I was thinking about the word "acyclic" meaning not having or containing a cycle. Then I thought of the word "bicycle" and wondered if it made sense to call something that an "acycle". As an example I would want to say that stilts are an acycle (because they do not inherently contain a cycle or cyclic motion).
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Referring to stilts as an "acycle" seems to me a bizarre formation. "Acyclic" is used to distinguish between things that might or should have a cycle but don't. Simply because stilts do not have a "cycle" does not make them acyclic, because stilts do not belong to a class of objects that could conceivably have a cycle. Neither do tree stumps, Frank Frazetta book covers, or fingernail parings, except in the sense that all things have a cycle of creation and destruction.
Acyclic refers to concepts like molecules that contain no rings of atoms, or women who don't have a menstrual cycle [see NOAD definition]. Both of those are commonly thought to have cycles, and so may require a term to describe the absence of what should be a normal property for them.
Calling stilts an acycle makes exactly as much sense as calling them a motorless.