Reconfigurable chains of bifurcating type III Bricard linkages

This paper presents the construction of a family of reconfigurable mechanisms composed of an unlimited number of doubly collapsible (type III) Bricard linkages. First, the geometries of these overconstrained six-hinge spatial loops are parameterized and their kinematics is investigated. The configurationspace curve is computed; its bifurcation behavior is analyzed and illustrated by projections. It is then shown that type III Bricard linkages can be connected in series in a one-degree-of-freedom chain. Such a multi-loop mechanism has the ability to reconfigure in multiple ways due to the bifurcations of the individual Bricard units. Consequently, the chain has multiple states where all joint axes are coplanar. In each such configuration, the physical links, every one realized as a planar figure, spread out to cover a curving stripe in the plane. Several simulations and case studies are performed.