Fluidic Fabric Muscle Sheets for
Wearable and Soft Robotics
Mengjia Zhu,1Thanh Nho Do,2Elliot Hawkes,3Yon Visell1,3∗
1Media Arts and Technology Program, Department of Electrical and Computer Engineering,
California NanoSystems Institute, and Center for Polymers and Organic Solids,
University of California, Santa Barbara, USA
2Graduate School of Biomedical Engineering, Faculty of Engineering,
University of New South Wales, Sydney, Australia
3Department of Mechanical Engineering, University of California, Santa Barbara, USA
∗To whom correspondence should be addressed; E-mail: firstname.lastname@example.org.
Conformable robotic systems are attractive for applications in which they can be
used to actuate structures with large surface areas, to provide forces through wear-
able garments, or to realize autonomous robotic systems. We present a new family
of soft actuators that we refer to as Fluidic Fabric Muscle Sheets (FFMS). They are
composite fabric structures that integrate ﬂuidic transmissions based on arrays of
elastic tubes. These sheet-like actuators can strain, squeeze, bend, and conform to
hard or soft objects of arbitrary shapes or sizes, including the human body. We show
how to design and fabricate FFMS actuators via facile apparel engineering methods,
including computerized sewing techniques. Together, these determine the distribu-
tions of stresses and strains that can be generated by the FFMS. We present a simple
mathematical model that proves effective for predicting their performance. FFMS
can operate at frequencies of 5 Hertz or more, achieve engineering strains exceeding
100%, and exert forces greater than 115 times their own weight. They can be safely
used in intimate contact with the human body even when delivering stresses exceed-
ing 106Pascals. We demonstrate their versatility for actuating a variety of bodies or
structures, and in conﬁgurations that perform multi-axis actuation, including bend-
ing and shape change. As we also show, FFMS can be used to exert forces on body
tissues for wearable and biomedical applications. We demonstrate several potential
use cases, including a miniature steerable robot, a glove for grasp assistance, gar-
ments for applying compression to the extremities, and devices for actuating small
body regions or tissues via localized skin stretch.
Keywords: Artiﬁcial muscles, Sheet-like actuators, Fluidic actuation, Wearables, Fabric, Textiles
Emerging soft actuator technologies are enabling applications in robotics, healthcare, haptics, assis-
tive technologies, and many other areas. Such soft actuators can interface with, conform to, exert
arXiv:1903.08253v1 [cs.RO] 19 Mar 2019
forces upon, or generate shape changes in complex or compliant structures.1–3 Wearable soft robotic
devices interfaced with the human body may prove valuable for rehabilitation, movement assistance,
or virtual reality.4–6 Soft actuators are also of interest for controlling motion in distributed or de-
formable structures. They can be used for tasks such as grasping, terrestrial locomotion, surgery, or
underwater operation.7–9 Such applications span systems of greatly varying length scales, ranging
from millimeter-scale biomedical robots to large, deployable structures.10,11
Biological systems provide a rich source of information to guide the design of soft robots.12 The
motile capabilities of animals are enabled by composite systems of muscle, connective, and other
tissues. The forces and motions they can produce depend on the properties of individual muscle
ﬁbers, the arrangement of ﬁbers, and the muscle morphology and attachments. Muscle morphologies
vary widely. There are fusiform shapes like the human biceps brachii, that produce large-amplitude
motion. There are also fan shapes, such as the pectoralis major, that yield larger forces, sphincter
morphologies that contract, and layered muscle sheets, like the transverse abdominis (Fig. 1A), that
compress or transfer forces around the torso.13 The great variety of biological muscles, and their
integration with other tissues, can inspire the design of soft robotic actuators, but much of the huge
potential design space remains unexplored.
Here, we describe a new family of muscle-inspired actuators that we refer to as Fluidic Fabric
Muscle Sheets (FFMS). They are composite fabric sheets that employ an integrated ﬂuidic transmis-
sion comprised of arrays of hollow elastic tubes to generate in-plane stresses or strains. We show how
to design and fabricate these devices using apparel engineering methods. As we demonstrate, FFMS
are stretchable, conformable, safe, efﬁcient, and scalable. In order to situate this work relative to prior
research, we begin with a review of several related technologies.
Many soft actuator technologies have been developed for applications in robotics, wearable devices,
healthcare, and other areas. The FFMS sheet actuators we present here build on prior research on
soft ﬂuidic actuators, including the sheet-like actuators described below. It is useful to compare the
materials, operating principle, methods of design and fabrication, and performance characteristics of
such devices. We highlight several salient examples below.
1.1.1 Fluidic actuators
Fluidic actuation technologies have attracted considerable attention for use in soft robotic systems
because of their intrinsic compliance and the ease with which the ﬂuids that transmit stresses may
be integrated into soft media.14 Fluidic power may be delivered in the form of ﬂuid pressure and
volume changes via a variety of pumps or charged reservoirs, enabling such systems to be designed to
match a wide range of requirements. Such devices can produce larger forces, displacements, or work
densities than are feasible with many emerging functional materials technologies (discussed below),
facilitating practical applications.
Pneumatic Artiﬁcial Muscles, which generally shorten when ﬁlled with compressed air, come in
many shapes and sizes.15 Among the many soft ﬂuidic actuators described in the literature, an early,
inﬂuential example is the McKibben actuator.16–19 It is a soft, pneumatic device that comprises an
airtight bladder with ﬁber constraints that cause it to contract when the internal volume is increased
through the application of pressure. The dimensions and working pressures of such actuators may
be selected to match application performance requirements. However, maximum strains are typically
limited to less than 35%,20, 21 limiting applications. Many soft, ﬂuidic actuators have been designed
for pneumatic operation via compressible gases. This causes energy to be stored in gas compression
during operation, which can lead to undesirable, rapid energy release on failure. Gas compression
also leads to thermodynamic losses. A smaller group of soft, ﬂuidic actuators have employed in-
compressible ﬂuids. FFMS actuators can use either approach. We review some of the advantages of
hydraulic operation below.
Many other variations on the idea of combining ﬂuidic actuation with ﬁber constraints have been
investigated.22,23 Recently, it has been observed that similar methods can be used to realize much
larger strains – approaching 300% – by means of actuators that contract when the internal volume
and pressure are reduced, in a manner inverse to the McKibben design. Such devices, including the
Inverse Pneumatic Artiﬁcial Muscle (IPAM)24 and Hydro-Muscle Actuators,25 integrate anisotropic
components that cause them to lengthen when pressurized. We leverage just such an “inverse” ﬂuidic
actuation strategy in the FFMS actuators described here. In contrast to the typically uniaxial and
tubular forms of prior devices, which evoke fusiform muscle structures, FFMS actuators are actuated
fabric-based structures, similar to muscle sheets. Anisotropic constraints in FFMS actuators are pro-
vided by the fabric structure. Different fabric patterns and assemblies can be used to realize a variety
of actuation modes, including uniaxial actuation, bending, multi-axis actuation, shape-changing, and
Several methods for creating mechanical anisotropies with fabrics have been previously investi-
gated to improve the performance of ﬂuidic actuators, such as devices based on individual tubes,25
air bladders,26 or other structures. In most cases, this is achieved through the intrinsic anisotropy of
integral ﬁbers. Fiber-reinforcement of the elastomer can be designed to produce desired anisotropy,
and hence motion, by specifying the threading angle of the ﬁbers,22, 23 although this complicates fab-
Other soft, ﬂuidic actuator designs, including origami-inspired devices, grow longer when positive
pressure is applied.27 However, the maximum forces that can be reproduced are limited by buckling
instabilities.28 Vacuum-driven soft actuators have also been realized, attaining large peak stresses,29
but often involve large changes in cross-section area.
1.1.2 Other Transduction Principles for Soft Actuators
Many other methods of soft actuation have been investigated, each involving different tradeoffs in
performance. Shape memory alloys yield strains of up to about 5% when heated.30 They can also
yield larger strains in other conﬁgurations, such as coils.31 Other thermally actuated transducers have
been based on shape memory polymers, nylon, polyethylene, or other ﬁbers.32–34 Such actuators of-
ten yield low efﬁciencies or low actuation speeds due to the intrinsic physics of the thermal processes
underlying actuation. Other devices based on shape memory polymers35,36 or electroactive polymer
technologies, including ionic polymer-metal composites37–39 have been designed to yield high strains,
but typically only generate small forces. Soft, electrostatic actuators, including dielectric elastomer
actuators, are fast and can be designed to produce large strains40 but require high voltages and care-
fully controlled fabrication processes and mechanisms that preclude their use in some applications.
Variations on such actuators that use ﬂuidic electrodes overcome some of the fabrication and design
challenges involved in employing such actuators, but high voltages are nonetheless required.41 Elec-
tromagnetic soft actuators can operate at low voltages,42,43 but often require an external magnetic
A more conventional approach to producing high forces and strains in soft, actuated structures
is based on tendon- or Bowden-cable transmissions.46–48 Achieving high performance actuation and
control with such devices depends on cable routing and friction management. In addition, careful
design is needed to ensure that the stresses that are produced are appropriately distributed.
1.1.3 Sheet-Like Soft Actuators
Various sheet-like soft actuators have been developed using actuation methods paralleling those de-
scribed above. Several groups have produced such sheet-like actuators based on shape memory alloys
or thermally actuated nylons, but the tradeoffs between actuation time, forces, and strains limit the
feasible mechanical power, speed, and reduce efﬁciencies.49–51 In addition, the temperatures or heat
exchange requirements may limit wearable applications.
Multi-layered artiﬁcial muscles made of electrostatic sheet actuators have been designed to pro-
duce large forces at moderately high voltages, but require careful control over their motion during
actuation, precluding out-of-plane deformation.52 Dielectric elastomer actuation principles have also
been used to realize compact sheet-like soft actuators, although large voltages (greater than 5 kV) are
Sheet-like soft actuators have also been designed using ﬂuidic actuation principles. This is achieved
by assembling discrete pneumatic artiﬁcial muscles within a fabric or other sheet-like assembly, or
through the design of integral ﬂuid-driven cavities. One conﬁguration comprised assemblies of McK-
ibben muscles within fabric layers.2Another consisted of thin McKibben muscles that were woven
into fabric structures.54 When driven to produce contraction along the axis of each muscle, the actu-
ators in such devices expand, causing undesired increases in thickness, adversely affecting potential
conformable or wearable applications and reducing efﬁciency. Other designs have resulted in low
forces that preclude many applications.55 In contrast, the FFMS actuators presented here increase in
nominal length, or decrease in contraction force, when ﬂuid pressure is applied. This is achieved with
negligible tangential expansion over the normal operating range of the actuator.
Other authors have used parallel cables or strings routed within fabric structures in order to achieve
composite, sheet-like actuators.56 Such designs can produce thin, fabric-like actuators, but require
careful attention to cable actuation and friction management in order to ensure that dynamic, fast, and
reversible actuation is possible. Because FFMS actuators transmit stresses via integral ﬂuids, losses,
due to viscosity and channel length (see Modeling, below) remain within ranges that permit highly
This paper presents FFMS, a new soft actuation technology. FFMS are planar, multimodal soft actu-
ators that are analogous to muscle sheets. Their design also builds upon prior “inverse-type’ uniaxial
actuators with tubular shapes that can be compared to fusiform muscles. Here, we describe the design
and fabrication of FFMS and show that this planar paradigm opens many new actuation capabilities
Design, Fabrication, and Modeling: We show how to design composite fabric structures to realize
mechanical anisotropies that enable FFMS to generate patterns of local contractions in a conformable,
planar surface as ﬂuid is withdrawn. FFMS can be efﬁciently fabricated using apparel engineering
methods including pattern making, computerized sewing, and wrinkling, and through the integration
of a ﬂuidic transmission based on hollow elastic tubes. We describe several alternatives for their
design and assembly. We analyze the effects of fabric selection and wrinkling, tube routing, thread
selection, and stitching selection, all of which can be used to tailor functionality and performance.
We also present a simple mathematical model that proves effective for predicting their performance
and aiding design.
Actuation Capabilities: FFMS actuators may be scaled to different sizes, depending on design re-
quirements. We demonstrate actuators with dimensions ranging from 1 to 34 millimeters in thickness,
and 30 to 1000 millimeters in length, yielding forces that can exceed 150 Newtons, and that can pro-
duce forces more than 115 times greater than their weight. FFMS actuators can also produce uniaxial
engineering strains exceeding 100%. Laboratory prototypes perform consistently in durability testing
during 5000 cycles or more, with less than 5% variation in displacement.
Applications: We demonstrate their use in actuating various bodies and mechanisms, and in con-
ﬁgurations that perform multi-axis actuation, including in- or out-of-plane bending and shape change.
We also demonstrate applications of FFMS methods for realizing low-proﬁle, fabric-based actuators
for new devices that exert forces on body tissues for wearable and biomedical applications. These
include a glove for grasp assistance, devices for compressing small body regions or tissues, and de-
vices for providing haptic compression or skin stretch to a ﬁnger, arm, or leg. Compression garments
formed from these actuators can produce dynamic compressive pressures that easily exceed 4000 Pa,
which is sufﬁcient for haptic feedback. Such compressions also meet requirements needed for many
musculoskeletal, circulatory, wound, and lymphatic compression therapies, including peristaltic com-
2 Design Concept and Operating Principle
The FFMS actuators presented here generate stresses or strains in a composite fabric sheet when
charged with a pressurized ﬂuid. The ﬂuid may be compressible (pneumatic operation) or incom-
pressible (hydraulic operation); we compare the relative merits of each approach later in the paper.
The routing of stresses and strains is accomplished via an integral ﬂuidic transmission composed of
hollow elastic tubes. The fabric assembly imposes mechanical anisotropies that locally direct stresses
along axis of channels that are sewn into the fabrics. As ﬂuid is pumped into the elastic tubes, their
internal volume is forced to increase. Circumferential constraints imposed by the fabric cause the
increased ﬂuid volume to produce a nominal lengthening of the structure along the axis of each tube
(Fig. 2A). This causes elastic energy to be stored in the tube-fabric structure. As the ﬂuid pressure
or volume is reduced, the stored elastic energy is released. When the FFMS is working against a
load, this reduction in pressure yields a contraction force. Thus, while increased pressure produces a
lengthening of the FFMS, external forces are normally produced via contraction, similar to biological
muscles (Fig. 1A).57 As we demonstrate, in other conﬁgurations the same principle can be used to
realize FFMS actuators that operate in hydrostatic mode, similar to muscular hydrostats such as the
tongue of many animals or trunk of the elephant. The ranges of forces and displacements that can be
produced depend on the dimensions of the FFMS, operating range of applied ﬂuids, actuation mode,
and materials involved. We present a simple mathematical description of the effects of these factors
Depending on actuation requirements, the FFMS can be operated to produce forces or displace-
ments. In force mode (Fig. 2B), a muscle is pre-stretched against a load via constraints at both
ends. At high ﬂuid pressures, the forces produced are low, while low pressures generate high forces.
Stresses are produced along the longitudinal axis of the elastic tubes. This can yield axial forces at the
ends of a fusiform-shaped FFMS, or compression forces, when the FFMS is wrapped in a nose-to-tail
conﬁguration around an object, such as a human limb (Fig. 10F). FFMS may also be used to generate
large strains or displacements (Fig. 2C). Changes in displacement can be used to displace loads or
to alter the shape of a structure through differential stresses or strains. Due to the radial constraint
imposed by the composite fabric structure, a change in ﬂuid volume creates a change in length. The
relationship between the ﬂuid volume in the FFMS and the channel length is approximately linear (see
Section 6). Such a displacement can be used to perform mechanical work. As we show, in multi-layer
structures, it can also be used to effect changes in the intrinsic shape of an FFMS assembly. Together,
these unique capabilities make FFMS amenable to various applications.
The fabrication of FFMS actuators involves three main steps: Construction, patterning, and assembly
of a multi-layer textile structure, routing of elastic tubes in the patterned fabric structure, and sealing
and attachment of tube ﬁttings, as illustrated in Figure 3A-E. The ﬁgure highlights a process based
on a conﬁguration of non-stretchable fabrics with stitching parallel to the channels. Other stitching
patterns, which are amenable to designs based on stretchable fabrics, are discussed in Section 4 below.
In a ﬁrst step, the fabric layers are aligned and stacked. The layers are then stitched to form con-
duits in between the fabric layers that allow the insertion of elastic tubes. The stitching patterns can be
designed to realize conﬁgurations using a single tube with a single ﬂuid input port (Fig. 3a), or mul-
tiple tubes with separate ports that allow the independent control of multiple channels (Fig. 3b). The
routing of channels in the fabric determines the distribution of strain and stress within the composite
textile, which need not be uniform. To radially constrain the tubes effectively, the conduit determined
by the stitching is designed to have a width equal to half of the tube diameter.
Different sewing methods can be used: hand sewing (Fig. 3F), machine sewing (Fig. 3G), and
computerized embroidery (Fig. 3H). When the size of the pattern ﬁts within the maximum embroi-
dery hoop size that the sewing machine can accommodate, computerized embroidery is preferred. It
provides great accuracy, ﬂexibility, and efﬁciency. When embroidery is impossible, machine sewing
may be used. This involves manual movement of the fabric under the sewing foot. This is often the
best option when stitching long actuators or very large surface areas. Hand sewing is the least efﬁ-
cient method, but can accommodate complex paths or non-ﬂat fabric surfaces, as are involved when
stitching the turning stitches that we apply following tube insertion (Fig. 3D).
After the sewing step, the elastic tubes are threaded through the stitched fabric conduits. To
achieve this, we use a slender rod that is inserted securely into one end of the elastic tube. Once
the tubes are completely inserted, the fabric is then wrinkled along the length of the tubes in order to
accommodate stretching in that direction. We have found that this wrinkling can readily be performed
in a uniform, controlled fashion. Together, the proportion of wrinkling and elastic properties of the
fabric and tube determine the maximum stretchability of the muscle. This process is best suited to
non-stretchable fabrics. If stretchable fabrics are used, the wrinkling step may be omitted. In a next
step, one end of the elastic tube is sealed with a ﬁxture, such as a knot, while the other is connected
to a barbed tube ﬁtting that allows the ﬂuid to be supplied to the muscle. For large-scale FFMS (Fig.
8A,B), one end of the tube may be sealed with a solid barbed end plug, rather than a knot, while the
other end is connected to a barbed tube ﬁtting. To strengthen the connection between the ﬁtting and
the elastic tube, clamps may be applied. In a next step, air is purged from the channels. To stabilize
the mechanical response, the muscle should be fully extended and contracted several times prior to
the ﬁrst usage.
4 Material Selection
The performance of FFMS actuators depends greatly on the selection of elastic material, fabric ma-
terial, and stitching pattern. The working ranges of displacements and forces are determined by the
applied ﬂuid pressure range, the fabric and elastic tube material properties and sizes, and the manner
of patterning and assembly.
4.1 Fabric and Stitch Selection
Forces and motions produced by the FFMS are determined by the relative magnitude of stored energy
generated by the elastic tubes and the ﬂuid pressure. To achieve the desired dynamic range of forces
and motions, the axial stretchability of the fabric conduit should be maximized, while the radial
expansion of the elastic tube in the operating range of ﬂuid pressures should be minimized. A ﬁrm
circumferential constraint is needed to ensure that stresses due to the ﬂuid are directed along the axis
of the tube and do not result in the tube expansion. Based on these criteria, an ideal fabric structure
should possess negligible stiffness in the axial direction of tube so that a high elongation from the
muscle can be achieved (we provide a quantitative discussion in the modeling section, below). This
requirement can be achieved through the use of non-stretchable fabrics, such as cotton weaves, in
tandem with the wrinkling process that is applied during assembly. In some applications, stretchable
fabric may be of interest. In such cases, cross stitching may be used to impose a radial constraint.
Such stretchable fabrics are uniaxially elastic (two-way stretch) or biaxially elastic (four-way stretch).
These fabrics are often made of elastic ﬁbers such as Spandex, that are spun into stretchable yarn, and
integrated along weft, warp, or both directions of the weave, yielding one- or two-way stretch fabric,
respectively. Alternatively, either elastic or non-elastic ﬁbers may be used to create a knit. In a
knit, stretchability depends on the design of the looping structure. This typically results in biaxial
stretchability. The axial stretchability of FFMS fabric structures using stretchable fabrics can also be
improved through the application of wrinkling, although we have not encountered practical situations
for which this is needed.
The routing of stresses or strains within the FFMS is achieved via fabric conduits formed from
stitching applied to the fabric sheets. The stitching involves three main factors: thread material,
stitch type, and stitch pattern. Near the elastic tubes, the stitching permits the fabric to impose a
circumferential constraint. This ensures that ﬂuidic stress or strain is directed along the axis of the
tube (see Section 2). Two design criteria are involved. First, the stitching must be strong enough to
constrain the fabric conduit around the elastic tubes over the entire operating regime of the FFMS.
Second, it must accommodate large strains along the axial direction of the tube, even in the absence
of wrinkled structure. Several different stitch designs, together with different choices of fabric, can
meet these requirements. The selection of each depends on application requirements. To illustrate
this, we compare three different combinations of fabric type and stitch design in Table 1. This table
shows that combinations yield distinct patterns of stretchability in the assembled FFMS (Table 1, blue
If a wrinkling step is omitted, a two-way or four-way stretchable fabric must be used in order
to accommodate the axial strains that are required for a FFMS actuator to function. A side or cross
stitch pattern may be used with either stretchable or non-stretchable fabrics, with or without wrinkling
constraints (Table 1, red arrows). Cross stitching is preferred for use with four-way stretch fabrics,
because it minimizes undesired radial expansion (i.e. ballooning) of the elastic tubes. Signiﬁcant
ballooning only occurs if side stitch patterns are used. Commercial two-way stretch fabrics (which
are typically knits) admit fabric extension in all directions. Thus, such fabrics yield undesirable
Table 1: Stitch and fabric selection for FFMS actuators. Red arrows represent the stretch directions
of the fabrics, and blue arrows represent the stretchability of the assembled FFMS. Longer arrows
denote greater stretchability. The conﬁguration in the red box is used for most prototypes in this
ballooning unless a cross stitch is used, which can result in failure (see Fig. 7C). When non-stretchable
fabric is used, wrinkling must be applied. In such cases, the range of extension is determined by the
extent of wrinkling. In practice, we have designed FFMS actuators capable of greater than 300%
strain using this technique. If a cross stitch is used, the amount of wrinkling is limited due to the
increased fabric constraint imposed by the cross stitch, thus limiting the extensibility of the FFMS.
Among thread types, inextensible high-strength nylon thread is one choice that is able to pro-
vide a sufﬁciently stiff constraint via a ﬁne thread. There are several possible combinations of stitch
designs, fabric stretchability, and wrinkling modes, which together yield distinct patterns of stretcha-
bility in the assembled FFMS (Table 1, blue arrows; longer arrows imply larger stretchability). When
side stitches are used, zig-zag stitching is recommended for use with stretchable fabrics in order
to preserve the fabric elasticity. Straight stitching is appropriate for non-stretchable fabrics, where
stretching is accommodated by wrinkling. To maximize stretchability in the axial direction, and min-
imize radial expansion, two-way stretch fabric with side stitches and wrinkling is optimal, although
non-stretch fabric with side stitches and wrinkling is also effective. Figure 4A shows four prototypes
with different combinations of fabrics and stitchings.
4.2 Tube and Fluid Selection
Another important material to specify is that of the elastic tube. This may be any elastomer that
is compatible with the working ﬂuid. For high force applications, tubing materials with high elas-
tic modulus and high extensibility would be preferred. The tube can have any diameter and length
compatible with the fabrication process, including very ﬁne silicone tubing,58 or larger diameter latex
rubber tubing. As noted below, FFMS using larger tubes generate higher force per unit length on the
threads, which can lead to failure for very large tubes. There are many options among commercially
available tubes (Fig. 4B). We present a model of the actuator performance accounting for effects of
tube size and material properties in Section 5 and present experimental results for several examples
in Section 6.
A variety of working ﬂuids may be used, depending on the performance requirements, materials,
and operating criteria. In hydraulic operation, FFMS can use incompressible ﬂuids such as oils or
waters, as illustrated in many of our experiments. This makes it possible to control the applied volume
in the actuator and hence the actuator length, due to the circumferential constraints. This renders the
quasi-static response of the actuator very simple, at the expense of increased viscosity and mass
(however, the ﬂuid mass in many of our prototypes is on the order of a few grams). Low viscosity
ﬂuids may be used to improve the actuation speed and efﬁciency. Pressures used with our prototypes
are generally much lower (less than 0.75 MPa) than those used in industrial hydraulics (20 MPa would
be typical). At such low working pressures, failures typically involve, at most, ﬂuid leakage.
In pneumatic operation, compressible ﬂuids such as air or other gases may be used. This can
minimize mass and viscosity. Over the operating range tested in our experiments, pneumatic opera-
tion leads to increased hysteresis, lower efﬁciency, and increased response latency (Fig. 6F). Further
discussion of hydraulic and pneumatic actuation methods are provided in the literature.59, 60
5 Analytical Modeling
As our experiments demonstrate, FFMS actuators may be operated to yield a variety of motion or
force patterns. The simplest involves the generation of axial forces through a parallel conﬁguration
of Nelastic tubes. Such a structure is similar to parallel muscle sheet architectures in biology. A net
external force, Fext, is produced by the actuator due to the stretching of the tubes, which produce a
net elastic force, Fel. The fabric can also contribute an elastic force, Ff ab. The force Fext exerted by
the actuator decreases with increasing ﬂuid pressure, p, due to the axial force, Ff luid, generated via
the ﬂuid pressure. Dissipative forces, Fd, include viscosity and friction. Combining these factors, one
can model the forces produced by the actuator as
Fext =Fel +Ffab −Ffluid +Fd(1)
The dissipative forces, Fd, include hydrodynamic ﬂow resistance, Fd,hyd, and dry friction at the tube
fabric interface, Fd,dry
Fd=Fd,hyd +Fd,dry (2)
Fd,hyd can be estimated from the Newton’s Law of viscosity,61
where τis the shear stress of the ﬂuid acting on the inner wall of the tube, Ais the contact area
between the ﬂuid and the tube, µis the kinematic viscosity, ρis the ﬂuid density, uis the ﬂow
velocity, ∂u/∂y is the rate of shear deformation, riis the tube inner radius, and Lis the tube length.
The dry friction Fd,dry is given by
Fd,dry =FNζ=N ζp Atf , Atf = 2πroL=Nζ p Atf ,(4)
where Nis the number of tubes, ζis the friction coefﬁcient, FNis the normal force between the tube
and fabric, Atf = 2πroLis the area of the tube-fabric interface, rois the tube outer radius, and pis
the ﬂuid pressure. We refer to such dissipative forces when interpreting measurements of actuator
efﬁciency and hysteresis.
In many embodiments, including the wrinkling construction described above, there is a small
relative motion of the tube and fabric, so Fd,dry may be neglected. In quasi-hydrostatic operation,
the forces due to ﬂow resistance Fd,hyd may also be neglected. For fabric that is wrinkled or easily
stretched in the axial direction, the fabric force, Ff ab may also be neglected.1Assuming that these
conditions hold, and assuming that the FFMS operates in a linear elastic regime with elastic modulus
Eand true strain , the net external force exerted by the actuator is:
Fext =Fel −Ffluid ,(5)
Fel =NEAtube =N E π(r2
Ffluid =NpAfluid =N pπr2
The result may be written
Fext =N(EAtube −pAf luid)(8)
The external force Fext,reaches its maximum value if the ﬂuid pressure p= 0,
pFext =Fext|p=0 =N EAtube (9)
The force can be maximized by increasing the value of the net cross section area, NAtube, the elastic
modulus, E, or the operating range of strains, . Increasing the strain may be accomplished via pre-
tensioning, which is also aided by wrinkling. The model given by Eq. 8 shows that Fext decreases
linearly with the increase in pressure, p. As our experiments demonstrate, despite the simpliﬁcations
involved in this model, it provides a good ﬁt to the behavior of FFMS actuators (Sec.6, Fig.5D4 and
The minimum external force magnitude occurs when the pressure is maximum, pmax. Since
pressure ﬂuctuates in dynamic operation, we take this to be the maximum quasi-hydrostatic pressure.
If the operating range of forces extends down to Fext = 0, the required maximum pressure, pmax is
determined by the ratio of tube and ﬂuid areas and tube elasticity,
where Atube is the inner cross section area of the tube. Conversely, if pmax is the maximum intended
pressure, the tube geometry, strain, and elasticity should be selected to ensure this expression holds.
In another conﬁguration, the actuator may be operated as a muscular hydrostat.62 For unsupported
(isochoric) operation, or for negative contraction forces, Fext <0, the muscle force may be produced
by applying a pressures higher than the one speciﬁed in (10). In the absence of an external load force,
Fext = 0, a pressure papplied to hydrostatic conﬁguration can yield a displacement, δL, with respect
to the initial tube length, L0,
δL =L0exp p
1Selecting a stiffer fabric, or adding non-ﬂuidic elastic ﬁbers to the structure, increases forces, but does not necessarily
improve actuator performance, because the added elasticity does not impart any added strength to the tube that would
enable it to operate at higher pressures.
Such modes of operation are analogous to muscular hydrostats in biology, such as the tongue of many
animals, or the elephant trunk.
FFMS actuators may also be used to compress enclosed objects. If an actuator with pressure
p > 0perfectly encloses a rigid cylindrical object, compressive pressures are generated as the ﬂuid
pressure pis reduced. For a cylinder of radius rch, where his the effective FFMS thickness, the
compressive pressure, pc, or force per unit area exerted on the cylinder, is
where AMis the net effective cross section area of the FFMS.
To evaluate the proposed FFMS actuators, we performed mechanical testing in several experimental
conﬁgurations and operating modes, using several FFMS actautors of different sizes. We also realized
functional prototypes for wearable devices, haptic feedback, and soft robotics.
6.1 Mechanical Testing
We used three testing conﬁgurations to measure axial forces, compressive forces, and axial displace-
ments. We complemented these evaluations with measurements of actuation efﬁciency and durability
over thousands of cycles.
Detailed mechanical testing was performed using two different prototypes (Fig. 5). The ﬁrst
comprised a smaller surface area FFMS with three elastic tubes (Fig. 5B) of dimensions 196 mm
(length), 25.2 mm (width), and 4.7 mm (thickness). The fabric channel width was 5 mm. The active
area spanned by the elastic tubes was measured to be 122.4 mm in length with no applied pressure.
The tubes were connected via a manifold to the ﬂuidic power source. We used latex tubes with outer
diameter 3.2 mm and inner diameter 1.6 mm.
The second prototype consisted of a larger surface area FFMS with ten parallel elastic tubes (Fig.
5C). The tubes in this prototype were connected in series, yielding a single ﬂuid port. The dimensions
of this prototype are 148.4 mm (length), 156.6 mm (width), and 4.9 mm (thickness) while the channel
width is 5 mm. The active region spanned by the elastic tubes (neglecting unwrinkled fabric end
sections) was 84.1 mm.
In all experiments, distilled water was used as a working ﬂuid. In a separate experiment, we
compared the operating efﬁciency of water (hydraulic mode) and air (pneumatic mode).
6.1.1 Axial Force Testing
Axial force testing was performed using an isometric test conﬁguration and apparatus (Fig. 5A). One
end of the FFMS was ﬁxed using a clamp ﬁxture while the other end was attached to a stationary
force gauge (M5-20, Mark 10). Fluid was supplied via three 10 mL syringes (inner diameter around
15 mm) driven by a displacement-controlled linear motor (A-BAR300BLC-E01, Zaber) and custom
ﬁxture. The syringe displacement was also measured via an optical encoder (S6S-1000-IB, US Dig-
ital). Fluid pressure was measured using a ﬂuid sensor (SSC Series Sensor, Honeywell) positioned
near the actuator port. The actuator was pre-pressurized to approximately 650 kPa and ﬁxed in an
isometric conﬁguration with sufﬁcient tension to ensure that the actuator remained during testing.
The FFMS was driven via sinusoidal ﬂuid displacement, at frequencies from 0.2 to 0.4 Hz. This
yielded time-varying (measured) pressures ranging from 200 kPa to 750 kPa. The signals were de-
coded synchronously using a computer-in-the-loop system (QPIDe, Quanser, Inc., with Simulink, The
Mathworks, Inc.). The instantaneous displacement of ﬂuid volume was calculated from the syringe
displacement and geometry.
The FFMS performance was consistent over repeated cycles. The generated axial force decreased
monotonically with the increase of ﬂuid pressure or volume (Fig. 5D-G). The results for a single cycle
(Fig. 5D2-D4) indicate that the range of forces Fext generated by the FFMS was 13 N (approximately
4.3 N per tube). This corresponded to a ﬂuid volume range of 1.78 mL. The volume-force and the
volume-pressure curves both exhibit hysteresis, indicating that energy was lost on each working cycle.
We will discuss such losses in the efﬁciency measurements below.
We compared the results with predictions of the analytical model (Eq. 8). To compute these
predictions, we used the geometric dimensions and measured the Young’s modulus of the elastic
tube. Using tensile testing, we determined the Young’s modulus to be 1.1MPa for true strains, ,
between 0 and 1. Other parameters used for model prediction were Atube = 5.9×10−6m2,= 0.8,
and Afluid = 7.7×10−6m2. The number of tubes was N= 3 for the ﬁrst and N= 10 for the second.
The experimental results and model predictions were in close agreement during slow actuation (Fig.
For different frequencies, ranging from 0.2 Hz to 5.0 Hz, the FFMS actuator responded in a
qualitatively similar manner (Fig. 5E,F). The response became somewhat more complex at the highest
frequencies. This can be explained by the inherent dynamics of ﬂuid-elastomer-fabric systems.
We obtained results when testing the larger FFMS actuator with 10 parallel tubes (Fig. 5G1-
G4). In this case, the FFMS produced forces ranging from 0 to 50 N with respect to the decrease of
ﬂuid volume (from 0 ml to 6 ml) or ﬂuid pressure (from 620 to 180 kPa). The FFMS performance
was also consistent over repeated testing cycles. Each of the ten tubes produced about 5 N. For the
smaller prototype, analytical modeling yielded qualitatively good agreement with the experimental
results (see Fig. 5G4). The results revealed nonlinear hysteresis between the pressure and force. This
can be attributed to the fact that the tubes were connected in series, requiring the ﬂuid to traverse a
much longer path. This indicates that series connections of elastic tubes, which simplify assembly,
may introduce modest response latency. From the experimental data, we estimated the latency to be
approximately 100 ms at 0.2 Hz. The volume-pressure and volume-force relationships also exhibited
nonlinear hysteresis, indicating that energy was lost on each cycle. For small changes in ﬂuid volume,
from 0 to 2 ml, the change in force with ﬂuid pressure was more gradual. However, the pressure-force
relationship remained approximately linear over most of the testing range.
6.1.2 Compression Testing
We evaluated the compression force Fc=pcAproduced using an FFMS prototype with 3 channels
(Fig. 5H), where pcwas the compressive pressure. The actuator was wrapped around a cylinder in
an isometric test ﬁxture using a force sensor (ATI Nano17, ATI Industrial Automation). The contact
area, A, was 209 mm2. We varied the applied ﬂuid volume from 0 to 2 mL (Fig. 5I). This yielded
compressive forces ranging from 0 to 10 N. These values were consistent with our predictions based
on the range of axial forces, Fext,produced by the same device: at ﬂuid pressure p= 250 kPa, we
measured the the axial force to be Fext = 13 N. The model predicts a compressive pressure pc= 44.5
kPa for our text ﬁxture conﬁguration, which implies Fc=pcA= 9.3N, in close agreement (error
<5%) with our measurements (Fig. 5K). The results varied little for speeds below 5.0 Hz.
We evaluated the FFMS performance in displacement testing using a test conﬁguration that was sim-
ilar to the one we used in axial force testing (Fig. 6A). For testing, a constant force retractor (Force
4.45N, model 61115A2, McMaster-Carr) was used to replace one of the isometric constraints in the
ﬁxture described above. An optical encoder was used to record the position for the distal end of
FFMS. Displacement increased with increases of ﬂuid volume or ﬂuid pressure. The results revealed
consistent displacement across repeated actuation (Fig. 6B1). As predicted, the relation between vol-
ume and displacement was almost perfectly linear, reﬂecting the incompressibility of the medium and
radial constraint provided by the textile (Fig. 6B2). When the ﬂuid volume reached 4.5 mL, the FFMS
attained a length increase of 70% (from 122.4 to 207.4 mm). In this case, the volume-pressure and
pressure-displacement relationships exhibited greater hysteresis. We attributed this to the deforma-
tion of the nonlinear elastic materials at large displacements or high ﬂuid volumes (Fig. 6B3-B4). The
analytical model correctly predicted the observed ranges of displacement, but because the model was
quasi-static, it did not capture the hysteresis. We plan to develop a dynamic model that can capture
such effects in future work. We also observed that the performance of FFMS remained consistent at
higher driving frequencies. The results for the larger FFMS with 10-channels were similar to those
that we observed for the smaller FFMS (see Fig. 6E1-E4).
We computed the energetic efﬁciency as the ratio of the input energy and the mechanical work over
one working cycle. We measured this for a single channel FFMS with different working ﬂuids,
comprising water (hydraulic mode) and air (pneumatic mode). The tested FFMS had a rest length of
16 mm, width of 3.7 mm, latex tube outer diameter of 6.4 mm, and tube inner diameter of 3.2 mm.
The FFMS lifted a load of mass magainst gravity at speed of v= 0.1mm/s to height h. Input work,
Win, was computed as the sum of (positive) mechanical work, W+,performed when extending the
actuator, and (negative) work, W−,performed when withdrawing the ﬂuid (during lifting), yielding
Win =W++W−. The energy efﬁciency, R, was R=Ug/Win,where Ug=mgh was the output
work, or change in potential energy of the mass over one working cycle. The results were averaged
over ﬁve working cycles in which the actuator returned to its initial state after displacing the mass.
The actuator efﬁciency was higher in hydraulic operation than in pneumatic operation (efﬁciency
R= 0.46 vs. 0.25, see Figure 6F). This can be explained by the additional thermodynamic losses
arising from the compression of air. Other losses included those due to ﬂuid viscosity, friction, and
thermoelastic heating of the elastomer. Prior authors25 computed the efﬁciency of a soft ﬂuidic actu-
ator by considering the work W−perormed when withdrawing the ﬂuid as an output of the system,
yielding R= (Ug+W−)/W+. However, such a calculation leads to erroneous results, since a system
can be designed to make the efﬁciency arbitrarily close to 1 by adding and removing an increment
of ﬂuidic energy at the input without any additional production of useful work (for example, this can
be achieved by adding a reservoir at the input). Applying this method to our actuator, we obtained a
(erroneous) higher efﬁciency of R= 0.83 in hydraulic operation.
We evaluated the durability of FFMS (three-channel prototype (Fig. 6G)) by actuating it over 5000
cycles to a maximum amplitude of 28 mm. The behavior was similar throughout testing. A 5%
reduction in displacement was observed after this testing cycle. We attributed this to initial relaxation
of elastic tube and fabric material. The relatively consistent performance may be attributed, in part,
to the operation of the tube within the elastic regime, which resulted in little plastic yielding.
6.1.6 Failure Modes
Actuator failure can arise due to improper selection of material, assembly, or to the operation regime.
Here, we highlight three typical failure modes observed in our prototypes during the experiments
(Fig. 7). As the ﬂuid pressure increases, the elastic tubes, enclosed fabrics, and stitches are subjected
to the increase of stresses. This can result in fabric tearing, stitch failure, or ballooning of the elastic
tube. Fabric tearing can be minimized through the use of high-strength or dense fabrics, ideally with
thread counts exceeding 300. One failure mode was associated with large cross section elastic tube.
For ﬁxed ﬂuid pressure, p, the force per unit length, ts,exerted by the stitch is proportional to pro,
where rois the tube outer radius. As the tube radius is increased, stitch failure will occur when ts
exceeds a critical value. Such stitch failures may be minimized through the use of high strength
threads, composed of materials such as polyester or Poly-paraphenylene terephthalamide (Kevlar),
through multiple (double or triple) stitching, and through the use of stronger fabrics. Another failure
mode arose from insufﬁcient radial constraints on the elastic tube, which yielded radial expansion
or ballooning of the tube. We observed this to occur due to imperfections in side stitching, due
to gaps between cross stitches, or due to the use of four-way stretchable fabrics. To mitigate such
failures, consistent stitching should be used, four-way stretch fabric should be avoided, and, where
two-way stretch fabrics are used, zig-zag conﬁgurations with smaller stitch distances (relative to the
tube diameter) should be used.
7 FFMS Embodiments and Applications
FFMS actuators are versatile, and capable of actuating a variety of bodies or structures of different
scales. They can be designed to realize multiple modes of actuation that are suited to applications in
robotics, healthcare, and wearable technologies, as we illustrate below.
FFMS actuators can be used to realize devices of different sizes, ranging from millimeter to meter
scale devices. The dimensional parameters of the FFMS include the lengths, L, of the elastic tubes,
their inner and outer radii, riand ro, and number, N, of elastic tubes. These parameters determine
the stitched conduit width, fabric length, and fabric width. For ﬁxed material, tube conﬁguration, and
strain, the maximum force is determined by r2
i. The maximum elongation, ∆L, is proportioned
to L. The required maximum pressure is scale-invariant (Eq. 10). Commercially available elastic
tubes can be used with widely varying radii, ri, ro, ranging from less than 1 mm to greater than 30
mm. We fabricated several prototypes to explore the scaling of FFMS actuators (Fig. 8) for different
applications (see Fig. 10). Small, low-proﬁle FFMS may be used in miniature biomedical or wearable
devices, while large FFMS can be employed in higher force applications, such as orthotics or soft
robotic construction machines.
7.2 Multimodal Actuation and Shape Change
Composite or multi-actuated FFMS can yield dynamic, multimodal motion or shape change. Here,
we show how FFMS actuators can be used to realize in-plane rotation, out-of-plane bending, and
biaxial bending motion (Fig. 9).
In-plane rotation may be realized by differentially driving multiple ﬂuid channels to steer an ac-
tuator in different extension modes. Such motions may be used in soft biomedical devices.63 In one
embodiment, a 3 cm FFMS is driven via 3 elastic tubes that are independently controlled. When one
of three lateral tubes is depressurized, a large-amplitude planar rotation can be achieved, yielding
turning angles approaching 90 degrees (Fig. 9A) due to differential elongation in the three tubes.
out-of-plane bending motion can be achieved via the FFMS actuators. When a passive layer
of ﬁberglass (with speciﬁed bending stiffness) is combined with the FFMS, continuous out-of-plane
bending can be generated. In one embodiment, a ﬁberglass sheet (thickness 0.38 mm) is pre-patterned
via laser engraving and stitched to the FFMS (Fig. 9B). Pressurizing the FFMS yields large-amplitude
bending, exceeding 180 degrees. Selecting the bending stiffness of the passive layer makes it possible
to tune the actuator stiffness and generated torques. Such a conﬁguration may be used in wearable or
soft robotics applications.64
If two FFMS layers are oriented in complementary directions, biaxial bending, or 3D shape
change, may be generated. To demonstrate this capability, we stitched two 7-channel FFMS lay-
ers together in orthogonal orientations (Fig. 9C). The whole composite structure remained ﬂat when
the applied ﬂuid pressure was equal in both FFMS layers. When the applied ﬂuid pressures was un-
equal in each layer, bending motion was initiated about each of two orthogonal in-plane axes. Biaxial
bending yielded 3D or hyperboloid shapes. Such a biaxial FFMS evokes the transversus and rectus
abdominis muscles in the human abdomen,13 which enable the bending of the thorax or compression
of the abdominal interior.
7.3 Device Conﬁgurations and Applications
FFMS sheets may be used to realize motion or provide forces in a variety of applications, including
soft robotic motion control, wearable actuators, assistive devices, and compression garments. We re-
alized several examples (Fig. 10 and Supplementary Video). Miniature FFMS can be used to produce
linear motion, to provide skin stretch haptic feedback, or to provide compression forces to small body
parts, such as a ﬁnger (Fig. 10D,E). We also fabricated a 3-channel FFMS that can contract from
10.5 mm in to 5 mm in length, lifting a mass of 500 g, while producing engineering strains up to
110% (Fig. 10A). Other compact devices can be used to apply constriction to small body parts (Fig.
10D, showing an FFMS of 1 mm thickness). They can also be used to realize wearable devices for
providing haptic feedback via skin-stretch, yielding highly palpable tactile sensations (Fig. 10E).
Larger scale FFMS actuators can perform greater mechanical work. For example, we fabricated
a 10-channel device that can lift a 3 kg mass (Fig. 5C). This was 115 times higher than the actuator
mass of 26 g (Fig. 10B, left). We realized a larger FFMS actuator with 3 tubes (inner latex tube of
diameter 25 mm, outer diameter of 32 mm), which lifted a 15 kg mass at ﬂuid pressures less than
276 kPa (Fig. 10B, right). This demonstrates how FFMS actuators can be used to perform signiﬁcant
FFMS actuators hold promise for wearable applications such as assistive devices. Here, we em-
ployed a conﬁguration similar to the one we used for out-of-plane bending (Fig. 9C) in order to
provide assistive ﬂexion forces for two ﬁngers during grasping (Fig. 10C). In this application, we
pre-tensioned the ﬁberglass sheet layers such that the device performed ﬂexion when pressurized and
extension when depressurized (Fig. 10C, bottom inset). The force was sufﬁcient to open and close
the hand for grasping. Such a device is useful for assisting conditions such as stroke that can often
lead to chronic ﬂexion of the ﬁngers, preventing grasping and adversely affecting many activities of
FFMS devices can also be used to provide compression to larger areas of the extremities. Such
compressive forces are of interest for haptic feedback,65 for preventative compression therapy in deep
vein thrombosis,66 for musculoskeletal recovery via blood ﬂow restriction therapy,67, 68 for lymphatic
or cardiovascular circulatory conditions,69,70 or other biomedical devices.71–74 We created an upper
limb compression device based on an FFMS arm band and measured the resulting compressive pres-
sures using thin-ﬁlm force sensors (FlexiForce A201, Tekscan Inc.). Withdrawing up to 3 mL of ﬂuid
from the band yielded uniform compression of up to 12 kPa, similar to pressures provided by blood
pressure cuffs. We also demonstrate a wearable compression garment for the lower limb (Fig. 10G).
This device is constructed from 3 elastic tubes arranged in three independently controlled sections
(Fig. 10G, dashed boxes). Supplying different ﬂuid pressures to different sections yields varied com-
pressive pressures across the limb. This can be used to provide bulk compression to the limb, which
is useful in recovery from some injuries or in disease treatment. It can also be used for providing
dynamic peristaltic motions that can be used for undulatory massage to augment lymph and blood
ﬂow. Such devices can meet the needs for pressure garment therapy,72 lymphedema treatments,73 or
venous closure treatments.74
This paper presents a new family of soft actuators that we refer to as Fluidic Fabric Muscle Sheets,
inspired by sheet-like biological muscles. These devices comprise fabric layers with integrated hy-
draulic transmissions formed from arrays of hollow elastic tubes routed in patterned fabric conduits.
We demonstrate how to design and fabricate these devices using facile methods that build on apparel
engineering techniques including computerized sewing processes. As we demonstrated, these devices
are stretchable, conformable, safe, efﬁcient, and scalable. They are applicable to small, millimeter-
scale actuators, and large meter-scale devices, and can yield forces exceeding 150 N, more than 115
times their weight, with engineering strains greater than 100%. Laboratory prototypes perform consis-
tently in testing over thousands of cycles. Their performance can be predicted via simple mechanical
modeling, aiding design. As we show, such FFMS actuators hold promise for applications in soft
robotic motion control and for wearable devices for haptics, healthcare, and assistive technologies.
The compressions they can produce meet requirements for several healthcare applications.
These results also point to several areas that are promising for future investigation. The fabrication
methods we describe are simple and ﬂexible, but further research is needed in order to align them with
potential manufacturing techniques. FFMS actuators prove capable of performance in axial actuation,
compression, and multimodal actuation, where dynamic shapes or stresses are enabled by designed
routings of ﬂuidic channels. New analytical and computational design methods would facilitate a
larger variety of programmable distributions of forces and strains, and would enable greater control
over such behaviors. The performance of FFMS actuators depends on the ﬂuidic power source that
is used. We highlighted advantages of hydraulic operation. Further research is needed on compact
hydraulic power sources. The analytical model we present was effective for predicting actuator per-
formance, but the model is quasi-static. In future work, we plan to extend this approach to account for
dynamics, aiding precise real-time control. Our devices employ open-loop control strategies, and the
performance of these devices would be further improved through the use of closed-loop controllers
relying on ﬂuidic or strain sensors. Intrinsic mechanical or physiological sensors would enable further
applications. The demonstration cases we present highlight potential applications in wearable devices
for human-computer interaction and virtual reality. We anticipate investigating these in future work.
Our demonstrations also point to a range of potential biomedical applications for assistive and ther-
apeutic devices. These merit further research. We have highlighted applications of FFMS actuators
in several forms of wearable devices. Our design and fabrication methods are amenable to realizing
integrated garments that may be applied to larger body areas, including the realization of whole-body
actuated suits or soft exoskeletons, which could greatly aid applications in haptic virtual reality, hu-
man space exploration, and rehabilitation. We intend to explore such garments and applications in
Ffluid Axial force produced via ﬂuid pressure
Fext Axial external load force
Fel Axial elastic force of tubing
Ffab Axial force due to fabric
FdDissipative forces including viscosity and friction
Fd,hyd Hydrodynamic ﬂow resistance force
Fd,dry Dry friction force at tube-fabric interface
τShear stress of ﬂuid at inner wall of tube
AContact area between ﬂuid and tube
µKinematic viscosity of ﬂuid
∂y Rate of shear deformation of ﬂuid
riTube inner radius
FNNormal force between tube and fabric
roTube outer radius
NNumber of elastic tubes
ETube elastic modulus
Tube true strain
Atf Area of the tube-fabric interface
Atube Cross section area of a single tube
Afluid Cross section area of ﬂuid inside a single tube
δL Tube displacement
L0Initial tube length
hEffective FFMS thickness
rcRadius of a cylindrical object
AMEffective axial cross section area of FFMS
This work was supported by the US National Science Foundation under awards NSF-1628831, NSF-
1623459, NSF-1751348 to Y.V.
Author Disclosure Statements
No competing ﬁnancial interests exist.
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Figure 1: A. Examples of muscle sheets in the human body that inspired the design of FFMS57
(reproduction rights pending). B. A functional prototype illustrating how FFMS are planar fabric
structures analogous to muscle sheets. C. FFMS comprise arrays of elastic tubes that function as
ﬂuidic transmissions. In this example, corresponding to the prototype of Fig. 1B, uniaxial extension
is produced when ﬂuid pressure is increased. D-G. FFMS may be applied in a variety of ways (see
Fig. 10): (D) deforming a soft object, (E) compressing a limb, (F) bending a ﬂexible structure, (G) in
bilayer structures that generate morphological change, among many other possibilities.
Figure 2: Fluidic Fabric Muscle Sheets: Concept and operating principle. A. Hollow elastic tubes are
integrated in a composite fabric structure. The tubes are routed in fabric conduits that provide circum-
ferential constraints, due to stitching. Left: When pressurized ﬂuid is pumped into the elastic tubes;
the tubes cannot swell radially due to the constraining stitches, and thus can produce a lengthening,
similar to a relaxing sheet of muscle. Right: When the ﬂuid pressure is removed, stored elastic energy
in the hollow tubes and elastic fabric is released, and the entire textile shortens, like a contracting
sheet of muscle. Pand Lrepresent ﬂuid pressure and actuator length, respectively. B. Left: When
the FFMS is operated to work against a load, as in the isometric conﬁguration shown here, forces are
produced. Middle: High pressures produce low forces, and vice versa. Right: A simple illustration
of the generation of axial forces. We present a mathematical model in a subsequent section. C. Left:
Cross section view of a single channel in the displacement operating mode. Middle: In displacement
mode, higher pressures produce larger displacements, and vice versa. Right: In such a displacement
mode, the FFMS may be used to do external work, such as lifting a mass, as shown here.
Figure 3: Fabricating planar ﬂuidic fabric muscles involves several steps based, in part, on apparel
engineering methods. For conﬁgurations based on non-stretchable fabrics, the fabric layers are ﬁrst
aligned and stacked. (A) The routing of elastic tubes is designed and layers are stitched to form
conduits (B) in a pattern that determines the routing. The stitched patterns can realize single (b) or
multiple (a) tube routings. The elastic tubes are then threaded (C) through the resulting fabric con-
duits. (D) For non-stretchable fabric layers, the fabric structure is wrinkled. (E) A port is established
at one end of each channel, whose remote end is then sealed. The stitching may be done via (F) hand
sewing, (G) machine sewing, or (H) computerized embroidery.
Figure 4: A1-A4. Four representative FFMS prototypes illustrating different fabric and stitch com-
binations. A1. Two-way stretch fabric using zig-zag side stitches without wrinkling. A2. Two-way
stretch fabric using zig-zag side stitches with wrinkling. A3. Two-way stretch fabric using zig-zag
cross stitches without wrinkling. A4. Non-stretch fabric using straight side stitches with wrinkling.
B. Cross section images of several commercially available tubes made of latex (top) and silicone
(bottom, note the smaller scale). The outer diameter of the silicone tube can reach sub-millimeter
Figure 5: Force testing. A. Apparatus for axial force testing. B. 3-channel FFMS. C. 10-channel
FFMS with brackets for test ﬁxture. D-F. Results for the 3-channel FFMS demonstrated consistent
performance over repeated actuation, similar behavior at different actuation speeds, and surprisingly
good agreement with the analytical model. G1-G4. The larger, 10-channel FFMS yielded similar
results to those that we obtained with the 3-channel device. The force range was 0 to 50 N. The
longer ﬂuid circuit yielded slightly greater response latency. H. Compression force testing apparatus.
I-K. The device produced compressive forces of 0 to 10 N, as 0 to 2 mL of ﬂuid was withdrawn. The
results were consistent with our analytical model, and varied little with speed.
Figure 6: Displacement and compression testing. A. Apparatus for displacement testing. B-D.
Results for the three-channel FFMS were consistent over repeated actuation. Similar behavior was
observed for different actuation speeds. The pressure-displacement relationships were consistent with
analytical predictions, despite dynamic effects, including hysteresis (see text). E1-E4. Results for the
larger, 10-channel FFMS were similar to those for the smaller FFMS. F. Hydraulic operation with
water was more efﬁcient than with air. Error bars: 95% conﬁdence intervals. G. Durability testing
revealed consistent performance over 5000 actuation cycles. A 5% reduction in displacement was
observed after this period, which we attributed to initial actuator relaxation.
Figure 7: Examples illustrating failure modes. A. Fabric tearing at stitch locations. B. Stitching
failure between fabric conduits. C. Tube ballooning between stitch locations.
Figure 8: FFMS actuators are readily scaled to small and large sizes. (A,B) A large example,
consisting of a 34.0 mm thickness FFMS (A: Top view, B: Side view), shown in contracted state,
was sufﬁcient to lift 15 kg (Fig. 10). (C-F) A small example, in contracted (C,D) and extended (E,F)
states; the thickness when extended is 1.0 mm. The large and small actuators were fabricated using
the same general process. A penny is used to illustrate the relative scale.
Figure 9: Composite or multi-actuated FFMS can realize dynamic, multimodal bending motion or
shape change. (A) In-plane rotation realized by differential pressurization of multiple ﬂuid channels.
(B) Out-of-plane bending is realized by combining an FFMS with a second, passive layer with spec-
iﬁed bending stiffness. (C) Biaxial bending is realized via a composite of two, orthogonally oriented
FFMS sheet actuators.
Figure 10: Demonstrations. (A,D,E) Miniature soft actuators for linear motion control or compres-
sion, capable of (A) lifting a small mass, (D) compressing small tissue areas, or (E) providing tactile
feedback via skin stretch. Inset: Skin stretch was easily perceived. (B) FFMS actuators can perform
large mechanical work. A 10-channel device lifts a 3 kg mass. A 4-channel structure (inner tube ra-
dius 2 cm) lifts a 15 kg cinder block and chain at pressures less than 276 kPa. (F,G) FFMS can be used
for compression garments for healthcare, training, and haptics. (F) A compression band yields uni-
form pressure on the upper limb, easily matching pressures provided by blood pressure cuffs. (G) A
compression garment for the lower limb comprises three independently addressable sections (dashed
boxes). Pressure variations can yield peristaltic motions suitable for undulatory massage in therapies
for lymphatic and blood circulation,72 such as lymphedema73 or venous closure.74