Abstract: Solid surface deployable antennas are widely used in wireless communication, deep space exploration and military reconnaissance due to their high profile accuracy and wide operating frequency bandwidth. In order to improve the storage ratio, synchronization and deployment reliability of solid surface deployable antennas, a solid surface deployable antenna based on the Bennett derivative mechanism is designed. Firstly, an antenna deployment scheme is proposed, and the parametric calculation process for the division of the reflection surface is then designed. Secondly, the bi-orthogonal axis of the reflection surface is equivalently transformed into a single rotation axis with quaternion, and the rotation axis is driven by the Bennett derivative mechanism to realize the expansion and contraction of the solid surface antenna. The research results in this paper provide a technical reference for the design of solid surface deployable antennas.