Amplifying the response of soft actuators by
harnessing snap-through instabilities
Johannes T. B. Overvelde
, Tamara Kloek
, Jonas J. A. D’haen
, and Katia Bertoldi
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; and
Kavli Institute, Harvard University,
Cambridge, MA 02138
Edited by John W. Hutchinson, Harvard University, Cambridge, MA, and approved July 21, 2015 (received for review March 11, 2015)
Soft, inflatable segments are the active elements responsible for
the actuation of soft machines and robots. Although current
designs of fluidic actuators achieve motion with large amplitudes,
they require large amounts of supplied volume, limiting their
speed and compactness. To circumvent these limitations, here we
embrace instabilities and show that they can be exploited to
amplify the response of the system. By combining experimental
and numerical tools we design and construct fluidic actuators in
which snap-through instabilities are harnessed to generate large
motion, high forces, and fast actuation at constant volume. Our
study opens avenues for the design of the next generation of soft
actuators and robots in which small amounts of volume are
sufficient to achieve significant ranges of motion.
The ability of elastomeric materials to undergo large de-
formation has recently enabled the design of actuators that
are inexpensive, easy to fabricate, and only require a single source of
pressure for their actuation, andstillachievecomplexmotion(1–5).
These unique characteristics have allowed for a variety of innovative
applications in areas as diverse as medical devices (6, 7), search and
rescue systems (8), and adaptive robots (9–11). However, existing
fluidic soft actuators typically show a continuous, quasi-monotonic
relation between input and output, so they rely on large amounts of
fluid to generate large deformations or exert high forces.
By contrast, it is well known that a variety of elastic instabilities
can be triggered in elastomeric films, resulting in sudden and
significant geometric changes (12, 13). Such instabilities have
traditionally been avoided as they often represent mechanical
failure. However, a new trend is emerging in which instabilities are
harnessed to enable new functionalities. For example, it has been
reported that buckling can be instrumental in the design of
stretchable soft electronics (14, 15), and tunable metamaterials
(16–18). Moreover, snap-through transitions have been shown to
result in instantaneous giant voltage-triggered deformation (19, 20).
Here, we introduce a class of soft actuators comprised of inter-
connected fluidic segments, and show that snap-through instabilities
in these systems can be harnessed to instantaneously trigger large
changes in internal pressure, extension, shape, and exerted force. By
combining experiments and numerical tools, we developed an ap-
proach that enables the design of customizable fluidic actuators for
which a small increment in supplied volume (input) is sufficient to
trigger large deformations or high forces (output).
Our work is inspired by the well-known two-balloon experiment,
in which two identical balloons, inflated to different diameters, are
connected to freely exchange air. Instead of the balloons becoming
equal in size, for most cases the smaller balloon becomes even
smaller and the balloon with the larger diameter further increases
in volume (Movie S1). This unexpected behavior originates from
the balloons’nonlinear relation between pressure and volume,
characterized by a pronounced pressure peak (21, 22). Interest-
ingly, for certain combinations of interconnected balloons, such
nonlinear response can result in snap-through instabilities at
constant volume, which lead to significant and sudden changes of
the membranes’diameters (Figs. S1 and S2). It is straightforward
to show analytically that these instabilities can be triggered only
if the pressure–volume relation of at least one of the membranes
is characterized by (i) a pronounced initial peak in pressure,
(ii) subsequent softening, and (iii) a final steep increase in pressure
(Analytical Exploration: Response of Interconnected Spherical
Membranes Upon Inflation).
Highly Nonlinear Fluidic Segments
To experimentally realize inflatable segments characterized by such
anonlinearpressure–volume relation, we initially fabricated fluidic
segments that consist of a soft latex tube of initial length Ltube, inner
radius R=6.35 mm, and thickness H=0.79 mm. We measured the
pressure–volume relation experimentally for three segments with
Ltube =22 −30 mm, and found that their response is not affected by
their length (Fig. S3). Moreover, the response does not show a final
steep increase in pressure. This is because latex has an almost
linear behavior, even at large strains.
Next, to construct fluidic segments with a final steep increase
in pressure and a response that can be easily tuned and con-
trolled, we enclosed the latex tube by longer and stiffer braids of
length Lbraid (Fig. 1A). It is important to note that the effect of
the stiff braids is twofold. First, as Lbraid >Ltube, the braids are in
a buckled state when connected to the latex tube (Fig. 1B), and
therefore apply an axial force, F, to the membrane. Second, at a
certain point during inflation when the membrane and the braids
come into contact, the overall response of the segments stiffens.
We derived a simple analytical model to predict the effect of
Lbraid and Ltube on the nonlinear response of these braided fluidic
segments (Simple Analytical Model to Predict the Response of the
Fluidic Segments). It is interesting to note that our analysis in-
dicates that for a latex tube of given length, shorter braids lower
the peak pressure due to larger axial forces (Fig. S4 Cand E).
Moreover, it also shows that Lbraid strongly affects the volume at
which stiffening occurs. In fact, the shorter the braids, the earlier
contact between the braids and the membrane occurs, reducing
the amount of supplied volume required to have a steep increase
Although instabilities have traditionally been avoided as they
often represent mechanical failure, here we embrace them to
amplify the response of fluidic soft actuators. Besides pre-
senting a robust strategy to trigger snap-through instabilities
at constant volume in soft fluidic actuators, we also show that
the energy released at the onset of the instabilities can be
harnessed to trigger instantaneous and significant changes in
internal pressure, extension, shape, and exerted force. There-
fore, in stark contrast to previously studied soft fluidic actuators,
we demonstrate that by harnessing snap-through instabilities it
is possible to design and construct systems with highly control-
lable nonlinear behavior, in which small amounts of fluid suffice
to generate large outputs.
Author contributions: J.T.B.O. and K.B. designed research; J.T.B.O., T.K., and J.J.A.D. performed
research; J.T.B.O., T.K., and K.B. analyzed data; and J.T.B.O. and K.B. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
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