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First published online January 30, 2009
Journal of Experimental Biology 212, 550-565 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.018093
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Exploring the mechanical basis for acceleration: pelvic limb locomotor function during accelerations in racing greyhounds (Canis familiaris)

S. B. Williams1,*, J. R. Usherwood2, K. Jespers2, A. J. Channon2 and A. M. Wilson2

1 Department of Veterinary Preclinical Sciences, Faculty of Veterinary Science, The University of Liverpool, Liverpool, UK
2 Structure and Motion Laboratory, The Royal Veterinary College, North Mymms, Hertfordshire, UK


Figure 1
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  		Fig. 1. Schematic diagram [adapted from Biewener (Biewener, 1989Go)] of effective mechanical advantage (EMA) about the ankle joint. r represents the moment arm of the ankle extensor muscles, whilst R represents the moment arm of the ground reaction force vector (GRFr). Fm is the force exerted by the ankle extensor muscles in order to counteract the force exerted by GRFr. This adaptation specifically illustrates how a high EMA (A) might increase the mechanical advantage for producing vertical GRFs (GRFv); however, a low EMA (B) can increase that for producing horizontal GRFs (GRFhz).

 

Figure 2
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  		Fig. 2. Definitions of joints and joint movement (i.e. flexion and extension) used in this study. The `flexor' aspect of each joint is highlighted by a red arc. MTP, metatarsophalangeal joint.

 

Figure 3
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  		Fig. 3. (A) Stance time, (B) swing time and (C) duty factor for hindlimbs versus mean acceleration within stance. Linear regressions for the lead limb are: stance time, y=0.01x+0.1, R2=0.17, P=0.03; swing time, y=–0.03x+0.35, R2=0.22, P=0.01; duty factor, y=0.04x+0.2, R2=0.51, P<0.0001. Linear regressions for the trailing limb are: stance time, y=0.01x+0.92, R2=0.25, P=0.003; swing time, y=–0.01x+0.32, R2=0.01, P=0.10; duty factor, y=0.03x+0.2, R2=0.39, P<0.0001. Shaded bars indicate the three acceleration groups used to categorise accelerations in Figs 7 and 9.

 

Figure 4
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  		Fig. 4. Patterns of medio-lateral (red), fore–aft (blue) and vertical (green) GRFs (solid line, mean; dotted line, s.d.) for trailing (A) and lead (B) hindlimbs. Data are grouped such that those displayed are for all low (N=11) and high (N=8) acceleration trials.

 

Figure 5
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  		Fig. 5. Horizontal (A) and vertical (B) impulse for lead (green; open symbols) and trailing (blue; filled symbols) hindlimbs versus acceleration. Linear regressions for horizontal impulse are: lead, y=4.08x+0.54, R2=0.64, P<0.0001; trailing, y=4.97x+0.37, R2=0.97, P<0.0001. Regressions for vertical impulse are: lead, y=2.0x–0.84, R2=0.33, P=0.004; trailing, y=1.66x–0.41, R2=0.2, P=0.07. Shaded bars indicate the three acceleration groups used to categorise accelerations in Figs 7 and 9.

 

Figure 6
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  		Fig. 6. Vertical:horizontal (V:H) impulse ratio for lead (green; open symbols) and trailing (blue; filled symbols) hindlimbs. Horizontal line indicates the asymptote around a ratio of 2.

 

Figure 7
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  		Fig. 7. Joint angles (solid line, mean; dotted line, s.d.) normalised to percentage stance for (A) hip, (B) stifle, (C) hock and (D) MTP joints. Data are grouped into low (mean±s.d., 0.9±0.4 m s–2), medium (2.0±0.3 m s–2) and high (3.2±0.6 m s–2) acceleration categories. Red lines represent trailing limbs whilst blue lines show lead limbs. Stick figures indicate the typical greyhound hindlimb posture at the beginning, middle and end of stance for low and high acceleration conditions. Note that y-axes are scaled differently for each joint.

 

Figure 8
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  		Fig. 8. Net change in joint angle versus acceleration for (A) hip, (B) stifle, (C) hock and (D) MTP joint of lead (green; open symbols) and trailing (blue; filled symbols) limbs. Linear regressions for lead limb are as follows: hip, y=2.6x+57.8, R2=0.36, P=0.011; stifle, y=4.1x+16.5, R2=0.63, P<0.0001; hock, y=6.3x+45.8, R2=0.40, P=0.007; MTP, y=3.3x+47.2, R2=0.07, P=0.32. Regressions for trailing limb: hip, y=4.6x+51.3, R2=0.64, P<0.0001; stifle, y=5.56x+14.9, R2=0.69, P<0.0001; hock, y=7.0x+43.1, R2=0.52, P<0.0001; MTP, y=2.7x+48.8, R2=0.03, P=0.42. Shaded bars indicate the three acceleration groups used to categorise accelerations in Figs 7 and 9.

 

Figure 9
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  		Fig. 9. External joint moments (solid line, mean; dotted line, s.d.) normalised to percentage stance for (A) hip, (B) stifle, (C) hock and (D) MTP joints. Data are grouped into low, medium and high acceleration categories. Red lines represent trailing limbs whilst blue lines show lead limbs. For details on groupings, see text or Fig. 7. Note that y-axes are scaled differently for each joint.

 

Figure 10
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  		Fig. 10. Hip (blue), stifle (red), hock (green), MTP (cyan) and total (summed) limb (black) power per kilogram body mass for a representative trial of each condition (A, low acceleration; B, medium acceleration; C, high acceleration).

 

Figure 11
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  		Fig. 11. (A) Net and (B) absolute positive limb work for trailing (blue; filled symbols) and lead (green; open symbols) hindlimbs versus acceleration. Linear regressions for A are: trailing limb, y=1.06x+1.38, R2=0.08, P=0.24; lead, y=2.10x+0.61, R2=0.60, P=0.0001. Regressions for B: trailing limb, y=0.24x+0.59, R2=0.39, P=0.002; lead, y=0.26x+0.72, R2=0.30, P=0.009. Shaded bars indicate the three acceleration groups used to categorise accelerations in Figs 7 and 9.

 

Figure 12
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  		Fig. 12. Net joint work produced per kilogram body mass at (A) hip, (B) stifle, (C) hock and (D) MTP joints versus acceleration for trailing (blue; filled symbols) and lead (green; open symbols) hindlimbs. Linear regressions for lead limbs are: hip, y=3.20x+1.40, R2=0.14, P=0.07; stifle, y=5.48x+1.65, R2=0.28, P=0.007; hock, y=3.27x+1.05, R2=0.41, P=0.001; MTP, y=1.39x+1.77, R2=0.03, P=0.45. Regressions for trailing limbs: hip, y=2.20x+1.54, R2=0.27, P=0.29; stifle, y=1.76x+1.77, R2=0.04, P=0.40; hock, y=0.80x+1.79, R2=0.04, P=0.41; MTP, y=–1.80x+2.10, R2=0.02, P=0.53. Shaded bars indicate the three acceleration groups used to categorise accelerations in Figs 7 and 9.

 

Figure 13
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  		Fig. 13. Absolute positive joint work produced per kilogram body mass at (A) hip, (B) stifle, (C) hock and (D) MTP joints versus acceleration for trailing (blue; filled symbols) and lead (green; open symbols) hindlimbs. Linear regressions for lead limbs are: hip, y=0.10x+0.26, R2=0.22, P=0.025; stifle, y=0.04x+0.008, R2=0.40, P=0.004; hock, y=0.06x+0.29, R2=0.26, P=0.026; MTP, y=0.01x+0.17, R2=0.01, P=0.70. Regressions for trailing limbs: hip, y=0.12x+0.17, R2=0.38, P=0.003; stifle, y=0.05x–0.006, R2=0.30, P=0.01; hock, y=0.06x+0.27, R2=0.19, P=0.046; MTP, y=0.01x+0.16, R2=0.005, P=0.75. Shaded bars indicate the three acceleration groups used to categorise accelerations in Figs 7 and 9.

 

Figure 14
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  		Fig. 14. Hindlimb EMA (A, vertical; B, horizontal) versus acceleration. (A) Linear regressions are: trailing limb (blue), y=–30.5x+13.7, R2=0.53, P=0.001; lead limb (green), y=–16.7x+8.35, R2=0.54, P=<0.0001. (B) Linear regressions: trailing limb, y=–0.02x+0.46, R2=0.22, P=0.003; lead limb, y=–0.02x+0.44, R2=0.53, P=0.001. Shaded bars indicate the three acceleration groups used to categorise accelerations in Figs 7 and 9.

 

Figure 15
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  		Fig. 15. `Gear ratio' (1/EMA) during stance (20–80%) for hip, stifle and hock joints during a low (A) and a high (B) acceleration trial.

 

Figure 16
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  		Fig. A1. Mean total joint moment at each hindlimb joint for a subset (N=4) of high acceleration trials. The red (solid) line indicates the moment as calculated by the GRFv approach (i.e. neglecting inertia and gravity). The dotted line indicates the total moment, including inertial and gravitational moments.

 

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© The Company of Biologists Ltd 2009