A New Approach to the Generation of Retractable Plate Structures Based on One-Uniform Tessellations

Abstract

Retractable plate structure (RPS) is a family of structures that is a set of cover plates connected by revolute joints. There exists wide range of possibilities related with these structures in architecture. Configuring the suitable shape of rigid plates that are able to be enclosed without any gaps or overlaps in both closed and open configurations and eliminating the possibility of contact between the plates during the deployment have been the most important issues in RPS design process. Many researchers have tried to find the most suitable shape by using kinematical or empirical analysis so far. This study presents a novel approach to find the suitable shape of the plates and their assembly order without any kinematical or empirical analysis. This approach is benefited from the one-uniform mathematical tessellation technique that gives the possibilities of tiling a plate using regular polygons without any gaps or overlaps. In the light of this technique, the shape of the plates is determined as regular polygons and two conditions are introduced to form RPS in which regular polygonal plates are connected by only revolute joints. It should be noted that these plates are not allowed to become overlapped during deployment and form gaps in closed configuration. Additionally, this study aims to reach a single degree-of-freedom (DoF) RPS. It presents a systematic method to convert multi-DoF RPS into single DoF RPS by using the similarity between graph theory and the duality of tessellation.