Design of Anti-Parallelogram Loop Assemblies

Abstract

Scissor mechanisms are frequently used for deployable structures and many studies have been conducted on the subject. Most of the studies consider scissor units as modules in the design process. An alternative approach is to utilize loops as the modules for design. In this paper, the design alternatives of single degree-of-freedom planar linkages comprising anti-parallelogram loops using the loop assembly method is presented. First, scissor mechanisms are reviewed. Next, the types of four-bar loops and the resulting linkages in the literature are introduced and those which are yet to be explored, anti-parallelogram being one of them, are identified. Then the loop assembly method and the examples in the literature are reviewed. As a method to form as many alternatives as possible, symmetry operations are proposed. Suitable frieze symmetry groups utilized for obtaining the assemblies are explained and the anti-parallelogram loop patterns are derived. Next, the single degree-of-freedom linkages are obtained from the loop assemblies. Finally, a selection of the resulting linkages with novel properties are presented. This study shows that loop assemblies are efficient in systematic type synthesis of scissor linkages, some types of which could not be foreseen by using units as modules.

Loop based classification of planar scissor linkages

“…Bai et al [35] assembled rhombus, parallelogram, kite and general quadrilateral loops for polygon scaling, where they discuss different ways to assemble these loops as well. Yar et al [36] used kite and dart loops and Gür et al [37][38] used anti-parallelogram loops to obtain planar scissor linkages, some of which are deployable, whereas some are transformable. Karagöz [39] presented examples of design formulations for several deployable and transformable scissor linkages using the loop assembly method.…”