On a type of radially retractable plate structures

The radially retractable plate structures (RPS) are a family of new retractable structures consisting of a set of cover plates connected by revolute hinges. The concept evolves from the foldable bar structures (FBS) by replacing the beams in an FBS with cover plates. With a single degree of freedom, the structures close to form a covered enclosure and expand to reveal a large central opening space, which makes them ideal for use as retractable roofs. In designing the plates of an RPS, two primary requirements have to be met. First, the boundary of these plates must be designed such that they form an enclosure without any gaps or overlaps in both closed and open configurations, and the plates do not interfere with each other during deployment. Second, all of the pivots of a beam must remain within the boundary of its corresponding RPS plate. This paper tackles the second problem. To meet the requirement, an analytical method is proposed. A feasible design area, defined by closed and open angles of the corresponding FBS, can be identified under this approach. The designers are no longer limited to use the empirical or numerical means to determine whether all of the pivots of a multi-angulated beam are within its corresponding plate. The analytical approach can be used regardless of the boundary’s profile. The approach can be extended into both symmetrical and non-symmetrical structures. Physical models built to validate our approach have shown that the analysis is correct.