A closed 6R linkage is generically rigid. Special cases may be mobile. Many families of mobile 6R linkages have been characterised 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.


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    Title :

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


    Contributors:


    Publication date :

    2015




    Type of media :

    Article (Journal)


    Type of material :

    Print


    Language :

    English



    Classification :

    BKL:    52.20 Antriebstechnik, Getriebelehre / 50.32 Dynamik, Schwingungslehre / 50.25 Robotertechnik