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First published online May 21, 2007
Journal of Experimental Biology 210, 1897-1911 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.002055

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Low speed maneuvering flight of the rose-breasted cockatoo (Eolophus roseicapillus). I. Kinematic and neuromuscular control of turning

T. L. Hedrick^1,* and A. A. Biewener²

¹ Department of Biology, CB 3280 Coker Hall, University of North Carolina, Chapel Hill, NC 27599-3280, USA
² Concord Field Station, MCZ, Harvard University, Old Causeway Road, Bedford, MA 01730, USA

View larger version (9K): [in this window] [in a new window]   Fig. 1. An overhead view of the maneuvering course showing the position of the video cameras and recording devices. The cockatoo and course are to scale, the shaded region in the middle of the maneuvering course approximates the volume in view from which we were able to acquire 3D kinematics. X, Y, Earth fixed coordinates.

View larger version (26K): [in this window] [in a new window]   Fig. 2. We recorded electromyograms from the pectoralis, supracoracoideus, biceps brachii, and extensor metacarpi radialis muscles, shown here in ventral view along with the proximal portion of the wing. Stars mark implant locations.

View larger version (8K): [in this window] [in a new window]   Fig. 3. (A) The local or anatomic coordinate system XbYbZb along with the roll, pitch and yaw axes. (B) Wing sweep angle (). Note that is positive for forward sweep of both the right and left wings. (C) Wing elevation angle (), which is positive for elevation of both the right and left wings. R, radius.

View larger version (23K): [in this window] [in a new window]   Fig. 4. (A) Body pitch, (B) roll and (C) yaw orientation through five wingbeats of a turn. Wingbeats are numbered across the top of the figure, with wingbeat 0 falling at mid-turn. Downstrokes are shaded gray. Solid lines are the data subject to normal processing, i.e. a 37 Hz low-pass filter. Broken lines were processed with a 4 Hz low-pass filter to show only the inter-wingbeat changes in orientation. Note negative pitch is `beak up' in the body coordinate system we used, thus the inverted axis in A.

View larger version (58K): [in this window] [in a new window]   Fig. 5. Wing angles (see Fig. 3) through five wingbeats of a left turn. (A) Wing elevation angle () and (B) sweep angle () measured at the wrist. (C) Elevation and (D) sweep angle measured at the tip. Both the wrist and tip angles contained right–left asymmetries throughout the wingbeat sequence. Asymmetries in position were most prominent at the stroke transitions and were much reduced by mid-stroke. Measurements made at the wrist typically encompassed a smaller range than measurements made at the tip because wrist flexion allows the tip continues to move ahead and below the bird near the end of downstroke while the wrist slows or even reverses direction.

View larger version (17K): [in this window] [in a new window]   Fig. 6. (A) An overhead view of an example flight through the maneuvering course (see Fig. 1) with numbered wingbeats, showing instantaneous heading at wingbeat 0. The numbered wingbeats correspond to the numbers between sections B and C. (B) Change in heading through time; gray shading indicates downstroke. (C) Rate of change in heading, the derivative of section B with respect to time. Changes in heading occur predominantly during downstroke.

View larger version (9K): [in this window] [in a new window]   Fig. 7. The mean rate of change in heading during a stroke was closely related to the roll angle measured at mid-downstroke. Individual points are the average response of a bird for a given wingbeat number and turn direction; N=59. Although the regression line and equation represent a simple linear regression between the two measurements, the r2 and P values reflect the partial correlation between the two variables, controlling for the temporal non-independence of roll angle as described in Materials and methods. The r2 for the simple linear regression was 0.953 with P<0.00001 and F=1264.

View larger version (43K): [in this window] [in a new window]   Fig. 8. Roll orientation through a left turn. (A) Changes in roll angle through time during a single trial, measured at the wing roots (Roll angle) and at the tail (Tail inclination angle). Roll angle changes both within and among wingbeats, typically reading a local minimum at mid-downstroke as the wings pass through the horizontal plane of the body coordinate system. (B) The power spectrum of the roll angle reveals that changes are largely confined to two frequencies, the bird's wingbeat frequency and a lower frequency encompassing approximately 3 wingbeats. (C) The peak-to-peak amplitude of the changes in roll near wingbeat frequency were approximately 16° and declined as the bird neared the end of the turn. In contrast, the peak-to-peak amplitude of the lower frequency, approximated by the red line in A, was approximately 45°.

View larger version (9K): [in this window] [in a new window]   Fig. 9. The simple physics simulation of a flapping cockatoo shows that asymmetric flapping causes instantaneous changes in roll angle. (A) The wing elevation angles used in the simulation. The amplitude difference of 20° approximates the larger amplitude asymmetries used by the turning cockatoos. (B) The roll angle associated with the asymmetric wing elevation angles. The simulated cockatoo has body and wing masses and moments of inertia identical to those collected from the cockatoos in the study, but flies in a null-gravity environment and generates no aerodynamic forces. Thus, all changes in roll orientation are due to the torque required to flap the wings. The somewhat non-sinusoidal behavior in the roll angle result is due to the passive hinge joint at the wrist. An animation of this simulation is available in supplementary material.

View larger version (16K): [in this window] [in a new window]   Fig. 10. (A) Relationship between instantaneous roll acceleration, measured at the midpoint of the first half of downstroke, and the difference in wrist velocity in the body coordinate system, measured at the same time. (B) Relationship between inter-wingbeat roll acceleration and the difference in world coordinate system wrist velocity at mid-downstroke. Note that the y-axis scale in A is an order of magnitude larger than that in B. In general, within-wingbeat roll accelerations were due to inertial effects and therefore related to movements in the body coordinate system. Inter-wingbeat roll accelerations include an aerodynamic component and therefore should be related to velocities in the world coordinate system. The instantaneous and inter-wingbeat roll accelerations were not correlated with one another, nor were the wrist velocity differences measured in the two coordinate systems.

View larger version (47K): [in this window] [in a new window]   Fig. 11. We observed a number of asymmetries in the wing kinematics of the cockatoos as they navigated the maneuvering course, including but not limited to the following. (A) Asymmetric wrist flexion angles at the start of downstroke, (B) asymmetric wrist angles and wingtip trajectories at the end of downstroke, and (C) asymmetric wing velocity vectors angles at the start of downstroke. These asymmetries all occur in the 3D reconstruction as well as the 2D projections given by the camera, although the camera views do accentuate some asymmetries. However, none of these asymmetries was significantly correlated with changes in heading or roll.

View larger version (41K): [in this window] [in a new window]   Fig. 12. Sample EMG sequence with shaded bars indicating the kinematic downstroke. The pectoralis, biceps and extensor metacarpi radialis were all generally activated approximately 0.025 s prior to the kinematic downstroke; activation in these three muscles ceases at approximately mid-downstroke. The supracoracoideus was typically activated just prior to the end of the kinematic downstroke and ceased activation near the middle of the kinematic upstroke just prior to the beginning of downstroke activation. Note that the right extensor metacarpi radialis recording in this example was from a failed implant.