The structure of a gear coupling consists of two outer gear sleeves 1 with the same number of teeth and two inner gear rings 5 with flanges. The two outer gear shaft sleeves are respectively connected and fixed to the shaft ends of the two linked shafts with keys. The inner teeth of the two inner gear rings mesh with the outer teeth on the shaft sleeves, and their flanges are connected with bolts to achieve the connection between the two shafts. The gears on the outer gear shaft sleeve and the inner gear ring are involute teeth with a meshing angle of a=20 °. In order to compensate for the relative angular displacement and radial displacement of two weeks, a certain amount of tooth flank clearance is provided during machining when the inner and outer teeth mesh. The tooth tip of the outer gear shaft sleeve is machined into a spherical surface, and the center of the spherical surface is located on the axis of the shaft sleeve. Obviously, when the relative angular position of the two shafts connected is large, the meshing tooth surfaces will only be able to make partial contact at both ends, which will inevitably affect the bearing capacity and service life of the coupling. Therefore, the outer teeth on the shaft sleeve can be changed from straight teeth to drum shaped teeth. At this point, not only can the contact between the gear teeth along the tooth width direction be improved, the load-bearing capacity be increased, and the service life be extended, but the compensation ability of the coupling for the relative angular displacement of the two shafts can also be enhanced.