Linkage origami is one effective approach for addressing stiffness and accommodating panels of finite size in origami models and tessellations. However, successfully implementing linkage origami in tessellations can be challenging. In this work, multiple theorems are presented that provide criteria for designing origami units or cells that can be assembled into arbitrarily large tessellations. The application of these theorems is demonstrated through examples of tessellations in two and three dimensions.

Folding is a manufacturing method which can create complex 3D geometries from flat materials and can be particularly useful in cost-sensitive or planar-limited fabrication applications. This paper introduces compliant mechanisms that employ folding techniques from origami to evolve from a flat material to deployed state. We present origami-inspired sacrificial joints, joints which have mobility during assembly of the mechanism but are rigid in their final position, to create regions of high and low stiffness and the proper alignment of compliant flexures in folded mechanisms. To demonstrate the method we fold steel sheet to create some well-known and complex compliant mechanisms.

Linkage origami is one effective approach for addressing stiffness and accommodating panels of finite size in origami models and tessellations. However, successfully implementing linkage origami in tessellations can be challenging. In this work, multiple theorems are presented that provide criteria for designing origami units or cells that can be assembled into arbitrarily large tessellations. The application of these theorems is demonstrated through examples of tessellations in two and three dimensions.