Geometric Design of Axisymmetric Spatial Structures Using Planar Angulated Members

Geometric design methods for deployable structures matured considerably during the latter half of the twentieth century. This article presents the geometric formulation for axisymmetric spatial structures using angulated scissor units. The formulas for the principal parameters, namely, the semilengths and kink angles of angulated members, are derived using three methods. One of them is a simplified semi-analytical method based on a unique property of isosceles trapezoids. The method lends itself for use in graphical and parametric computer programs. It was found that predetermined shapes dictated by architectural or other reasons may not deploy or compact fully. The packaging of forms can be improved by using more polygon sides and fewer vertical layers. To calculate fully deployable and compact forms, a compactness criterion is defined and discussed. The influence of shape and geometric parameters is described to motivate intuitive understanding for the design of any axisymmetric form. Although research on geometric design seems to have advanced considerably, there is still scope for improved and simplified methods that lend themselves to implementation in graphical computer programs.