Coupling capable of realizing continuous fine-adjustment of angular directions without power cutoff and automatic adjustment method

The invention discloses a coupling capable of realizing continuous fine-adjustment of angular directions without power cutoff and an automatic adjustment method and belongs to the technical field of machinery. One end of a first shaft is connected with a first gear, the first gear is connected with a box body by the aid of a bearing, one end of a second shaft is connected with a second gear, the second gear is connected with the box body by the aid of a bearing, the first gear is meshed with a third gear, the second gear is meshed with a fourth gear, the fourth gear and the third gear are connected with a transmission shaft by the aid of a common key and a sliding key, the transmission shaft, a first mandrel and the third gear are connected by the aid of straight pins, inner holes in two ends of the transmission shaft are in clearance fit with the first mandrel so as to limit radial movement of the first mandrel, the transmission shaft is connected with the bearings, the bearings are connected with the box bo