# Research on the Dynamics of the Space Tubular Expandable Structure Driving Deployment Unit
###### Abstract  
The limitations associated with traditional screw-based and cable-based deployment mechanisms for space deployable structures, such as deployment stiffness, accuracy, and distance, are effectively overcome by introducing the concept of a variable diameter internal drive device. To enhance stability during the discontinuous surface transition phase inside the tubular structure, a thin-walled flexible beam structure is adopted for the driving deployment unit. The analysis employs the spatial absolute nodal coordinate formulation, integrating the pose states of each node into the global coordinate system. The three-dimensional displacement field and rotational angle changes at different time intervals are obtained using the unit shape function matrix and Kirchhoff theory. Subsequently, a dynamic model of the corresponding spatial nodes is established using the virtual work principle. This significant improvement enhances the dynamic characteristics of the coupled rigid-flexible deformation of the driving deployment unit under radial and axial external forces, surpassing the previously used flexible beam structure. The dynamic simulation analysis is performed using the finite element method and validated through experimental tests. The experimental results confirm the driving deployment unit's stability and successful achievement of the desired functionalities, as demonstrated by the endpoint displacement, three-dimensional centroid displacement, and trajectory rotation angle. Mast (TTM) developed by Northrop Grumman for the ISIS (Inflatable Sunshield In Space) system achieved a fully extended length of 6.70 m [10]. Mechanical analysis conducted by [PERSON] et al. on the deployment and retraction of TTM, as shown in Figure 1b, demonstrated that its stiffness and frequencies were better suited for space applications compared to other space deployable mechanisms [11]. Additionally, [PERSON] et al. investigated the TTM in the sunshield deployment mechanism of a space telescope and simulated its structural status under axial loads in space, proving that the 8 m long TTM could stably move under a 50 N axial load [12]. However, current fixed-drive devices (screw-nut or cable-driven) used in the TTM result in a short deployment distance and a heavy mass [13; 14; 15]. To address this issue, a three-dimensional structure called the variable radial internal drive device (Figure 2) was developed to achieve step-by-step deployment with a smaller mass for the tubular structure while maximizing the extension distance. The effective and stable transition between the non-continuous surfaces at different stages within the tubular structure is currently a critical technical challenge that needs to be addressed to ensure the successful deployment of space telescopes. To overcome this challenge, conducting a flexible multibody dynamics analysis on the non-continuous surfaces during the transitional phase of the variable radial internal drive device is of utmost importance, as it will provide valuable insights into the behavior and reliability of the system. In recent years, researchers both domestically and internationally have extensively studied the flexible multibody dynamics analysis of structures with thin-walled characteristics or flexible beam structures, due to their importance in various engineering applications. These structures often exhibit complex deformations and require accurate analysis methods to understand their behavior. The earliest approach used the [PERSON]'s Equations of Motion (KED) method [16] to address flexible multibody dynamics. However, this method neglected the  
Figure 1: (**a**) Tubular (TTM) space deployable mechanism; (**b**) Mechanical testing of the 34.4 m TTM. Figure 2: Schematic diagram of the variable radial internal drive device in TTM. effects of elastic components' motion within their range and gradually revealed limitations in the analysis of coupled fields.