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Robosnail 1 Snail-Inspired Fluid Locomotion. Brian Chan, M.S Theresa Guo, undergraduate researcher Advisors: Anette Hosoi, Julio Guerrero (SLB) Hatsopolous Microfluids Laboratory Department of Mechanical Engineering Massachusetts Institute of Technology Schlumberger - Doll Research, SDR. - PowerPoint PPT Presentation
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Robosnail 1 Snail-Inspired Fluid Locomotion
Brian Chan, M.STheresa Guo, undergraduate researcherAdvisors: Anette Hosoi, Julio Guerrero (SLB)
Hatsopolous Microfluids LaboratoryDepartment of Mechanical EngineeringMassachusetts Institute of Technology
Schlumberger - Doll Research, SDR
Contents:
Snail locomotion Type 1 Robosnails
Theory Simulations
Robosnail 1A Design Experiment
Robosnail 1B Design Experiment
Robosnail 1C In progress
Conclusions
Robosnail 1A
Robosnail 1B
MotivationTo evaluate the feasibility of using
snail-like locomotion, and to optimize the performance of mechanical Robosnails.
Advantages of snail locomotion: can be configured as a versatile
flexible robot A sealed Robosnail mechanism
can be robust in muddy conditions
Effective locomotion for environments with little or no traction
Snail Locomotion basics
- All snails are separated from the substrate by a fluid layer (mucus)- Locomotive forces must be transferred through this layer to the
substrate- Snails, equipped with a single flexible foot must find a way to generate
fluid forces parallel to the substrate.
Classifying Snail locomotion:
Direct waves/Retrograde waves (Denny 1989)
Direct waves: waves of compression (used by most land snails)
Retrograde waves: waves of expansion (used by most aquatic snails) – also possible flapping motion …
Limax maximus (moving with direct waves)
Robosnail 1: Design using Retrograde Waves(Joint SLB/MIT U.S. Patent Pending)
Driving a flexible waving membrane with a motor
Governing physics:Analysis of thin fluid layers: Lubrication Theory
Assumptions: Height scale much smaller
than length scale pressure varies only in the x
direction Inertia effects negligible
The lubrication equation:
(slight modifications for non-Newtonian fluids)
Conservation of momentum
Robosnail 1: Theory - Physical mechanism
Using lubrication pressures for propulsion
Pressure under a sinusoidal flapping membrane (1 wavelength):
Immediately before the wave trough, fluid is being compressed (high pressure),
Behind the wave trough, fluid is being pulled apart (low pressure)
Pressure acting on sloped surface creates a propulsive force.
x – velocity profile
Volume flux Q:
Pressure p:
From conservation of momentum and mass we find velocity
Robosnail 1: 2D Theory
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Robosnail 1: 2D Theory
Steady- state horizontal force balance: horizontal component of pressure force and shear stress at membrane balances tractoring force
sxpxx FFF ,,
dxdy
dudx
dx
dhpF
h
LL
x 00
Robosnail 1: 2D Theory
We derive a simple linear tractoring force – velocity function, which resembles a motor torque-speed curve.
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where
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Robosnail 1: Full 3D TheoryFor real Robosnails, we always experience side leakage, hence losses. By
analyzing a differential control volume, we can derive a 3D lubrication equation.
hph 123
Where p is pressure, h is height, and η is viscosity.
Robosnail 1: Full 3D TheoryDeriving a force-speed relationship
[A]: stalled robosnail [B] pure shearing force
In 3D, the force-velocity relationship is still linear
dxh
vFL
sB 0
1dxdz
dudx
dx
dhpF
L
hz
L
A
00
BAt FFF
Robosnail 1: 3D SimulationsNumerical solutions for the pressure show the losses due to leakage; we can
integrate pressure to solve for the tractoring force (maximum, stalled)
Robosnail 1: 3D SimulationsSinusoidal foot profile:
Comparing the tractoring force of 3D Robosnails to the ideal 2D case:
As we expect, the wider the foot, the closer it behaves like the 2D snail.
Robosnail 1A: Experiment
Robosnail 1A: Results: Free velocity
Fluid: glycerol
b/l = 0.6
Robosnail 1A: Results: Stall Force
Fluid: Silicone oil
b/l = 0.6
Strain gauge
Robosnail 1A: Results: Force-velocity
Fluid: Silicone oil
b/l = 0.6
By varying the payload m and the waving velocity vw, we measure different values of vs
Robosnail 1B: Apparatus
- Periodic foot design to eliminate entrance/exit anomalies.
- Replaceable tracks define the height profile.
Robosnail 1B: Apparatus
Core mechanism:
Various replaceable tracks:
Robosnail 1B: Experiment
Robosnail 1B: Results: Free Velocity (Sinusoidal foot)
RS-1B performs better than the 3d solution (due to partial sealing effect of the tank walls) but understandably still not as well as the 2D solution.
Robosnail 1C: Faster-than-wave locomotion
Snail speed is a function of wave shape. For some non-sinusoidal wave shapes we can predict Vs/Vw >1.
That is, a Robosnail that moves faster than it ‘steps’!
We replace the sinusoidal foot with a foot composed of two parabolas, varying the size ratios:
Conclusions
- Lubrication theory predicts a linear force and velocity relationship for both 2D and 3D Robosnails.
- Analytic solutions exist for the 2D case for any given wave height function.
- Numerical simulations give a similar linear force-velocity relation for 3D snails, but with losses dependent on the ratio of snail width to length.
- We have experimental data for sinusoidal wave Robosnails that confirms the numerical results.
- In theory, certain wave shapes exhibit regimes where the snail speed is faster than the wave speed; future experiments will test this theory.
Appendix: 2D theory (detail)
To more easily analyze the fluid flow in the lubrication layer we switch to a reference frame following the waves.
In the new reference frame, Q = constant.
h
ws
h
zvh
zzv
hzz
dx
dpdzuQ
0
223
0 2232
1
hvv
hdx
dpw
s
212
1 3
03322 *
112
*
1
2
12pdx
ha
QLdx
hv
v
a
Lxp w
s
ws vh
zvhzz
dx
dpu
1
2
1 2
Appendix: Dimensionless variables
Experimental constants:L wavelengthμ viscosityh0 average fluid thicknessvw waving velocity
Dimensional variables:x* x-positionb* half-width of footp* pressureh* heighta* foot amplitudevs* snail velocityFx* tractoring force
Dimensionless variablesx = x*/Lb = b*/L
p = *
*
Lbv
ph
w
h = h*/h0
a = a*/h0
vs= vs*/ vw
Fx=w
x
v
hF
**
Acknowledgements
National Science Foundation
Schlumberger Limited
References
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