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The trend toward smaller mechanism footprints and volumes, while maintaining the ability to perform complex tasks, presents the opportunity for exploration of hypercompact mechanical systems integrated with curved surfaces. Developable surfaces are shapes that a flat sheet can take without tearing or stretching, and they represent a wide range of manufactured surfaces. This work introduces “developable mechanisms” as devices that emerge from or conform to developable surfaces. They are made possible by aligning hinge axes with developable surface ruling lines to enable mobility. Because rigid-link motion depends on the relative orientation of hinge axes and not link geometry, links can take the shape of the corresponding developable surface. Mechanisms are classified by their associated surface type, and these relationships are defined and demonstrated by example. Developable mechanisms show promise for meeting unfilled needs using systems not previously envisioned. 

Origami concepts show promise for creating complex deployable systems. However, translating origami to thick (non-paper) materials introduces challenges, including that thick panels do not flex to facilitate folding and the chances for self-intersection of components increase. This work introduces methods for creating permutations of linkage-based, origami-inspired mechanisms that retain desired kinematics but avoid self-intersection and enable their connection into deployable networks. Methods for reconfiguring overconstrained linkages and implementing them as modified origami-inspired mechanisms are proved and demonstrated for multiple linkage examples. Equations are derived describing the folding behavior of these implementations. An approach for designing networks of linkage-based origami vertices is demonstrated and applications for tessellations are described. The results offer the opportunity to exploit origami principles to create deployable systems not previously feasible.

 

A variety of electronic phases in solid-state systems can be understood by abstracting away microscopic details and refocusing on how Fermi surface topology interacts with band structure to define available electron states1. In fact, topological concepts are broadly applicable to non-electronic materials and can be used to understand a variety of seemingly unrelated phenomena2,3,4,5,6. Here, we apply topological principles to origami-inspired mechanical metamaterials7,8,9,10,11,12, and demonstrate how to guide bulk kinematics by tailoring the crease configuration-space topology. Specifically, we show that by simply changing the crease angles, we modify the configuration-space topology, and drive origami structures to dramatically change their kinematics from being smoothly and continuously deformable to mechanically bistable and rigid. In addition, we examine how a topologically disjointed configuration space can be used to constrain the locally accessible deformations of a single folded sheet. While analyses of origami structures are typically dependent on the energetics of constitutive relations11,12,13,14, the topological abstractions introduced here are a separate and independent consideration that we use to analyse, understand and design these metamaterials. 

The design and manufacture of an origami‐based liver‐on‐a‐chip device is presented, together with demonstrations of the chip's effectiveness at recapitulating some of the liver's key in vivo architecture, physical microenvironment, and functions. Laser‐cut layers of polyimide tape are folded together with polycarbonate nanoporous membranes to create a stack of three adjacent flow chambers separated by the membranes. Endothelial cells are seeded in the upper and lower flow chambers to simulate sinusoids, and hepatocytes are seeded in the middle flow chamber. Nutrients and metabolites flow through the simulated sinusoids and diffuse between the vascular pathways and the hepatocyte layers, mimicking physiological microcirculation. Studies of cell viability, metabolic functions, and hepatotoxicity of pharmaceutical compounds show that the endothelialized liver‐on‐a‐chip model is conducive to maintaining hepatocyte functions and evaluation of the hepatotoxicity of drugs. The unique origami approach speeds chip development and optimization, effectively simplifying the laboratory‐scale fabrication of on‐chip models of human tissues without necessarily reducing their structural and functional sophistication.