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First published online December 15, 2004
Journal of Experimental Biology 208, 41-53 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01305

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Joint work and power associated with acceleration and deceleration in tammar wallabies (Macropus eugenii)

C. P. McGowan^1,*, R. V. Baudinette² and A. A. Biewener¹

¹ Concord Field Station, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
² Department of Environmental Biology, University of Adelaide, Adelaide, SA 5003, Australia

View larger version (17K): [in a new window]   Fig. 1. A schematic diagram of the linked segment model used to calculate joint moments, power and work. (A) The internal angles that were measured. Angles () were measured at hip (h), knee (k), ankle (a) and metatarsophalageal joint (MP). (B) Elements of the linked segment model used in the inverse dynamics calculations, where m is the mass of each segment, I is the mass moment of inertia of each segment and Fx and Fy are the horizontal and vertical ground reaction forces (GRF), respectively. The center of pressure of the GRF on the foot was determined by the force plate.

View larger version (16K): [in a new window]   Fig. 2. Representative GRF recordings from (A) a large acceleration trial, (B) a steady speed trial and (C) a large deceleration trial, normalized to percentage of stance time. The insets show the average limb position at the time of first contact, midstance and last contact relative to the orientation of the GRF vector (red broken line). Note the broken red line does not represent the magnitude of the GRF.

View larger version (13K): [in a new window]   Fig. 3. The mean vertical (VGRF, squares), propulsive (+HGRF, triangles) and breaking (-HGRF, circles) forces in xBW versus acceleration. During accelerations, both VGRF and +HGRF increased with acceleration; however, the trend for VGRF was not significant (r2=0.93, P<0.0001; r2=0.23, P=0.072, respectively). During decelerations, only -HGRF was significantly correlated with acceleration (r2=0.89, P<0.0001).

View larger version (12K): [in a new window]   Fig. 4. Graphs of (A) limb protraction angle, (B) limb retraction angle and (C) limb excursion angle versus acceleration. During acceleration trials (triangles), limb protraction angle did not change significantly with acceleration, while retraction angle increased with increasing accelerations. In deceleration trails (squares), both limb protraction and retraction angles increased with increasing deceleration magnitude. Limb excursion angle increased linearly with both acceleration and deceleration magnitude. See text for further details.

View larger version (15K): [in a new window]   Fig. 5. Graphs of the average change in joint angle during stance for the hip, knee, ankle and metatarsophalageal joint (MP) during accelerations (green), steady speed (black) and decelerations (red). Solid lines are the average of four trials for each condition. The mean accelerations of these groups were: 5.88±0.80 m s-2, -0.07±0.45 m s-2 and -5.27±0.86 m s-2 for accelerations, steady speed and decelerations, respectively. Standard errors for each joint angle curve have been omitted for the sake of clarity.

View larger version (15K): [in a new window]   Fig. 6. A graph showing the net angle change during stance at each joint as a function of acceleration. Positive values represent net joint extension while negative values represent net joint flexion. The results of linear regressions showed significant correlations at all joints (hip: r2=0.50, P<0.0001; knee: r2=0.47, P<0.0001; ankle: r2=0.51, P<0.0001; MP: r2=0.19, P=0.017).

View larger version (17K): [in a new window]   Fig. 7. Graphs of total joint moments (tot), including inertial and gravitational components (solid lines) and external joint moments (ext, dotted lines) from a representative trial for each condition: (A) acceleration, 5.97 m s-2, (B) steady speed, -0.41 m s-2 and (C) deceleration, -5.99 m s-2. During accelerations, moments reach a peak later in stance and are maintained for a longer duration of the stance period, as compared to steady speed trials. Conversely, during decelerations the moments reach a peak early in stance and fall to near zero for the later part of stance. Peak moments for all joints remains relatively constant across trails. Note that the difference between total joint moments and external joint moments is small and can only be seen at the hip.

View larger version (17K): [in a new window]   Fig. 8. Total joint power (tot, solid colored lines), external joint power (ext, dotted colored lines) and summed limb power (broken black lines) for the representative trials shown in Fig. 6. The majority of the power for changing speed is produced at the hip (red) and ankle (blue). Peak powers at the knee (green) increase during accelerations and decelerations, but the net work remains relatively constant. The MP (black) produces more negative power with increased accelerations.

View larger version (12K): [in a new window]   Fig. 9. Net work produced at each joint per kg body mass versus acceleration. The slope of regression lines was steepest at the ankle, indicating that the modulation of limb work during accelerations and decelerations occurred primarily at this joint. Work at the hip and MP also had a significant relationships with acceleration but with shallower slopes than at the ankle. The amount of work done at the knee was low and independent of acceleration. Linear regressions are: hip, y=0.095x+0.954, r2=0.035, P<0.001; knee, y=0.021x+0.347, r2=0.05, P=0.256; ankle, y=0.302x+0.024, r2=0.83, P<0.0001; MP, y=-0.08x-0.997, r2=0.39, P<0.001.

View larger version (17K): [in a new window]   Fig. 10. Center of mass (CoM) work (filled triangles) and summed limb work (open squares) plotted against acceleration. The slope of the regression line for the summed limb work (broken line) was significantly lower then that for the center of mass work (solid line). Thus, at the maximum accelerations and decelerations, the work done by the limbs did not account for all of the work done on the center of mass. This suggests that the trunk and tail may also be recruited to power changes in speed (see Discussion). Linear regressions are: CoM work, y=0.530x+0.022, r2=0.97, P<0.0001; limb work, y=0.338x+0.328, r2=0.87, P<0.0001.