Contact-Time Bounds for Paired Gait Angles: Signed Phase Differences and Sampled-Signal Error

Abstract

Errors in the two contacts delimiting a gait cycle alter the angles compared at a common normalized phase. To determine the signed angular differences that persist under bounded contact-time corrections and sampled-signal error. Start- and end-contact intervals were projected through affine cycle normalization. Signal extrema on the resulting time intervals gave exact difference limits for independently selectable correction sets. Four trajectories were evaluated in 180 combinations of cycle duration and endpoint bounds; 216 sampled-signal combinations assessed linear interpolation with bounded sample perturbations. A four-event predictive box was calibrated from 199 exchangeable correction tuples. Opposite 10 ms contact-label offsets generated a nominal root-mean-square difference of 1.985^∘ between identical trajectories. A 5^∘ angular offset exceeded 2^∘ for every admitted correction over 85.26%, 41.58% and 12.16% of phase at 10, 20 and 40 ms radii. Taylor bounds containing a curvature remainder enclosed the exact limits in all 144 smooth-trajectory combinations; first-order bounds omitted a limit in each combination. Their median mean-width ratio was 1.309. All 21,600 sampled-signal correction tuples satisfied the reconstruction-expanded limits at the evaluated phases. Across 200 calibration runs, mean joint coverage was 94.91%, with Monte Carlo standard error 0.12 percentage points. Contact-time intervals quantify the angular consequences of uncertain cycle boundaries. Shared corrections, local curvature and interpolation error determine the resulting limits. The retained phase fraction describes signed threshold exceedance under the stated measurement assumptions; participant-level treatment effects require a separate statistical analysis.