Geometric method to design bistable and non - bistable deployable structures of straight scissors based on the convergence surface

Abstract

Since Leonardo Da Vinci designed the first deployable structure with scissors some centuries ago, many authors have tried to improve its designs using new geometries. However, these strategies to make deployable structures have limits because they can only be applied in some geometries and the level of the resolution obtained is limited. In this paper a new geometric method to design bistable and non – bistable deployable structures with straight scissors is going to be developed. Using this method, the only limit in the design of deployable structures with straight scissors is the designer's imagination, for example, with this method the designer will be able to design as deployable the Sydney Opera House or a common building with pillars, etc. Consequently, this method is not based on load or forces that can be applied in the structure. An application example is the figure attached in this Abstract where the reader can see the Manantiales Restaurant in Xochimilco designed with straight scissors and without any geometric incompatibility.