Reprogrammable Kinematic Branches in Tessellated Origami Structures

We analyze the folding kinematics of a recently proposed origami-based tessellated structure called the Morph pattern, using thin, rigid panel assumptions. We discuss the geometry of the Morph unit cell that can exist in two characteristic modes differing in the mountain/valley assignment of a degree-four vertex and explain how a single tessellation of the Morph structure can undergo morphing through rigid origami kinematics resulting in multiple hybrid states. We describe the kinematics of the tessellated Morph pattern through multiple branches, each path leading to different sets of hybrid states. We study the kinematics of the tessellated structure through local and global Poisson's ratios and derive an analytical condition for which the global ratio switches between negative and positive values. We show that the interplay between the local and global kinematics results in folding deformations in which the hybrid states are either locked in their current modes or are transformable to other modes of the kinematic branches, leading to a reprogrammable morphing behavior of the system. Finally, using a bar-and-hinge model-based numerical framework, we simulate the nonlinear folding behavior of the hybrid systems and verify the deformation characteristics that are predicted analytically. ; © 2021 by ASME. Contributed by Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received September 27, 2020; final manuscript received January 18, 2021; published online March 12, 2021. Assoc. Editor: Philip A. Voglewede. We acknowledge support from the National Science Foundation (NSF) through grant CMMI 1538830, and from the endowment provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology. PPP acknowledges the support from the Indian Institute of Technology Madras and the Science & Engineering Research Board (SERB) of the Department of Science & Technology, Government of India, through award SRG/2019/000999. SPV acknowledges the ...