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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).

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    Perhaps it is undulating. maybe it’s even conformal undulation. – Jim Aug 31 '18 at 0:59
  • 'serpentine' is literally like a snake. Did you check a thesaurus for similar? – Mitch Aug 31 '18 at 1:04
  • @Mitch I did but those synonyms tend to emphasize the curvyness whereas I just used a snake as a generic example to avoid the narrow scope of a straight rod moving along its own axis. – Museful Aug 31 '18 at 1:10
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    If the question is not about snake-like movement, then why does the title ask for movement resembling a snake? This is confusing. Do you just want 'the segment is following the curve'? – Mitch Aug 31 '18 at 3:20
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    Could you add three example sentences (one for the verb, one each for adver/adjective)? – loonquawl Aug 31 '18 at 7:37
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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.

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I'll focus on the perceived quality of all parts following in a given (if previously unseen) track, while neglecting any allusions to a specific way of movement:

To troop: Assumes multiple objects moving in a coherent manner along a common path.

To flock: As troop, but with less internal order, also usually towards some point.

To file: As troop, but with a definite, simple, order.

To journey: As troop, but possible for a single object.

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