Introduction
Reconfigurable structures can transform their shapes without entailing the redesign of their achitectures\cite{Yim_2007,Hawkes_2010,Haghpanah_2016,Rocklin_2017}. Recently, origami has gained increasing attention from the scientific and engineering community, because we can construct various types of reconfigurable cellular structures by simply folding surface materials. Examples include interleaved tube cellular structures\cite{Cheung_2014}, zipper-coupled tubes\cite{Filipov_2015}, waterbomb origami\cite{Hanna_2014,Chen_2016} and prismatic architected materials based on snapology\cite{Overvelde_2016,Overvelde_2017}. These origami-based cellular structures exhibit great ability to transform their shape from one state to another. However, one of the major concerns of these structures is to solve the conflict between reconfigurable and load-bearing capabilities. Typically, reconfigurability needs structural flexibility, while load-bearing capability requires structural rigidity.
One way to achieve load-supporting property in origami is a self-blocking mechanism. For example, a stacked Miura-ori structure can significantly increase its maximum load capacity, once it reaches a densification stage\cite{Schenk_2013,Fang_2018}. This mechanism harnesses internal contact between layers, which constrains further deformation of the entire structure. While this mechanism brings a notable enhancement of structural stiffness in origami, such a structure inevitably hits the singular state (i.e., blocked state), from which its kinematic path becomes unpredictable. This makes the system impossible to be reconfigured back to the original state.
Previous studies have also reported non-locking mechanisms to achieve simultaneously reconfigurable and load-bearing capabilities\cite{Cheung_2014,Filipov_2015,Overvelde_2016} by constructing highly overconstrained mechanisms. However, it remains a formidable challenge to switch freely between the reconfigurable and load-bearing modes. Another approach shows the potential of programmable structures switching between different cross sections\cite{Filipov_2016}. This method utilizes the kinematic bifurcation the singular state, leading to an exponential number of modes because of its combinational nature of the kinematics. The controlled actuation from such a kinematically singular state causes the uncertainty of the folding motion\cite{Tachi_2017}, making it theoretically impossible to switch reliably between modes.
Here, we show a new method of realizing a reliable switching between load-bearing capability and folding nature in origami-based cellular structures. Specifically, we exploit the mechanical bifurcation of the Tachi-Miura Polyhedron (TMP)\cite{tachi2010,miura2012,Yasuda_2015}, which exhibits the in-situ transition between two drastically different states: collapsible and load-bearing configurations (see Fig.\ref{944278}A for the conceptual illustration). This behavior is attributed to pure kinematic motions of the TMP cells, which possess a single folding path but with multiple local minima in its dimensions. Depending on the configuration of the TMP unit cell, the structure can be folded into the completely flat (see the schematic illustration marked by (i) in Fig.\ref{944278}B), or loading-carrying shape (see (ii) in Fig.\ref{944278}B, and the photograph for the corresponding paper prototype carrying approximately 17 times its own weight). It should be noted that this dual folding mechanism is based on a rigid origami motion, which means that all deformation takes place only along crease lines, without incurring elastic deformation or plastic buckling of planar facets. This is particularly important for engineering applications to construct a 3D architecture, because it would not necessitate curved or deformable facets. Moreover, the kinematic path depicted in the fold angle parameter space is regular between the states, meaning that the mechanism does not hit kinematic singularity and thus eliminating the uncertainty in the mode switch. Therefore, to actuate this structure, we only need to control the folding angle of the crease lines. To prove this concept, we analytically study the nonlinear kinematic behavior of TMP cells, fabricate paper-based TMP prototypes using a simple self-folding technique, and eventually demonstrate their self-folding actuation to trigger the in-situ transition between collapsible and load-carrying states.