Foldable Hexagonal Structures Based on the Threefold-Symmetric Bricard Linkage

Abstract The threefold-symmetric Bricard linkage, a special type of Bricard linkage, is able to generate spatial motion in 3D space with well-defined threefold rotational symmetries and three symmetric planes, which makes it a robust base linkage in designing many one-degrees-of-freedom (DOF) foldable structures. However, its practical applications are limited, as the design method with the consideration of the actual assembly is still an ambiguous area. In this paper, a foldable hexagonal structure based on the alternative form of the threefold-symmetric Bricard linkage is designed and manufactured. Geometric conditions for achieving the desired deployment are analyzed at first. Then the relationship among kinematic variables of the linkage and the geometric parameters of physical bars with a regular triangular cross-section are set up. Finally, an intuitive approach is presented to detect two types of physical blockages in the motion paths of deployment. The proposed method supplies a convenient way to design foldable hexagonal structures for potential practical applications.