Which parts may not share a plane: crank rocker

One node per link and one edge per pair that cannot be in the same plane. Joined pairs (solid) share a pin, so both surround it and neither can be where the other is; overlapping pairs (dashed) are links with no pin in common whose material is in the same place at some position of the drive. The colours are a layer assignment: 3 planes, which is the fewest this graph admits. Nothing in the mechanism's constraint equations mentions any of it — a mobility of one is a statement about the Jacobian, and this is a statement about the material.