Geometric variety of scissor linkages according to loop geometry: A case study of a canopy design

Abstract

Scissor linkages are used in various applications since they provide many advantages in comparison to other types of deployable structures. In literature there are two geometric design methods for these linkages: unit-assembly method and loop-assembly method. The unit-assembly method is an inductive method based on the serial multiplication of scissor units. On the contrary the loop-assembly method is a deductive method which is based on the alignment of selected loop types on the desired base curve. Due to its design methodology the loop-assembly method allows creating not only various scissor linkages with different primary units but also different geometric configurations for the initial curve. This paper aims to investigate geometric varieties of scissor linkages generated using the loop-assembly method and to reveal their potential applications. For this purpose first quadrilateral loops loop-assembly method and kinematic analysis of a sample scissor linkage based on the quadrilateral loops have been presented. Then five different scissor linkages having the same curvilinear geometry in their initial configurations have been generated and the variations in their deployment behaviors due to the loop types have been presented. Finally a canopy structure composed of kite loops has been proposed and its transformation capability has been discussed.