Geometric and analytical design of angulated scissor structures

Abstract

Deployable scissor structures are capable of large geometric transformations between predefined configurations thanks to their extension and rotation properties. These structures are formed by connecting translational, polar or angulated units that are composed of scissor-like elements. The studies especially on the angulated scissor structures mostly concentrate on developing certain types of planar or spatial structures; thus, they do not present a systematic form-finding method for different types of angulated units lying on different path-curves. This paper aims to introduce two design methods including geometrical method based on drawings and analytical method based on mathematical equations both for generating various angulated scissor structures and facilitating the design of asymmetric and polycentric structures. First, basic design principles of the angulated scissor structures are investigated. Then, proper solutions are proposed to design such planar structures using both geometrical and analytical methods. Various planar angulated scissor structures are generated lying on monocentric and polycentric curves or straight-line in the deployed, fully deployed, and undeployed configurations. Finally, a case study as a numerical model of a sunshade with monocentric curve is presented.