Loop based classification of planar scissor linkages

Abstract

Scissor linkages have been used for several applications since ancient Greeks and Romans. In addition to simple scissor linkages with straight rods, linkages with angulated elements have been introduced in the last decades. In the related literature, two methods have been used to design scissor linkages, one of which is based on scissor elements, and the other is based on assembling loops. This study presents a systematic classification of scissor linkages as assemblies of rhombus, kite, dart, parallelogram and anti-parallelogram loops using frieze patterns and long-short diagonal connections. After the loops are replicated along a curve as a pattern, the linkages are obtained by selection of proper common link sections for adjacent loops. The resulting linkages are analyzed for their motions and they are classified as realizing scaling deployable, angular deployable or transformable motion. Some of the linkages obtained are novel. Totally 10 scalable deployable, 1 angular deployable and 8 transformable scissor linkages are listed. Designers in architecture and engineering can use this list of linkages as a library of scissor linkage topologies.