Displacement–closure equations of the unspecialised double-Hookeʹs-joint linkage

Despite the widespread application of the double-Hookeʹs-joint linkage, there has been no published account of the displacement–closure equations which govern the motion of its unspecialised form. We provide one here after an examination of the two typical special cases. We go on to consider a generalisation of the chain, and are led to postulate the existence of an even more general loop. In an appendix we present a new listing of all known 6R linkages.