Multiple linkage forms and bifurcation behaviours of the double-subtractive-Goldberg 6R linkage

In this paper, a particular type of double-subtractive-Goldberg 6R linkage is obtained by combining two subtractive Goldberg 5R linkages on the commonly shared ‘roof-links’ through the common link-pair method and common Bennett-linkage method. Two distinct linkage forms are obtained with the identical geometry conditions, yet different closure equations. Bifurcation behaviours of these two forms are analysed, leading to the discovery of two more linkage forms of this linkage, which cannot be constructed with Bennett linkages or Goldberg linkages directly. From the construction process, this 6R linkage belongs to the Bennett-based linkages. But about the bifurcation behaviours, it is closely related to the line-symmetric Bricard linkage because of its hidden symmetric property. Therefore, it could play an important role in exploring the relationship between the Bennett-based linkages and the Bricard linkages.