Mobile assemblies of Bennett linkages from four-crease origami patterns.

This paper deals with constructing mobile assemblies of Bennett linkages inspired by four-crease origami patterns. A transition technique has been proposed by taking the thick-panel form of an origami pattern as an intermediate bridge. A zero-thickness rigid origami pattern and its thick-panel form share the same sector angles and folding behaviours, while the thick-panel origami and the mobile assembly of linkages are kinematically equivalent with differences only in link profiles. Applying this transition technique to typical four-crease origami patterns, we have found that the Miura-ori and graded Miura-ori patterns lead to assemblies of Bennett linkages with identical link lengths. The supplementary-type origami patterns with different mountain-valley crease assignments correspond to different types of Bennett linkage assemblies with negative link lengths. And the identical linkage-type origami pattern generates a new mobile assembly. Hence, the transition technique offers a novel approach to constructing mobile assemblies of spatial linkages from origami patterns.