Geometric and Kinematic Analysis of Deployable Doubly Ruled Hyperboloids

Abstract

ÖZThis 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. Keywords: Deployable hyperboloids; doubly-ruled surfaces; kinetic structures; structural mechanisms. ABSTRACT IntroductionThe geometrical simplicity and structural advantages of doubly curved anticlastic surfaces opened a wide range of applications in architecture and engineering. Pioneered by Vladimir Shukhov, Antoni Gaudi and Félix Candela, anticlastic surfaces such as hyperboloid of one sheet and hyperbolic paraboloid (hypar) have been used for cooling towers, oil and water storage tanks, radio and transmission masts, offshore structures and other industrial premises. Over the last century, various different types of structures in the forms of hyperboloid and hypar have been built around the world. Hyperboloid geometry's surface generation method and its form based structural behavior played a fundamental role in constructing hyperboloid structures. Since the straight-line generators can form the anticlastic surface, concrete shell structures have been easily constructed by using straight wooden boards, which not only simplified the formwork but also provided efficient use of construction materials. Hence, various elegant structures with different curvatures could be realized to span over large areas. Likewise, steel and timber grid shells made with lattice of straight beams have been developed to obtain not only

Design Optimization of Hyperboloid Wooden House Concerning Structural, Cost, and Daylight Performance

“…Then, as seen in Figure 2b, the skew line is rotated clockwise along the z-axis with the selected phase angle. Following that, with the same twist angle, the same skew line that is mirrored around the vertical axis is rotated counterclockwise (Figure 2c) [17]. The properties of a hyperboloid can also be described by the relation of one point to another.…”

“…The results showed how the MOO can produce attractive, creative, and high-performance design that There are several advantages to the use of the hyperboloid structure. It is associated with aesthetics, structural integrity, and efficiency that influence modern architecture [17]. Firstly, it is very resistant to buckling due to the straight member.…”