Spherical gear couplings are a type of toothed coupling where the external spline usually requires highly crowned tooth surfaces to absorb high misalignments. The teeth of the external spline (or hub) may present cross sections with undercutting, particularly when the tooth number is small and the hub teeth are manufactured directly on a shaft. These peculiarities make it difficult to generate accurate hub geometries with the existing models in the literature. This paper proposes a method of generation of the hub tooth surfaces by a hob thread surface, simulating the hobbing process of the external spline and generating undercut profiles. The proposed hub model is compared with existing models where a cutting edge is considered as a generating tool of the hub. The comparison shows that the normal deviations between the hub tooth surfaces of the considered models are significant, especially when high misalignments (typically above 3${}^{\circ }$) are present and highly crowned tooth surfaces are required. Differences in the location where undercut profiles appear are also observed between the proposed model and those of the literature. Moreover, from the application of unloaded tooth contact analysis and clearance determination, disparities are observed when a misalignment angle is present.

球面齿轮联轴器是一种齿式联轴器，其中外花键通常需要高冠度的齿面来吸收高不对中。外花键（或轮毂）的齿可能具有带底切的横截面，特别是当齿数较小且轮毂齿直接在轴上制造时。这些特性使得很难使用文献中的现有模型生成准确的轮毂几何形状。本文提出了一种通过滚刀螺纹表面生成轮毂齿面的方法，模拟外花键的滚齿过程并生成咬边轮廓。将所提出的轮毂模型与现有模型进行比较，其中将切削刃视为轮毂的生成工具。${}^{\circ }$) 存在并且需要高度冠的牙齿表面。在提议的模型和文献中的模型之间也观察到底切轮廓出现的位置的差异。此外，从卸载齿接触分析和间隙确定的应用来看，当存在错位角时观察到差异。