In order to effectively improve the single-ring truss deployable antenna mechanism due to the large aperture caused by the problem with low structural strength and low-profile accuracy, a series of double-ring truss deployable antenna mechanisms (DRTDAM) are proposed with constant height during folding and deployment process. First, a variety of DRTDAMs are proposed based on tetrahedral units and their topologies are analyzed. Secondly, degree-of-freedom (DOF) characteristics of DRTDAM proposed in this paper are analyzed based on the screw theory and screw-constrained topological graphs and based on this, the kinematic characteristics of DRTDAM is investigated. Thirdly, the dynamics of the whole DRTDAM is built with Newton-Euler equations of multi-rigid body system. Finally, the correctness of above analysis is verified through dynamics analysis software ADAMS and numerical analysis software MATLAB, and the principle prototype is produced to verify the correctness of DOF analysis. The mechanism proposed in this paper enriches the configuration of DRTDAM, and the process of kinematic characterization method is clear and simple, which is meaningful for the research in space complex mechanism.