New Mechanical Generators of Schoenflies Motion Implementing Bennett Linkages

Based on the Bennett 4R chain, we construct a rotating loop by fixing one R axis to the frame and the fixed R becomes a coaxial double R pair. The R pair opposite to the fixed double R is replaced by a spherical S pair which can be equivalent to a (RRR) open chain with non-coplanar intersecting axes. In the (RRR) sub-chain, we choose special axes and derive R|- R|(R(RRR)R chain moving with 2 DoFs. That moving R becomes a coaxial double R with the addition of another rigid body and the obtained chain with hybrid topology generates a 3-dof motion, which is mathematically modeled by a 3D submanifold of a 4D group of X motions. Because of the product closure in an X-motion group, adding an H pair with any pitch and an axis parallel to the fixed R axis leads to a mechanical generator of a 4D X-motion group. Then, parallel arrangement of two generators of the same X motion gives a new parallel generator of X motion, which can be actuated by four fixed R pairs; the two Hs must have distinct pitches. A special design with four collinear actuated axes is revealed too.