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Once a train breaks down on a busy railway line, it will affect the whole traffic network. However, when a rescue locomotive is hooked up to the broken train for towing it to the next station, it is common that coupling dislocation occurs, which results in damages to couplers and the driver's cab. To ensure the safety of the trains during the coupling, it becomes crucial to determine whether they can be linked safely and automatically under different line conditions. In this paper, position and pose of the rescue locomotive and the broken train on the line are calculated by geometric analytical calculation method, which determines the position relation of their couplers. Then a so-called "coupling characteristic triangle" was proposed to determine whether trains can be safely and automatically linked on the railway line. The triangles are constructed by the peak points of the couplers head of the front vehicle and the rear one and border lines of secure coupling area on the couplers. By judging the shape of the triangle, it can directly judge whether their couplers can be connected successfully. The method has been applied to check the safety of the trains during coupling on the Nanchang urban railway Line 4. The results show that the maximum swing angle of the coupler reaches 17.3957° in the straight–curve section with a radius of 325 m. At this time, coupling is most difficult, and trains need to be connected manually through the tractor; all the calculation results are verified in the actual line. By comparing different calculation methods for judging coupling safety, it is shown that the method proposed in this paper is accurate, efficient, and users can judge coupling safety more intuitively. [ABSTRACT FROM AUTHOR]