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Figures
- Fig. 1.
Schematic view of a frog jump. (A) Top view showing bones in the horizontal plane with rotation axes (φ) oriented vertically resulting in horizontal jumps (ψ=0). (B) Side view showing bones in the sagittal plane with rotation axes oriented horizontally to produce a vertical jump (ψ=90). (C) Three-dimensional view showing rotation axes at 45 deg within a hypothetical ‘extension plane’ (white box) within which the bones rotate to determine the inclination of the take-off angle. Extension of the joints in this configuration results in both forward (Vthrust) and upward velocity (Velevation). (D) Rear view showing how joint rotation axes need not be tied to the extension plane. For example, the ankle orientation can shift to a different orientation (blue lines) independent of the orientation of the knee. Note that A and B are extreme cases for illustrative purposes only and are not actually observed in frog jumping.
- Fig. 2.
Box and whisker plot showing the interquartile range (IQR; grey box) and median (white line) of jump angle data for n=50 trials pooled over four animals (different colours). Low jumps (squares) fall below the median whereas high jumps (triangles) are above 1.5×IQR. The remaining represent intermediate jumps (circles).
- Fig. 3.
Three-dimensional leg kinematics from an example jump. (A) Three-dimensional view and rear view (inset) schematic showing kinematics from five key frames of an example jump. The black spheres are skin marker landmarks for the right leg and body (red), mirrored for the left (grey). Subsequent frames show right leg only, offset in space for clarity. Shaded areas are hip and ankle ‘3D extension angles’ with their respective rotation axes (blue lines), similarly labelled for the rear view (inset). For illustration, axes lengths are scaled to snout–vent length. The knee axis (dashed) is omitted from the 3D view for clarity. Note the reorientation of rotation axes as they align at the final frame. (B) Three-dimensional angles for sacroiliac (SI; green), hip (black), knee (red), ankle (blue) and TMT (orange) from the example trial in A. Note that the sacroiliac joint is not depicted in the illustrations, but is represented as a rotation axis in the horizontal plane (green, dashed line).
- Fig. 4.
Translational and rotational COM velocity (see Materials and methods). Resultant (black), horizontal (red) and vertical (grey) translational velocity components are shown for low (A), intermediate (B) and high angle jumps (C), and similarly for rotational velocity (D–F), where positive versus negative values indicate pitching upwards versus downwards, respectively. Time is relative to contact time (tc; see Materials and methods). Data are means±s.d. for n=50 trials pooled over four animals.
- Fig. 5.
Leg segment kinematics across a range of jump angles. Limb segment protraction–retraction angles for the low, intermediate and high angle jumps (A–C, respectively) and abduction–adduction angles (D–F, respectively). Traces are for thigh (black), shank (red) and proximal foot (blue). The black dashed line (A–C) represents a line drawn posterior from the hip joint from which protraction–retraction angles were referenced (see Fig. 1). Trending towards the line (arrows) denotes retraction. The x-axis (D–F) represents the horizontal axis. Downward slopes indicate adduction. Time is relative to contact time (tc; see Materials and methods). Data are means±s.d. for n=50 trials pooled over four animals.
- Fig. 6.
Joint rotation axis orientations across a range of jump angles. Orientations of hip (black), knee (red) and ankle (blue) axes of rotation for low (A), intermediate (B) and high angle jumps (C). Angles are drawn with respect to the horizontal plane such that 0 deg is horizontal and 90 deg is vertical, indicating pure adduction/abduction or retraction/protraction, respectively. Time is relative to contact time (tc; see Materials and methods). Data are means±s.d. for n=50 trials pooled over four animals.
- Fig. 7.
Inverse kinematics (IK) predictions based on an average intermediate angle jump. Radial plots show the hypothetical influences of hip (black), knee (red) and ankle (blue) 3D extension on instantaneous body velocity angle (ψ) for (A) 0% time and (B) 80% time. The blue-to-red gradient indicates positive-to-negative contributions. The dashed line indicates 0. Note the negative values for the hip at time 80% – i.e. hypothetically, the hip would be required to flex to reorient the limb to angles greater than ∼45 deg. (C) Influence of knee axis orientation on body rotational velocity (dψ/dt) through time. The black line indicates the mean knee axis orientation for intermediate angle jumps. Note the increase in dψ/dt as the knee rotation axis orientation decreases.
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