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screw motor. Thanks. I googled an image of that and it all made sense. Pretty sweet. And based on that, the motor doesn't seem like it would have any impact on the minimum difference between height settings. It would just a question of some kind of control that converts the remote signal into a burst of on or off for the motor. So likely there are an infinite number of positions the bed could achieve because holding the the button would be nondeterministic as to how far it would move. Thanks.
Yep.
Don't even need a stepper or servo motor. Any old motor will do.