Deployable space structures have long been investigated as a means for packaging the desired solution within the confines of the launch environment. In this study, the design of a highly compact reflector that can be stowed in a 1U CubeSat is addressed. The ideal diameter of the finished reflector is 1 meter. In order to accomplish this objective, a folding method is developed and design constraints are derived from the packaging requirement. A design method is presented in which the deployed shape is divided into gores and flattened for manufacturing. Constraints on the shape of the gores are imposed in order to produce a flat configuration with desirable stowing characteristics. Two iterations of the design are presented with deployed diameters of 0.8 and 0.5m and final stowed diameters of 16 and 14cm respectively.
This paper presents a novel scheme to biaxially package and deploy flat membranes, in which the thickness of the membrane is accounted for through the novel concept of slipping folds. The membrane is divided into parallel strips connected by slipping folds, and specially chosen wrapping profiles that require zero slip along the edges of the membrane are identified. This packaging scheme avoids the kinematic incompatibilities that in other schemes result in local buckles and wrinkles that increase the deployment force and permanently deform the membrane. The paper also presents a scheme to apply uniform uniaxial prestress to the deployed membrane, as well as a two-stage deployment scheme. Packaging efficiencies of up to 83% have been demonstrated for meter-scale models, although for large membranes the packaging efficiency approaches 100%.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.