Design Theory Of Double Chain Mechanism And Its Application In Retractable Structures

In this dissertation, we explore the possibilities of constructing new deployable structures using a family of over-constrained mechanisms named planar Double Chain linkages with only revolute joints as basic elements. These deployable structures only own a single degree of freedom, which makes them ideal for use as retractable roofs.The first part of the dissertation is devoted to review the history of planar closed loop over-constrained linkages and classify these linkages. Meanwhile, according to the requirement of this dissertation, two analytical methods, the complex vector method and the matrix method, are developed.The second part of the dissertation deals with the planar closed loop Double Chain linkages consisting of a series of scissor like pairs connected by hinges. According to the mathematical and topological derivation, a series of rules are proposed, which have been extended to form two classifications of Double Chain linkages. One classification of Double Chain is based on the assumption, i.e., the angulated elements of Double Chain subtend a constant angle as their rods rotate. The condition for the angulated elements with this characteristic has been derived. Furthermore, the problem of connecting these angulated elements into a mobile Double Chain, which other researchers were unable to solve, has also been solved. The other classification of Double Chain is made of a serious of loop parallelograms, i.e., in the assemblies each set of four neighbouring hinges form a parallelogram. Three cases of mobile assemblies have been identified: the chains with intersecting and non-intersecting pairs as well as a mixture of both pairs. The corresponding mobility conditions are derived. In addition, a simple method to extend Double Chain has been introduced. A study into the fixed points of Double Chain has also been done, i.e., Double Chain is always mobile when they rotate with these fixed points.The third part of the dissertation is concerned with module techniques in order to develop an approach for determining the layout of mobile assemblies. Starting with the tiling techniques and the study of polygonal array, it has been found that the rules of polygonal array can be applied completely in Double Chain to construct large deployable structures. Furthermore, in-depth research into the symmetrical Double Chain, including combined rules and types, module compatibility and opening rate, has also been conducted. Based on this approach, the construction of large deployable structures can be divided into three steps: selection of suitable tiling, construction of over-constrained units and validation of compatibility. Finally, three possible configurations with module techniques are discussed, including mobile plate assemblies, mobile pyramidal assemblies and mobile projective assemblies. These configurations have been successfully applied to the construction of the structural mechanisms based on Double Chain.The final part of the dissertation is a study into the radially retractable plate structures (RPS) which are a family of new retractable structures consisting of a set of cover plates connected by revolute hinges. In the current designing of an RPS, two obvious shortcomings are in existence. First, there is a lack of a convenient way to keep all the pivots of an angulated beam within the boundary of its corresponding RPS plate. Secondly, the stiffness of the RPS is too small to resist external loads, which limits the practical application of this structure. This part aims to tackle these two problems. To solve the first problem, a mathematical method is proposed to determine whether all of the pivots of a multi-angulated beam are within its corresponding plate. The mathematical approach can be used regardless of the boundary's profile. The approach can be extended into both symmetrical and non-symmetrical structures. To increase the stiffness of the RPS, a few support conditions for the RPS are discussed and the structural behavior of numerical simulated models under different support conditions is investigated. Moreover, some measures to increase the stiffness of the RPS are proposed, providing additional choice to the designers.All of the novel Double Chain and their assemblies presented in this dissertation contain only revolute joints, have a single degree of mobility, are over-constrained and physically modeled to demonstrate that the design theory in this dissertation is correct. Research work reported in this dissertation could lead to substantial advancement in building large spatial deployable structures.