Fig 1.
Phases of the flick, delivered by the fencer on the right (black filled) against the fencer on the left (gray filled), are illustrated by a cartoon. En garde: The initial posture prior to commencing the flick. Backward rotation: The base of the blade is rotated backward, causing the blade to bend forward. Peak backward rotation: The backward rotation of the base of the blade stops causing the blade to bend backwards. Forward rotation: Rapid forward rotation of the base of blade causes the blade to further bend backwards. Deceleration: The forward rotation of the blade is abruptly stopped, causing the blade to markedly bend forward toward the target. If contact is made with adequate force a point, or touch, is scored.
Fig 2.
(A) Single video frame from the en garde phase of the flick shows the experimental arrangement of the nine tracking markers, scoring box, fencing dummy, back drop and target. The 5 cm target was created by electrically conductive lamé material wrapped around a 30.5 cm long aluminum plate covered in non-conductive fabric. (B) Single video frame with superimposed tracked trajectories of the 9 markers over the entire duration of flick. (C) Diagram illustrates the Cartesian coordination system whose origin is at the center of the target and the calculated joint and blade angles. Green circles are markers and red lines highlight the limb-blade kinematic chain. The direction of joint angle arcs indicate increasing angle.
Fig 3.
Stiffness measurement and target construction.
(A) Lab-made device to measure stiffness. Weights are at the top and height is measured by the location of the black dot relative to the ruler. (B) Arrangement for applying the weighted cylinder to the shoulder and recording by camera. (C) Stiffness across the shoulder was relatively constant. (D) Average compression and mass over all locations. Stiffness across the shoulder was relatively constant. (E) Comparison of the average stiffness for the shoulder (blue), several candidate rubber surfaces (green and red), and the one chosen (green).
Table 1.
Variables.
Fig 4.
Stick figure progression of a single, typical flick for both A and B fencers. The nine tracked features are shown for 35 equally spaced (every 10th frame, or 15 ms) frames. Markers, shown as small filled circles, are connected by linear interpolation for all but the blade between the tip and base (between markers 2 and 3), which is connected by second order polynomial interpolation. The hand, represented by the wrist marker (marker 6), is a larger blue filled circle. Limb segments are identified by color (torso → shoulder, cyan; shoulder → elbow, blue; elbow → writs, green; wrist → hand, magenta; hand to lower blade, back). The blade is colored red for the en garde and backward rotation phase and green for the forward rotation phase of the flick. The tip and blade segments are thickened.
Fig 5.
Differences between fencers: Path and trajectories of the foil tip.
(A) Paths in the Cartesian coordinate system of the foil tip for all of fencer A’s (n = 67, black) and fencer B’s (n = 78, red) trials. Fencer icons represent the approximate phase of the flick. (B,C) Trajectories of the foil tip over time for both distance (B) and height (C) for both fencers (fencer A black, fencer B red). Time is reversed, progressing from right to left, with the last point on the left immediately before the foil tip contacted with the target. The thick lines represent average trajectory (Fencer A dark blue, Fencer B light blue). The average trajectories are truncated to the duration of the briefest trajectory. Icons indicate approximate progression of the flick.
Fig 6.
Differences between fencers: Limb joint angular velocity trajectories.
Trajectories of finger, wrist, elbow and shoulder joint angle velocities for all of fencer A’s (n = 67, black) and fencer B’s (n = 78, red) trials. Time is reversed, progressing from right to left, with the last point on the left immediately before the foil tip contacted with the target. Shoulder angular velocity axis is reversed. Inset graphs depict mean joint angle for both fencers over time.
Fig 7.
Differences between fencers: Peak limb angular velocity variables.
Violin plots show medians and distributions of peak angular velocities around the finger, wrist, elbow and shoulder joints for both fencers A (black) and B (red). Peak velocities were calculated over the full duration except finger peak joint velocity was calculated over frames beyond 60ms (see Fig 5). P-values for all for joints are p<0.000001 (n = 67 for fencer A and n = 78 for fencer B; Mann-Whitney). Effect sizes, expressed as percent differences between medians, are 176%, 138%, 142% and 114% for the finger, wrist, elbow and shoulder joints respectively.
Fig 8.
Differences between fencers: Principal component analysis of limb joint angle trajectories.
(A) Principal component coefficients (loadings; PCA 1, PCA 2, PCA 3, PCA 4) for the trajectories of the four limb joint angles (finger, wrist, elbow and shoulder) for both fencer A (n = 67 trials) and fencer B (n = 98 trials). Colored (black, red) bars show components retained based on the amount of variance explained (see (B)). Maximum normalized coefficient is 0.86 for the elbow of fencer B. Error bars, which are small, are standard error of the mean. (B) Scree plot shows that the total variance explained by the first two principal components (PCA 1 and PCA 2) for Fencer A (black filled circles) is 94% but for Fencer B (red filled circles) was 89% for two components and 98% for three components. 90% was the cut-off for retaining principal components in (A).
Fig 9.
Significant direct and indirect relationships.
Diagram depicts significant relationships for both direct (left of “scoring”; limb effects on scoring) and indirect (right of “scoring”; tip effects on scoring, blade effects on tip variables, limb effects on blade variables). Number represent standardized slopes (linear regression) and odds ratios (logistic regression; values less than one are inverted).
Fig 10.
Effects of tip variables on scoring.
Dichotomous scoring is jittered and corresponds to either success (1) or a miss (0). Variables are expressed in dimensionless standardized units. The continuous curve correspond to probability. Fencer A: The probability of scoring by fencer A was increased by decreased reflected tip distance (logistic regression, n = 67, r2 = 0.24, %explained = 61/77; p = 0.002, oddsstd = 2.9, r2 = 0.24). Not significantly related to scoring (not shown) were tip velocity (p = 0.4), reflected tip velocity (p = 0.1), distance (p = 0.8), tip angle (p = 0.2), and reflected tip angle (p = 1.0). Fencer B: The probability of scoring by fencer B was affected by both reflected tip distance and tip velocity (logistic regression, n = 78, %explained 53/78, r2 = 0.29). Decreased reflected tip distance (p = 0.007, oddsstd = 0.4) and increased tip velocity (p = 0.002, oddsstd = 2.4) increased scoring probability. Graphs are not partial plots. Not significantly related to scoring were reflected tip velocity (p = 0.4), distance (p = 0.3), tip angle (p = 0.4), and reflected tip angle (p = 0.3).
Fig 11.
Effects of blade variables on tip variables.
Variables are expressed in dimensionless standardized units. Fencer A: Reflected tip distance increased with increased reflected blade distance (linear regression, both variables square root transformed for regression but not plotting, n = 67, p = 0.00016, r2 = 0.20, slopestd = 0.45, plot). Not significantly related to reflected tip distance (forward step-wise linear regression) were angular blade velocity (p = 0.8), reflected blade velocity (p = 0.2), blade height (p = 0.9), reflected blade height (p = 0.05), and blade distance (p = 0.03). Fencer B. Reflected tip distance increased with increased reflected blade distance (linear regression, both variables square-root transformed for regression, n = 78, p<0.000001, r2 = 0.29, slope = 0.62 based on non-transformed data). Not significantly related to blade velocity (p = 0.7), reflected blade velocity (p = 0.6), blade height (p = 0.3), reflected blade height (p = 0.2), or blade distance (p = 0.0005). Tip velocity was affected by both angular blade velocity and blade height (linear regression, n = 78, r2 = 0.44). Tip velocity increased with increased angular blade velocity (multiple linear regression, n = 78, p<0.00001, slopestd = 0.59, partial plot). Tip velocity increased with decreased blade height (multiple linear regression, n = 78, p<0.00001, slopestd = -0.65, partial plot). Not significantly related to tip velocity (forward step-wise linear regression) were reflected angular velocity (p = 0.02), reflected blade height (p = 0.8), blade distance (p = 0.1), reflected blade distance (p = 0.6).
Fig 12.
Effects of limb variables on blade variables.
Variables are expressed in dimensionless standardized units. Fencer A: Reflected blade distance increased with increased reflected hand distance (linear regression, both variables square root transformed for regression, n = 67, p<0.000001, r2 = 0.94, slopestd = 0.97). Not significantly related to reflected tip distance (forward step-wise linear regression) were finger velocity (p = 0.5), reflected finger velocity (p = 0.4), wrist velocity (p = 0.6), reflected wrist velocity 0.8), elbow velocity (p = 0.92, reflected elbow velocity (p = 0.8), shoulder velocity (p = 0.6), reflected shoulder velocity (p = 0.3), hand height, (p = 0.9) reflected hand height (p = 0.9), hand distance (p = 0.01). Fencer B: Blade velocity was affected by both wrist and shoulder velocity (linear regression, n = 78, r2 = 0.23). Blade velocity increased with increased wrist velocity (linear regression, n = 78, p<0.0002, r2 = 0.21, slopestd = 0.42, partial plot). Blade velocity increased with increased shoulder velocity (linear regression, n = 78, p<0.001, r2 = 0.13, slopestd = 0.36, partial plot). Not significantly related to reflected blade velocity (forward step-wise linear regression) were finger velocity (p = 0.11), reflected finger velocity (p = 0.44), reflected wrist velocity (p = 0.99), elbow velocity (p = 0.6), reflected shoulder velocity (p = 0.9), hand height (p = 0.2), reflected hand height (p = 0.4), hand distance (p = 0.2), reflected hand distance (p = 0.32). Blade height increased with increased hand height (linear regression, n = 78, p<0.00001, r2 = 0.97, standardized slope = 0.99, plot). Not significantly related to reflected tip distance (forward step-wise linear regression) were finger velocity (p = 0.9), reflected finger velocity (p = 0.3), wrist velocity (p = 0.15), reflected wrist velocity (p = 0.3), elbow velocity (p = 0.35), reflected elbow velocity (p = 0.1), reflected shoulder velocity (p = 0.6), reflected hand height (p = 0.6), hand distance (p = 0.18), reflected hand distance (p = 0.3). Reflected blade distance increased with increased reflected hand distance (linear regression, both variables square root transformed for regression, n = 78, p<0.000001, r2 = 0.94, slopestd = 0.97 for non-transformed variables, partial plot). Not significantly related to reflected tip distance (forward step-wise linear regression) were finger velocity (p = 0.5), reflected finger velocity (p = 0.8), wrist velocity (p = 0.2), reflected wrist velocity 0.8), elbow velocity (p = 0.2), reflected elbow velocity (p = 0.6), shoulder velocity (p = 0.9), reflected shoulder velocity (p = 0.4), hand height (p = 0.3), reflected hand height (p = 0.1), hand distance (p = 0.003).
Fig 13.
Effects of limb variables on scoring.
Dichotomous scoring is jittered and corresponds to either success (1) or a miss (0). Variables are expressed in dimensionless standardized units. The continuous curve correspond to probability. Fencer A: The probability of scoring was increased by decreased reflected hand distance (logistic regression, n = 67, r2 = 0.04, %explained = 37/67; p = 0.14, oddsstd = 0.67). Not significantly related to scoring were finger velocity (p = 0.9), reflected finger velocity (p = 0.4), wrist velocity (p = 0.3), reflected wrist velocity (p = 0.7), elbow velocity (p = 0.4), reflected elbow velocity (p = 0.4), shoulder velocity (p = 0.6), reflected shoulder velocity (p = 0.2), hand height (p = 0.9), reflected hand height (p = 0.3), hand distance (p = 0.3). Fencer B: The probability of scoring was influenced by finger velocity, reflected wrist velocity, hand height and reflected hand distance (logistic regression, n = 78, r2 = 0.22, %explained = 8/77). The probability of scoring was increased by finger velocity (logistic regression, n = 78, p = 0.0005, oddsstd = 3.8). The probability of scoring was decreased by absolute wrist velocity (logistic regression, n = 78, p = 0.003, oddsstd = 0.37). The probability of scoring was increased by hand height (logistic regression, n = 78, p = 0.009, oddsstd = 2.2). The probability of scoring was decreased by reflected hand distance (logistic regression, n = 78, p = 0.04, oddsstd = 0.48). Graphs are not partial plots, thus under-estimating the strength of the relationship. Not significantly related to scoring were reflected finger velocity (p = 0.2), wrist velocity (p = 0.7), elbow velocity (p = 0.3), reflected elbow velocity (p = 0.1), shoulder velocity (p = 0.4), reflected shoulder velocity (p = 0.4), reflected hand height (p = 0.5), and distance (p = 0.3).
Fig 14.
Relations for significant linear relationships between tip velocity and peak joint velocities. (A) Tip velocity increased significantly with increased finger velocity (p<0.00001, r2 = 0.46, slopestd = 0.67, linear regression) and (B) increased finger velocity (p = 0.00001, r2 = 0.23, slopestd = 2.7, linear regression).