Analysis of angular errors of the planar multi-closed-loop deployable mechanism with link deviations and revolute joint clearances

Accuracy is of great importance for deployable mechanisms because it greatly determines the performance of the antenna. The main purpose of this paper is to propose a method to analyze the angular errors of the multi-closed-loop deployable mechanism of the planar synthetic-aperture radar antenna considering link deviations and joint clearances. First, a two-link unit is explored to calculate the position errors of the joints due to the manufacturing imperfection only in the assembly process. On this basis, conducting a geometrical analysis, the formulations of the studied angular errors of two planar antenna panels after the introduction of clearances are established. Utilizing the rotatability law of the single-loop linkage, the worst-case scenario associated with a chaotic clearance-induced uncertainty is reduced to a purely geometrical problem. Accordingly, the maximum angular errors caused by these two error sources are obtained in an intuitive manner. Finally, the proposed method is demonstrated by a numerical example of the deployable mechanism and verified by experimental measurements.