Rigid-foldable tapered multi-tubular structures by extending type III Bricard octahedra

This paper investigates the construction and kinematics of rigid-foldable tapered multi-tubular structures derived from type III Bricard octahedra (BOIII). The partially folded BOIII can be recursively extended in the longitudinal direction to form larger tapered tubes. We further introduce a novel transverse extension of the BOIII, enabling the formation of composite BOIIIs with a single degree of freedom. When longitudinally extended, the composite BOIIIs generate rigid-foldable multi-tubular structures. Specifically, we examine plane-symmetric multi-tubular structures and demonstrate the creation of structures with adjustable zigzag and spiral profiles by varying input sector angles. Like the BOIII, these multi-tubular structures exhibit two distinct collapsible or flat states, allowing for compact storage and a large deployment ratio. Both sides of these structures are origami patterns that are free from self-intersection at the initial flat state, facilitating efficient fabrication through folding and subsequent assembly. The resulting multi-tubular structures have potential applications in reconfigurable heat and air conduction tubes, robotic arms, meta-materials, and architectural design.