I don't think it's the motion of the ring, it's getting energy from Harry when he moves his arms. Putting it on something moving wouldn't do anything, even another person might need attunement or something.
Remember that Elaine could recharge her thorn-wand by just plugging into a wall-socket, and she's got similar training to Harry (she's just "more elegant").
I think Harry's rings are (or could easily be re-made) similarly-amenable to mechanical recharge.
It might have to be more linear than rotational, though -- the force rings are pretty explicitly one trick, linear thrust (though if he does have to re-make them anyhow, he might include some rotational and other variants).
Maybe he could find a supermarket or similar, with a sliding-door that opens & closes many times per hour, all day long...