# Research on the Dynamics of the Space Tubular Expandable Structure Driving Deployment Unit
###### Abstract
By using gradient coordinates instead of traditional angular coordinates in the global coordinate system, they established a mapping relationship between parameters in the current configuration and the reference configuration. This method offers an effective means to analyze the behavior of flexible structures under different loading conditions. [PERSON] and colleagues [29] applied the absolute nodal coordinate formulation to beam structures and derived motion equations for axial motion beams based on the generalized Lagrange equations in the Lagrange-Euler sense. This research contributes to the understanding of the dynamic behavior of beams and their applications in various engineering systems. [PERSON] [30] treated the dynamic platform of a parallel mechanism as a thin plate element based on the absolute nodal coordinate formulation. By employing the elastic middle surface method, they effectively reduced high-frequency vibration modes, improving the stability and performance of the dynamic platform. The introduction of tangent coordinates to define joint coordinate systems further enhanced the modeling and analysis of flexible-rigid coupled systems. [PERSON] and colleagues [31] proposed a recursive algorithm based on the absolute nodal coordinate formulation for dynamic analysis of multi-flexible-body systems with nonlinear large deformations. By describing flexible bodies using ANCF and establishing kinematic and dynamic recursive relationships based on the Articulated Body Algorithm (ABA), the study provides a powerful and efficient method for analyzing complex flexible multibody systems. [PERSON] and colleagues [32] developed a new combined element model based on the absolute nodal coordinate formulation, which derived consistent deformation conditions for two thin plate contact interfaces. This study contributes to the accurate and reliable modeling of contact interactions in thin plate structures, making it valuable for various engineering applications. [PERSON] and colleagues [33] introduced a new model based on the absolute nodal coordinate formulation using the gradient method. By applying this model to nonlinear dynamic analysis of elastic line structures under tension and deformation conditions, the study demonstrated good accuracy and computational efficiency in obtaining results, providing a promising approach for analyzing complex line structures. Based on extensive research conducted by domestic and international scholars on flexible beam structures or thin-walled flexible beam structures, it has been found that the use of the absolute nodal coordinate formulation (ANCF) offers significant advantages over other flexible multibody dynamic analysis methods in terms of computational accuracy and cost. However, there is limited literature on the application of spatial ANCF for the dynamic analysis of the parallel triangular configuration of thin-walled flexible beam structures, especially in the context of inner-drive unit components of deployable cylindrical structures. To address this gap, this paper first constructs a flexible multibody dynamic analysis model for the inner-drive unit of a deployable cylindrical structure based on the spatial ANCF. This model analyzes the motion states of the driving deployment unit and dynamically models the parallel triangular configuration of the thin-walled flexible beam structure using ANCF. The proposed planar triangular element configuration, with its unique design, aims to enhance the adaptability of the coupled rigid-flexible structure within the deployable cylindrical structure of a space telescope when subjected to radial and axial external forces. By superimposing this coupled rigid-flexible structure in spatial orientation, a parallel configuration is formed, ensuring structural integrity during deployment. To validate the proposed model and assess its performance, finite element analysis is employed to simulate and analyze a virtual prototype. Subsequently, a 1:1 experimental prototype is established to conduct stability tests on the driving deployment unit.