  We characterise the kinematic image of the constraint variety of a 2R dyad as
a regular ruled quadric in a 3-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.
