Mechanical Devices for Snail-like Locomotion
BRIAN CHAN, SUSAN JI, CATHERINE KOVEAL
AND
A. E. HOSOI*
Hatsopolous Microfluids Laboratory, Department of Mechanical Engineering
Massachusetts Institute of Technology, Cambridge, MA, USA
ABSTRACT: We have constructed two mechanical snails, Robosnail 1 and Robosnail 2,
inspired by the propulsion mechanisms of live gastropods. Each uses a different mechanical
strategy to move on a thin layer of viscous fluid. Robosnail 1 uses a flexible flapping sheet
to generate lubrication pressures in a viscous Newtonian fluid which in turn propel the
snail. Robosnail 2 uses a compressible sliding sheet on a layer of Laponite, a non-Newtonian,
finite-yield stress fluid.
Key Words: Author please supply Keywords???
INTRODUCTION
such as snails and slugs (with the
exception of free-swimming species) move over
solid surfaces lubricated by a thin layer of pedal mucus.
It has been noted (Vles, 1907) that when snails move,
they generate a train of moving waves along the foot
(Figure 1). Depending on the type of snail, the waves
may be compression waves moving from tail to head
(direct waves) or expansion waves from head to tail
(retrograde waves) (Ruppert and Barnes; Wilbur and
Yonge, 1964; Moore, 2001). Close observation shows
that the foot is stationary and affixed by mucus to the
substrate in the area between waves (the interwave) yet
moves within the wave. This mode of locomotion has
been termed adhesive locomotion by (Denny, 1981, 1984,
1989). It is commonly observed that most land snails use
direct waves, while most aquatic snails use retrograde
waves. This correlation between habitat and locomotion
method leads us to believe that terrestrial and marine
species may have evolved significantly different physical
mechanisms for motion.
Construction of biomimetic robots allows engineers
not only to reproduce the motions of animals, thus
testing the feasibility of applying natural mechanisms
to manmade mechanisms, but also to explore the effect
of varying parameters affecting the phenomena. By
changing those parameters it is possible to optimize the
mechanisms for a range of applications, some of which
may be very different from the natural counterpart.
There exists a myriad of examples of biomimetic robots
built for the study of locomotion. Among them are
G
ASTROPODS
*Author to whom correspondence should be addressed. E-mail: [email protected]
Figures 1, 3 and 6 appear in color online: http://jim.sagepub.com
JOURNAL
OF INTELLIGENT
robots for fluid locomotion such as Robofly (Birch and
Dickinson, 2001), Robotuna (Kagemoto et al.), a
mechanical eel (McIsaac and Ostrowski, 2002), and
other robotic fishes (Yu et al., 2004); for surface
locomotion Robostrider (Hu and Bush, 2003); and for
walking robots there are robotic lobsters (Ayers, 2004),
scorpions (Klaassen et al., 2002), roaches (Bailey et al.,
2001), and devices with various numbers of legs.
However, no known free-standing systems for lubrication layer locomotion or adhesive locomotion exist.
The closest work is that done by (Ito and Yasukawa,
2000) in their study of a waving sheet used to convey
objects (essentially an upside-down Robosnail 1).
However, unlike the crawlers presented in the current
study, Ito’s snail requires mechanical energy input from
the environment.
We have built two mechanical snails as prototypes
to reproduce the locomotion mechanisms of retrograde
wave and of direct wave snails, respectively. This
study will briefly describe the mechanical designs and
discuss preliminary data. Extensive tests have not
been performed as of yet, as the reliability and ease
of parameter variation need to be improved before
undertaking extensive experimentation. The primary
goal in the present designs is to demonstrate and
investigate the feasibility of using adhesive locomotion
in mechanical designs.
ROBOSNAIL 1
Robosnail 1 was built to explore the possibility that
marine snails and other aquatic creatures such as
flatworms use backwards waving deformations of
the body to generate thrust via forces in a thin layer
of viscous fluid. As the foot of the snail waves over a
MATERIAL SYSTEMS
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STRUCTURES, Vol. 00—Month 200?
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DOI: 10.1177/1045389X0?063464
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thin film of Newtonian fluid, it generates a high pressure
near the ground where fluid is squeezed into a narrow
gap and a low pressure where the fluid is pulled apart.
The pressure forces acting on the sloped areas of the
sinusoidal foot act to propel the snail. This means of
locomotion bears considerable similarity to peristaltic
pumping of fluids through flexible channels (Childress,
1997; Ajdari and Stone, 1999; Dobrolyubov and
Douchy, 2002). The primary difference is that the
force applied by the boundary and transmitted through
the fluid to the substrate is used to move both the
boundary and the fluid, rather than being used to pump
the fluid alone.
Robosnail 1 has a solid polycarbonate body
(Figure 2) with a total weight force of 1.67 N. Its foot
is powered by an external DC power source, capable of
Rim
Interwave
Wave
1 cm
Figure 1. Underside of Leopard slug Limax maximus during
locomotion showing wave and interwave segments. Here, waves
propagate in the direction of locomotion.
AL.
supplying 1.5, 3.0, and 4.5 V. The motor is connected
to a variable-speed gearbox. A toothed pulley connects
the gearbox to a shallow brass helix which passes
through an array of aluminum sheets perforated with
slots. Each of the sheet is constrained to vertical motion
as they ride in equally spaced slots along the body.
The bottom edges of the sheets are glued onto a flexible
foam sheet. When the helix is spun by the motor and
gearbox, it causes the plates to translate up and down
inside their tracks in a moving sinusoidal wave
(evident when viewed from the side). The wave is
transferred directly to the foam sheet. This sinusoidal
wave generates regions of high pressure in front of
the wave, where the fluid is squeezed into a narrow
gap, and regions of low pressure behind the wave
where the fluid is allowed to expand. These pressures
in turn generate forces normal to the interface,
driving the snail in the opposite direction of the wave
(reminiscent of the retrograde waves observed in marine
snails).
To test the efficacy of this mechanism, a track slightly
larger than the width of the snail, to minimize the
leakage of fluid past the open sides of the foot, was
constructed. A laser, fitted with a lens to emit a plane of
light, was fixed at an angle of 45 degrees with respect
to the bottom of the clear channel. The line of the laser
hitting the foam sole, seen from the underside, reflects
the height of the wave relative to the bottom of the
channel, and the profile of the film thickness becomes
clearly visible from below. The track was filled with
0.5 mm thick layer of glycerol and the Robosnail was
activated on top of the layer. After the motion
reached steady state, measurements of wave speed,
foot height (revealed by the laser), and snail speed
were recorded. Robosnail 1 was tested using four
varying wave speeds and as expected, the direction
DC motor
Planetary
gearbox
Pulleys
and belt
Aluminum sheets
Foam rubber
sole
Helix
Motor mount
Figure 2. Exploded view of Robosnail 1.
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Mechanical Devices for Snail-like Locomotion
of motion was found to be opposite to the direction of
wave propagation.
Performing a two-dimensional lubrication analysis
on the thin film of Newtonian fluid (Chan et al., 2005),
we predict that, for a sinusoidal wave, the velocity of the
snail scales linearly with wave speed1:
vs
3ða=h0 Þ2
¼
vw 1 þ 2ða=h0 Þ2
where vs is the velocity of the snail, vw is the velocity
of the wave, h0 is the average height of the fluid layer,
and a is the amplitude of the waving foot. Here, the
snail velocity and waving amplitude are made nondimensional by dividing by vw and h0 respectively.
The correct scaling for the snail velocity was observed
experimentally (Figure 3), however, the coefficient
was considerably smaller than the value predicted by
the analytical solution, i.e., the best fit to the data
corresponds to a larger gap (a/h0 ¼ 0.5) than was
measured in the experiment (a/h0 1). This discrepancy
is most likely due to the leakage of fluid from the side
of the finite-width robot, which reduces the effectiveness
of the propulsion mechanism.
ROBOSNAIL 2
Robosnail 2 was built to mimic the direct wave
motion of land snails. The bottom interwave area of a
snail’s foot is adhered to the substrate via the fluid layer
while an in-plane traveling wave of compression causes
a small net translation as it propagates from one end of
the foot to the other.
Unlike real snails, the foot of Robosnail 2 is made
of five discrete, sliding sections, while live snails have a
continuous foot of muscle. Each of the five foot sections
of Robosnail 2 move forward by a small fixed amount
in relation to the body, after which they all return to
their original positions. These small motions occur
in sequence as illustrated in Figure 4. Rheological
properties of the interstitial fluid play a key role in the
propulsion mechanism of Robosnail 2. As each wave
propagates forward, the interwave areas must adhere
to the substrate to prevent the snail from slipping
backwards. Conversely, the moving portion of the foot
must be allowed to slide freely forwards. This is only
possible if the interstitial fluid possesses a finite yield
stress. In the interwave regions, the fluid is unstressed
and acts as a solid gluing the foot to the substrate; in
the wave regions, the snail must provide sufficient stress
to induce the non-Newtonian fluid to yield a lubricating
layer for the wave.
1
The snail velocity scales linearly with the wave speed regardless of the
shape of the foot. However, the coefficient is a function of the wave shape
(Chan et al., 2005).
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Instead of mucus as a lubricating layer, Laponite
was used, chosen for its pronounced shear thinning
effects (Laponite Synthetic Layered Silicate-its
Chemistry, Structure, and Relationship to Natural
Clays; Willenbacher, 1996), finite yield stress and
availability. Though the mechanical properties of
Laponite and snail mucus are quantitatively different,
both exhibit the finite yield stress: i.e., the stress at zero
shear-rate is nonzero. This quality is what allows snails
(and Robosnail 2) to adhere to walls while moving.
In order that the snail propels itself forward, the force
provided by the viscous shear of the moving segment
must balance (or be exceeded by) the force sustained by
the stationary foot segments. When the speed of the
moving foot section is small such that the viscous stress
is much less than the yield stress, one can approximate
the stress underneath the shearing Laponite by the
yield stress value of about 100 Pa, and the force on the
moving part of the foot to be the product of the area
of the moving section and the yield stress, allowing us to
determine the required actuation force.
Robosnail 2 was designed to mimic the vertical
wall-climbing ability of adhesive locomotion using a
finite-yield stress fluid. For wall-climbing to be possible,
the force per unit area of stationary foot area must
be less than the yield stress of Laponite. In vertical
wall-climbing, this force is dominated by the weight
of the snail. Since the yield stress of Laponite is only
about 100 Pa, reducing the weight of the robot presented
a serious challenge in the design of the crawler. To save
weight, Robosnail 2 is actuated using five 10 cm lengths
of Nitinol shape-memory alloy wire (Gilbertson, 2000)
rather than electric motors. The finished prototype
weighed 0.31 N. The five Nitinol wires are attached to
nylon cords wrapped 180 degrees around a pulley and
tied to five sheets of polycarbonate (Figure 5). Each of
the sheets is attached to a pair of guides that allow only
fore–aft translation. A leaf spring held by the main body
returns each of the sheets to its original position when
there is no other force. The springs apply the restoring
forces necessary to return the wires to their original
outstretched positions. The wires are crimped in loops at
the ends, one end is tied to the cords controlling the foot,
and the other end of each wire is looped around
adjustable brass fasteners to allow proper tightening
of the wire and cords. It was important for the wires to
be correctly tensioned such that the springs succeed in
re-stretching the wires, but not so tight as to limit the
motion of the muscle wires. The tightness adjustment is
achieved by turning the screws through which the wire
mounts are threaded.
To test the wall climbing ability of Robosnail 2, we
mounted it on a tiltable platform covered in a 1.5 mm
thick layer of Laponite. The bulk of the Laponite was
observed to hold its form as a fixed layer on the
platform as the robot slid along. This observation
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1
0.9
0.9
0.8
0.8
0.7
0.7
Vsnail , cm/s
1
0.6
VX/VW
AL.
0.5
0.4
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
Data
Best fit
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
a/h0
0.2
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0.9
1
Vwave , cm/s
Figure 3. (Left) Analytical solution for an infinite waving sheet, and (Right) experimental results. The best fit of the linear coefficient in the
experimental data corresponded to a value of a/h0 ¼ 0.5.
Figure 4. Action sequence of Robosnail 2 foot segments. Black segments represent interwave or stationary areas; grey segments indicate wave
areas of propagation. In the final frame, the body shifts forward relieving the tension in the leaf springs.
Tensioning screw
Nitinol shape memory alloy 'muscle wires'
Guide rail
Foot segments
Return spring
Nylon string
Foam rubber sole
Figure 5. Exploded view of Robosnail 2.
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0.7
0.6
d/∆L per cycle
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100 120 140 160
180
Incline (°)
Figure 6. Testing the inverted locomotion capability of Robosnail 2 and displacement per cycle graph of Robosnail 2.
suggests that only a small layer of the Laponite touching
the foot segment yielded into liquid form, while the rest
remained solid. For each angular increment, Robosnail
2 was activated for twenty complete cycles and the
total displacement was recorded. Robosnail 2 was able
to climb the Laponite-coated surface tilted at any angle,
including both a vertical and fully inverted position
(Figure 6).
The snail displacement has been made nondimensional by dividing it by the step length L. The
experiment showed that the motion per cycle is in all
cases slightly less than the translation of one foot.
Ideally the slip velocity should be zero and the snail
displacement per cycle d should be L (i.e., along
the line d/L ¼ 1 in Figure 6). The slipping effect of
the stationary sections can be explained by several
phenomena: neither the Laponite layer nor the foam
rubber of Robosnail’s foot sections was perfectly flat,
therefore if the moving section hits a lump or other
imperfection in the Laponite, the local stress would
exceed the yield stress. Another cause for slippage is that
the Laponite under the stationary sections may not have
had enough time to re-solidify. This last problem can be
remedied by increasing the time of each cycle, to allow
the Laponite to re-solidify at the expense of slowing
down the translational speed of the snail. Finally, it was
observed that there was de-lamination of the Laponite
layer from the segments of the foot, decreasing the
traction of the stationary foot segments. The most slip
occurs between 60 and about 120 , when the high angle
of tilt decreased the normal force of the robot’s weight
and thus the traction. At high tilt, much of the adhesive
force of the Laponite supports both the weight of the
snail and the viscous resistance of the moving foot
section, while at near-flat angles near 0 and 180 , the
adhesive force primarily resists the friction on the
moving foot. We should expect a minimum displacement somewhere between 90 and 180 , where gravity
works to decrease traction and to increase the resistive
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force of the weight; this is indeed supported by the
data. Though there was some slipping at all angles of
incline, Robosnail 2 was able to consistently propel itself
forward at all inclined angles.
CONCLUSIONS
The results of these experiments confirm the feasibility
of snail-like motion for small machines, and introduce
a new type of application for unconventional actuators
for robots and related machines. Although the actual
speeds of the devices did not reach the values predicted
by theory, the fundamental concept is proven by the
motion of the devices. Furthermore, there is room for
more work in improving efficiency and optimization
of both mechanisms. Future studies will adapt the
mechanisms to handle rigorous experimentation and
introduce new synthetic working fluids.
ACKNOWLEDGMENTS
This research was partially funded by the National
Science Foundation and Schlumberger-Doll Research.
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