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.

在最近关于直剪刀可展开结构设计的发表之后，已经表明这种结构的应用可能性是巨大的：有机几何、双稳态控制等。然而，其中一个方面仍然没有研究的是使用相同元素的特殊情况。一方面，满足这种几何条件意味着结构行为以及制造和组装过程中的优势，但另一方面，这种几何约束也限制了设计的可能性，如本文将要证明的那样。因此，这项研究将开发一个数学过程来证明只有非双稳态平面，