Double Bennett Mechanisms with Assembly Modes of Different Dimensions

By considering the geometry of the Bennett 3R open-chain linkage it is possible to predict the possible configuration spaces of 6R closed loop mechanisms formed by joining pairs of Bennett linkages. Attention is confined to cases where the configuration space can be described by the intersection of three quadric surfaces in a three-dimensional projective space. There are just five possibilities which contain a component of dimension one. Two of these possibilities correspond to well-known constructions for forming mobile overconstrained 6R mechanisms from Bennett linkages. The geometry shows that these configuration spaces must also contain a number of isolated configurations, a result we believe to be new. Finally we are able to show that one of the other five geometric possibilities cannot occur as the configuration space of a double Bennett mechanism.