A technique for deriving equational conditions on the Denavit–Hartenberg parameters of 6R linkages that are necessary for movability

• We compute the configuration space of a 6R linkage.
• We give necessary conditions for the mobility.
• We give a new mobile 6R linkage.

A closed 6R linkage is generically rigid. Special cases may be mobile. Many families of mobile 6R linkages have been characterized in terms of the invariant Denavit–Hartenberg parameters of the linkage. In other words, many sufficient conditions for mobility are known. In this paper we give, for the first time, equational conditions on the invariant Denavit–Hartenberg parameters that are necessary for mobility. The method is based on the theory of bonds. We illustrate the method by deriving the equational conditions for various well-known linkages (Bricard's line symmetric linkage, Hooke's linkage, Dietmaier's linkage, and recent a generalization of Bricard's orthogonal linkage), starting from their bond diagrams; and by deriving the equations for another bond diagram, thereby discovering a new mobile 6R linkage.