Kinematic Solutions and Bifurcation Analysis of Single Vertex Origami Pattern

The bifurcation behavior of deployable structures has received significant attention from different fields. Apart from pin-jointed structures, origami, as a thriving inspiration for valuable and practical deployable structures, develops singular configurations along its kinematic paths. The kinematic behaviors of single vertex origami patterns are studied in this work. General four-crease patterns and symmetric six-crease patterns are thoroughly investigated based on the analytical solutions obtained by constraint equations. Moreover, the corresponding motion paths are described to discuss the bifurcation behavior. A comparative analysis of kinematic behaviors with the different actuating coordinates is performed. Three types of bifurcation are analyzed, concluding that three different motion paths cannot occur at the same time. The research findings of the present work can contribute to the development of novel deployable structures and mechanical systems.