A technical term for constrained motion resembling that of a snake

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).

Solution 1:

I think you may have found the best answer yourself: Constrained is used to mean something similar, including by you, though you'd have to make it clear that your snake is constrained to the curve. Refer to the snake as a (curve) segment and you wouldn't have to, but then you need to be clear not to imply a part of the original curve, but something following it. The curve it follows might be described as a path

Guided might also be of interest, though it feels like it should apply to an animate entity rather than a simple object.

I doubt you'll find a perfect single word, but with the right context at first you can probably refer to the constraints in subsequent mentions. Perhaps you could even define path-constrained, as the unusual term makes it clear that you're not referring to arbitrary constraints. In fact path-constraint is used in this context in the CAD world.