On syncopated and augmented six-revolute linkages

Among the known six-revolute linkages, the two “syncopated” loops appear as peculiar by virtue of the formulation of their governing equations. The first was due to Goldberg and the second was found some four decades later by applying his technique to a different hybrid chain. A re-examination here of the latter solution leads to a third syncopated loop. Further investigation and a related method of synthesis, dubbed “augmentation”, yields a second new linkage which is found to have as particular cases the family of “foldable” six-bars recently reported.