Figures and data
(a) Illustration of the kangaroo model. Total leg length was calculated as the sum of the segment lengths (solid black lines) in the hindlimb and compared to minimum pelvis-to-toe distance (dashed line) to calculate the crouch factor. Joint angles were determined for the hip, h, knee, k, ankle, a, and metatarsophalangeal, m, joints. The model markers (red circles) indicate the position of the reflective markers placed on the kangaroos in the experimental trials and were used to characterize the movement of segments in the musculoskeletal model. (b) Illustration of ankle effective mechanical advantage, EMA, muscle moment arm, r, and external moment arm, R, as the perpendicular distance to the Achilles tendon line of action and ground reaction force (GRF) vector, respectively.
Horizontal (dashed lines) and vertical (solid lines) components of the ground reaction force (GRF) (a) coloured by body mass subsets (small 17.6±2.96 kg, medium 21.5±0.74 kg, large 24.0±1.46 kg) and (b) coloured by speed subsets (slow 2.52±0.25 m s-1, medium 3.11±0.16 m s-1, fast 3.79±0.27 m s-1). In (a) and (b) the medial-lateral component of the GRF is not shown as it remained close to zero, as expected for animals moving in a straight-line path. Lower panels show average time-varying EMA for the ankle joint subset by (c) body mass and (d) speed.
Average time-varying crouch factor of the kangaroo hindlimb grouped by (a) body mass and (c) speed. Position of the limb segments during % stance intervals (b). Average time-varying joint angles for the hip (solid lines) and knee (dashed lines) displayed for kangaroos grouped by (d) body mass and (e) speed. Average time-varying joint angles for the ankle (solid lines) and metatarsophalangeal (MTP) joints (dashed lines) displayed for kangaroos grouped by (f) body mass and (g) speed. Body mass subsets: small 17.6±2.96 kg, medium 21.5±0.74 kg, large 24.0±1.46 kg. Speed subsets: slow 2.52±0.25 m s-1, medium 3.11±0.16 m s-1, fast 3.79±0.27 m s-1.
Average time-varying joint powers for the hip (a,b), knee (c, d), ankle (e, f), and MTP (g, h) displayed for kangaroos grouped by body mass (a, c, e, g) and speed (b, d, f, h). Body mass subsets: small 17.6±2.96 kg, medium 21.5±0.74 kg, large 24.0±1.46 kg. Speed subsets: slow 2.52±0.25 m s-1, medium 3.11±0.16 m s-1, fast 3.79±0.27 m s-1.
Variation with speed of (a) positive and negative ankle work, and (b) net ankle work.
How the relationship between posture and speed is proposed to change tendon stress. Forces are not to scale and joint angles are exaggerated for illustrative clarity. A slow hop (left panel) compared to a fast hop (right panel). The increase in ground reaction force (GRF) with speed, while a more crouched posture changes the muscle moment arm, r, and external moment arm, R, which allows the ankle to do more negative work (storing elastic potential energy in the tendons due to higher tendon stresses), without increasing net work, and thereby metabolic cost.
(a) Relationship between ankle effective mechanical advantage, EMA, at midstance and Achilles tendon stress (stress = 11.6 EMA-1.04, R2=0.593) (black), with other mammals (green). (b) Scaling of mean ankle EMA at midstance for each individual kangaroo against body mass (black), with data for a wider range of macropods (purple) (Bennett and Taylor 1995), and other mammals (green, EMA = 0.269 M0.259, shaded area 95% confidence interval) (Biewener 1990) shown.
a) Mean vertical and horizontal components of whole body acceleration for kangaroos in the slow, medium and fast subsets (respectively: 2.52±0.25 m s-1, 3.11±0.16 m s-1, 3.79±0.27 m s-1). (b) Ground contact duration across hopping speeds from current study (black circles) and for red kangaroos reported in Kram and Dawson (1998) (red circles). Regression equation: tc = 0.342speed-0.477 where tc is contact duration and s is hopping speed. (c) Relationship between stride length and speed, and (d) stride frequency and speed.
(a) Relationship between peak vertical GRF as a multiple of body weight (BW) with body mass and (b) with speed. Dotted line is insignificant and solid line is significant, see Table 2 for interaction.
Average time-varying muscle moment arm, r, grouped by (a) body mass and (b) speed; external moment arm, R, grouped by (c) body mass and (d) speed. Vertical displacement of the ankle marker from the ground throughout stance grouped by (e) body mass and (f) speed. Ankle angles and corresponding r arm length (g). Body mass subsets: small 17.6±2.96 kg, medium 21.5±0.74 kg, large 24.0±1.46 kg. Speed subsets: slow 2.52±0.25 m s-1, medium 3.11±0.16 m s-1, fast 3.79±0.27 m s-1.
Average time-varying net joint moments (dimensionless, as moments were divided by body weight * leg length) for the hip (solid lines) and knee (dotted lines) displayed for kangaroos grouped by (a) body mass and (b) speed. Average time-varying net joint moments (dimensionless) for the ankle (solid lines) and metatarsophalangeal (MTP; dotted lines) joints displayed for kangaroos grouped by (c) body mass and (d) speed. Data for tammar wallabies was also included (McGowan et al. 2005) in green. Peak ankle moment occurred at 47.37±4.91 % of the stance phase. Positive values represent extensor moments and negative values represent flexor moments. Body mass subsets: small 17.6±2.96 kg, medium 21.5±0.74 kg, large 24.0±1.46 kg. Speed subsets: slow 2.52±0.25 m s-1, medium 3.11±0.16 m s-1, fast 3.79±0.27 m s-1.
Positive (purple) and negative (green) joint work over stance for the hip, knee, ankle and MTP plotted against body mass (a,c,e,g) and speed (b,d,f,h). Solid lines represent significant trends, dotted lines are not significant (see Suppl Table 6).
Net joint work for the hip, knee, ankle and MTP joint over stance plotted against body mass (a,c,e,g) and speed (b,d,f,h). Solid lines represent significant trends, dotted lines are not significant (see Suppl Table 6).
Negative (a) (Β=-3.04, SE=0.75, P<0.001, R2=0.155), positive (b) (Β=-7.42, SE=0.61, P<0.001, R2=0.622), and net ankle work (c) (Β=-4.37, SE=0.84, P<0.001, R2=0.230) plotted against EMA at 50% of stance.
Mean instantaneous positive (top panel) and negative (bottom panel) power for each hindlimb joint expressed as a percentage of total limb power (sum of instantaneous joint powers). Means were calculated at 10% stance intervals.
Peak vertical ground reaction force (GRF) plotted against tendon stress (Β=0.080, SE=0.009, P<0.001, R2=0.486).
Stride parameter multiple linear regression results as slopes, standard errors and P-values. Models with a significant interaction are displayed in full, and as a simplified model without the interaction term included (marked *). The fit of the model is represented by R2 and relationships are considered significant at P<0.05.
Ground reaction force and centre of pressure (CoP) multiple linear regression results as slopes, standard errors and P-values. Models with a significant interaction are displayed in full, and as a simplified model without the interaction term included (marked *). The fit of the model is represented by R2 and relationships are considered significant at P<0.05.
Crouch factor (CF) and kinematics multiple linear regression results as slopes, standard errors and P-values. Models with a significant interaction are displayed in full, and as a simplified model without the interaction term included (marked *). The fit of the model is represented by R2 and relationships are considered significant at P<0.05.
Multiple linear regression results of dimensionless peak joint moments as slopes, standard errors and P-values. Models with a significant interaction are displayed in full, and as a simplified model without the interaction term included (marked *). The fit of the model is represented by R2 and relationships are considered significant at P<0.05.
Tendon stress and EMA multiple linear regression results as slopes, standard errors and P-values. Models with a significant interaction are displayed in full, and as a simplified model without the interaction term included (marked *). The fit of the model is represented by R2 and relationships are considered significant at P<0.05.
Joint net positive, negative and net work simple linear regression (lm(joint work ∼ mass), lm(joint work ∼ speed)) results as slopes, standard errors and P-values. Work is normalised by body mass (BM). The fit of the model is represented by R2 and relationships are considered significant at P<0.05.
Positive, negative and net joint work multiple linear regression results as slopes, standard errors and P-values. Work is normalised by body mass (BM). Models with a significant interaction are displayed in full, and as a simplified model without the interaction term included (marked *). The fit of the model is represented by R2 and relationships are considered significant at P<0.05.
