Rigid origami of thick panels and deployable membranes

Rigid origami is about folding flat inextensional facets which are connected by creases. It is gaining popularity and being used in an increasing number of engineering applications. Since this is a relatively new field, a number of challenges exist, e.g., folding facets with a finite thickness and achieving folding compactness. This dissertation summarises two attempts to address these two issues. Specific attention has been drawn to the offset crease technique and the wrapping membrane patterns. In the first part of this dissertation, I have established a kinematic model describing the offset crease models, which leads to a proof that the motion of the thick panel folding is kinematically equivalent to that of its parent pattern with zero thickness. A detailed design approach for adapting this technique has been proposed and proven to be effective by various physical implementations. In order to achieve a higher compactness, an anisotropic tessellation has been derived from the traditional Miura-ori pattern. Its compatibility with pre-existing thickness accommodation approaches has been demonstrated via thick-panel models. The second part of the dissertation examines a number of deployable membrane patterns. Firstly, the hexagonal winding membrane has been validated with a strict mathematical proof that a rigid transition is non-existent. Therefore, a number of newly proposed wrapping patterns have been designed and their motions have been studied via numerical simulation to discover the adequate rigid-foldable patterns. The algorithm of the simulation has been synthesised to create visualisation software for simulating general origami patterns. Furthermore, we have proposed a comprehensive scheme to allow arbitrary material thickness to be accommodated for the wrapping patterns. Finally, a sequential square twist pattern with a high deployed-to-stowed ratio has been created.