Forest Higgs posts an interesting approach to a key problem in building a self-replicating 3D printer. This of course, is the main objective of the RepRap project. They've actually performed a replication already, but there are always ideas for improvement.
That's where the idea of a linkage comes in. As you might imagine, the 3D printer's key operation is straight and accurate movement of the print head that deposits the 3D media. Normally, this might be done with very accurately constructed rails. However, if the device is to reproduce itself, it should do so in the most efficient manner.
The proposal is to use linkages (pictured) instead of rails, as they could be more efficient and accurate. Be sure to watch the animation at the link below. as Higgs says, "I've found watching it move is positively hypnotic".