This paper designs a deployment mechanism based on sliding disc for solid surface deployable antenna. Firstly, a method for determining the folded petal posture based on particle swarm optimization algorithm is proposed, combined with the equivalent axis angle theorem to achieve the 1DOF deployment requirement. The deployment mechanism of solid surface deployable antenna is abstracted as a single closed-loop parallel platform. Based on the calculation of spatial mechanism degrees of freedom, the configuration synthesis of this type of antenna is established, and 136 feasible configurations are topologically identified. A detailed design analysis is conducted using the PUSR mechanism as an example. A kinematic model of the PUSR mechanism is constructed based on the closed vector method. The analysis results showed that the deployment process is stable and reliable, verifying the feasibility of the design scheme. Meanwhile, the analysis methods and conclusions can provide technical references for the design of solid surface deployable antennas.