Geometric Design of Planar Scissor Linkages with Hybrid Loop Assemblies

Due to their expansion capabilities and the simplicity of their design, scissor linkages have been used in both architecture and engineering for various applications, such as expandable roofs and shelters, movable bridges, furniture, and as parts of mechanisms. The two main design methods used for scissor linkages are the unit-based method and the loop-based method. While the unit-based method is based on serial multiplication of the scissor units, the loop-based method is based on aligning predefined loop types onto the desired curve. When the input parameter is the desired curvature for the finally deployed configuration of the linkage, the loop-based method is easier and more convenient for defining the scissor units to create the whole linkage geometry. Most of the existing studies on the loop-based method deal with identical or arbitrary loops. Hybrid loop assemblies have not yet been studied, although they may offer different geometric alternatives. This work aimed to fill this gap in the literature and present a geometric design approach for scissor linkages composed of hybrid loop assemblies using frieze patterns. First, the basic terminology, such as loop types, loop assemblies, and frieze patterns, is introduced. Then, we discuss scissor linkages using hybrid loops, generated using a predefined rectilinear geometry in which frieze groups are used to provide diverse variations. The kinematic definitions of the represented linkages are then explained. To reveal the potential applications of the scissor linkages composed of hybrid loops, a case study was conducted in which the proposed linkages were used as a canopy structure. After discussing the potential for using hybrid loops, and their deployment, we present the concluding remarks and make suggestions for future research.