Vertical Ground Reaction Force Morphology Is Determined by Step-to-Step Transition Mechanical Energy Imbalance During Human Walking

Abstract

Vertical ground reaction force (vGRF) profiles during walking typically exhibit a double-peaked structure with a mid-stance trough, yet the mechanical conditions governing this morphology remain incompletely defined. In this study, we examined how the balance between push-off and collision impulses during the step-to-step transition influences the temporal and structural characteristics of the vGRF trajectory. Empirical relationships describing push-off and collision work were used to compute transition impulses across walking speeds ranging from 0.8 to 1.4 m{middle dot}s{square}1. A normalized Impulse Balance Index (IBI) was defined to quantify the relative dominance of push-off and collision impulses. The temporal position of the mid-stance trough was quantified using a Trough Deficit Index (TDI) derived from quadratic fits of the vGRF trajectory. Across walking speeds, push-off and collision variations produced step-to-step active work performance imbalance. Push-off and collision became approximately balanced near 1.2 m{middle dot}s{square}1, corresponding to the mechanically preferred walking speed. Deviations from this balanced condition were associated with systematic shifts in trough timing: the trough occurred 1.83% and 1.56% earlier in stance at 0.8 and 1.0 m{middle dot}s{square}1, respectively, and 1.31% later at 1.4 m{middle dot}s{square}1 relative to the reference speed. TDI exhibited a strong inverse relationship with impulse balance (IBI), indicating that vGRF morphology is tightly coupled to the mechanical balance of the step transition. A simplified pendular model further demonstrated that active torque, representing work, during single support shifts the quadratic vertex of the force trajectory by approximately 48.6-51.1% of stance, consistent with the observed trough timing variations. These results show that vertical GRF morphology reflects the imbalance between push-off and collision provides a simple signal of step-to-step transition mechanics, that may be used for rehabilitation and exoskeleton modulation.