Limitations in the design of deployable structures with straight scissors using identical elements

After the recent publications on the design of deployable structures with straight scissors, it has been shown that the possibilities in the application of this type of structure are enormous: organic geometries, bistability control, etc. However, one of the aspects that have still not been studied is the particular case of using identical elements. On the one hand, the satisfaction of this geometric condition implies advantages in the structural behaviour and in the manufacturing and assembly process, but, on the other hand, this geometric constraint also limits design possibilities as will be demonstrated in this paper. Consequently, this research will develop a mathematical process to demonstrate that only non-bistable planes, non-bistable cylinders with a circle base and non-bistable spheres can be designed as deployable if straight scissors and identical elements are used.