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First published online November 14, 2008
Journal of Experimental Biology 211, 3744-3749 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.023416
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Compass gait mechanics account for top walking speeds in ducks and humans

James R. Usherwood*, Katie L. Szymanek and Monica A. Daley

Structure and Motion Laboratory, The Royal Veterinary College, North Mymms, Hatfield, Hertfordshire AL9 7TA, UK


Figure 1
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Fig. 1. Energy recoveries (ERs) for Aylesbury (red), Mallard (blue) and Indian Runner (green) ducks including (B) and excluding (C) the kinetic energy (Ek) associated with lateral motions (the difference is displayed in D). An ER of 1 indicates that changes in potential and kinetic energies of the centre of mass throughout a step has the potential to be completely passive, consistent with inverted-pendulum mechanics. Different symbols indicate different individuals. Vertical broken lines indicate Froude number=0.5 for reference; the horizontal broken line (in B) shows the cut-off used to distinguish between walking and running for Fig. 3.

 

Figure 2
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Fig. 2. Step angle as a function of speed from theoretical compass gait predictions (A), and from forceplate observations of Mallard and Aylesbury ducks, coded by energy recovery (ER) (B). Perfectly passive (ER=1), stiff-limbed compass gait walking constrains both lower (i) and upper (ii) speeds (black area in A); with a small energy input (ER≤Formula), the low-speed constraint is lost (red area); without any passive potential-kinetic energy interchange (ER=0) higher step angles and speeds are possible (blue line) until V=1. Underlying grey curves (in B) indicate the contours associated with step frequencies normalized by the ideal pendular frequency of the swing leg with point mass at the foot. Ducks walk (with high ERs, yellows and reds) with near-passive step frequencies and transition to running (low ERs, blues and black) at higher speeds, with higher-than-passive step frequencies.

 

Figure 3
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Fig. 3. Step angle as a function of speed for `walking' ducks [A, determined as having energy recovery (ER)≥0.2] or `running' ducks (B, ER<0.2), and walking and running humans [C, walking in red (N=11 subjects), running in blue (N=5 subjects)], with running at below maximum possible walking speed with grey fills). Ducks are coloured according to breed, with symbols denoting subject, as for Fig. 1. Underlying black and grey lines indicate the compass gait boundary and step frequencies described for Fig. 2. The vertical grey broken line denotes V=0.7 (Fr=0.5), usually identified as the walk–run transition speed for humans. Vertical broken black lines in C mark the range in maximum speeds predicted if humans walked both with passive swing limbs and while constrained by compass gait mechanics. fnat,human indicates the frequency consistent with a passive, pendular swing leg action for humans.

 

Figure 4
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Fig. 4. CoM trajectories (black arrows) for compass gait walking and motions of the effective pendulum length (EPL) (red arrows) for the swing leg for (A) walking ducks assuming the swing leg is passive, and with EPL appropriate for mean observed walking frequencies; (B) a walking human with passive swing leg if the mass distribution were such that the step frequency was that observed at high speeds (f=2; EPL=Lleg/4); (C) a walking human with EPL appropriate for reported mass distributions. Fast human walking cannot be achieved with a passive swing leg.

 

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© The Company of Biologists Ltd 2008