Spatial 6R linkages based on the combination of two Goldberg 5R linkages

In this paper, we report the creation of a pair of 6R linkages by combining Goldberg 5R linkages. The new linkages are similar to the Bennett-joint 6R linkages proposed by Mavroidis and Roth. However, unlike the Bennett-joint 6R linkages, the Bennett ratio, defined as the ratio between the sinusoidal value of the twist over a link and the length of the link, is not necessarily to be the same for all of the six links. The geometric parameters of the new linkages are defined and the closure equations have been derived. Physical models of the new linkages were constructed which validates our derivation.