A Multi-Bennett 8R Mechanism Obtained From Factorization of Bivariate Motion Polynomials

Overconstrained linkages is a long-lasting but still highly active topic of research in mechanism science. For several decades, researchers focused on overconstrained mechanisms consisting of a single loop of n 6 revolute joints (R), prismatic joints (P), or, sometimes, helical joints (H). New linkages of that type are continuously being discovered, often by craftily combining known linkages [2, 3, 28], sometimes via novel concepts for their construction. One of these concepts is the factorization of motion polynomials [8]. It gave rise to the construction of the only class of overconstrained 6R linkages with still unknown relations between its Denavit-Hartenberg parameters. In [6, 9, 17-20], motion polynomial factorization was exploited for the synthesis of linkages. In spite of some attempts, a complete classification of overconstrained single-loop linkages is currently out of reach. It is thus natural that research efforts shifted towards the investigation of single-loop linkages consisting of n 7 links with, generically, n 6 1 degrees of freedom.