Modular origami is a type of origami where multiple pieces of paper are folded into modules, and these modules are then interlocked with each other forming an assembly. Some of them turn out to be capable of large scale shape transformation, making them ideal to create metamaterials with tuned mechanical properties. In this paper, we carry out a fundamental research on 2D modular origami assemblies using mathematical tiling and patterns and mechanism analysis, which leads to the development of various patterns consisting of interconnected quadrilateral modules. Due to the existence of 4R linkages within the patterns, they become transformable, and can be compactly packaged. Moreover, by the introduction of paired modules, we are able to adjust the expansion ratio of the pattern. Additionally, we also show that transformable patterns with higher mobility exist for other polygonal modules. Our findings provide more design flexibility to achieve truly programmable metamaterials.

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