Figure 1.
Modifications to the bat hindlimb skeleton.
Posterior view of the pelvis and left femur in (A) a bat and (B) a tree shrew, illustrative of the ancestral condition for bats. The arrow indicates the orientation of the acetabulum. The arc indicates the angle between the acetabulum and the shaft of the femur. Modified from [4].
Figure 2.
The hindlimb serves as a boundary condition for the wing membrane.
(A) Posterior view of Rousettus aegyptiacus (Family: Pteropodidae) in flight; flight kinematics in this species are similar to those of Cynopterus brachyotis [14]. A plane transects the wing membrane adjacent to the body, femur, and tibia. The wing profile approximates the geometry of these elements where they directly support the skin. (B) A perspective-corrected wing profile view. The orange circle indicates the left hip location. Photo courtesy of Brock Fenton.
Figure 3.
Illustration of the eight anatomical markers used in this study and the parameters measured.
The orange circle indicates the left hip marker location. (A) Lateral view from late upstroke. F/E (blue) indicates the amplitude of flexion/extension of the ankle marker in the parasagittal (xz-) plane. (B) Posterior view from early downstroke. Inset, below: magnified view of the wing membrane trailing edge attaching at the ankle. θ (magenta) indicates the angle of the trailing edge at the ankle relative to the y-axis, in the transverse (yz-) plane.
Figure 4.
Ankle position was variable among wingbeats.
Variation in ankle motion amplitude and path. Letters α-ε each represent a separate wingbeat. The wingbeats are assigned alphabetically from greatest to smallest dorsoventral amplitude. (A) Angular amplitude of the ankle relative to the hip for flexion/extension (F/E) and abduction/adduction (Ab/Ad), separated by individual. A given letter within an individual is for a single wingbeat, across the F/E and Ab/Ad columns. When letters overlap, they are slightly offset along the horizontal axis. (B, C) Ankle motion over the wingbeat cycle, for a single wingbeat from each individual. Wingbeats were selected to convey the full range of kinematic variation. The orange circle indicates the left hip location in the insets, which provide expanded views. (B) Lateral view from late upstroke, (C) posterior view from early downstroke.
Figure 5.
Direction of ankle motion was consistent among wingbeats.
Angular velocity of the ankle with respect to the hip in (A) the parasagittal (xz-) plane, with positive indicating dorsal extension, and (B) the frontal (xy-) plane, with positive indicating abduction. Solid line is median; aqua shaded envelope is bounded by the first and third quartiles over N = 5 individuals, 25 wingbeat cycles. Downstroke is shaded in gray.
Figure 6.
Wing membrane tension varied in a consistent pattern among wingbeats.
Proxies for magnitude and orientation of forcing of the ankle by the wing membrane through the wingbeat cycle. (A) Length of the trailing edge normalized by maximum length, a proxy for the magnitude of force. (B) Projected on the transverse (yz-) plane, angle of the trailing edge at the ankle relative to the y-axis (θ), a proxy for the direction of force. Solid line is median; aqua shaded envelope is bounded by the first and third quartiles over N = 4 individuals, 17 wingbeat cycles. Downstroke is shaded in gray.
Figure 7.
Ankle motion consistently resisted wing membrane tension.
Left ankle motion and approximate wing membrane tension through one wingbeat cycle in the transverse (yz-) plane (view as in Fig. 3B). Filled markers indicate movement during downstroke; open markers indicate movement during upstroke. Blue arrows indicate direction and approximate magnitude of wing membrane tension on the ankle, at 10% intervals across the wingbeat cycle. Black arrows indicate direction of ankle motion. Orange circle indicates location of left hip. Data is from individual 4, wingbeat β.