The six-revolute hybrids of four-revolute loops and their single reciprocal screws

Most of the known six-revolute linkages are hybrid in character. The six simplest of these synthesised loops arise by combining a pair of four-bars along a common joint axis. Because displacement–closure equations have not been previously developed for all of them, the task is undertaken in this article. Contributing to the examination is a scrutiny of the single motion screw reciprocal to the joint screws of a resultant loop. It is an unconventional approach, but one that is flexible and offers useful insights into the nature of a kinematic chain's mobility.