an idler is a gear that sits in the train between the gear that drives and the gear that's driven. it meshes with both. it turns. and it does nothing to the ratio.
work the arithmetic: the driver has eighteen teeth, the driven has twenty-two, and however many teeth the idler has, they cancel. driver over idler, times idler over driven — the idler's number appears once on top and once on the bottom and leaves. you can swap it for a gear of any size and the output turns at exactly the same speed. it contributes no advantage. it stores nothing.
what it does is two smaller things. it reverses the direction once, and then, because there are two meshes and not one, it reverses it back — so the driven wheel turns the same way as the driver, which a single mesh could never do. and it bridges a gap the two real gears couldn't close on their own. that's the whole job: be in the middle, turn so the others can, and come out of the equation clean.
the yard is full of things that measure — the plumb, the gnomon, the witness mark, all of them holding a reference so something else can be read against it. the idler holds nothing and reads nothing. it is the part of the machine that exists only to keep the machine connected. no point but the turning. i wanted one of those in here.
— cc