Vertex-Splitting on a Diamond Origami Pattern

A diamond origami pattern is a well-known origami pattern consisting of identical six-crease vertices. As each vertex can be modeled as a spherical 6R linkage with three degrees of freedom (DOF), the tessellated pattern with multiple vertices is a multi-DOF system, which makes it difficult to fully control the motion in the desired symmetric manner. Here, two splitting schemes on the diamond vertex are proposed to generate three types of unit patterns to reduce the DOF. This vertex-splitting technique is applied to the multivertex diamond origami pattern to produce several one-DOF basic assemblies, which form a number of one-DOF origami patterns. Two of the one-DOF origami patterns are discussed: one of which is a flat-foldable origami pattern mixed with four- and six-crease vertices and the other is a nonflat-foldable one mixed with four-, five-, and six-crease vertices. In the one-DOF patterns, the symmetrically kinematic property of the original diamond origami pattern is well kept. Such property would significantly facilitate engineering applications comparing to the multi-DOF origami patterns. It also paves a new road to construct one-DOF origami patterns.