Robosnail 1 Snail-Inspired Fluid Locomotion

2. 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

3. 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

4. Motivation To 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

5. 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.

6. Classifying Snail locomotion: Retrograde waves: waves of expansion (used by most aquatic snails) – also possible flapping motion … Direct waves: waves of compression (used by most land snails) Direct waves/Retrograde waves (Denny 1989) Limax maximus (moving with direct waves)

7. Robosnail 1: Design using Retrograde Waves(Joint SLB/MIT U.S. Patent Pending) Driving a flexible waving membrane with a motor

8. 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

9. 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.

10. Robosnail 1: 2D Theory x – velocity profile Volume fluxQ: Pressurep: From conservation of momentum and mass we find velocity

11. Robosnail 1: 2D Theory Steady- state horizontal force balance: horizontal component of pressure force and shear stress at membrane balances tractoring force

12. Robosnail 1: 2D Theory We derive a simple linear tractoring force – velocity function, which resembles a motor torque-speed curve. where

13. Robosnail 1: Full 3D Theory For real Robosnails, we always experience side leakage, hence losses. By analyzing a differential control volume, we can derive a 3D lubrication equation. Where p is pressure, h is height, and ηis viscosity.

14. Robosnail 1: Full 3D Theory Deriving a force-speed relationship [A]: stalled robosnail [B] pure shearing force In 3D, the force-velocity relationship is still linear

15. Robosnail 1: 3D Simulations Numerical solutions for the pressure show the losses due to leakage; we can integrate pressure to solve for the tractoring force (maximum, stalled)

16. Robosnail 1: 3D Simulations Sinusoidal 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.

17. Robosnail 1A: Experiment

18. Robosnail 1A: Results: Free velocity Fluid: glycerol b/l = 0.6

19. Robosnail 1A: Results: Stall Force Strain gauge Fluid: Silicone oil b/l = 0.6

20. 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

21. Robosnail 1B: Apparatus • Periodic foot design to eliminate entrance/exit anomalies. • Replaceable tracks define the height profile.

22. Robosnail 1B: Apparatus Core mechanism: Various replaceable tracks:

23. Robosnail 1B: Experiment

24. 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.

25. 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:

26. 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.

27. 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.

28. Appendix: Dimensionless variables Experimental constants: Lwavelength μ viscosity h0average fluid thickness vwwaving velocity Dimensional variables: x*x-position b*half-width of foot p*pressure h*height a* foot amplitude vs* snail velocity Fx* tractoring force Dimensionless variables x = x*/L b = b*/L p = h = h*/h0 a = a*/h0 vs= vs*/ vw Fx=

29. Acknowledgements • National Science Foundation • Schlumberger Limited

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