The Kinematic Image of 2R Dyads and Exact Synthesis of 5R Linkages

We characterise the kinematic image of the constraint variety of a 2R dyad as a regular ruled quadric in a three-space that contains a “null quadrilateral”. Three prescribed poses determine, in general, two such quadrics. This allows us to modify a recent algorithm for the synthesis of 6R linkages in such a way that two consecutive revolute axes coincide, thus producing a 5R linkage. Using the classical geometry of twisted cubics on a quadric, we explain some of the peculiar properties of the the resulting synthesis procedure for 5R linkages.