Push-off in human walking emerges from support-limited feasibility not propulsion capacity

Late stance push-off is widely interpreted as the mechanical expression of propulsion capacity in human walking. Here we show that this interpretation is incomplete: push-off is not a direct consequence of forward propulsion, but a conditional outcome governed by system level mechanical feasibility. Using an analytical model of step-to-step transition with empirical measurements of post-stroke hemiparetic walking, we identify two feasibility boundaries that constrain push-off. The first is a support threshold, defined by the minimum vertical force required to maintain body weight support during double support. The second is a higher transition requirement associated with redirecting the center of mass (COM) between successive stance limbs. Optimization of force limited transitions predicts that late stance push-off is mechanically infeasible below the support threshold, emerges abruptly once support feasibility is satisfied, and increases progressively toward transition defined work as available force capacity increases. Empirical analyses of ground reaction force derived COM power confirm these predictions. Forward directed propulsive impulse persists even when push-off work is absent, demonstrating that propulsion can occur without performing positive COM work. Push-off emerges only when system-level vertical feasibility becomes sufficient, and its subsequent growth is associated with increased vertical unloading and redistribution of mechanical work across the gait cycle. These results establish a hierarchical organization of walking mechanics in which feasibility precedes efficiency. Vertical support feasibility governs push-off emergence, whereas the transition requirement governs its mechanically sufficient expression. The abrupt loss of push-off therefore reflects a change in mechanically feasible locomotor solutions rather than reduced propulsive capacity.