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RESEARCH PAPERS

# An Investigation Into the Use of Springs and Wing Motions to Minimize the Power Expended by a Pigeon-Sized Mechanical Bird for Steady Flight

[+] Author and Article Information
K. Kurien Issac1

Mechanical Systems Laboratory, Department of Mechanical Engineering,  University of Delaware, Newark, DE 19716issac@me.udel.edu

Sunil K. Agrawal

Mechanical Systems Laboratory, Department of Mechanical Engineering,  University of Delaware, Newark, DE 19716agrawal@me.udel.edu

1

On sabbatical from Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.

J. Mech. Des 129(4), 381-389 (Apr 28, 2006) (9 pages) doi:10.1115/1.2429696 History: Received June 07, 2005; Revised April 28, 2006

## Abstract

In this paper, we investigate the effect of using springs and wing motions to minimize the power required by a mechanical bird to fly. Inertia forces as well as aerodynamic forces on the wing are included. The design takes into account different flight speeds in the range from 0 to $20m∕s$. Four ways in which springs can be attached, are considered. The frequency of wing beat is kept fixed and both flapping and feathering are assumed to be simple harmonic. Constraints are imposed on the maximum power expended by the two actuators of a wing. The results show that introduction of springs increases the power required at lower speeds, marginally reducing the power at higher speeds. In the manner in which they are used here, springs do not appear to be useful to reduce power. However, the optimal solutions obtained without springs indicate that it is possible to develop pigeon-like mechanical birds which can hover and fly steadily up to $20m∕s$.

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## Figures

Figure 3

Force on a strip of the wing

Figure 4

Experimentally measured and theoretically calculated force variations during (a) upstroke and (b) downstroke, for 46° flapping amplitude and 75° feathering amplitude (9)

Figure 5

(a) Lift and drag forces on an airfoil; (b)CL and CD versus α

Figure 1

(a) Bird model in flying posture (facing away from the reader); (b) dimensions of body and wings

Figure 2

(a) Coordinate systems and angles associated with the wing, shown for the left side wing; (b) arrangement of joints and actuators of the wing

Figure 9

Components of feathering power. θ is shown for reference and is not to scale.

Figure 6

Comparison of power with and without wing inertia

Figure 7

Comparison of optimum power obtained without springs and with four combinations of springs. The legend gives the order in which bars are placed. p‐s stands for parallel-serial combination.

Figure 8

Components of flapping power. ϕ is shown for reference and is not to scale.

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