Origami based deployable surfaces: an optimization approach

This thesis explores using origami and optimisation approaches for designing deployable structures. In particular, the problem of solid-surface deployable reflectors is studied, and optimal designs are pursued under simultaneous constraints including rigid foldability, double curvature and complex collision between finite thickness components. The research includes three aspects. First, optimality of origami designs is pursued. Many origami designs as well as deployable reflector designs are defined and presented without discussion of whether they are the best possible design. Here, an optimisation approach is used to produce best results for predefined design problems with specific requirements. Second, a formalised design methodology is pursued. A process is developed where a deployable structure design problem is translated into an origami design problem, and the origami design problem into an optimisation problem. This provides a formalised and mostly automated path towards optimal deployable structures designs. Third, design results for the class of stringent design problems studied here are explored. Complex local constraints such as collision are solved via adjustment of the global folding kinematics. It is shown that using the novel design approach developed here, optimal results with tangible improvement upon previous designs, as well as unforeseen features can be obtained. The two main foci of the work included in this thesis are two deployable reflector concepts based on the flasher and Miura-ori pattern respectively. The former introduces a new variant of the flasher pattern involving cut creases. Advances include achievement of full rigid foldability under double curvature, optimised compact stowage, and details such as elimination of gaps between panels, all of which are rarely achieved by similar designs. The latter concept uses the Miura-ori pattern and the Hoberman linkage to construct a novel kinematic architecture which has fully adjustable geometry for both the deployed and stowed states, whilst simultaneously achieving single-degree-of-freedom folding.