Three-dimensional hind limb kinematics of a sidestep maneuver to the right. (A) Four frames of X-ray video showing the bird performing a split (1–2), shifting on two legs (2–3) and converging (3–4). (B) Plots of pelvic yaw (blue), pitch (green) and roll (red) as well as flexion/extension (FE, blue), abduction/adduction (ABAD, green) and long-axis rotation (LAR, red) angles of the hip, knee and ankle joints for the right (solid) and left (dotted) limbs versus time. Numbered arrows show the timing of the four X-ray frames pictured in A. (C) Pelvic translations along the craniocaudal (red), right–left (green) and vertical (blue) axes relative to the starting position. The 12.5 cm shift to the right is the dominant movement as seen in Fig. 1A. (D) LAR angles of the right (solid) and left (dotted) hips tightly correlate with transverse distance between the feet (E, inset; also see Fig. 11B). During the split phase, the right, leading foot is lifted and both femora rotate internally, spreading the feet. In double support the left hip continues to internally rotate while the right rotates externally to shift the body. During the converge phase, the left, trailing foot is lifted and bilateral external LAR brings the feet back together.

Bilateral hip and knee LAR of yaws and turns to the right. (A) A sidestep yaw of 84 deg entails significant LAR of the femora and tibiotarsi, which counter-rotate to spread, converge and reorient the feet as in Fig. 1B. (B) Reversing the sequence of hip and knee LAR results in both feet passing the midline in a crossover yaw of 38 deg as in Fig. 1C. (C) A sidestep turn reorients the pelvis 73 deg while laterally displacing the pelvis 5 cm as in Fig. 1D. Almost 120 deg of total foot yaw is associated with external knee LAR. (D) A crossover turn with 78 deg of yaw and 5 cm of lateral displacement as in Fig. 1E is dominated by internal knee LAR. At the top of the figure, caudal views (yaw removed) of the sidestep and crossover yaws demonstrate the spreading and converging of the feet (A,B) at the four times indicated by arrows. Pairs of digital axis angles at the three time points indicated by the arrows for the sidestep and crossover turns are given in C and D (see Fig. 11B).

Bilateral hip and knee LAR during a complex maneuvering sequence. (A) Plot of pelvic yaw. Overhead views show poses at the time points indicated by the arrows. (B) Plots of hip and knee LAR for right (solid) and left (dotted) limbs demonstrate that multiple maneuvers are strung together in series during the course of the trial. The left knee rotates through more than 65 deg over the sequence. (C) Transverse distances vary dramatically over the course of the maneuver as split, shift and crossover components are freely mixed. Gray boxes highlight specific coordination patterns discussed in Results.

A sample of non-planar limb poses. Cranial views of limbs deviating widely from parasagittal. Right and left limbs move symmetrically or asymmetrically as the situation requires. However awkward and unlikely looking, all were freely performed by the maneuvering birds.

LAR at similar FE angles within the same sequence. (A) Craniolateral view of the left femur relative to a fixed pelvis at two different hip LAR angles (−10 deg, 15 deg) for the same FE angle (42 deg). (B) Cranial view of the left tibiotarsus relative to a fixed femur at two different knee LAR angles (0 deg, 37 deg) for the same FE angle (79 deg). (C) Proximal articular view of the knee in the same poses as in B.

Ranges of observed joint angles. For each joint, the difference between the maximum and minimum values of FE, ABAD and LAR angle were calculated across the six trials figured in this paper. L, left; R, right.

Individual and combined consequences of LAR. (A) Cranial view of a neutral pose. (B) Internal hip LAR (orange) moves the right foot laterally while external hip LAR (purple) moves the foot medially. (C) External knee LAR (orange) moves the right foot laterally and toes out while internal knee LAR (purple) moves the foot medially and toes in. (D) Internal hip LAR and external knee LAR (orange) are additive, as are external hip LAR and internal knee LAR (purple). (E) Combining internal (orange) and external (purple) LARs generates a range of digital axis angles at a similar toe position.

Marker-based XROMM using carbide points. (A–C) Three steps in the fabrication of a conical marker from a stock rod. (D) The thinned blade is strong enough to allow manual insertion, but weak enough for the tip to snap off when bent. (E) Planar X-ray of points implanted into the proximal and distal femur. (F) Implant sites shown by polygonal marker models (red) within their respective bone models.

Experimental setup reconstructed as a Maya scene. (A) Top view of the maneuvering chamber representing the two X-ray systems as a pair of virtual X-ray cameras with overlapping yellow and blue beams. Two calibrated standard cameras (red and green fields of view) provide external imaging of the whole bird and feet. (B) Perspective view of the scene showing the reconstructed skeletal model in place between the four image planes textured with frames of video. (C–F) When viewed through each virtual camera, bone models are registered to their X-ray shadows as well as to the standard video images.

Quantifying 3D skeletal motion. (A) Semi-transparent anterolateral view of the pelvis and hind limbs showing the anatomical coordinate system (ACS)-based joint coordinate systems (JCSs) by which FE (blue axes), ABAD (green axes) and LAR (red axes) rotations were measured at the hips, knees and ankles. (B) Top view showing how the position and orientation of the tarsometatarsus were measured relative to a median sagittal plane (thin vertical line bisecting the pelvis). Transverse distances for each foot (positive laterally) were summed to measure spreading of the feet (thick double-headed arrow). Virtual digital axes extending forward from the condyle of digit III were calculated at the intersection of each tarsometatarsal sagittal plane (magenta) with horizontal (light gray). Digital axis angle measured the toe out (positive) or toe in (negative) deviation of each digital axis from a sagittal plane.

ACS conventions for each bone. (A) Craniolateral and lateral views of the pelvic ACS. (B) Craniolateral view of the pelvis showing acetabular ACSs for the right and left hip. (C) Craniolateral and dorsal views of the right femur demonstrating the proximal and distal femoral ACSs. (D) Craniolateral and lateral views of the right tibiotarsus showing the proximal and distal ACSs. (E) Craniolateral and lateral views of the right tarsometatarsus with proximal and distal ACSs.