Design of structural mechanisms - Chen, Y; Y. Chen (2003)
In this dissertation, we explore the possibilities of systematically constructing large structural mechanisms using existing spatial overconstrained linkages with only revolute joints as basic elements. The first part of the dissertation is devoted to structural mechanisms (networks) based on the Bennett linkage, a well-known spatial 4R linkage. This special linkage has been used as the basic element. A particular layout of the structures has been identified allowing unlimited extension of the network by repeating elements. As a result, a family of structural mechanisms has been found which form single-layer structural mechanisms. In general, these structures deploy into profiles of cylindrical surface. Meanwhile, two special cases of the single-layer structures have been extended to form multi-layer structures. In addition, according to the mathematical derivation, the problem of connecting two similar Bennett linkages into a mobile structure, which other researchers were unable to solve, has also been solved. A study into the existence of alternative forms of the Bennett linkage has also been done. The condition for the alternative forms to achieve the compact folding and maximum expansion has been derived. This work has resulted in the creation of the most effective deployable element based on the Bennett linkage. A simple method to build the Bennett linkage in its alternative form has been introduced and verified. The corresponding networks have been obtained following the similar layout of the original Bennett linkage. The second effort has been made to construct large overconstrained structural mechanisms using hybrid Bricard linkages as basic elements. The hybrid Bricard linkage is a special case of the Bricard linkage, which is overconstrained and with a single degree of mobility. Starting with the derivation of the compatibility condition and the study of its deployment behaviour, it has been found that for some particular twists, the hybrid Bricard linkage can be folded completely into a bundle and deployed to a flat triangular profile. Based on this linkage, a network of hybrid Bricard linkages has been produced. Furthermore, in-depth research into the deployment characteristics, including kinematic bifurcation and the alternative forms of the hybrid Bricard linkage, has also been conducted. The final part of the dissertation is a study into tiling techniques in order to develop a systematic approach for determining the layout of mobile assemblies. A general approach to constructing large structural mechanisms has been proposed, which can be divided into three steps: selection of suitable tilings, construction of overconstrained units and validation of compatibility. This approach has been successfully applied to the construction of the structural mechanisms based on Bennett linkages and hybrid Bricard linkages. Several possible configurations are discussed including those described previously. All of the novel structural mechanisms presented in this dissertation contain only revolute joints, have a single degree of mobility and are geometrically overconstrained. Research work reported in this dissertation could lead to substantial advancement in building large spatial deployable structures.