On the Singularity Analysis of Origami Using Graph and Screw Theories

This paper presents a comprehensive study on the mobility and redundancies of an origami in its fully unfolded, partially folded, and fully folded configurations by applying graph and screw theories via Davies' method. It seeks to take advantage of the existing analogies between origami and spherical mechanisms to apply the Davies method in the kinematic analysis of origami. A detailed calculation of the mobility of two origamis is performed, identifying redundant constraints in each configuration. In addition, the singular positions of the origami in each state are explored, providing an in-depth understanding of their behavior under different conditions. These results not only provide a comprehensive insight into origami kinematics, but also have significant implications for the design and application of origami-inspired mechanisms in various fields, ranging from robotics to structural engineering.