A family of mixed double-Goldberg 6R linkages

Abstract

A complete family of double-Goldberg 6R linkages is reported in this article by combining a subtractive Goldberg 5R linkage and a Goldberg 5R linkage through the common link-pair or common Bennett-linkage method. A number of distinct types of overconstrained linkages are built, namely the mixed double-Goldberg 6R linkages. They all have one degree of freedom and their closure equations are derived in detail. One of them degenerates into a Goldberg 5R linkage. From the construction process and geometry conditions, the corresponding relationship between the newly found 6R linkages and the double-Goldberg 6R linkages, constructed from two Goldberg 5R linkages or two subtractive Goldberg 5R linkages, has been established.