Figure 3.

The path of the left wing-tip for one hummingbird flap from (a) lateral, (b) rear and (c) overhead viewpoints. The shoulder position is indicated with an orange square and the path of the wing-tip is shown by the heavy black line. The cyan line shows the tip path if the humeral long-axis rotation angle ϕ is held constant at its mid-downstroke value throughout the flap but humeral rotation angle θ and all other kinematic chain angles allowed to vary. The magenta line shows the wing-tip path if humeral rotation angle θ is held constant but all other angles, including humeral long-axis rotation angle ϕ are allowed to vary. See electronic supplementary material, movies S1–S3 for an animation of the wing movement without contributions from all measured joints.