Kinematic Modeling and Analysis of a Space Bionic Tree Deployable Antenna Mechanism

Objective Space deployable antennas are a new type of space structure developed with the rapid advancement of aerospace technology. In recent years, with China's increasing frequency of space exploration activities, ranging from the Earth-Moon system to interplanetary space, subsequent aerospace engineering projects have raised urgent demands for deployable antennas that must balance comprehensive performance indicators, including large aperture, lightweight design, and high precision. Meanwhile, kinematic characteristic analysis serves as a crucial approach to validate the feasibility of innovative mechanism designs. Nevertheless, there are relatively few studies on the kinematic modeling of complex space deployable antennas that can be transformed into planar mechanisms. Accordingly, this paper proposes a new configuration of a bionic tree-like deployable antenna mechanism and investigates its kinematic characteristics as a multi-stage, multi-closed-loop mechanism. Methods First, by analyzing the bionic mechanisms of tree branching structures and large-span tree-like support structures and considering the practical design requirements of deployable antennas, design principles for bionic tree-like deployable antenna mechanisms are proposed. Based on the proposed antenna configuration, the overall design and deployment principle are introduced. Second, based on the closed-loop vector method and coordinate transformation method, the rib units are divided into sub-units, and the internal closed-loop circuits within these sub-units are decomposed. Accordingly, the kinematic models of the rib unit and the entire antenna structure are established, which consist of multi-level deployable units connected in series and nested closed-loop circuits. By analyzing the motion characteristics of the outer branching beam and its spatial geometric relationships, spatial coordinate models of key nodes are established. In addition, a driving strategy of "outer rotation parallel, inner rotation zeroing" is formulated, and a corresponding driving strategy model is established for the branching outer beam to avoid interference during the deployment process. Finally, the antenna kinematic model and the branching outer beam driving strategy model are simulated and analyzed using numerical software such as MATLAB, while the branch slider displacements and the key angular displacements during the deployment process are selected for validation. The 30 m-class antenna scaled model is imported into ADAMS for further comparative validation and analysis. Results and Discussions The simulation results indicate that, for the driven branching outer beam, there are displacement deviations between the two simulation results obtained using ADAMS and MATLAB. However, the motion trends are consistent, thereby verifying the correctness of the modeling. The primary cause of the error appears to be inaccuracies in the calculation of the spatial coordinate transformation angles. Additionally, the larger size of the antenna appears to amplify the error. At time t = 0 s, the antenna mechanisms are in a fully retracted state, and there is no interference between the rib units. In the initial phase ( t = 1 ≈ 6 s), the antenna mechanism undergoes a gradual deployment process. The key point J3 of the fixed branching outer beam enters the danger zone after t = 2 s, thereby causing interference. Concurrently, the driven branching outer beam maintains parallel alignment with the plane of the trunk deployable unit through continuous external rotation. Notably, the key point does not enter the danger zone during this period. At t = 50 s, the driven branching outer beam has moved away from the danger zone and is in a state of internal rotation. At this time, the antenna has nearly completed deployment, with most of the displacement achieved. This indicates that, although the trunk slider moves at a uniform speed, the synchronized deployment of the branching deployable unit is mainly concentrated within the first 50 s and is therefore not a uniform-speed motion. At t = 100 s, the antenna is fully deployed. The fixed branching outer beam does not reach its preset position due to the absence of internal rotation to offset both the initial angular displacement and that generated by external rotation. In contrast, the driven branching outer beam reaches the preset position through internal rotation. At this stage, the branching outer beam is coplanar with the branching deployable unit, ensuring that the outer layer of the rope is smoothly tensioned. The branching slider displacement and angular displacement first gradually increase and then gradually decrease during t = 1 ≈ 6 s, and the trend of the curves is consistent with the motion trajectory of the key point. Conclusions In this paper, to address the urgent requirements of future large-scale development, a novel configuration of a large-aperture bionic tree-like deployable antenna mechanism is proposed. The antenna mechanism takes the tree branching structure as the bionic prototype, and kinematic modeling, motion characteristic analysis, and numerical simulation are conducted to investigate its performance. By analyzing the bionic mechanism of tree branching geometry, design criteria applicable to deployable antennas are extracted, thereby providing a theoretical reference for the systematic design of antenna configurations. On this basis, a kinematic parametric model of a deployable antenna with multilevel deployable units connected in series and multiple nested closed-loop mechanisms is established, and the mutual coupling relationships between the antenna structural parameters are clarified, which provides a basis for subsequent optimization of antenna structural design. Furthermore, by analyzing the kinematic characteristics of the antenna branching outer beam during the deployment process, a driving strategy of "parallel external rotation and zero internal rotation" is proposed. This strategy has been shown to be effective in avoiding interference during the deployment process of the branching outer beam. The validity and correctness of this strategy are verified through numerical simulation analysis.