Generalized geometry of foldable scissor grids based on polar units

Deployable scissor structures are hinged-bar mechanisms that can rapidly transform between different configurations. The past decades many different types of scissor structures have been developed for various applications. Double curvature is often desired to obtain functional and appealing shapes with a good structural performance. Consequently polar scissor units have been extensively studied for their ability to generate doubly curved scissor structures that can undergo large volume expansions. Unfortunately this double curvature could only be spherical. We propose a generalization of the polar scissor unit that can be used to translate the existing spherical scissor grids into non-spherical ones while maintaining their kinematic behaviour. Therefore it uncovers a large unexplored potential and broadens the applicability of this scissor grid type. This paper presents this innovative method together with a new joint model that preserves the geometric compatibility. Scale models are used to verify and illustrate the concepts presented in this paper.

Keywords:transformable structures, deployable scissor structures, geometric design, non-spherical double curvature, generalization, mechanism, joints, scale model, polar units