Displacement Analysis of Foldable V-Polyhedra Based on Dual Quaternions

V-polyhedra is a Kokotsakis-type flat foldable rigid origami with increasing application in the engineering field. Currently, researches on origami mainly focused on foldability and mobility. In order to apply V-polyhedra in practical engineering, the analysis of kinematic characteristics is in need. This paper presents a displacement analysis methodology for the generic point belonging to any surfaces of foldable V-polyhedra. The rigid foldability of four-faced V-polyhedra and that of nine-faced V-polyhedra were discussed first. Then, the corresponding mathematical models are established with the rotating vector model constructed by dual quaternions. Finally, the correctness of the proposed method is verified through application of a symmetric pair of nine-faced V-polyhedra.