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Research Papers

Passive Aerodynamic Drag Balancing in a Flapping-Wing Robotic Insect

[+] Author and Article Information
P. S. Sreetharan1

School of Engineering and Applied Science, Harvard University, 60 Oxford Street, Cambridge, MA 02138-1903pratheev@post.harvard.edu

R. J. Wood

School of Engineering and Applied Science, Harvard University, 60 Oxford Street, Cambridge, MA 02138-1903

1

Corresponding author.

J. Mech. Des 132(5), 051006 (May 03, 2010) (11 pages) doi:10.1115/1.4001379 History: Received August 19, 2009; Revised February 02, 2010; Published May 03, 2010

Flapping-wing robotic platforms based on Dipteran insects have demonstrated lift to weight ratios greater than 1, but research into regulating the aerodynamic forces produced by their wings has largely focused on active wing trajectory control. In an alternate approach, a flapping-wing drivetrain design that passively balances aerodynamic drag torques is presented. A discussion of the dynamic properties of this millimeter-scale underactuated planar linkage accompanies an experimental test of an at-scale device. This mechanism introduces a novel strategy for regulating forces and torques from flapping wings, using passive mechanical elements to potentially simplify control systems for mass and power limited flapping-wing robotic platforms.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Kinematic diagram and representative block diagram for the simple HMF transmission

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Figure 2

A simplified automobile drivetrain, analogous to the HMF transmission

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Figure 3

Kinematic diagram and representative block diagram for the PARITy drivetrain

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Figure 4

A classic automobile drivetrain, analogous to the PARITy design, incorporating a transmission and a differential

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Figure 5

PARITy drivetrain with links labeled and various angles and torques indicated. The shaded links are affixed to a mechanical ground or, in a free flying structure, an airframe. Input power is applied to the hatched input platform.

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Figure 6

The torque transmission ratio TR(q1,q2) (normalized to its neutral configuration value of −6.25) plotted as a function of wing angle θwR(q1,q2) for the simulated and constructed PARITy design under the expected operating condition q2⪡1

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Figure 7

Wings affixed to the PARITy drivetrain in a representative MAV. Vertical aerodynamic forces constitute lift while drag forces are perpendicular to the wing. For this experiment, wings remain perpendicular to their direction of motion, implying a fixed angle of attack α=90 deg.

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Figure 8

Theoretical torques τw,dragR and τw,inertialR applied by the right wing in a symmetric system. In shaded regions, |τw,dragR|>|τw,inertialR|.

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Figure 9

Simulated drag torque magnitudes. For both results, the right wing has a torque parameter ΩR=31.3 mg mm2. The left wing drag parameter ΩL has been reduced to (a) 0.599⋅ΩR and (b) 0.420⋅ΩR.

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Figure 10

Solid lines indicate the instantaneous torque discrepancy Δτw,drag between wings over a single cycle when (a) ΩcontrolL=ΩR, (b) Ω1-cutL=0.599⋅ΩR, and (c) Ω2-cutL=0.420⋅ΩR. The dashed lines describe the recovery of the torque imbalance from a 2 rad/s perturbation applied to the balance beam rotational velocity q̇2 at time t=0.

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Figure 11

The experimental test structure

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Figure 12

Images of the left wing membrane as used for each trial, along with the associated planforms used to calculate the drag parameter ΩL using the blade-element model. Units are in millimeters. (a) Control trial, ΩcontrolL=31.3 mg mm2. (b) 1-cut trial, Ω1-cutL=18.8 mg mm2. (c) 2-cut trial, Ω2-cutL=13.2 mg mm2.

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Figure 13

The PARITy drivetrain (a) before and (b) after folding

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Figure 14

Theoretical predictions versus experimental wing trajectories for (a) the control trial, (b) the 1-cut trial, and (c) the 2-cut trial. (d) Experimentally observed left wing velocities, low-pass filtered with an 800 Hz cutoff frequency.

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Figure 15

Image sequence from the 2-cut trial high speed video illustrating increased amplitude of θwL compared with θwR. From left to right, the elapsed time between adjacent images is 1.5 ms. The checkerboard contains 1×1 mm2 squares and is used for scale.

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