# Dynamics Modelling and Simulation for Deployment Characteristics of Mesh Reflector Antennas
## 5 Conclusions  
The presented work aims at the analysis of the deployment dynamics of a hoop truss considering the effect of the torsional spring and a time-varying attenuation coefficient of driving force. With the employment of the ANCF method, large deformation of the cable net during deployment of the deployable antenna can be predicted accurately. Based on the derived dynamic governing equations, dynamic simulation can be performed numerically. From the results obtained, the phenomenon of unsynchronized deployment during the latter phase can be observed, which results from the attenuation of driving force caused by the friction effect of the pulley. Furthermore, with the increase in the deployable angle, the tension of the cable net increases with oscillation. Particularly, an intense augment in cable tension arises in the final phase of deployment, which implies that the driving force affects the tension significantly. Additionally, the impact force induced by the lock mechanism will exert an influence on the tension of the cable net. The flexibility of the truss is neglected in this study; further investigation considering the effect of the flexible rod should be conducted in the future.  
[PERSON] conceived the proposal of the paper, performed the simulation, and analyzed the data. Z  
**Funding:** This research received no external funding.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
\begin{tabular}{l l} \(A\) & cross-sectional area of cable \\ \(c\) & damping coefficient of the torsional spring \\ \(\mathbf{C}\) & vector of constraint equations \\ \(\mathbf{C_{q}}\) & Jacobian matrix of the constraint equations \\ \(\mathbf{e}\) & generalized coordinates of cable element \\ \(E\) & elastic modulus of cable \\ \(f\) & frictional coefficient \\ \(F\) & equivalent driving force \\ \(F_{n},F_{n+1}\) & driving forces on the pulley \\ \(F_{\lambda}\) & synthetic moment load \\ \(F_{r}\) & radial force of the bearing \\ \(i\) & clockwise number of the cell \\ \(\mathbf{I}\) & identity matrix \\ \(K\) & stiffness coefficient of the torsional spring \\ \(L_{1}\) & length of the vertical rod \\ \(L_{2}\) & length of the horizontal rod \\ \(L\) & length of the cable element \\ \(m_{t}\) & equivalent mass of the truss cell \\ \(m_{e}\) & mass of the cable element \\ \(m_{p}\) & mass of the pulley \\ \(\mathbf{M}\) & mass matrix of the antenna system \\ \(\mathbf{M}_{e}\) & mass matrix of the cable element \\ \(M\) & frictional moment \\ \(n\) & number of the truss cells \\ \(\mathbf{q}\) & vector of generalized coordinates of antenna \\ \(U_{e}\) & strain energy of the cable element \\ \(U_{c}\) & strain energy of the cable \\ \(\mathbf{v}\) & global velocity vector of the truss \\ \(\mathbf{p}_{i}\) & local position vector of the truss \\ \(\mathbf{Q}_{e}\) & vector of external forces \\ \(\mathbf{r}\) & global position vector of cable element \\ \(R_{n},R_{n+1}\) & driving force from the center of pulley to the action point \\ \(\mathbf{s}\) & global position vector of the truss \\ \(\mathbf{S}\) & shape function matrix of cable element \\ \(T_{t}\) & kinetic energy of the truss \\ \(T_{e}\) & kinetic energy of the cable element \\ \(\alpha\) & angle between horizontal rod and perpendicular rod \\ \(\varphi\) & angle between two body coordinate frames \\ \(\theta\) & deployment angle \\ \(\mathbf{\theta}\) & Vector of the generalized coordinates \\ \(\lambda\) & Lagrange multiplier \\ \(\tau\) & torque of the torsional spring \\ \end{tabular}