This idea came to me in a dream: [1]
(This is likely to be more useful for up escalators, so that's what I'll describe. If you want to replace all
'up's with 'down's and read it that way, go ahead—it should make sense that way too.)
Imagine an escalator. The steps move upward on the upper surface,
and downward underneath to circle
back around. Each step moves upward at constant velocity, pulled along by a chain, and humans ride
them. Sometimes, humans walk up them in the typical manner of ascending stairs, rather than riding
passively. This idea aims to make that active ascent more efficient.
Take that escalator you're imagining, and change the connection between the steps and the chain, as
well as the mating faces of the steps, such that each step can hinge up and down about the rear edge
of its tread (where the tread meets the riser of the next step up) [2] or somewhere near that location.
Next, add some mechanism to actuate each step up and down in sequence, so as to form a wave motion
moving up the escalator. For example, this mechanism could be a pinion gear associated with each
step, riding on a stationary gear rack that goes up the length of the escalator's stair flight, and
connected to a crank that controls the angle of the step. The mechanisms will need to be calibrated
and synchronized so as to produce a useful wave. (A wave-shaped track along the flight, with a
follower on each step, would produce a standing wave, not a traveling wave: not useful.)
The effect of this is a traveling wave going up the escalator at a rate ideally equal to the rate of ascent
of a person actively climbing the escalator. This should make it more efficient for those users to
ascend, if they synchronize their ascent with the wave so as to have shorter steps to climb, while not
impacting the overall ascent rate of passive riders. (It remains to be seen whether the wave-influenced
upward velocity is acceptably unannoying to passive riders.)