Accuracy analysis of spatial overconstrained extendible support structures considering geometric errors, joint clearances and link flexibility

The extendible support structure (ESS) is designed for ensuring the antenna panel of the synthetic aperture radar in a precise configuration. Therefore, the accuracy of the ESS is critical to the overall success of the radar mission. However, its accuracy is significantly affected by geometric errors, joint clearances and link flexibility. Taking into account all deviation sources simultaneously, a novel deterministic method is proposed to predict the pose error of the overconstrained ESS. Firstly, based on the comprehensive kinematic model of revolute joints with radial and axial clearances, the algorithm of contact detection between the journal and the bearing is developed with combination of the contact conditions and structural constraints. Next, the condensed stiffness matrices that merge flexible links and adjacent joints together are developed for the clearance-affected kinematic pairs, and the matrix structural analysis is adopted to generate the global stiffness matrix of the ESS. Finally, the accuracy of the ESS is determined by the elastostatic analysis and the virtual work principle, and the proposed method is validated through comparison between the numerical predictions and the experimental results.