Deployable structures are a good solution for emergency buildings, due to their lightness and compact nature which means they can be transported to where they are needed. Nevertheless, the deployable structures studied to date have the drawback of being too deformable, so that larger and therefore heavier sections had to be used. This paper proposes a new type of deployable structure that uses reciprocal linkages which give rise to greater strength and rigidity. The geometrical and mechanical conditions of the linkages are analysed, as several different types which perform better can be designed, and a calculation method is developed to analyse structures of this type. The features and behaviour of a flat mesh with articulated reciprocal linkages are also compared analytically and experimentally. The theoretical calculations and experimental tests make it possible to prove the viability and efficacy of this new structural type.