SCIENCE ADVANCES | RESEARCH ARTICLE
MATERIALS SCIENCE

Reprogrammable soft actuation and shape-shifting
via tensile jamming
Bilige Yang†, Robert Baines†, Dylan Shah, Sreekalyan Patiballa, Eugene Thomas,
Madhusudhan Venkadesan, Rebecca Kramer-Bottiglio*
The emerging generation of robots composed of soft materials strives to match biological motor adaptation skills
via shape-shifting. Soft robots often harness volumetric expansion directed by strain limiters to deform in complex ways. Traditionally, strain limiters have been inert materials embedded within a system to prescribe a single
deformation. Under changing task demands, a fixed deformation mode limits adaptability. Recent technologies
for on-demand reprogrammable deformation of soft bodies, including thermally activated variable stiffness
materials and jamming systems, presently suffer from long actuation times or introduce unwanted bending stiffness. We present fibers that switch tensile stiffness via jamming of segmented elastic fibrils. When jammed, tensile
stiffness increases more than 20× in less than 0.1 s, but bending stiffness increases only 2×. When adhered to an inflating body, jamming fibers locally limit surface tensile strains, unlocking myriad programmable deformations.
The proposed jamming technology is scalable, enabling adaptive behaviors in emerging robotic materials thatinteract with unstructured environments.

Biological organisms are able to adjust their anatomical structures,stiffness, and behaviors to accommodate a variety of tasks and environmental demands (1). Octopus tentacles, for example, can accessnearly infinite trajectories, yet also form joint-like structures to adapt
articulated limb control strategies for precise point-to-point movements (2, 3). Caterpillars undulate and engage in inchworm gaits
but can rapidly curl into a wheel form and propel themselves awayfrom predators (4, 5). Rapid reconfiguration capabilities make a bodyversatile; they are a hallmark of biological systems that thrive in thenatural, unstructured world. Yet, these capabilities have long eluded
conventional robots, which are limited by rigid structures and discrete joints.
To extend reconfiguration capabilities to artificial systems, researchers have leveraged continuously deformable materials to create
soft robot bodies and actuators. Commonly, multiple actuators arepatterned into a soft robot body, and a subset of those actuators is
activated to achieve a desired body configuration (6–10). For example,
several works have presented three–degree of freedom actuator
modules containing three pneumatic actuators evenly spaced in acylindrical configuration (11–15). These pneumatic multi-actuatorsystems are capable of bending in various directions, yet multiple
chambers take up substantial radial space and make miniaturizing
such systems difficult for applications like minimally invasive surgery, where a smaller outer diameter is desired (16, 17).
As an alternative to multichamber actuators, a single volumetrically
expanding soft body can achieve controlled and complex motion
when coupled with thin strain-limiting components (like woven
meshes or fibers) that bias deformation in a programmed way(18–21). Several recent studies have attempted to create inflatable soft
actuators with reprogrammable strain-limiting layers, thereby enabling a single actuator to attain multiple trajectories by controlling
School of Engineering & Applied Science, Yale University, 10 Hillhouse Avenue, New
Haven, CT 06520, USA.
*Corresponding author. Email: rebecca.kramer@yale.edu†These authors contributed equally to this work.
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material properties at the actuator surface. One approach used reconfigurable tensile strain-limiting adhesive patches that can be
manually repositioned over the soft body to direct inflation (22).
Other approaches relied on thermally responsive materials, such as
low–melting point alloy (LMPA) particulate composites (23, 24)
and shape memory polymer (SMP) (25, 26) that change stiffness uponheating to influence the trajectory of pneumatic actuators. Although
thermally activated variable stiffness mechanisms are disposed to large
modulus changes and require no human intervention, they often
suffer from long response times (27). Furthermore, when in the rigid,
bulk state (28, 29), materials like LMPA and SMP compromise thedeformation ability of soft systems because they have coupled tensile and bending stiffnesses. Electrostatic clutches can also modulatetensile stiffness (30, 31). However, these clutches require high voltages (>300 V) to operate, posing risks for human-orientated applications, and the nonstretchable, two-dimensional (2D) componentsof the clutches limit their free bending in 3D.
A growing body of work seeks to use jamming, the sudden changeof modulus due to interactions of many constituent parts within asystem, to achieve rapid stiffness change in soft robots (32–35). Existing
jamming technologies predominately trigger interactions between
subcomponents by applying a vacuum to a sealed domain of material, inducing a compressive force that drives the material together.
There are three established classes of jamming—granular jamming,
layer jamming, and fiber jamming. Each class is associated with adifferent dimensionality and tunes stiffness along particular axes
(Fig. 1D). Granular jamming tunes the compressive and bending
stiffnesses of a consolidated volume of particles (36–40). Vacuum-­
packed granules are unable to resist tensile force that exceeds thevacuum pressure, making granular jamming unsuitable for constraining tensile strain on an inflating actuator. Layer jamming tunes thebending stiffness of surfaces consisting of stacked, flexible sheets(41–43). Traditional layer jamming does not have any degrees of
freedom in-plane because the layers are stiff and homogeneously
connected to all sides of the system. Layer jamming thus cannot be used
to tune tensile stiffness from the surface. Fiber jamming changes thebending stiffness of 1D elements composed of flexible fibers (44–47).
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INTRODUCTION

Copyright © 2021
The Authors, somerights reserved;
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for the Advancementof Science. No claim to
original U.S. Government
Works. Distributed
under a Creative
Commons Attribution
NonCommercial
License 4.0 (CC BY-NC).

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Similar to layer jamming, fiber jamming designs in the literature
have used homogeneous, inextensible fibers connected to both ends
of a system and consequently cannot be used to modulate tensile
stiffness. Moreover, current fiber jamming systems have a relatively
high bending stiffness (even in the unjammed state) due to theincorporation of stiff fibers. High bending stiffness impedes large
deformations and creates an undesirable rigid interface. Although all
three jamming systems have been integrated with actively actuating
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structures like soft inflating bodies, their applications have been primarily restricted to locking shape (37, 40, 45, 48) or varying bending
angles (42, 49, 50). The inability to independently tune tensile stiffness impedes current jamming systems from actively regulating thesurface strains of soft systems to shift shape.
A recent variant of layer jamming technology, which we will refer to as “stretchable layer jamming,” allows the tuning of tensile
stiffness (51–53). In this technology, individual layers are not connected
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Fig. 1. Tensile jamming fiber with SEFs. (A) Schematic of SEFs and jamming fiber. Only two SEFs are shown inside the jamming fiber for clarity. Real system has 4 to 10 SEFs.
Detailed fabrication process in fig. S2. (B) Jamming fiber with eight SEFs inside is highly flexible (scale bars, 1 cm). Fibers are 12 cm long. Close-up images of SEFs and asingle polyester-silicone interface [scale bars, 900 m (top) and 500 m (bottom)]. (C) Upon application of vacuum, SEFs agglomerate and overlapping polyester sections
yield high shear strength through friction, increasing tensile stiffness of the fiber. At atmospheric pressure, SEFs in the fiber can individually stretch and slide over eachother. With a mass of 200 g attached to its end, the unjammed fiber (atmospheric pressure) stretched to 88% strain, while the jammed fiber (−80 kPa) stretched to only
4% strain. Scale bars, 2 cm. (D) Stiffness change ratios of jamming systems. Tensile jamming fibers occupy the desired range: low bending stiffness change and large
tensile stiffness change. (E) Radially constrained pneumatic actuator with three jamming fibers around its perimeter. The actuator executes different trajectories depending on which fibers are jammed. (F) A pneumatic membrane with jamming fibers attached to the top and bottom orthotropically expands when fibers are unjammed (topleft). By jamming certain fibers, the membrane can attain shapes with zero (bottom left), positive (top right), and negative (bottom right) Gaussian curvatures. Photo
credit: Robert Baines, Yale University.

SCIENCE ADVANCES | RESEARCH ARTICLERESULTS

Segmented elastic fibrils
The technology underpinning tensile jamming fibers is the SEFs.
We developed two SEF architectures, each consisting of different
interspersed segments of polyester and silicone, labeled as “type A”
and “type B” in Fig. 1A. To make a jamming fiber, equal numbers oftype A and type B SEFs are aligned and joined at their ends. They
are then placed inside a sealed silicone envelope and connected to a
vacuum source. Further manufacturing details can be found inMaterials and Methods, while an illustration of the process can befound in fig. S2. Within each type of SEF, the length of polyester
content is higher than 50% of the total SEF length. This way, there
will be overlapping polyester sections when the two types of SEF areplaced adjacent to one another in the silicone envelope.
We conducted tension tests on SEFs with varying polyester length
percentages () to understand how  influences stiffness and maximum elongation before failure (fig. S3). As  increases, so does thestiffness, which is consistent with our understanding of the mechanicsof an SEF from the rule of mixtures​  ​​​		​​E​ SEF​​  = γ ​E​ f​​ + (1 − γ ) ​Em(1)

where ESEF is the Young’s modulus of an SEF, and Ef and Em are
Young’s moduli of polyester and silicone matrix, respectively.
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Tensile jamming fibers
We found that we could tune the tensile force (F) required to stretcha tensile jamming fiber to a prescribed displacement () and thereby_F​​) by varying the magnitude of vacuum
the fiber’s tensile stiffness (​k = ​δ(P) (Fig. 2A). The ratio of jammed to unjammed stiffness rises toa maximum of more than 20× with increasing pressure (Fig. 2B).
Despite this high tensile stiffness ratio, the fibers retain low bending
stiffness in two orthogonal directions (Fig. 2, C and D). Three-point
bending tests (details in note S1) reveal that the system has a bending
stiffness of 0.0021 and 0.0048 N/mm when unjammed and jammed
at −85 kPa, respectively. Thus, transitioning from unjammed tojammed, the bending stiffness increases about 2×. Note that thesebending stiffnesses (unjammed and jammed) are less than 1/80 of
the reported stiffnesses of a benchmark fiber jamming system withsimilar dimensions (44).
Other design parameters contribute to a tensile jamming fiber’s
effectiveness. We therefore derived a relationship between k and design parameters including , vacuum pressure, and number of SEFs
(N) (see note S2). The analytical model considers the interfacial shear
stiffness (kshear) between SEFs as the primary contribution to the overalltensile stiffness (see fig. S1). We express the interfacial stiffness as
GA ​​	
	​​k​ shear​​  = α ​ ─t(2)where  is the effective contact ratio (a fitting parameter to account for_imperfect contact), G is the shear modulus of silicone (​G = 2(1​  E+ ν)​​,where E is Young’s modulus and  is the Poisson ratio), A is the areaof contact, and t is the thickness of the silicone under shear on one
fibril. t is a function of the applied pressure, because pressure willsqueeze and flatten the silicone in the linear elastic regime according
ΔP​​ ​​​​, where t0 is the initial thickness of the silicone
to ​​t(ΔP ) = ​t​ 0​​​(​​1 − ​_E)interface. Because the shear interfaces are parallel, the total stiffnessof the jamming fiber is the sum of kshear from all interfaces (eqs.
S13 to S17).
In the model, we also considered SEF slippage that captures thenonlinearity of the force-displacement response. Slip happens when
the shear force in the interface exceeds the maximum static frictionthat can be sustained by the silicone interface between polyester
threads in adjacent fibrils. After slip, some interfacial stress is relieved(eqs. S18 and S19).
With only three fitting parameters [effective contact ratio (),shear area ratio (e), and coefficient of friction ()], our model is able
to predict the jamming behavior reasonably well. The model predicts
that jamming fiber stiffness will increase with increasing , N, andP. This prediction is consistent with uniaxial quasistatic tension
tests conducted on jamming fibers while varying the same parameters(fig. S4, A and B). Theoretical predictions from the model are plotted in Fig. 2A as a dashed line. The average percentage error of force
prediction at the maximum tested displacement of 8 mm is 8.60%.
On the basis of the results of the tension tests, we chose to proceedwith  = 70% and N = 8 (referred to as 70% N8 in subsequent text)
for further testing and demonstrations because it exhibited the highest
tensile stiffness ratio, 22.2, between the jammed and unjammed statesfor P = −40 kPa (fig. S4, C and D).
Having quantified the influence of critical design variables on a
jamming fiber’s tensile stiffness, we evaluated the reliability of thefiber jamming mechanism in two ways. First, to assess how well the
jammed fibers could induce the same actuator trajectory multiple
times, we kept a fiber jammed and subjected it to 1000 cyclic tensile
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to all sides of the device, enabling the layers to slide past each otherwhen pulled. Stretchable layer jamming could potentially be applied
to modulate moderate tensile strains (<40%) but at the cost of
markedly increased bending stiffness (see Fig. 1D), which severely
limits the achievable curvature if it is incorporated as a strain limiter.
Stretchable layer jamming sheets also cannot bend in all directionsin space—even if made into long, narrow sheets resembling a fiber,these sheets only bend easily along the axis with minimal second
moment of area and thus would constrain the potential deformationsof the soft system. The ability to control tensile stiffness while retaining
low bending stiffness in any direction is crucial for jamming-based
strain-limiting technology and remains an unsolved problem.
In this work, we introduce “tensile jamming fibers,” a system that
rapidly modulates its tensile stiffness while maintaining low bending stiffness in all directions. Tensile jamming fibers are the first
technology to occupy the desired range in Fig. 1D. A jamming fiber
comprises a collection of segmented elastic fibrils (SEFs) (Fig. 1C).
One SEF consists of an alternating pattern of inextensible polyester
thread and elastic springs (see Fig. 1, A and B). The segmented design of SEFs allows a jamming fiber to be highly stretchable—up to
200% of its original length without failure (fig. S5)—in the absenceof vacuum (unjammed). When vacuum is applied, the SEFs press
together, and the interfaces between overlapping sections withembedded polyester thread generate high shear force that resists tensileloads (jammed).
After affixing these jamming fibers to the surface of a single-­chamber inflatable actuator, we tune the local tensile stiffness torapidly and predictably change its trajectory (Fig. 1E). In addition,
we integrate our jamming fibers into a planarly expanding actuator
to create a rapidly shape-shifting bilayer capable of forming surfaces
with zero, positive, and negative Gaussian curvatures (Fig. 1F). Thesedemonstrations pave the way for shape-shifting robots and dynamic
camouflage systems.

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loads. After 1000 cycles, the fiber retained more than 70% of its
original tensile force (dropping from 5.1 to 3.6 N) (Fig. 3A). Second,
to test how well the fibers would fare in reconfigurable applications(jamming and then unjamming to facilitate different sets of motions),
we applied vacuum every other cycle for 100 cycles of tensile load.
Throughout the 100 cycles of intermittent jamming and unjamming,
we observed negligible change in F, despite reaching the same  eachcycle (Fig. 3B). The effective maintenance of k throughout the jam-­unjam cycles gave us confidence that jamming fibers could be jammed
and unjammed repeatedly to perform reconfiguration tasks.
To quantify the time scale of stiffness change in a jamming fiber,
we initiated jamming partway through a tensile test while monitoring
the mechanical response (see Fig. 3C and additional data in fig. S6A).
The jamming transition was rapid, stiffening the fiber within 1/10 ofa second and stabilizing in the new jammed state in less than half ofa second (see inset of Fig. 3C). The reverse process, going from thejammed state to the unjammed state, was also rapid and exhibitedno residual forces (see Fig. 3D and additional data in fig. S6B). From
this test, we also observed that force sustained in the jammed state
appears to be independent of the prestrain on a fiber at the onset of
jamming. For example, the maximum value attained by curves in thetwo gray shaded regions in Fig. 3 (C to H) is within 5% of one
another. Invariance in the mechanical response of jamming fibers
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to moderate prestrains allows stiffness changes during inflation ofan actuator, as shown in movie S4.
Modular variable trajectory actuatorTo achieve multiple trajectories using a single actuator, we integrated
three jamming fibers around the circumference of a modular, verticallyextending pneumatic chamber. By applying vacuum to subsets of
the jamming fibers, the actuator could bend along various trajectories (Fig. 4A). The range of attainable trajectories grows combinatorially with increased resolution in pressures: Even with only two levelsof pressure (P = −10 and −40 kPa), the actuator generated 12 distinct
swept trajectories (Fig. 4B). Beyond the rapidity of reconfiguration,
attaining 12 distinct trajectories sets us apart from multitrajectory
actuators based on phase-change materials like LMPA (23, 24), where
only two states—ON and OFF—are available. Our demonstration
represents a single-core soft actuator with the largest number ofprogrammable trajectories to date. With finer variations in pressure,the actuator is able to bend in more directions, without requiring
additional pneumatic chambers. As a conceptual illustration, we
generated 24 distinct trajectories by varying the stiffness of fibers
further in finite-element (FE) simulation (fig. S8 and note S5).
Analytical and FE models were used to predict the deformation
trajectories of the single actuator outfitted with jamming fibers (Fig. 4A).
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Fig. 2. Mechanical characterization of jamming fibers. (A) Tensile behavior at selected jamming pressures for fibers with the parameters of 70% polyester length
fraction and eight SEFs (70% N8). Each solid line represents the average behavior of three specimens. Clouds indicate 1 SD from the mean. Dashed lines are predictions
from the analytical model. (B) Ratio of jammed stiffness over unjammed tensile stiffness as a function of vacuum pressure for the 70% N8 specimens. Average of three
specimens reported. Bars represent 1 SD above and below the mean. (C and D) Three-point bending of tensile jamming fibers. When jammed (at vacuum pressure of −85 kPa),
the fiber is approximately 2× stiffer than when unjammed. However, the magnitude of the forces it sustains when deforming is still very low. (D) is test conducted withspecimen rotated 90° from (C). Approximately the same force values are reached, testifying to the fact that the tensile jamming fiber has isotropic bending stiffness.
Confidence cloud shows SD. Solid line indicates the mean.

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For derivation and simulation details, see notes S3 and S5. With theanalytical model, we can predict fairly well both the bending direction and the bending curvature of the actuator. The bending direction
can be approximated by calculating the geometric circumferential
midpoint of the jammed fibers, while a hyperelastic constitutive
model reasonably predicts the magnitude of curvature (fig. S7 andnote S3). With the FE model, we were able to capture more nuanced
phenomena. These include how jamming multiple fibers to bisect a
trajectory decreases curvature at a fixed pressure and how jammingat intermediate pressures can be used to further hone bending angle anddirection. We juxtaposed
the end effector distances defined by the_
Euclidean distance, √​​ ​x​​  2​ + ​y​​  2​ + ​z​​  2​ ​​, from its starting position withthose predicted by the models (Fig. 4C, left axis). The small discrepancies suggest that both models are useful in the design of variable
trajectory actuators. However, while the analytical model offers
predictions with less required computation, it cannot predict theeffects of jamming at intermediate pressures.
We also calculated the angular deviation of the actuator’s swept
path from the intended path, which was to divide the hemisphere
into 12 equal parts (Fig. 4D, right axis). The trajectories with least
absolute angle error (1, 5, and 11) arose from different jamming
configurations: single fiber jammed, two fibers jammed, and fiber
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partially jammed, respectively. This result suggests that a desired
direction—whether it is along the direction of one fiber or in between
two fibers—can be achieved with high accuracy. By the same token,
the result suggests that deformation trajectories, and in our case,angular deviations from perfect divisions of the x-y plane, are sensitive
to fiber placement and actuator dynamics (see oscillations of swept
paths projected in the x-y plane in Fig. 4B, especially trajectories
2, 3, 7, and 12).
Enhancing performance by combinations of modules
Jamming fiber–enabled modular variable trajectory actuators can be
combined to create agile, reconfigurable soft robots. The resulting
systems have myriad deformation modes, enabled by the versatility
and modularity of individual variable trajectory actuators. To demonstrate potential applications for this principle, we created a multimodal gripper and a multitrajectory continuum arm (Fig. 5A).
To make a multimodal gripper, we mounted three actuators (eachequipped with three jamming fibers) in parallel to an acrylic baseplate (Fig. 5B). Depending on the set of fibers that was jammed, thefingers engaged in three kinematically distinct grasping modes. Whenthe fibers on the inside of the fingers were jammed, the gripper
executed a “pinching grasp” for picking up relatively small objects.
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Fig. 3. Cyclic and dynamic behavior of jamming fibers. (A) Cyclic tensile testing up to a displacement of 8 mm while jammed at −40 kPa. (B) Cyclic tensile testing up toa displacement of 8 mm, jammed at −40 kPa and unjammed for every other cycle. Average of three specimens reported. Error clouds represent 1 SD from the mean. Top
green curve shows the jammed response, and bottom black curve shows the unjammed response. Insets show the force versus displacement curve for the last two cycles(jammed and unjammed). (C) Dynamic transition from unjammed to jammed at displacement of 6 mm during a tensile pull to 12 mm. Inset shows the derivative of force
with regard to displacement (instantaneous stiffness) plotted against time to display the rapid time scale of the stiffness response. (D) Dynamic transition from jammed
to unjammed at displacement of 6 mm during a tensile pull to 12 mm. In (C) and (D), data from only one of the three specimens tested are plotted for clarity. Additional
data in fig. S6.

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Jamming the outside fibers of each actuator led to an “outward-­
hooking” motion for latching onto the inside of concave objects. Last,
when two fibers on the oblique side of the fingers were jammed, thegripper executed a “twisting” motion. Using the three grasp modes
separately, the gripper was able to pick up a Rubik’s cube, lift a bowl,
and twist the cap off of a jar. We also show how two grasping motions(pinching and outward-hooking) can be combined in sequence to
execute a pick-and-place operation (movie S3). The ability to achieve
diverse grasping modes within the same gripper with a single positive
pressure input shows the enhanced reprogrammability of motion
trajectories enabled by tensile jamming. A superposition of these grasp
modes, or optimization of fiber placement, could potentially open
up a wider grasping space.
In addition to the parallel configuration embodied by the gripper,
we joined two actuators in series to create a continuum manipulator
with seven controllable degrees of freedom (six fibers and one contiguous inflating core) (Fig. 5C). By jamming the fibers of each segmenton the same side, the whole manipulator bent to that side; by jamming
fibers on different sides of each segment, the manipulator bent into
more complex configurations. Such motions are reminiscent of thevariety of deformation modes of biological hydrostats (54, 55). In eachcase, the deformed state was predicted well by FE analysis (FEA),
reinforcing its utility as a design tool for jamming fiber–based robots.
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Shape-changing membrane
The ability to adapt shape to environmental and developmental
triggers is a core function of living beings and a grand challenge for
artificial machines (1). Many studies, those in both simulation (56)and hardware (10, 57–61), attest to the benefits shape change confers on robots under changing task demands. Soft robots, in particular,
hold promise as the next generation of shape-changing robots dueto their capability to undergo large deformations. Inspired by botany[unfolding of flowers (62) and natural curling of seed pods (63)],
researchers have programmed thin, planar sheets to morph into complex surfaces through in-plane growth and out-of-plane buckling (64).
Such an arrangement enables local control of the shape tensor, thereby
giving rise to a rich diversity of shapes.
Current artificial shape-changing sheets—those made from composite hydrogels (65) or elastomers (66), for example—often have
only one programmed shape and a slow response time. Recent workon liquid crystal elastomer composite shape-morphing surfaces increased the number of possible deformations with a single systembut still required minutes to switch between shapes (61). Fast shape-­changing systems can be achieved by applying jamming fibers toplanar inflatable geometries. The capability of the fibers to tune tensile
stiffness on a higher magnitude than bending stiffness allows effective redistribution of the elastic energy on the thin sheet between
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Fig. 4. Modular variable trajectory actuator. (A) Experimental setup and simulation visualizations. The FEA model generated 12 trajectories, including some configurations with two different pressures and thus two sets of stiffness, as was done in the experiment. However, our analytical model could only account for one stiffness, limiting it to prediction of six of the tested trajectories. (B) Comparison of motion capture data for the actuator’s end effector and the predictions from the analytical and FEA
models. We labeled the trajectories 1 to 12, corresponding to combinations of jammed fibers. Trajectories 1 to 3 (blue) are achieved by jamming a single fiber to P = 40 kPa,
4 to 6 (red) by jamming two adjacent fibers to P = 40 kPa, and 7 to 12 (green) by jamming two adjacent fibers at different pressures (P = 10 and 40 kPa and vice versa). (C) Leftaxis and blue markers show final resting distance of the end effector from the origin. Right axis and orange markers show error between the measured bending angle of
the actuator (as projected into the x-y plane) and the angles expected from an ideal subdivision of the plane into 12 equal parts.

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stretching and bending, thus effectively altering the resulting shapewithin seconds. Here, we demonstrate this concept by applying
jamming fibers in a grid-like arrangement on each side of a planar
pneumatic bladder (Fig. 6).
The top and bottom faces of the bladder are connected by silicone
pillars, preventing expansion through the thickness and creating amembrane that expands in-plane orthotropically (see fig. S9 andnote S4). When the membrane’s surface is asymmetrically or anisotropically constrained by jamming fibers during inflation, the membrane bends out of plane as it equilibrates to a minimum energy state.
For example, by jamming the top longitudinal fibers, the inflated
bladder bent around a single axis into a cylindrical arch (zero Gauss
curvature; Fig. 6A). Jamming the bottom longitudinal and bottom
latitudinal fibers, the bladder assumed the shape of a bowl or dome
(positive Gauss curvature; Fig. 6B). Last, jamming the top longitudinal and bottom latitudinal fibers yielded a saddle shape (negative
Gauss curvature; Fig. 6C). This is the first demonstration of a bilayerthat is able to independently switch between all three types ofGaussian curvatures within seconds.
The qualitative deformation behavior of the bladder outfitted in
jamming fibers is described well by FEA, while analytical methods
reasonably predict deformation of the midplane (notes S4 and S5).
We expect that the local control of shape furnished by the jamming
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fibers will propel the field of shape-morphing structures to the nextlevel. As a demonstration of concept, we simulated a large-scale
membrane with patterned jamming fibers and found that it was able
to morph to distinct and complex topologies contingent on the subsets of locally jammed fibers (fig. S10).
DISCUSSION

The ability to actively tune stiffness is critical to devising next-­
generation robots that replicate the control and fluidity of biologicalorganisms’ motions and shape changes. In lieu of traditional approaches
that rely on strain limiters with immutable material properties, here,
we introduce controllable tensile strain limiters. Jamming fibers
combine the desirable features from many different existing stiffness modulation techniques, such as state-of-the-art jamming andthermally activated variable stiffness materials. Jamming fibers exhibit marked tensile stiffness changes, rapid response times, minimal
contribution to system bulk properties or weight, and highly isolatedmaterial changes. They stand in contrast to thermal stiffness-changing
systems, where heat diffusion leads to undesired local interference,and stretchable layer jamming, where bending stiffness and tensile
stiffness are coupled. At atmospheric pressure, the jamming fibers
stretch with low tensile stiffness, having little influence on the trajectory
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Fig. 5. Modular actuators combined to make multimodal three-finger gripper and two-segment continuum arm. (A) Schematics for the modular actuators.
(B) Three grasping modes enabled by fiber jamming. Top row depicts jamming states of the three actuators. Middle row shows pictures from grasping trials: pinching a
Rubik’s cube, hooking a metal bowl, and twisting a lid. Bottom row shows the FEA-simulated prediction of actuator positions in the absence of an object. (C) Multimodal
two-segment arm. Left column shows the final shapes the arm attained after jamming different sets of fibers (scale bar, 4 cm). Right column shows the simulated arm
position prediction with FEA. Photo credit: Bilige Yang, Yale University.

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of an actuator. When vacuum is applied, the jamming fibers’ tensile
stiffness increases by more than 20× in less than 1/10 of a second,
imposing strong directional bias while retaining flexibility in bending.
Tensile jamming technology demonstrates far-reaching potential in soft robotics, enabling great improvements to the workspacesof single-chamber, volumetrically expanding soft actuators without
adding large volume or inducing high bending stiffness. With rapid
response and an ability to influence actuator dynamics mid-inflation,such multimodal actuators are more responsive in applications compared to thermally activated strain-limiting components and safer
for human-oriented applications than high voltage–activated clutches.
This improvement in control of trajectories without undesired increases in volume is especially relevant for applications where thecross-sectional area of the actuator needs to be minimized, such as
in endoscopic minimally invasive surgery. Our radially constrained
single-chamber actuator, with small-footprint 1D elements (tensile
jamming fibers), can potentially be made more slender than current
multichamber actuators (16, 17) and avoid the large radial expansion needed for multichamber actuators to achieve bending.
In the surface (2D) cases, varying tensile stiffness (coupled with
underlying inflation) allows control of Gaussian curvature. The
result is the first demonstration of active transition between three
types of Gaussian curvatures—on the order of seconds—within thesame system. The ability of the tensile jamming fibers to increase
tensile stiffness while maintaining a low bending stiffness enables aredistribution between bending energy and stretching energy for thethin surface, which facilitates marked shape change. Theoretically,
with sufficient number of jamming fibers, an inflating 2D sheet cangrow into any target surface (64) and then change between such shapes.
Yang et al., Sci. Adv. 2021; 7 : eabh2073

1 October 2021

This demonstration paves the way for next-generation shape-shifting
robots with ability to adapt to environmental demands and adopt
shapes for dynamic camouflage.
Beyond the robotics space, we foresee jamming fibers as a usefultechnology in exosuit-assisted rehabilitation, where selective mobility
is tantamount to patient recovery. Additional possible use cases include on-demand sizing for smart garments and other applications
where predictable, rapid, and localized tensile stiffness changes aredesired.
MATERIALS AND METHODSManufacturing of fibers
Each SEF had segments of polyester thread embedded discontinuously
in a thin silicone substrate (Ecoflex 50, Smooth-On). Several SEFs
were stacked and glued together on both ends with a silicone-based
adhesive (Sil-Poxy, Smooth-On). A small amount of cornstarch wasapplied to the surfaces of SEFs to prevent adhesion of silicone. The
bundle of SEFs was put inside a silicone membrane and sealed with
Sil-Poxy. The detailed manufacturing process is depicted in fig. S2.
Several designs were manufactured, with different linear loading
fractions of SEF ( = 0, 60, 70, and 100%) and different numbers of
SEFs per fiber (N = 4, 6, 8, and 10).
Mechanical testing
Quasistatic tensile testing of jamming fibers was done using an
Instron 3345 material tester. For pull-to-failure and nondynamic
tensile tests, extension was applied at 20 mm/min. For three-point
bending, compression was applied at 1 mm/min. For cyclic testing,
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Fig. 6. Shape-changing membrane enabled by tensile jamming fibers. A circular planarly expanding actuator was made and equipped with grids of jamming fibers.
By jamming different sets of fibers, this unit was able to manifest ranges of Gaussian curvatures. FEA and analytical modeling were used to predict and understand theeffect of varied tensile stiffness on the 2D actuator. (A) Top longitudinal fibers jammed to create an arch (zero Gaussian curvature). (B) Top longitudinal and latitudinal
fibers jammed to create a bowl (positive Gaussian curvature). (C) Top longitudinal and bottom latitudinal fibers jammed to create a saddle shape (negative Gaussian
curvature). Scale bars, 4 cm. Photo credit: Bilige Yang, Yale University.

SCIENCE ADVANCES | RESEARCH ARTICLE
extension was applied at 60 mm/min. Additional details and results regarding characterization are presented in the Supplementary Materials.
Fabrication of actuators
The omnidirectional actuators were made by first creating a silicone(Ecoflex 50, Smooth-On) membrane with embedded parallel polyester threads and then wrapping the membrane into a cylinder, as
described in previous work (22). Jamming fibers were attached on
the outside of this cylinder, at even spacing (every 120°). A modular
connection, made out of acrylic and Luer lock connectors (51525K123
and 51525K213, McMaster-Carr), was added to each end of thecylindrical actuator using Sil-Poxy. For the gripper demonstration,
three modules were attached to an acrylic plate, in a circular pattern(radius of 300 mm), at equal spacing (120°). The continuum arm was
manufactured by attaching two omnidirectional actuators in series
and mounting the free end of one of them to a base plate. The shape-­
shifting membrane was fabricated by casting silicone (Ecoflex 30,
Smooth-On) in an acrylic mold (fig. S9) and attaching 3 × 3 grids ofjamming fibers on both sides of the membrane with Sil-Poxy. The
resulting bilayer membrane is about 10 mm thick.
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Submitted 22 February 2021
Accepted 10 August 2021
Published 1 October 2021
10.1126/sciadv.abh2073
Citation: B. Yang, R. Baines, D. Shah, S. Patiballa, E. Thomas, M. Venkadesan, R. Kramer-Bottiglio,
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Reprogrammable soft actuation and shape-shifting via tensile jamming
Bilige YangRobert BainesDylan ShahSreekalyan PatiballaEugene ThomasMadhusudhan VenkadesanRebecca KramerBottiglio

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