This study designs a deployment mechanism based on the Bennett mechanism to address the synchronization and reliability issues of solid surface deployment antennas （SSDAs） caused by independent rotation around two axes. First， a position determination algorithm for the antenna petal based on a particle swarm optimization algorithm is proposed. Combined with the axis-angle theorem， the parameters of uniaxial deployment are obtained， and the deployment mechanism based on the Bennett mechanism is designed. Furthermore， the design scheme of the petal frame is proposed with topology optimization methods based on the motion trajectories of adjacent petals. The analysis results show that the design frame can reduce the reflector deformation by 62.5% and enhance the fundamental frequency by four times， which fully proves the effectiveness of the frame design. Using a 10 m aperture SSDA as an example， the deployment mechanism is established， whereas the kinematic and dynamic parameters during the deployment process are analyzed. The deployment mechanism is further derived into a non-overconstrained mechanism by introducing negative kinematic pairs. The results show that the deployment process of SSDA is stable and reliable； the package ratio reaches 0.384. The research methods and conclusions in this study provide technical references for the design of SSDA.