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Architected modular origami structures show potential for future robotic matter owing to their reconfigurability with multiple mobilities. Similar to modular robots, the units of modular origami structures do not need to be assembled in a fully packed fashion; in fact, disconnection can provide more freedom for the design of mobility and functionality. Despite the potential of expanded design freedom, the effect of the disconnection of units on the mobility and physical properties has not yet been explored in modular origami structures. Determining the mobility and weak spots of modular origami structures is significant to enable transformation with minimum energy. Herein, we investigate the effect of the disconnection of units on the mobility and stiffness of architected modular origami structures with deformable units using angular kinematics of geometry and topology of units and closed loops. Angular kinematics provides a valuable tool for investigating the complex mobility of architected modular origami structures with the disconnection of loops. The mobility of the network structure is a function not only of the number of disconnections but also of the topology of the loop. In contrast to the conventional negative perception of defects or disconnection in these materials, the disconnection can potentially be used to expand the design space of mobility for future robotic matter. Our findings can be used to develop powerful design guidelines for topologically reconfigurable structures for soft modular robots, active architected materials, implanted modular devices, deployable structures, thermal metamaterials, and active acoustic metamaterials.

Effect of disconnection of deformable units on the mobility and stiffness of 3D prismatic modular origami structures using angular kinematics