Shape-Morphing Space Frame (SMSF) Using Quadrilateral Bistable Unit-Cell Elements

This paper presents a new concept: a Shape-Morphing Space Frame (SMSF) using quadrilateral bistable unit-cell elements. The unit-cells are composed of either eight-bar or seven-bar mechanisms in which design constraints, system of elimination and graph theory are used to design, as a proof of concept, a disk like structure with the ability to morph into a sphere. Or specifically, the circumference of a disk structure is approximated by a ten-sided polygon that would then morph into a hollow sphere structure that is approximated by 60-sided polyhedron. The disk-to-sphere structure is tessellated into ten sides for the latitudes circles and 12 sides for the longitude circles; the disk’s thickness and radius are chosen at the design stage. The strategy in morphing the initial shape of the structure (disk) into its final shape (sphere) is that the radial lines on the surface of the disk bend but do not stretch, whereas the circumferential lines compress. Moreover, the radial lines on the disk become longitude lines on the sphere and the circumferential lines become latitude lines on the sphere. The disk’s thickness splits in half, the upper half becomes the thickness of the upper hemisphere and the lower half becomes the thickness of the lower hemisphere. The concept was successfully prototyped and actuation forces were measured.