The Kinematic Image of 2R Dyads and Exact Synthesis of 5R Linkages
This work addresses a specific problem in mechanical engineering for linkage design, but it appears incremental as it builds on prior algorithms for 6R linkages.
The authors tackled the problem of synthesizing 5R linkages by characterizing the kinematic image of 2R dyads as a regular ruled quadric and modifying an existing algorithm for 6R linkages to produce 5R linkages, resulting in a method that explains peculiar properties using classical geometry.
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.