resulting from its anisotropic properties. is actuator was tested at 10 Hz and an actuating length of
26 mm was determined to match the natural frequency of the actuator at this actuation frequency. Results for a
complete cycle during 0.1 s showing the tip deformation and twisting angle of this actuator at this frequency is
shown in Fig.8. Results show that this actuator produces large bending deformations that are coupled with a large
twisting deformation.
Actuator Deformation Control.  e deformation of the actuator can be varied by changing the current
applied to the SMA wire without any eect on the actuation stability and on the natural frequency of the actu-
ator. To verify this an experiment was conducted for an actuator with a length 56 mm, a small lament gap and
using a xed frequency of 10 Hz while the range of bending deformations were measured for applied currents
ranging from 1.2 to 2.8 A. As the applied current to the SMA wire increased, the maximum tip deformation and
maximum apping angle are increased as shown in Fig.9(a). e error remains constantly small for all applied
currents, which shows that the deformation of the actuator can be controlled independently of the frequency of
the actuator. is is in contrast with the length of the actuator where the actuation speed and natural frequency of
the actuator need to be matched to obtain a stable actuation pattern.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
e deformation can also be controlled such that the actuator bends more towards one direction than the
other by applying a dierent current for each direction of actuation. is was tested using the conguration of
the previous experiment for dierent applied currents of 1.2 A, 2.0 A, 3.8 A with dierent combinations of these
applied currents of the le and right sides. e results of this experiment are shown in Fig.9(b). If the same
magnitude of current I0 is applied to the both le and right side of SMA wires (L, R: I0), the actuator shows a
symmetrical large tip deformation and apping angle in both directions. However, when a smaller current of
2.0 A is applied to the le side and a current of 3.8 A is maintained to the right side (L: I1/R: I0), then right side
shows a larger deformation than the le side. If the smaller current is further decreased to 1.2 A (L: I2/R: I0), then
the dierence in bending amplitude between the le and right deformations is further increased. It is to be men-
tioned that there is a reduction in bending amplitude even on the side where the applied current is maintained at
the higher current, but that it is much smaller than on the other side such that this represents a viable strategy to
produce an asymmetric deformation. Similar results were also obtained for inversed current input for the le side.
is shows that the current can be used to control both the bending amplitude and to introduce an imbalance in
bending amplitude between both sides of the actuator.
Figure 7. Actuating performance according to the layered reinforcement structure deign. (a) Actuating
speed and maximum tip deformation for both layered reinforcement structure designs. (b) Actuation speed and
maximum tip deformation per actuator length for both layered reinforcement structure designs.
(c) Comparison of calculated and measured values for both layered reinforcement structure designs.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
Payload Eect on the Actuator Performance.  In order to see the eect of a payload on the actuator per-
formance, the maximum tip deformation and maximum apping angle were measured for dierent loads applied
at the tip of the actuator. e weight was attached directly at the tip of the actuator and the actuator length that
corresponds to a resonant frequency of 10 Hz was obtained experimentally, and the experiment was repeated for
payload weights ranging 0.3 g to 3.0 g. As the payload is increased, the actuator length corresponding to a natural
frequency of 10 Hz decreases as shown in Fig.10(a). is is due to the natural frequency of the actuator changing
due to the added mass, so the expected actuator length correspond to the resonance can be calculated using the
modied equation (2) for a dierent payload mass ml as follows.
.+(+ )=
bt mm
e results of this model for the tested actuator to obtain a natural frequency of 10 Hz with dierent payload
masses is also shown Fig.10(a). e results for the maximum tip deformation and apping angle is shown in
Fig.10(b) where it can be seen that the tip deformation decreases steadily while the apping angle stays constant
until a payload mass of 1.2 g and then diminishes. ese results show that the payload mass has an eect on the
actuation properties, but that the design is able to perform well even with a non-signicant payload mass and that
it is possible to predict the eect of this added mass on the natural frequency of the actuator.
A novel SSC actuator is presented in this work that combines multiple SMA wires with small cross-sections, a so
polymeric matrix and an ABS layered reinforcement structure where the actuation speed of the actuator corre-
sponds to its natural frequency and the resonant amplication of the actuator increases the amplitude of actuation
of the actuator such that large deformations will occur. e actuator requires a few actuation cycles to reach and
then maintain its maximum tip deformation. is type of actuator was demonstrated to be capable of large defor-
mations at actuation speeds up to 35 Hz, which is two order higher than the fastest SMA-based bending actuator
found in the surveyed literature which had an actuation speed of 0.3 Hz. It is also the smart material-based so
actuator with the largest deformations in the 10–35 Hz range within the surveyed literature.
It was found that the actuating length of the actuator should be shortened for faster actuating speeds in order
to increase the natural frequency of the actuator to match the actuating frequency. However, tailoring of the
conguration of the layered reinforcement structure within the actuator allows to modify the actuation char-
acteristics of the actuator and thus to target a specic actuator length, tip deformation and actuation frequency.
Figure 8. Bending-twisting coupled mode of actuation. (a) Photographs showing the bending-twisting
coupled behavior of an actuator with a [30/45/30] layered reinforcement structure at an actuation speed of
10 Hz. (b) Tip deformation and twisting angle of the bending-twisting coupled mode actuator at an actuation
speed of 10 Hz.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
Furthermore, the conguration of the layered reinforcement structure can also be changed to induce anisotropic
properties to the actuator and thus produce a motion with a coupled bend-twist deformation. Although the actu-
ation frequency of the actuator cannot be changed during use, the maximum tip deformation and maximum ap-
ping angle could be controlled by changing the applied current. e performance of actuator for dierent loads
were also measured and the expected actuator length corresponds to the resonance at given loaded condition
could be calculated by proposed model. Also, from the small deviation of deformation, it could be veried that
the hysteresis of SMA did not have a signicant eect on the behavior of the actuator. However, the relatively high
energy consumption ( 50 W) of the developed actuator could pose limitations for certain types of applications.
Future work will focus on the dynamic modeling of the actuator including the temperature of the SMA wires.
By combining the model of the SMA with a modal analysis of structure, it should be possible to predict the
actuation performance. Also, a real-time, precise and fast temperature measurement system for the actuator will
be used to validate the results from the model. Other optimization avenues such as changing the material of the
matrix and the use of SMA coatings will be investigated in order to further improve the cooling speed of the
actuator and to reach higher actuation speeds. e developed actuator capable of fast bending actuation will also
be applied to various elds where fast actuation speeds with large deformations is required such as apping based
ying robots or underwater swimming robots.
Actuator performance measurement.  e actuator is xed to a xture which clamps it at a specic posi-
tion along the length of the actuator, which allows to obtain a specic active length of the actuator. e actuator
is then actuated using a current generator to generate the current patterns that is controlled using Labview and a
Figure 9. Control of the amplitude of deformation. (a) Control of the amplitude by changing the applied
current and (b) asymmetric bending deformations using asymmetric applied current.
Scientific RepoRts | 6:21118 | DOI: 10.1038/srep21118
CompactRIO real-time controller. e applied current magnitude is 2.8 A for all SMA wires with the square wave
current pattern shown in Supplementary Fig. S2. e start and end time for the actuation of each set of SMA wires
depends on the cycle time T of the intended actuation frequency. A ruler is xed below the actuator which is used
to measure the deformation in both bending directions, and a high speed camera (Ultima APX-RS, by Photron)
set at 500 frames per second (FPS) is used to record the deformation of the actuator. e deformation magnitude
is dened as the tip deformation in each bending direction, and the maximum tip deformation is dened as the
sum of the tip deformations in both directions. e apping angle is dened in each bending direction and the
maximum apping angle is dened as the sum of the apping angles in both directions. e tip deformations and
apping angles are measured visually from the obtained videos using the high speed camera. e video used to
measure the performance of the actuator is collected aer 2 seconds of actuation to allow the actuator to reach its
steady state performance.
Experimental modal analysis.  The natural frequency of the actuator is measured at different actua-
tor lengths using an exciter. e actuator is xed at a desired length by xing it using the xture to the tip of
the stinger. e exciter used during this test is a 4854 Modal Exciter (Bruel & Kjaer Instruments, Inc.) using a
Macro-tech 1202 (Crown, Inc.) power amplier. e sinusoidal excitation signal at each given frequency is con-
trolled using the Pulse Labshop 16.0 soware (Bruel & Kjaer Instruments, Inc.) and generated using the LAN-XI
Type 3160 Front end (Bruel & Kjaer Instruments, Inc.). To measure the response of actuator at each frequency
input, the high speed camera (Ultima APX-RS, by Photron) is used to measure the tip displacement of the actu-
ator with respect to the actuators xture.
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is work was supported by the Industrial Strategic technology development program (10049258) funded by
the Ministry of Knowledge Economy (MKE, Korea), Bio-Mimetic Robot Research Center funded by Defense
Acquisition Program Administration, and by Agency for Defense Development (UD130070ID) and National
Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP)(No. 2012R1A3A2048841).
Author Contributions
S.H.A. conceived the idea, supervised the research. S.H.S. designed the study and performed the experiments.
J.Y.L developed the control system. S.H.S and H.R. analyzed the data. I.S.C and Y.J.K developed system for the
modal analysis. S.H.S., H.R. and S.H.A wrote the manuscript and all authors commented on the manuscript.
Additional Information
Supplementary information accompanies this paper at
Competing nancial interests: e authors declare no competing nancial interests.
How to cite this article: Song, S.-H. et al. 35 Hz shape memory alloy actuator with bending-twisting mode. Sci.
Rep. 6, 21118; doi: 10.1038/srep21118 (2016).
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Supplementary resource (1)

... There are many different approaches used for cooling system for SMA material including natural air cooling, active air cooling and active liquid cooling. The natural air-cooling system decreases temperature by using heat convection principle to remove the heat generation [13]. It relays on the surrounding temperature of the environment including the room temperature and SMA temperature. ...
... This energy dissipation can be expressed as volume power density and can be calculated using the Eq. (13). The variables is defined as spectrum electrical conductivity, is the electrical field strength and is current density. ...
Shape Memory Alloy (SMA) possess memory capability to revert its original shape when exposed to load or temperature changes. This unique thermomechanical property occurs during solid state phase transformations which corresponds to functional properties of SMA, shape memory effect (SME) and super elasticity (SE). The significant coupling behaviour of SMA can be utilized as actuator in aerospace, automotive, electrical and civil fields. However, in practical applications, the coupling behaviour of SMA are non-linear and hysteretic. The control mechanism of SMA coupling behaviour is complex. Therefore, in order to achieve good control of thermomechanical properties, a highly controllable and promising heating technique is required. Thus, this paper reviewed the existing heating techniques for the SMA intending to find a controllable heating technique for the SMA. Besides that, this review suggested the promising induction heating for SMA thermomechanical characterization which offer temperature controllability and faster heating capability. However, till date most of research works are purely empirical. The present paper is able to provide an insight on the experimental approaches toward induction heating of SMA. Thus, the main aim of this paper is to provide a better understanding on the heating mechanism of SMA to develop an optimized utilization of SMA as an actuator.
... However, the actuation frequency of SMA wires (usually ≤ 10 Hz) is limited due to the long duration of cooling by natural convection mode of heat transfer [36]. Research is underway to elevate the operating actuation frequency either by using innovative methods of cooling [37,38] or by tuning the geometric configuration of SMA wires [39,40]. The objective of this paper is to demonstrate how the parametric instabilities caused by non-linear system parameters can be controlled by incorporating SMA wires as actuators. ...
PurposeVibration control of pipes conveying fluid at high pressure and pulsating velocity has been a key area of research for many engineering applications. The variation of velocity of flowing fluid with time leads to parametric instabilities in the transverse motion of the pipe. The objective of the present work is to effectively control the parametric instabilities of flexible pipes conveying pulsating fluid (sinusoidal velocity profile) by applying shape memory alloy (SMA) based actuation.Methods The Equivalent Coefficient of Thermal Expansion (ECTE) based SMA model has been employed to assimilate the actuator effect as part of the governing equation. Bolotin’s approach has been used to investigate the principal primary and secondary instability regions due to pulsating flow in a pipe with and without the actuator.ResultsIt is observed that the extent of the instability region increases with a rise in flow velocity of the fluid, however, the inclusion of SMA wire actuator causes a significant reduction in the region of principal primaryinstability. The effect of other parameters like fluid-pipe mass ratio, and mean component of fluid velocity on both primary and secondary instabilities of the system is also addressed.ConclusionSMA actuators could be effectively used for the vibration control of pipes containing pulsating flows, as long as the harmonic component of the fluctuation of the flow is within a specific limit.
... In order to achieve higher levels of strain, the SMA can be paired with a passive material in a unimorph or bimorph configuration (Kennedy et al., 2020;Song et al., 2016). These configurations have been previously used in piezoelectric composite actuators to increase their deformation. ...
Shape memory alloys (SMAs) can contract their length via a crystalline phase transition that is dependent upon their temperature and stress state. SMAs have been used as linear micro-actuators due to their high strength to weight ratio and compact structure. However, the relatively low linear contraction ([Formula: see text]4%–5% in length) limits their use. To remedy this, the SMA can be offset from a passive structure, which acts to magnify the deformation. The resulting amount of deformation depends upon the material properties and geometry of both the SMA and the passive structure. In this work, geometrically exact beam theory (also known as Cosserat theory) is coupled with SMA constitutive relations to model the maximum deformation configuration of these actuators. Four of these actuators of various lengths were fabricated and tested to verify the model. For the four actuators tested, the mean squared error between the experimental results and the Cosserat model were between 0.0702 mm (0.1% error) for the shortest actuator (66 mm in length) and 3.59 mm (2.7% error) for the longest actuator (135 mm in length). These results show that the closed form solution derived for this Cosserat beam model can accurately model the deformation of these active structures.
... На более высоких частотах кончик кантиловера не достигал максимального отклонения, что говорит о наступлении режима, когда тепло не может быть отведено от устройства достаточно быстро, чтобы обеспечить полное охлаждение. В [6] авторами был предложен интеллектуальный мягкий композитный актюатор, способный быстро изгибаться с большими деформациями под воздействием джоулева нагрева. Он представляет собой конструкцию, состоящую из мягкой матрицы, нескольких встроенных проволок из материала с ЭПФ и анизотропной многослойной армирующей структуры. ...
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The kinetic properties and high-speed processes during phase transformations and related effects of giant deformations in micro- and nanosamples of functional nanomaterials in alternating electric and thermal fields have been studied. Theoretically studied the processes of controlled deformation (activation) and heat distribution at small sample sizes, in which the manifestation of such phenomena as thermoelastic martensitic phase transition and associated shape memory effect (SME) is possible. A computing model of the speedwork of a composite actuator has been constructed and the dependence of the maximum activation frequency on the linear dimensions of the micro-actuator has been determined.
... Taking this into account, a significant amount of research has been conducted in the field of SMAbased actuators. It is imperative to note that SMA-based actuators have been designed to deliver both translational and rotational motion for variety of applications [13][14][15] . While some rotary actuators have been developed, researchers have been particularly interested in linear actuators. ...
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Actuators are ubiquitous to generate controlled motion through the application of suitable excitation force or torque to perform various operations in manufacturing and industrial automation. The demands placed on faster, smaller, and efficient actuators drive innovation in actuator development. Shape memory alloy (SMA) based actuators have multiple advantages over conventional actuators, including high power-to-weight ratio. This paper integrates the advantages of pennate muscle of a biological system and the unique properties of SMA to develop SMA-based bipennate actuator. The present study explores and expands on the previous SMA actuators by developing the mathematical model of the new actuator based on the bipennate arrangement of the SMA wires and experimentally validating it. The new actuator is found to deliver at least five times higher actuation forces (up to 150 N) in comparison to the reported SMA-based actuators. The corresponding weight reduction is about 67%. The results from the sensitivity analysis of the mathematical model facilitates customization of the design parameters and understanding critical parameters. This study further introduces an Nth level hierarchical actuator that can be deployed for further amplification of actuation forces. The SMA-based bipennate muscle actuator has broad applications ranging from building automation controls to precise drug delivery systems.
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The choice of actuators dictates how an implantable biomedical device moves. Specifically, the concept of implantable robots consists of the three pillars: actuators, sensors, and powering. Robotic devices that require active motion are driven by a biocompatible actuator. Depending on the actuating mechanism, different types of actuators vary remarkably in strain/stress output, frequency, power consumption, and durability. Most reviews to date focus on specific type of actuating mechanism (electric, photonic, electrothermal, etc.) for biomedical applications. With a rapidly expanding library of novel actuators, however, the granular boundaries between subcategories turns the selection of actuators a laborious task, which can be particularly time-consuming to those unfamiliar with actuation. To offer a broad view, this study (1) showcases the recent advances in various types of actuating technologies that can be potentially implemented in vivo, (2) outlines technical advantages and the limitations of each type, and (3) provides use-specific suggestions on actuator choice for applications such as drug delivery, cardiovascular, and endoscopy implants.
This chapter tries to move away from any magical context by examining, as scientifically as possible, how by various stimulations a form can change spatially or in functionality, alone in a homogeneous way or by association with materials. It summarizes the developments in 4D printing, with a focus on the materials and methods used for the manufacture of 4D printed objects and structures. Although printed structures exhibit self‐healing, self‐diagnosing, self‐acting and self‐sensing capabilities, etc., the chapter illustrates attractive possibilities and also highlights some difficulties. To meet the specificities of 4D printing, the actuators, integrated or not, must satisfy the following: a resolution below a certain threshold, allowing a given stroke, depending on the application, a reasonable speed and a mechanical strength adapted to the objective, and the ability to be totally or partially integrable in the 4D device.
Four-dimensional (4D) printed structures fabricated from shape memory polymers (SMPs) are typically one-way actuators, that is, for each actuation cycle, they must be programmed to deform from the original (as-printed) shape to a secondary (programmed) shape. This is done by applying a combination of thermal and mechanical loads. Then, they restore the initial shape during the actuation process by applying a thermal load. Here, we generalize this concept to fabricate two-way actuators by embedding shape memory alloy (SMA) wires into the printed SMP structures. To explain this in greater detail, we describe the printing process of a two-way bending actuator whose bilayer hinges consist of stiff SMPs as well as elastomers with low modulus. Joule heating was employed to modulate the hinges bending stiffness. To this end, electrical current was applied to the resistive wires inserted into the hinges SMP layer to control their temperature. On the other hand, thermomechanical programming of the SMA wires, which were integrated into the actuator, provided the bending actuation force. The fabricated actuator was able to bend, maintain the deformed shape, and recover the as-fabricated shape in a fully automated manner. Further potentials of this design methodology were assessed using a nonlinear finite element model. The model incorporated user-defined subroutines to incorporate complex material behaviors of SMAs and SMPs.
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This paper presents a comparative theoretical study of the performance of a set of controllers for improving the speed of actuators based on shape memory alloys (SMAs), especially on Nitinol (NiTi). To prevent overheating and thermal fatigue, these controllers take into account the maximum heating current at which a NiTi element can safely be heated. The thermal behaviour of NiTi is first modelled for calculating the time response and, based on the suggested model, it is shown that hysteresis due to phase transformation can be neglected for rapid heating, thus simplifying the model to a linear problem. The design and performance of a set of linear controllers is then presented. Simulation results show a substantial increase in actuation speed.
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Poly(vinylidene fluoride) (PVDF) based polymers are attractive for applications for artificial muscles, high energy density storage devices etc. Recently these polymers have been found great potential for being used as actuators for refreshable full-page Braille displays for visually impaired people in terms of light weight, miniaturized size, and larger displacement, compared with currently used lead zirconate titanate ceramic actuators. The applied voltages of published polymer actuators, however, cannot be reduced to meet the requirements of using city power. Here, we report the polymer actuator generating quite large displacement and blocking force at a voltage close to the city power. Our embodiments also show good self-healing performance and disuse of lead-containing material, which makes the Braille device safer, more reliable and more environment-friendly.
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This paper introduces a novel geometry for a pure-twisting soft morphing actuator that improves the stability of the actuator and allows it to obtain a larger twisting angle. The smart soft composite (SSC) actuator uses pair of NiTi shape memory alloy (SMA) wires embedded in a cross-shaped polydimethylsiloxane (PDMS) matrix at constant and opposite eccentricity across the cross-section in opposite directions in order to produce a twisting motion. To evaluate the twisting performance of the cross-shaped actuator, specimens with rectangular cross-sections and cross-shaped cross-sections are made and their twist angles are measured and compared. Results show that the cross-shaped actuator is capable of a higher twisting rate by using a thinner flange due to a more stable twisting motion.
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Piezoelectric bending actuators utilise the inverse piezoelectric effect to convert input electric energy to useful mechanical work. A comprehensive analytical model of the dynamic electromechanical behaviour of a unimorph piezoelectric actuator has been developed and successfully validated against experimental data. The model provides a mapping between force, displacement, voltage and charge. Damping is modelled using experimental data. Experimental validation is based on measurement of mode shape and frequency response of a series of unimorph beams of varying length but of the same thickness and material. The experimental frequency response is weakly nonlinear with excitation voltage, with a reduction in natural frequency and increase in damping with increasing excitation amplitude. An expression for the electromechanical coupling factor has been extracted from the analytical model and is used as the objective for parametric design studies. The design parameters are thickness and Young’s modulus ratios of the elastic and piezoceramic layers, and the piezoelectric constant k 31. The operational design point is defined by the damping ratio. It is found that the relative variation in the electromechanical coupling factor with the design parameters for dynamic operation is similar to static operation; however, for light damping, the magnitude of the peak electromechanical coupling factor will typically be an order of magnitude greater than that of static operation. For the actuator configuration considered in this study, it is shown that the absolute variation in electromechanical coupling factor with thickness ratio for dynamic operation is same as that for static operation when the damping ratio is 0.44.
In the previous paper based on this study, the authors proposed a high-speed ON/OFF digital valve driven by a laminated piezoelectric (PZT) actuator. One drawback of this digital valve was that the PZT actuator could not produce enough displacement in order to actuate the main valve. Additionally, it may be pointed out that the laminated PZT actuator is considerably expensive for general consumer use. In this study, for the purpose of overcoming such drawbacks, an improved type of high-speed digital valve was developed by adopting a bimorph PZT actuator in place of a laminated actuator. The bimorph PZT is cost-effective to produce and can realize a large displacement; the valve will be financially practical and capable of high performance. To actuate the spool valve, a nozzle-and-flapper mechanism was adopted in the proposed valve. The static and dynamic characteristics of the new device were investigated by experiment and digital simulation. As a result, we found that the valve could be driven by frequencies of a PWM carrier wave as high as 200 Hz.