Imagine a point moving along a curve. This point is simply traversing the curve, I suppose.
But now imagine a little "curve-segment" moving along the same curve, while conforming to the curve at all times. So no part of the curve-segment ever strays from the greater curve.
Now forget about the greater curve and focus on the moving curve-segment. What word describes this motion?
It moves like a snake, or like the wire on a bicycle brake, but I'm hoping for a word in the register of Reciprocate and Articulated, not Slither. The word can refer to either the motion (verb) or the constraint (adverb or adjective), whatever is most suggestive of the constrained nature of the motion.
EDIT: I should add that the curve need not necessarily be curvy. It just may be straight by coincidence. Therefore the emphasis is on the conformity between motion and shape.
EDIT2: Another example: Picture the way a train moves, but forget about the tracks (to avoid words like Ride).