Correction of initial velocity conditions for calculation of the guinea fowl's COM path. Initial velocity conditions derived using standard methods result in a path that diverges considerably from kinematic observation. The calculated vertical position (A, broken red line) and the observed kinematic estimates (black dots) relate to the left axes in A and B, and show a discrepancy represented as the squared difference at each point (grey vertical bars, right axes in A and B). The sum of the squared differences through the step period (SSD, inset in A and B) is used as a statistic for selecting the V_i,v that minimizes the divergence between the two vertical paths. The V_i values resulting in the closest path match for the vertical (B, solid blue line) and horizontal components (not displayed, but identical principles), are then used as the integration constants in the calculation of instantaneous velocities from the ground reaction force data (Eqn 5, 6).

(A) COM paths over a step cycle for one individual during the three treatments: control (C), unexpected substrate drops (U) and visible substrate drops (V). All U trials for this individual are shown to illustrate within-subject variation (solid blue lines), with a representative V trial (dotted red line) and C step (broken green line) drawn for comparison. Thin gray lines represent the aerial phase of the step. In (B) the periods of analysis are schematically illustrated. In all cases, the COM trajectory was calculated between subsequent aerial phase peaks in COM height. During level running this corresponded to subsequent COM apexes, where E_Kv is zero and E_P is at a maximum. However, in the U and V trials the COM generally did not return to stable periodic motion within the perturbed step, and the COM was often moving downward at the beginning of the aerial phase following the perturbation. In these cases, there was a net gain in E_Kv, and the aerial phase peak in COM height occurred at the beginning of the flight phase. ThisΔ E_Kv must be dealt with during the next stance phase because total vertical energy (E_V=E_P+E_Kv), total horizontal energy (E_H=E_Kh) and total mechanical energy (E_com) can change only during ground contact.

Summary of COM mechanics during C, U and V treatments (A,B,C, respectively). Silhouettes of the bird with corresponding limb stick figures at three points during the perturbed step: toe-down, midstance, and toe-off. The broken silhouette and stick figure represent the time of tissue paper contact in the U treatment. The COM path is overlaid for the time interval illustrated in Fig. 3B, along with the corresponding net change in height (Δs_v, blue), GRF impulse vector (J, red, summed over the stance phase), and initial and final velocity vectors (V_i and V_f, respectively, green) to illustrate differences among treatments.

Net changes in gravitational potential (ΔE_P), horizontal and vertical kinetic (ΔE_Kh andΔ E_Kv, respectively), and total mechanical energy (ΔE_com) of the COM over the course of one step for the C, U and V treatments. The broken gray line indicates theΔ E_P that would occur if the birds fell the entire substrate drop (ΔH=8.5 cm). Values are means ± s.e.m for all individuals (N=5). The net changes in energy were determined over the time interval illustrated in Fig. 3B.

Comparison of mechanical variables across C (black bars), U (pale grey bars) and V (dark grey bars) treatments, with U trials subdivided into energy exchange modes. Values are means ± s.e.m for all instances of each response. Initial horizontal velocity (V_i,h) was measured at the COM apex during the flight phase prior to the measured step (`begin' point in Fig. 3B). The net change in COM height (Δs_v) was determined over the time interval illustrated in Fig. 3B. The other mechanical variables were measured over the period of ground contact.

Ground reaction force (top), and COM energy changes (below) over time for the step period for representative trials, comparing steady, spring-like dynamics of level running (A) to the three energy responses observed during U perturbations: (B) `E<sub>Kh</sub> mode', (C) `E_com mode' and (D) `E_Kv mode'. The time interval shown is that illustrated in Fig. 3B. Bold and dotted lines in top panels indicate instantaneous vertical (f_v) and horizontal (f_h) GRF, respectively. The dotted vertical lines indicate time of tissue paper contact, and gray bars indicate duration of ground contact. Gravitational potential (E_P), horizontal kinetic (E_Kh) and vertical kinetic (E_Kv) energies are shown over time, with dotted horizontal lines to indicate the initial energy. Two energy sums, total vertical energy (E_V=E_P+E_Kv) and total COM energy (E_com=E_P+E_Ktot), allow distinction between energy conversion (e.g. E_P→E_Kh as in B and net energy absorption (as in C). Note that at the point of ground contact in U trials (B-D), E_Kv is greater than in level running (A) because the body falls during the perturbation.

The COM mechanics occur along a continuum related to how well the limb supported body weight BW and whether it produced or absorbed net energy. Different symbols represent different `energy mode' categories. The GRF impulse magnitude and direction (|J| and ϕ) distinguish the different response patterns, as illustrated by their relationship with two energy ratios. (A) The vertical energy ratio (ΔE<sub>Kv</sub>: ΔE<sub>P</sub>) strongly correlates with |J|, and indicates the level of BW support (0 indicates full BW support, 1.0 indicates free fall). We categorized trials in which the E<sub>V</sub> ratio ≥0.5 as `E_Kv' mode (dotted line). (B) The perturbation energy ratio (ΔE_com: ΔE_V) correlates with ϕ, and distinguishes energy redistribution vs actuation by the limb. A value of zero indicates that theΔ E_V was converted to E_Kh (ΔE_V→ΔE_Kh), with no net muscular work, consistent with spring-like limb function. A value of 1.0 indicates that all of ΔE_V is absorbed, a value> 1.0 indicates deceleration (-ΔE_Kh) and a value<0 indicates acceleration (+ ΔE_Kh). We categorized trials in which the perturbation energy ratio ≥0.5 as `E_com' mode (dotted line).