Geometric Design of Deployable Spatial Structures Made of Three-Dimensional Angulated Members

During their early development, deployable structures were constructed using translational and polar scissor units. The discovery of angulated units revolutionized the field and popularized radially deployable geometries. This paper presents a geometric design method for axisymmetric grid structures made of three-dimensional angulated scissor units on a regular polygonal base. The method is applied to a series of forms, namely: Positive, zero, and negative curvature shapes, and validated using a graphical procedure. The paper also describes the kinematic analysis of deployable planar rings and three-dimensional axisymmetric grids. Position, velocity, and acceleration (PVA) analyses provided insights into the structures' motion characteristics and the influence of geometric parameters on their deployment and folding.