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Hydrodynamics maneuver of a single helical flagellum swimming robot at low-Reynolds condition

  • Hassan Sayyaadi
  • Shahnaz Bahmanyar
Research Paper
  • 72 Downloads

Abstract

Helical swimming robots with a capable propulsion system at low-Reynolds numbers have been proposed for many applications. Although linear propulsion characteristics of swimming robots with a single helical flagellum have been extensively studied, the characteristics of maneuverability have not been completely investigated yet. This study presents a new method for the maneuverability of the helical swimming robot with a single helical flagellum. This mechanism is based on the change in the angle between the helical and body axes. This study shows that a change in the aforementioned angle can enable the swimming robot to have turning maneuvers in clockwise or counterclockwise directions. Moreover, the swimming robot will move in a straight line if the helical and body axes are parallel. To investigate this new method and predict the robot’s behavior at various inclination angles, a hydrodynamics model is used. To validate the hydrodynamics model, an experimental prototype of a macro-size swimming robot with specific inclination angles is fabricated. The results indicate that the helical swimming robot swims on circular trajectories through specific inclination angles between the helical flagellum and the body axis. Moreover, the radius of curvature decreases by increasing the inclination angle. Results of the validated hydrodynamics model indicate that the turning velocity has approximately a constant value at different inclination angles depending on the rotational frequency and geometrical parameters of the swimming robot. Finally, the effects of geometrical parameters of the body and the helical flagellum on the radius of curvature and turning velocity are investigated through the proposed hydrodynamics model. The verified results indicate that the hydrodynamics model provides a viable alternative model to predict the behavior of a helical swimming robot at various inclination angles within a range of design variables. This new method can be introduced as a mechanism for maneuverability of the helical swimming robots with a single helical flagellum and will be able to control the parameters in this type of swimmers for the implementation of predefined missions.

Keywords

Helical swimmer robot Single helical flagellum Hydrodynamics maneuver Flagellum inclination angle 

Abbreviations

dbody

Cylindrical body diameter (mm)

Lbody

Cylindrical body length (mm)

2b

Helical tail diameter (mm)

2hhelix

Helical wave amplitude (mm)

Ltail

Helical tail’s length (mm)

Ltotal

Overall length of swimmer robot (body length + helical tail) (mm)

β

Pitch angle (°)

α

Inclination angle (°)

λ

Helical wave length (mm)

n

Number of wavelengths (−)

W

Total weight (g)

Dmotor

DC-motor diameter (mm)

Lmotor

DC-motor length (mm)

Vmotor

Voltage of motor (V)

volbattery

Volume of battery (m3)

Vbattery

Voltage of battery (V)

ρ

Density of test fluid (Kg/m3)

v

Kinematic viscosity (cSt)

f

Spinal propulsive frequency (Hz)

G

The center of mass \(G=\left({x}_{g},{y}_{g},{z}_{g}\right)\) (mm)

B

The center of buoyancy \(B=\left({x}_{B},{y}_{B},{z}_{B}\right)\)(mm)

\({\overrightarrow{F}}_{\rm helix}\)

Propulsive force in x-direction

\({\overrightarrow{M}}_{\rm helix}\)

Torque resulting from fluid reaction on the helical tail

\({\overrightarrow{F}}_{\rm body}, {\overrightarrow{M}}_{\rm body}\)

Viscous drag and torque acting on the body

\({\overrightarrow{F}}_{\rm e}, {\overrightarrow{M}}_{\rm e}\)

External forces and torques that affect the swimmer

\({df}_{n}, {df}_{t}\)

Hydrodynamic forces acting on a cylindrical element of local length

\({ \xi }_{n}, { \xi }_{t}\)

Local drag coefficient for motion normal and tangential to local length

\({ \upsilon }_{n}, { \upsilon }_{t}\)

Components of local normal and tangential to local length (mm/s)

\({G}_{body}\)

The resistive matrix for the body

\({G}_{helix}\)

The resistive matrix for the helical flagella

\(\varOmega\)

Angular velocity of the swimmer robot in inertial coordinates \({\Omega }=\left(\dot{{\theta }},\dot{{\phi }},\dot{{\Psi }}\right)\) (rad/s)

\(R\)

Radius of curvature (mm)

\(U\)

Planer velocity of swimmer robot \((\text{mm/s})\)

\(v\)

Velocity of the swimmer robot in body-fixed coordinates \(v=\left({v}_{x},{v}_{y},{v}_{z}\right)\) \((\text{mm/s})\)

V

Velocity of the swimmer robot in inertial coordinates \(V=\left({V}_{x},{V}_{y},{V}_{z}\right)\) \((\text{mm/s})\)

Ω

Angular velocity of the swimmer robot in body-fixed coordinates \(\varOmega =\left({\varOmega }_{x},{\varOmega }_{y},{\varOmega }_{z}\right)\)(\(\text{rad/s}\))

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Center of Excellence in Hydrodynamics and Dynamics of Marine VehiclesSharif University of TechnologyTehranIran

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