Blender Underground

I'm working on a really simple animation of gears. The first small gear copies the rotation of an empty. A gear three times larger than the first copies 0.333333 of the rotation of the first gear, then has another gear the same size as the first copying it's rotation exactly, which has a larger gear and so on.

This works fine through the first two pairs, but on the third, this weird snapping motion i've noticed before crops up. On the midpoint of the animated action, it suddenly snaps so the gear is "a tooth" further along the rotation than it should be. This also happens when you use too slow a rotation copy [I started trying to have the slowest gear in the sequence being a 0.1 copy and working up but that didn't work out]

Can anyone explain to me why this happens and how to avoid it? For reference, the action used is a 360 rotation of the empty every 300 frames, so the jump happens at or around 150 frames.