Geometric and Kinematic Analysis of Deployable Doubly Ruled Hyperboloids

This paper aims to develop deployable doubly ruled hyperboloid surfaces that can be used in architectural applications. First, the study systematically analyzes the geometric principles of hyperboloids generated by the ruled surface generation method and examines the morphology to generate different types of hyperboloids. Then, a method is introduced to construct deployable doubly ruled hyperboloid surfaces. The study demonstrates that deployment behavior of the hyperboloid is directly related to joint types used at the intersection points of the bars. Based on kinematic analysis, the study establishes that deployable hyperboloids with a single degree of freedom can be constructed only by revolute and spherical joints. Finally, various hyperboloids having different number of intersections are constructed according to the proposed joint types and their deployment capabilities are discussed.