Figure 1.

Hummingbird kinematic markers and methods: (a) and (b) show original X-ray video images of the hummingbird from an overhead and lateral view, respectively. Arrows indicate the location of the different platinum markers; orange arrows point to the three body markers, green indicate the left wing shoulder markers, red the elbow markers, dark blue the manus markers and yellow the manus tip marker. The right wing markers are not indicated. (c) Planar view of the left wing and indicates the location of the different wing markers as follows: the filled diamond lies on the distal leading edge, the filled circle at the wing-tip, the open square at the tip of the fourth primary, the open diamond at the tip of the first secondary and the open circle at the tip of the fourth secondary. (d) Kinematic chain segments and joints used to model the movements of the hummingbird wing skeleton and their rotations, θ (spherical rotation), ϕ (long-axis rotation) and ω (polar rotation). The shoulder and wrist joints have three degrees of freedom while the elbow has one. (e) Calculation of angle α, the local supination angle of the wing. p1 is a trailing edge wing marker, p2 the nearest point on the leading edge of the wing, and X′ lies perpendicular to gravity and parallel to the projection of p1–p2 in the horizontal plane. (f) Calculation of angle γ, the angle between the long axis of the humerus and the leading edge of the wing.