The large deployable mechanisms can be constructed by a set of basic deployable mechanical modules via mobile connection between the modules, i.e., the necessary mobility of each module is retained after connecting to other modules. In the large deployable mechanical networks, however, the mobility is always overconstrained due to the multiple close-loop structures in the mechanisms. This fact makes the mechanisms easily become rigid structures that are not movable even if small dimensional error happens to the mechanisms. Thus, eliminating redundant constraints so that the mechanisms still movable under the possible geometric dimensional errors, is very important for this kind of mechanisms. In this paper, efficient methods for the mobile connection between deployable single loop mechanisms (DSLMs) are first synthesized systematically; using some of these methods, lots of deployable units can be repeatedly used to build large deployable mechanical networks. A theoretic approach for eliminating the redundant constraints in the large deployable networks is proposed to make the deployable networks not so sensitive to dimensional errors. Finally, physical prototypes are fabricated to illustrate the feasibility of the proposed approach.