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This Communication presents a class of soft actuated materials that can achieve lifelike motion. By embedding pneumatic actuators in a soft material inspired by biological muscle fibril architecture, and developing a simple finite element simulation of same, we can achieve tunable biomimetic motion with fully soft structures, exemplified here by an active left ventricle simulator.
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A Bioinspired Soft Actuated Material
Ellen T. Roche , Robert Wohlfarth , Johannes T. B. Overvelde , Nikolay V. Vasilyev ,
Frank A. Pigula , David J. Mooney , Katia Bertoldi , and Conor J. Walsh *
E. T. Roche, J. T.B. Overvelde, Prof. D. J. Mooney,
Prof. K. Bertoldi, Prof. C. J. Walsh
School of Engineering and Applied Sciences
Harvard University
Pierce Hall, 29 Oxford Street
Cambridge , MA , 02138 , USA
E-mail: walsh@seas.harvard.edu
E. T. Roche, Prof. D. J. Mooney, Prof. C. J. Walsh
Wyss Institute for Biologically Inspired Engineering
Harvard University
3 Blackfan circle , Boston , MA , 02155 , USA
R. Wohlfarth
Technical University of Munich
Germany , Arcisstr. 21 , D-80333 , Munich , Germany
J. T. B. Overvelde, Prof. K. Bertoldi
Kavli Institute for Bionano Science and Technology
Harvard University
29 Oxford Street , Cambridge , MA , 02138 , USA
Dr. N. V. Vasilyev, Dr. F. A. Pigula
Department of Cardiac Surgery
Boston Children’s Hospital
300 Longwood Ave , Boston , MA , 02115 , USA
DOI: 10.1002/adma.201304018
Nature has abundant examples of soft muscular systems; exam-
ples of these in the human body are the stomach, tongue, dia-
phragm and heart. In fact, musculature has been deemed the
“prototypical soft actuator” because it can achieve fast, strong
actuation and remarkably complex patterns of movement.
[ 1 ]
Replication of these motions with traditional robotic systems
is challenging, and involves complex mechanisms and many
actuators. Furthermore, while the impedance of a robotic
system can be modulated using force feedback and advanced
control methods, it is diffi cult to achieve values similar to bio-
logical tissue. The emerging fi eld of “soft robotics” lends itself
to replicating biomimetic motions, having simple and low
cost actuation and the capability to achieve bending, twisting,
extension and fl exion with non-rigid materials. However, com-
plex motion often requires specifi cally designed actuators with
multiple internal channels or complex cavities for actuation.
[ 1–6 ]
As depicted in Figure 1 a, if we look to biology for inspiration,
complex motion in soft muscular structures is often achieved
through the functional arrangement of many simple contrac-
tile elements arranged spatially in a soft matrix (Figure 1 b), and
actuated synergistically.
In this communication we begin by realizing a soft con-
tractile actuator that lends itself to being made from, and
embedded in, an elastomeric matrix with mechanical proper-
ties similar to tissue (Figure 1 c). Through the specifi c arrange-
ment of the contractile elements and their selective activation,
a wide variety of motions can be achieved relatively simply and
inexpensively (Figure 1 d). By varying matrix material, width,
number of actuators and actuator spacing we characterize
effects on horizontal and vertical strain distribution, and total
force generation for a variety of test specimens. Furthermore,
we develop methods for numerically simulating these materials
that can provide design guidelines on how the material and geo-
metric properties of both the contractile elements and matrices
affect the resultant movement. To demonstrate the modeling
approach and manufacturing capabilities of this new platform
of materials, we present a specifi c case study of a material that
mimics the biological form/function relationship of the left
ventricle of the heart (Figure 1 e). This modeling approach was
verifi ed via a prototype fabricated with a multi-step molding
process that included features to aid with three dimensional
measurement of movement (Figure 1 f). This class of program-
mable, soft actuated material with multiple degrees of freedom
has potential for a huge range of applications including simu-
lating normal physiological and pathological motion, in addi-
tion to replacing or restoring the function of failing organs.
We selected McKibben pneumatic artifi cial muscles (PAMs)
[ 7–9 ]
to act as the contractile elements for this platform of materials.
These are the most highly developed and studied class of soft
actuators
[ 1 ] . They consist of an infl atable bladder surrounded
by a braided mesh. The rationale for selection of these PAMs
were multiple; (i) they can be fabricated to be fully soft,
[ 10 ]
(ii) they can be actuated to achieve signifi cant contraction with
low pressures (demonstrating a load-length behaviour similar
to muscle),
[ 1 ] (ii) they can be actuated quickly (0.05 seconds
dynamic response time)
[ 10 ] and (iv) they can be easily inte-
grated into the manufacture of three dimensional soft actuated
materials through a multi-step co-molding process. PAMs are
limited in that they can only have one mode of actuation; axial
contraction with an accompanied radial expansion in response
to an increase in pressure. However, if arranged spatially in a
matrix according to a desired function, they may be analogous
to individual contractile elements such as muscle fi brils
[ 1 ] and
more complex three dimensional resultant motions can be
achieved. For our application, soft low-threshold pressure actu-
ators were fabricated as described previously
[ 10 ] but scaled down
in size to a nominal length and diameter of 75 mm and 5 mm
respectively. Figure 2 a shows the fabrication of the actuators. A
3D printed mold (Objet Connex 500, Stratasys) was used to cast
inner tubes from elastomer (Ecofl ex 00–30, Smooth-on Inc.).
The process is described further in the Supporting Information
(Figure S1). A mesh was then placed around this inner tube
and an air supply tube was secured inside actuator with nylon
thread. Finally the mesh and inner tube were covered with
an additional layer of elastomer. The principle of operation of
the PAMs is shown in Figure 2 b and Supporting Information
Movie S1. Their longitudinal contraction and radial expansion
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were characterized, and are plotted as a function of input pres-
sure (Figure 2 c). As can be seen, the majority of the contrac-
tion/expansion occurs at low pressures due to the low durom-
eter of the inner elastomeric tube.
In order to understand the behavior of a composite material
consisting of actuators embedded in an elastomeric matrix, we
manufactured a number of two dimensional test specimens
with varying material properties and actuator number and
spacing. Figure 2 d shows the process for fab-
rication of dog-bone shaped test specimens
with embedded actuators (one or three) with
two different elastomeric matrices (Ecofl ex
00–30, Smooth-on Inc. and Elastosil M4601,
Wacker Chemie AG). Two-part molds were
3D printed that included interdigitating fea-
tures to provide increased tensile strength at
the material interface between the specimen
and its ends that were clamped in the tensile
testing machine. Before casting the speci-
mens, the actuator and supply lines were
placed in the mold and PDMS and Ecofl ex
elastomer were poured into the ends and
main cavity respectively and the two mate-
rials bonded at the interdigitating interface.
Optical markers were added to test speci-
mens with a template and a Matlab (Math-
works Inc.) interface was used to track them.
Strain measurements were made according
to the equations in Figure 2 e. Testing for
force and strain at various input pressures
was carried out as described in the experi-
mental section, with more detail and results
in supporting information (Supporting Infor-
mation Figure S4 and S5 and Movie S2).
Ecofl ex 00–30 was selected as the matrix
for fabrication of the soft actuated material
due to the ability to generate larger strains,
and because its reported modulus 125kPa
[ 11 ]
was within the range of reported values
for myocardial tissue (203.3 ± 55.6 kPa for
healthy myocardium and 117.3 ± 37.0 kPa for
infarcted myocardium).
[ 12 ]
Having ascertained the properties of the
individual actuator and composite actuator-
matrix specimens, we developed a method-
ology for creating numerical simulations of
our soft actuated materials. The simulations
were performed using the nonlinear fi nite
element (FE) code ABAQUS/Explicit and
provide a means to predict the performance
of different design iterations of the soft active
materials. To model the response of the
actuators to an increase in pressure, without
the need for a detailed model of the braided
mesh, we used temperature and orthotropic
coeffi cients of thermal expansion to model
their anisotropic strain response. PAMs
were assigned an experimentally derived
modulus of 1.78MPa (described further in
Experimental Section and Supporting Information Figure S1)
and orthotropic thermal expansion coeffi cients according to
experimentally derived strains that were negative in the lon-
gitudinal direction and positive in the radial direction for a
positive change in pressure (Figure 2 c). The host elastomeric
matrix was modeled as an elastic material as strains were in
the linear elastic range. It was assigned a thermal expansion
coeffi cient of zero. The model of the matrix and the PAMs were
Figure 1. Inspiration, concept and realization of bioinspired soft actuated material for physi-
ological motion generation. a) The arrangement of fi bers in the heart, stomach and skeletal
muscle can inspire soft actuated materials. b) Arrangement of fi bers in the heart. c) Pneumatic
air muscle showing displacement when actuated with air, and process of embedding actuators
in a soft matrix. d) Selective activation of individual contractile elements. e) Resulting active left
ventricle that can achieve twisting motion. f) Casting of actuators in a simplifi ed bioinspired
3D structure.
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optical markers. Also, as we would expect, we observe a trend
towards decreasing strain as matrix width or actuator spacing
increases. The total force produced by the specimens is less
affected by matrix width and actuator spacing (Figures 2 g and
2 j). Discrepancies between the experimental and numerically
predicted force were observed (Figure 2 j) with the experimental
force being less than the numerical prediction. This may be
attributed to some slippage of the test specimens from the grips
of the tensile testing machine, or some slight de-lamination at
merged in ABAQUS before applying a uniform temperature
(corresponding to actuation pressure) to the entire assembly.
The output for each specimen was the reaction force at fi xed
ends and displacement for selected nodes corresponding to
the optically tracked markers on the physical specimens. In
Figure 2 f–j we compare numerical and experimental strain and
force results for single and multiple actuators, respectively. We
see very good agreement for strain; as shown in Figure 2 f and
2 i, with discrepancies likely due to quality and consistency of
Figure 2. a) Molding process for actuators 1: An elastomeric tube is molded and capped with a 3D printed mold, and centre rod 2: Tube is demolded
3: A mesh is placed over the elastomeric tube, secured to an air supply tube, and 4: Actuator is embedded in a thin layer of elastomer. b) Operation
of actuators: when pressure is applied the actuator shortens and expands radially. c) Percentage longitudinal shortening and radial expansion for each
pressure. d) Fabrication process for test specimens. e) Test specimen showing optical marker placement for horizontal and vertical strain calculations
and dimensions. f) Experimental and FE strain for various matrix widths. g) Experimental and FE force prediction for various matrix widths (h–j) as
above for various actuator spacing (S) in terms of resting diameter of actuator, D = 5 mm.
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corresponding to the experimental boundary condition.
Experimental measurements on the physical prototype closely
matched that of the FE model with an agreement of 98.5%.
The average experimental rotation was 7.89° ± 0.59° (Figure 3 f,
Movie S4 and S5). Differences between numerical and experi-
mental results are likely due to slight discrepancies in sensor
positioning in the physical prototype. Discrepancies are lower
than the 2D test specimens because the electromagnetic
trackers are smaller and more accurate than optical marker
tracking. Both numerical and experimental values for rota-
tion fall within the ranges of clinical values of 6.8° ± 2.5° as
reported by Nagel et al.
[ 13 ] Furthermore, when the physical
model was supported by a fl exible band rather than a rigid
support to allow apical and basal rotation (end of Movie S4),
apical rotation of 6.25° ± 1.73° (counterclockwise when viewed
from apex) and basal rotation of 2.78°± 0.45° (clockwise) could
be achieved. These values were also in the range of clinical
values for apical and basal rotation respectively (6.8° ± 2.5° and
4.4° ± 1.6°) (Figure 3 g). The validation of the FE model with
experimental testing, and the close correlation of both with
clinical data is a key result that demonstrates the applicability
of this class of materials.
Left ventricular twist is a useful index of cardiac performance
and myocardial mechanics, and can be affected by a range of
diseases.
[ 14 ] For example, if muscles are injured by ischemia
(insuffi cient supply of blood, usually due to a blocked artery)
it can lead to tissue death or infarction. This injury can render
them non-contractile, leading to local akinesia (no motion)
or dyskinesia (local movement that opposes that of the viable
myocardium). The three-dimensional simulation and physical
prototype we developed were also used to explore how damage
to individual contractile elements can result in akinetic motion.
This could be accomplished by selective deactivation of the
PAMs, representing a transmural infarct where both sup-
epicardial and sub-endocardial fi bers are injured by ischemia
and rendered non-contractile.
[ 17 ] Figure 4 highlights this key
feature of our approach: the ability to selectively deactivate
individual PAMs in both numerical simulation (Figure 4 a–c,
Movie S7) and our experimental model (Figure 4 d, Movie S6).
Pathological motion was simulated by setting isotropic thermal
coeffi cients of selected PAMs to zero in the FE model and by
disconnecting the air supply for the deactivated muscles in
the physical prototype. The plot in Figure 4 e shows the total
rotation from each of the four markers in the apical plane (FE
simulation and experimental measurements) as the PAMs are
sequentially deactivated. Overall rotation decreases as PAMs
are deactivated sequentially. The discrepancy between simula-
tion and experiment is likely due to slight movement of the ini-
tial marker positions when deactivating the PAMs in the phys-
ical prototype. As the results demonstrate, the contribution to
rotation from markers 1 and 2, (positioned in the region where
PAMs were deactivated) decreases with each PAM deactivation.
Although this trend is evident for markers 1 and 2, it is more
signifi cant for marker 2 (positioned between 2 muscles that
are ultimately deactivated) than marker 1 (positioned between
activated and deactivated PAMs). This is analagous to a higher
reduction in rotation in an infarcted region (akinetic motion)
compared to a lower reduction in rotation in a peri-infarct or
border zone region (dyskinetic motion).
the actuator/matrix or matrix/PDMS interface, although meas-
ures were taken to minimize these experimental artifacts. In
addition, a limitation of the numerical modeling approach is
that it is not as accurate for higher pressures and higher mod-
ulus matrices.
Upon establishing the fabrication method, completing the
experimental characterization, and developing and validating
a numerical simulation approach, we then took inspiration
from nature to create a three dimensional soft active material.
The left ventricle of the heart is a muscular structure capable
of achieving complex motion through oriented active con-
tractile elements. During the contraction phase of the cardiac
cycle the apex of the left ventricle twists anti-clockwise approx-
imately 6–10° when viewed from the apex while the base of
the heart has a net clockwise rotation of 2–4°.
[ 13,14 ] Figure 3 a
describes the resultant complex left ventricular (LV) twisting
motion, with the apex and base rotating in opposite directions.
Twist is governed by parameters including orientation of the
heart muscle (myocardial) fi bers and the balance between
the contraction of the outer (sub-epicardial) and inner (sub-
endocardial) fi bers which are arranged in opposing helices
(Figure 3 b). [ 15 ]
Once we had validated our modeling approach, we cre-
ated a three-dimensional FE model that represented a sim-
plifi ed version of the left ventricle (LV) structure (Figure 3 d
and e, Supporting Information Movie S3). Specifi cally, an
ellipsoid LV geometry was generated in Solidworks (Dassault
Systemes) using dimensions in the range of a previously
reported simplifi ed model
[ 16 ] (specifi cally; base to apex 71 mm,
wall thickness 10mm, radius 42mm). As the sub-epicardial
bers dominate the motion of the LV, the simplifi ed model
includes this layer alone (Figure 3 b). The PAMs were oriented
in a left-handed helix to mimic the architecture of the fi bers
of the sub-epicardial layer and were oriented, at an inclination
of 60° with respect to the basal plane as described by Young
and Cowan.
[ 17 ] Three transverse reference planes (apical, mid
and basal) were created in the LV model (Figure 3 b) and four
equally spaced nodes were created on each plane coincident
with the outside of the LV wall for outputting displacement
data. The simulations were run as described for the 2D speci-
mens. The boundary conditions matched that of the physical
prototype when the displacement of the nodes at the base was
xed in all directions. Positional coordinates of each displace-
ment tracking node were measured for actuation of PAMs at
different pressures. Guided by this numerical simulation, a
physical prototype was fabricated with identical dimensions
(Figure 3 c). Figure S6 describes the multi-step molding pro-
cess with reconfi gurable 3D printed molds that include align-
ment features for accurately embedding multiple actuators in
an elastomeric LV structure. Motion was tracked using elec-
tromagnetic trackers (3D Guidance trakSTAR system, Ascen-
sion Technology Corporation) placed in the LV model at loca-
tions corresponding to the displacement tracking nodes in the
FE model (Figure S8). Rotation of each node in the basal and
apical plane for incremental pressures was calculated from
these coordinates using equation 2 (Supporting Information).
The FE model predicted an apical rotation of 7.78° ± 0.55°
(average of rotations for four nodes corresponding to EM
trackers) when the LV is rigidly supported at the base,
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based methodology was developed and validated for simulating
such composite materials. A case study was presented that was
inspired by the structure and dominant muscle layer of the
myocardial architecture of the left ventricle. We demonstrated
In this communication we have described the simulation,
fabrication and experimental characterization of a soft active
material concept comprising linear contractile elements com-
pletely embedded in an elastomeric matrix. A fi nite element
Figure 3. a) Heart with opposing rotation at apex (counter-clockwise) and base (clockwise). b) Sub-epicardial and sub-endocardial fi bers are arranged
in opposing helices. Sub-epicardial fi bers dominate overall motion due to a larger radius, thus a greater moment arm. c) Physical prototype at various
pressure increments. d) Mesh showing deformation at corresponding pressures. e) Displacement contour plot in isometric view showing the displace-
ment (U) of the ventricle at corresponding pressures. f) Apical rotation (average of 4 markers in apical plane) for FE and physical model when LV is
supported at the base compared to clinical values.
[ 13 ] g) Apical and basal rotation (average of 4 markers) when LV is supported by fl exible band between
base and apex compared to clinical values.
[ 13 ]
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actuated materials are vast. The method of fabrication is simple,
low cost and fl exible. We demonstrate that by varying the matrix
material, the number of actuators, actuator spacing and degree
of actuation (Supporting Information, Figure S5) that we can
tune the motion to match both physiological and pathological
motion. In addition to increasing our understanding of these
motions, this material platform can function as a test-bed for
therapeutics. Additionally, as the PAMs can be further actuated,
the platform could have potential as a device for the mechanical
assist or replacement of organs. The elastomeric materials used
in the creation of these soft active materials have a modulus
on the order of 125 kPa which is closely matched to that of
biological tissue, providing an inherently safer alternative for
interfacing with biological tissue compared to other robotic
approaches. Further tuning of the material platform could
involve using an inhomogeneous or graded modulus matrix
to tune the compliance of the material, or using other actuator
types to achieve additional patterns of movement.
Experimental Section
Experimental Characterization of Actuators : In order to characterize
longitudinal shortening and radial expansion of the actuator, one end
was fi xed as it was infl ated to a given pressure. Length and diameter
of the actuator were measured at each pressure increment. Young’s
that by mimicking the orientation of the contractile elements in
a soft elastomeric material in shape similar to the left ventricle,
an accurate representation of apical twist could be achieved.
Furthermore, we showed that the approach could be used to
predict the effect of damage to a select number of contrac-
tile elements on cardiac motion by selectively disengaging a
number of PAMs. In future studies, other parameters such as
changing the geometry, number and orientation of PAMS or
material properties of the elastomeric matrix, could be modifi ed
to see the effect on motion. Due to the fact that physiological
or pathological twist has a critical impact on the performance
of implantable cardiac devices such as prosthetic valves and
intracardiac defect repair devices, an ideal bench-top cardiac
simulator would mimic the soft and active contractile motion of
the natural heart tissue in addition to replicating physiological
and pathological motions. Here, we demonstrate a soft cardiac
simulator with an actively twisting component whose motion
agrees well with numerical simulation and physiological clin-
ical ranges. Given that the majority of therapy delivered to treat
cardiac disease is associated with pathological motion, we also
demonstrate the ability to generate pathological-like motion
with our simulations and experiments by deactivating select
PAMs, a key feature not present in other silicone models.
[ 18 ]
Looking beyond the exemplifi cation of the left ventricle sim-
ulator, the possible applications for this tunable platform of soft
Figure 4. a) FE model showing sequential deactivation of PAMs (all at 20 psi). Displacement contour plot for each case at 20 psi viewed from anterior
view (b) and apex (c), respectively. d) Physical prototype at 20 psi with 0, 1, 2, and 3 muscles deactivated (shown in red). e) Total rotation for FE model
and experimental showing a decrease in rotation of markers 1 and 2 that lie in the “akinetic region”.
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Acknowledgements
Funding was from the Fulbright International Science and Technology
Award, the Wyss Institute, and Harvard SEAS. We would like to thank
Sicong Shan for initial Matlab code for optical marker tracking, Jongmin
Shim and Panagiotis Polygerinos for input to FE simulation, Steven
Obiajulu for help with initial actuator fabrication, the Wyss Institute for
use of Object Connex 500 3D printer and Kathleen O’Donnell for help
with illustrations.
Received: August 9, 2013
Revised: August 30, 2013
Published online:
[1] F. Ilievski , A. D. Mazzeo , R. F. Shepherd , X. Chen , G. M. Whitesides ,
Angew. Chem. Int. Ed. 2011 , 50 , 1890 .
[2] R. V Martinez , J. L. Branch , C. R. Fish , L. Jin , R. F. Shepherd ,
R. M. D. Nunes , Z. Suo , G. M. Whitesides , Adv. Mater. 2013 , 25 ,
205 .
[3] R. V. Martinez , C. R. Fish , X. Chen , G. M. Whitesides , Adv. Funct.
Mater. 2012 , 22 , 1376 .
[4] R. F. Shepherd , F. Ilievski , W. Choi , S. a. Morin , A. a. Stokes ,
A. D. Mazzeo , X. Chen , M. Wang , G. M. Whitesides , Proc. Natl.
Acad.Sci. USA 2011 , 4 .
[5] K. Suzumori , S. Endo , T. Kanda , IEEE Int. Conf. Robot. 2007 ,
4975 .
[6] K. Suzumori , T. Maeda , H. Watanabe , T. Hisada , IEEE/ASME T.
Mechatron. 1997 , 2 , 281 .
[7] H. A. Baldwin , in Proceedings of the Furdt Rock Biomechanics Sympo-
sium 1969 , 139 .
[8] H. Schulte , Natl. Acad. Sci. 1961 , H , 94 .
[9] M. Gavrilovic , M. R. Maric , Med. Biol. Eng. 1969 , 7 , 77 .
[10] S. C. Obiajulu , E. T. Roche , F. A. Pigula , C. J. Walsh , in Proc. ASME
IDETC 2013 , in press
[11] Y.-L. Park , B. Chen , D. Young , L. Stirling , R. J. Wood , E. Goldfi eld ,
R. Nagpal , IEEE Int. Conf. Robot. 2011 , 4488 .
[12] T. Shishido , M. Sugimachi , O. Kawaguchi , H. Miyano , T. Kawada ,
W. Matsuura , Y. Ikeda , T. Sato , J. O. E. Alexander , K. Sunagawa ,
H. Miyano , T. Kawada , Y. Ikeda , T. Sato , J. Alex , Am. J. Physiol. 1998 ,
274 , H1404 .
[13] E. Nagel , M. Stuber , B. Burkhard , S. E. Fischer , M. B. Scheidegger ,
P. Boesiger , O. M. Hess , Eur. Heart J. 2000 , 21 , 582 .
[14] C. H. Lorenz , J. S. Pastorek , J. M. Bundy , J. Cardiovasc. Magn. R.
2000 , 2 , 97 .
[15] S. Nakatani , J. Cardiovasc. Ultrasound 2011 , 19 , 1 .
[16] S. Göktepe , O. J. Abilez , K. K. Parker , E. Kuhl , J. Theor. Biol. 2010 ,
265 , 433 .
[17] A. A . Young , B. R. Cowan , J. Cardiovasc. Magn. R. 2012 , 14 ,
49 .
[18] E. R. Chamberlain , (The Chamberlain Group), Patent US 6,685,481
B2 , 2004.
modulus of the PAMs was determined at a range of pressure increments
on a mechanical tensile tester (Instron 5566, 2kN load cell) at a grip-
to-grip spacing of 50mm. The crosshead was manually lowered to zero
force, and then returned to the original gauge length at a speed of
200 mm/min while measuring force (Figure S2).
Experimental Characterization of Test Specimens : Specimens were
gripped by rigid ends at a in a mechanical tensile tester (Instron
5566, 2kN load cell). Pressure used to actuate PAMs was varied with
a regulator (Campbell Hausfeld) and measured with a sensor (Balluff
BSP000W). A photo was taken at each pressure with a remote-controlled
camera positioned at a fi xed distance from the test specimen. Optical
markers were then tracked with a camera and a customized Matlab script
in order to output axial and radial strain at each pressure (Figure S4).
FE Model of Test Specimens and Left Ventricle : Quadratic tetrahedral
solid hybrid elements (ABAQUS standard element type C3D10H) were
used. Under large strains, Ecofl ex 00–30 behaves as a hyperelastic
material but strains encountered in the experiments presented are within
the linear elastic range so it was modeled as a linear elastic material with
properties from supplier material data sheets (density of 1.07 × 10
–9 g/cm 3
and Young’s modulus of 68.9kPa, the tensile strength at 100%
strain) and a Poisson’s ratio of 0.499. A linear elastic model was also
used for the PAMs. The Young’s modulus of the PAMs under tension
in the axial direction was experimentally determined by measuring the
force/length slope of an infl ated PAM at various pressure increments
(Figure S2). The composite density of the actuator was derived by the
volumetric percentage of its components (elastomer, mesh, and air) and
calculated at 0.45 × 10
−9 g/cm 3 . Air supply tube geometry and inactive
ends were incorporated into the model and assigned appropriate
material properties and a coeffi cient of thermal expansion. For the test
specimens, the accuracy of the mesh was ascertained through a mesh
refi nement study, resulting in a mesh seeding size of 1.5 mm in the
matrix and PAMs, and 4.9 mm throughout clamped ends. For the left
ventricle mesh seeding size was 3.2 mm. Displacement of the nodes on
the clamped ends of the samples was fi xed for test specimens, and nodes
at the base of the left ventricle were fi xed. Orientation assignment for the
PAMs in the left ventricle model is described in Supporting Information.
Experimental Characterization of Motion : Motion tracking of the
physical prototype was achieved with the 3D Guidance trakSTAR
(Ascension Technology Corporation) and Model 90 6DOF freedom
sensors (0.9 mm). The transmitter and the base of heart were fi xed in
the same plane using a customized plastic holder so that the apex was
free to move. One sensor was placed at the center of the base plane,
and assigned as the origin. Each of eleven additional trackers were
then placed at molded alignment features on the LV and then fi nely,
symmetrically positioned with Cubes software (Ascension Technology
Corporation). Insertion into the elastomer was achieved by piercing
a hole with a 22 gauge needle then inserting the 0.9 mm trackers so
that elastomer would self-seal around the trackers, enabling them to be
secured to the elastomer. The LV was actuated in discrete pressure steps
and positional data was acquired 5 times at each pressure and averaged.
Supporting Information
Supporting Information is available from Wiley Online Library or from
the author.
Adv. Mater. 2013,
DOI: 10.1002/adma.201304018
... In recent years, a variety of soft actuators have been developed with the aim to replicate mechanical features; for example, dielectric elastomers [4][5][6][7], shape-memory alloys [8][9][10], fiber-based and polymer carbon artificial muscles [11][12][13], and fluidic actuators [14][15][16][17][18][19][20]. All artificial actuators demonstrated here can achieve linear contraction, high strain/stress, and intrinsic mechanical properties. ...
... The interaction of contractile units, pennation angle, and flexible behavior of connective tissue remains unknown. Roche et al. [15,18] reported a pneumatic artificial heart by embedding contractile units into a flexible matrix to achieve a heart-like rotational motion. Actuation of the myocardium is different from skeletal muscle but provides a valuable reference for the design of skeletal muscle, as natural muscle actuation can be achieved by arranging muscle fibers parallel within the connective tissue [2,3,23]. ...
... The model of MFUs and flexible matrix were assumed to be isotropic with linear elastic material properties. The contractile units (Young's modulus 1.5 MPa, Poisson's ratio 0.31) [18], double symmetrical rebar layers (Young's modulus 100 MPa, Poisson's ratio 0.3) [28] with linear elastic material, and the flexible matrix with Young's modulus of 0.6 MPa and Poisson's ratio of 0.475 [28]. The interaction between the contractile units and the flexible matrix was defined as a tie constraint; the inflation behavior of the contractile units was simulated with a fluid cavity; and the applied pressure was the same as that of the pressure during the experiment. ...
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Pennate muscle is characterized by muscle fibers that are oriented at a certain angle (pennation angle) relative to the muscle’s line of action and rotation during contraction. This fiber rotation amplifies the shortening velocity of muscle, to match loading conditions without any control system. This unique variable gearing mechanism, which characterized by Architecture Gear Ratio (AGR), is involves complex interaction among three key elements: muscle fibers, connective tissue, and the pennation angle. However, how three elements determine the AGR of muscle-like actuator is still unknown. This study introduces a Himisk actuator that arranges five contractile units at a certain pennation angle in a flexible matrix, the experiment and simulation results demonstrated that the proposed actuator could vary AGR automatically in response to variable loading conditions. Based on this actuator, we present a series of actuators by simulations with the varying pennation angle ( P ), elastic modulus of the flexible matrix ( E ), and number of contractile units ( N ) to analyze their effects on AGR, and their interaction by three-factor analysis of variance. The results demonstrated that P and N effect on the AGR significantly, while E effects on AGR slightly, which supported the idea that the P is the essential factor for the AGR, and N is also an important factor due to the capability of force generation. This provides a better understanding of mechanical behavior and an effective optimizing strategy to muscle-like soft actuator.
... An overview of the FEM procedure is shown in Fig. 2. FEM has been used to analyze and optimize the various soft actuator designs discussed in Section II, such as pneumatic network [98], [113], [114], fiber-reinforced [76], [78], [122], omnidirectional [86], [108], [140] and 3D-printed actuators [18], [50], [87], [151]. The aforementioned packages also allow for force measurements, modeling of the interaction with other objects, and analysis of multiphysics phenomenon such as fluid-structure interaction [241] and thermostructural analysis [242], [243]. Open-source alternatives for the simulation of soft actuators are MOOSE and VegaFEM. ...
... Soft robotic devices for the heart, including ventricular assist and direct cardiac compression devices, have received significant attention due to their relatively simple function (similar to a pump) and can assist cardiac function, which may be required before transplant. A soft robotic sleeve with embedded McKibben-based actuators is proposed in [242], [568] (Fig. 9d), which is implanted around the heart and actively compresses and twists to act as a cardiac ventricular assist device. Alternatively, individual McKibben actuators are wrapped around the heart ventricles in [612] to contract and relax in synchrony with the beating heart. ...
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Soft robotics is a rapidly evolving field where robots are fabricated using highly deformable materials and usually follow a bioinspired design. Their high dexterity and safety make them ideal for applications such as gripping, locomotion, and biomedical devices, where the environment is highly dynamic and sensitive to physical interaction. Pneumatic actuation remains the dominant technology in soft robotics due to its low cost and mass, fast response time, and easy implementation. Given the significant number of publications in soft robotics over recent years, newcomers and even established researchers may have difficulty assessing the state of the art. To address this issue, this article summarizes the development of soft pneumatic actuators and robots up until the date of publication. The scope of this article includes the design, modeling, fabrication, actuation, characterization, sensing, control, and applications of soft robotic devices. In addition to a historical overview, there is a special emphasis on recent advances such as novel designs, differential simulators, analytical and numerical modeling methods, topology optimization, data-driven modeling and control methods, hardware control boards, and nonlinear estimation and control techniques. Finally, the capabilities and limitations of soft pneumatic actuators and robots are discussed and directions for future research are identified.
... Inspired by living organisms, soft robots are developed from intrinsically compliant materials, enabling continuous motions that mimic animal and vegetal movement 1 . In soft robots, the canonical hinges and bolts are replaced by elastomers assembled into actuators programmed to change shape following the application of stimuli, for example pneumatic inflation [2][3][4][5] . The morphing information is typically directly embedded within the shape of these actuators, whose assembly is facilitated by recent advances in rapid prototyping techniques [6][7][8][9][10][11] . ...
... Soft robots can achieve complex tasks such as gentle gripping, crawling or swimming 3,12,13 using low-complexity, muscle-like soft actuators that bend, twist, contract or elongate on demand 2,5,[14][15][16] . This unique combination of softness and bioinspired motion make soft robots appealing for a variety of innovative applications where rigid robots would fail 17 . ...
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Inspired by living organisms, soft robots are developed from intrinsically compliant materials, enabling continuous motions that mimic animal and vegetal movement1. In soft robots, the canonical hinges and bolts are replaced by elastomers assembled into actuators programmed to change shape following the application of stimuli, for example pneumatic inflation2–5. The morphing information is typically directly embedded within the shape of these actuators, whose assembly is facilitated by recent advances in rapid prototyping techniques6–11. Yet, these manufacturing processes have limitations in scalability, design flexibility and robustness. Here we demonstrate a new all-in-one methodology for the fabrication and the programming of soft machines. Instead of relying on the assembly of individual parts, our approach harnesses interfacial flows in elastomers that progressively cure to robustly produce monolithic pneumatic actuators whose shape can easily be tailored to suit applications ranging from artificial muscles to grippers. We rationalize the fluid mechanics at play in the assembly of our actuators and model their subsequent morphing. We leverage this quantitative knowledge to program these soft machines and produce complex functionalities, for example sequential motion obtained from a monotonic stimulus. We expect that the flexibility, robustness and predictive nature of our methodology will accelerate the proliferation of soft robotics by enabling the assembly of complex actuators, for example long, tortuous or vascular structures, thereby paving the way towards new functionalities stemming from geometric and material nonlinearities. An all-in-one methodology for fabricating soft robotics reported here uses interfacial flows in elastomers that cure to produce actuators that can be tailored to suit applications from artificial muscles to grippers.
... When safe human-machine interaction is paramount, the design of smart devices and robotic systems often relies on inflatables and cylindrical structures as they support a variety of possible deformations. [1][2][3][4][5][6][7] However, a vast majority of these suffer from an intrinsic one-to-one relationship between input pressure and output deformation. In other words, they exhibit programmed to snap at different pressure thresholds and assembled in various order and orientation to form structures capable of multimodal deformation. ...
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Inflatable structures have become essential components in the design of soft robots and deployable systems as they enable dramatic shape change from a single pressure inlet. This simplicity, however, often brings a strict limitation: unimodal deformation upon inflation. Here, multistability is embraced to design modular, inflatable structures that can switch between distinct deformation modes as a response to a single input signal. This system comprises bistable origami modules in which pressure is used to trigger a snap‐through transition between a state of deformation characterized by simple deployment to a state characterized by bending deformation. By assembling different modules and tuning their geometry to cause snapping at different pressure thresholds, structures capable of complex deformations that can be pre‐programmed and activated using only one pressure source are created. This approach puts forward multistability as a paradigm to eliminate a one‐to‐one relation between input signal and deformation mode in inflatable systems.
... In the biomedical field, Belforte et al. (2014) created many McKibben actuator-inspired prototypes of similar fabric-reinforced soft actuators for various biomedical purposes, such as massage therapy for patients suffering from lymph edema. Roche et al. (2014) used McKibben actuators completely embedded in an elastomeric matrix to facilitate complex deformation modes in a synthetic model of the human left ventricle. Natividad et al. (Natividad and Yeow, 2016) used an elastomeric ''bladder'' surrounded by a heat-sealed fabric jacket and placed on the brachium as an assistive device for shoulder abduction for people with cerebral palsy. ...
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Compliant elastomer tubing with a fabric ‘jacket’ has been essential in various applications as soft robotic actuators, such as in biomedical exomuscles and massage therapy implements. Here, our study shows that a similar design concept can be an effective strategy in realizing passive regulation in the tube’s distension, as well as in preventing aneurysm-like asymmetric rupture of the tube. A custom hydraulic pressure testing rig was built to perform experiments. The jacketed tubes initially deform rapidly as pressure increases, but a self-regulation behavior suppresses the tube’s continued distension by strain-stiffening of the ‘jacket’. In addition, highly asymmetric distension, common to elastomeric tubes due to imperfection in fabrication, is prevented dramatically by the ‘jacket’. A three-dimensional finite element model predicts the distension of all tested tubes quantitatively across the entire experimental pressure ranges and beyond. Incorporating custom-designed kirigami relief patterns in the ‘jackets’ expands the potential of the elastomeric tubes.
... The three samples shown in Fig. 10 were chosen for the validation of our proposed method. [26,27,59,60] in the clinical environment. ...
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This paper proposes a novel method for estimating the reaction force, the Stereovision Based Force Estimation Method (SBFEM), with deep learning techniques to predict the interaction force of the surgical procedures. The interaction force is estimated through SBFEM combined with computer vision and neural networks instead of using direct force sensors due to the difficulty of adapting them to tools due to biocompatibility, sterilizability, and integration issues. The proposed model processes both spatial and temporal information acquired from the vision and tool data. The LSTM-RNN framework, along with dimensionality reduction, is trained with In-Vivo-experimental data of porcine skin, and the cyclical learning rate method is suggested for fine-tuning the network. The analyses are based on three distinct datasets, each with three cases to validate the result. The proposed method, RNN-LSTM + DR + CLR, outperforms the RNN and RNN-LSTM without dimensionality reduction by 8.46% and 3.98% in force prediction accuracy, respectively. Interestingly, this work reports an average RMSE of 0.01 N in the force component and 0.03Nm in the torque component in the applied force direction. The result shows that estimated force quality is better when reducing dimensionality on extracted features and processing both tool and vision data together. The network performed better when optimized with the loss function, root mean square error, and the cyclical learning rate method as an optimizer for fewer datasets with a minimum computational cost. Finally, the Mann–Whitney U test shows that the predicted force components are adaptable to any dataset.
... For example, the locomotion of soft robots can be influenced by embedding dissipative components in their bodies [71]. For instance, the control of motion can be reduced to the control of flow rate in pneumatic soft actuators [88,85]. For example, at larger scales, dissipative mechanisms in wearable devices and soft exo-suits [89] can promote the design of such soft systems by reducing the duty of active elements and annexing memory. ...
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