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Aeromechanics of passive rotation in flapping flight

Published online by Cambridge University Press:  27 July 2010

J. P. WHITNEY  and
R. J. WOOD
J. P. WHITNEY*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
R. J. WOOD
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
*
†Email address for correspondence: jwhitney@fas.harvard.edu
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Abstract

Flying insects and robots that mimic them flap and rotate (or ‘pitch’) their wings with large angular amplitudes. The reciprocating nature of flapping requires rotation of the wing at the end of each stroke. Insects or flapping-wing robots could achieve this by directly exerting moments about the axis of rotation using auxiliary muscles or actuators. However, completely passive rotational dynamics might be preferred for efficiency purposes, or, in the case of a robot, decreased mechanical complexity and reduced system mass. Herein, the detailed equations of motion are derived for wing rotational dynamics, and a blade-element model is used to supply aerodynamic force and moment estimates. Passive-rotation flapping experiments with insect-scale mechanically driven artificial wings are conducted to simultaneously measure aerodynamic forces and three-degree-of-freedom kinematics (flapping, rotation and out-of-plane deviation), allowing a detailed evaluation of the blade-element model and the derived equations of motion. Variations in flapping kinematics, wing-beat frequency, stroke amplitude and torsional compliance are made to test the generality of the model. All experiments showed strong agreement with predicted forces and kinematics, without variation or fitting of model parameters.

JFM classification

Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 660 , 10 October 2010 , pp. 197 - 220
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Andersen, A., Pesavento, U. & Wang, Z. J. 2005 Unsteady aerodynamics of fluttering and tumbling plates. J. Fluid Mech. 541, 65–90.CrossRefGoogle Scholar
Bergou, A. J., Xu, S. & Wang, Z. J. 2007 Passive wing pitch reversal in insect flight. J. Fluid Mech. 591, 321–337.CrossRefGoogle Scholar
Bouguet, J.-Y. 2008 Camera Calibration Toolbox for Matlab. Available at: http://www.vision.caltech.edu/bouguetj/calib_doc/.Google Scholar
Daniel, T. L. & Combes, S. A. 2002 Flexing wings and fins: bending by inertial or fluid-dynamic forces? Intgr. Comp. Biol. 42 (5), 1044–1049.CrossRefGoogle ScholarPubMed
Dickinson, M. H., Lehmann, F.-O. & Sane, S. P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954–1960.CrossRefGoogle ScholarPubMed
Dickson, W. B., Straw, A. D., Poelma, C. & Dickinson, M. H. 2006 An integrative model of insect flight control. In Proceedings of the AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV.Google Scholar
Doman, D. B. & Oppenheimer, M. W. 2009 Dynamics and control of a minimally actuated biomimetic vehicle: Part I. Aerodynamic model. In Proceedings of the AIAA Guidance, Navigation, and Control Conference, San Francisco, CA.Google Scholar
Dudley, R. 2000 The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press.CrossRefGoogle Scholar
Ellington, C. P. 1984 The aerodynamics of insect flight. II. Morphological parameters. Phil. Trans. R. Soc. Lond. B 305, 17–40.Google Scholar
Ennos, A. R. 1988 a The importance of torsion in the design of insect wings. J. Exp. Biol. 140, 137–160.CrossRefGoogle Scholar
Ennos, A. R. 1988 b The inertial cause of wing rotation in Diptera. J. Exp. Biol. 140, 161–169.CrossRefGoogle Scholar
Fry, S. N., Sayaman, R. & Dickinson, M. H. 2003 The aerodynamics of free-flight maneuvers in Drosophila. Science 300, 495–498.Google Scholar
Graetzel, C. 2008 MEMS & high speed vision: development and application to reverse-engineer Drosophila flight control. PhD thesis, ETH Zurich.Google Scholar
Graetzel, C. F., Fry, S. N., Beyeler, F., Sun, Y. & Nelson, B. J. 2008 Real-time microforce sensors and high speed vision system for insect flight control analysis. In Experimental Robotics: The 10th International Symposium on Experimental Robotics, p. 451. Springer.CrossRefGoogle Scholar
Lentink, D. & Dickinson, M. H. 2009 Rotational accelerations stabilize leading edge vortices on revolving fly wings. J. Exp. Biol. 212 (16), 2705.CrossRefGoogle ScholarPubMed
Pesavento, U. & Wang, Z. J. 2009 Flapping wing flight can save aerodynamic power compared to steady flight. Phys. Rev. Lett. 103 (11), 118102.CrossRefGoogle ScholarPubMed
Ristroph, L., Berman, G., Bergou, A., Wang, Z. J. & Cohen, I. 2009 Automated hull reconstruction motion tracking (HRMT) applied to sideways maneuvers of free-flying insects. J. Exp. Biol. 212, 1324–1335.CrossRefGoogle ScholarPubMed
Sane, S. P. 2003 The aerodynamics of insect flight. J. Exp. Biol. 206 (23), 4191.CrossRefGoogle ScholarPubMed
Sane, S. P. & Dickinson, M. H. 2002 The aerodynamic effects of wing rotation and a revised quasi-steady model of flapping flight. J. Exp. Biol. 205, 1087–1096.CrossRefGoogle Scholar
Sedov, L. I. 1965 Two-Dimensional Problems in Hydrodynamics and Aerodynamics. Interscience.CrossRefGoogle Scholar
Walker, S. M., Thomas, A. L. R. & Taylor, G. K. 2009 Photogrammetric reconstruction of high-resolution surface topographies and deformable wing kinematics of tethered locusts and free-flying hoverflies. J. R. Soc. Interface 6 (33), 351.CrossRefGoogle ScholarPubMed
Wang, Z. J. 2000 Two-dimensional mechanism for insect hovering. Phys. Rev. Lett. 85 (10).Google Scholar
Wang, Z. J., Birch, J. & Dickinson, M. H. 2004 Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments. J. Exp. Biol. 207, 449.CrossRefGoogle ScholarPubMed
Wood, R. J. 2007 Design, fabrication, and analysis of a 3 DOF, 3 cm flapping-wing MAV. In IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1576–1581.Google Scholar
Wood, R. J. 2008 The first takeoff of a biologically inspired at-scale robotic insect. IEEE Trans. Robot. 24, 341–347.CrossRefGoogle Scholar
Wood, R. J., Cho, K. J. & Hoffman, K. 2009 A novel multi-axis force sensor for microrobotics applications. Smart Mater. Struct. 18, 125002.CrossRefGoogle Scholar
Wood, R. J., Steltz, E. & Fearing, R. S. 2005 Nonlinear performance limits for high energy density piezoelectric bending actuators. In IEEE International Conference on Robotics and Automation, pp. 3633–3640.Google Scholar
Wu, J. H. & Sun, M. 2004 Unsteady aerodynamic forces of a flapping wing. J. Exp. Biol. 207, 1137–1150.CrossRefGoogle ScholarPubMed
Yih, C. S. 1977 Fluid Mechanics: A Concise Introduction to the Theory. West River Press.Google Scholar
Young, J., Walker, S. M., Bomphrey, R. J., Taylor, G. K. & Thomas, A. L. R. 2009 Details of insect wing design and deformation enhance aerodynamic function and flight efficiency. Science 325 (5947), 1549–1552.CrossRefGoogle ScholarPubMed
Zhang, Z. 2000 A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 22 (11), 1330–1334.CrossRefGoogle Scholar