On the generation of new linkages from Bennett loops

Abstract We expound the geometrical principles which underlie the combining of Bennett chains to produce new 5-R and 6-R linkages. Waldron's hybrid chain and Goldberg's generalised primary chains are directly compared and related to well established mobility criteria. Goldberg's generalised 5-R chain is shown to be a degeneracy of a special form of Waldron's hybrid loop. Syncopated linkages are also considered, and the geometrical criteria for their mobility are shown to be consistent with currently accepted ones. A syncopation of a hybrid linkage is constructed for the first time. The linkages examined are further delineated and compared by determining their equations.