A method of calculating the degree of freedom of foldable plate rigid origami with adjacency matrix

Abstract

The mechanism with good fold performance derived from rigid origami is widely used in the field of engineering. In this article, the adjacency matrix method was proposed to analyze the degree of freedom of foldable plate rigid origami. This method can also judge the number of redundant constraints while calculating the degree of freedom of the rigid origami. First, the adjacency matrix between vertices of origami structure was established. Then the elimination matrix was introduced, and the process of determining the motion state of vertices was described by matrix product. The degree of freedom of rigid origami was determined by calculating the number of constraints introduced. A method for judging redundant constraints of rigid origami was proposed, and the number of redundant constraints was determined by computing the sum of the row elements corresponding to the vertices. The motion state of the cross-crease vertex was analyzed, and the computational error of the degree of freedom at the cross-crease vertex was avoided by the method of classification and simplification. The degree of freedom of the ring pattern was discussed, and the calculation method of the degree of freedom of whole pattern with many ring patterns was summarized. Finally, the degree of freedom of typical rigid origami was analyzed.