The reflective surface of a large 6-degree of freedom （DOF） solid-surface antenna has a problem of free swing during deployment. In order to reduce the difficulty of active control， the torque of the torsion spring at each joint needs to be designed reasonably. For this dynamic problem， the second Lagrange equation is used to derive the dynamic model from 1-DOF to n-DOF. Matlab is used to solve the model numerically， and the relationship between the torque of the torsion spring and the expansion process in the case of 6-DOF is studied and assisted verification through Adams. The calculation of the dynamic model has obtained a set of reasonable torsion spring torque values. Without external force constraints， each reflecting surface can be deployed at a coordinated speed and a prescribed trend. This research method can obtain the design scheme of the torque of the torsion spring under specific conditions， and reduce the difficulty of active control during the deployment of the antenna reflector.