As to the position of the rotation centers, it seems to me that they need to ba based on the inside radius of the links. Assuming a vertical chain with the first link at the bottom, one axis of rotation would be at the center of a circle drawn at the inside top of the link below the link in question, the other at the inside bottom of the link in question itself. These two axes are equidistant from the point where the two links touch. In chains produced by the chain_maker the bottom axis is the real origin, and the top axis is the "fake origin", though I suppose it might just as easily be done the other way round.

Messing with the rotation orders of the chain links, I realize just how little I understand about rotation orders and how to set them appropriately. At the moment my method is pure trial and error. I may see if I can make something to shed some light on this.