Motion singularity analysis of the thick-panel kirigami

Abstract

Thick-panel kirigami, constructed by cutting open creases on origami structures, can be applied to deployable structures with different Gaussian curvatures. By converting creases to rotational hinges, thick-panel kirigami can be treated as the assembly of spatial linkage, which provides accurate and precise deployment motion. Compared with origami, kirigami structures are able to optimize jagged deployed surfaces by geometry parameter adjustment. However, replacing several creases with slits in structures may lead to shortcomings in kinematics, i.e., motion singularity. In this study, motion singularity of thick-panel kirigami structure is discussed. Starting with kirigami units, bifurcation paths are detected and followed by the predictor-corrector numerical method. We then check the corresponding extension kirigami arrays and explore their complex bifurcation behaviors. The result indicates that the bifurcation motion paths within kirigami structures may lead to incomplete deployment. Physical prototypes are carried out, which successfully validate the singularity analysis. Also, motor- and spring-based hinges are arranged for driving, and the redundant actuator method is considered to avoid bifurcations and accomplish the full deployment. The findings are applicable to the design of kirigami-inspired deployable structures for engineering applications in the future.