On mobile assemblies of Bennett linkages

This paper deals with deployable structures formed by interconnected Bennett linkages. A total of eight cases that allow mobile assemblies of Bennett linkages being built have been found by considering the links that may contain sections with negative length. Among the eight assemblies, four are distinct ones, including the one that we reported previously, and the remaining can be obtained by modifying the four cases. All these assemblies consist of a grid of nested Bennett linkages. The layout of the assemblies can be repeated to form a large deployable structure. When the Bennett linkages are equilateral, the assemblies expand to form arches. For a non-equilateral case, the assemblies deploy into a helical shape with a cylindrical profile. They are geometrically overconstrained with a single degree of mobility. The newly found assemblies provide more choices in the design of deployable structures.