This study is oriented to elaborating mathematical models for the synthesis and analysis of Wildhaber-type globoid worm gear mechanisms, which are distinct within the worm gear transmission group for their integration of a cylindrical gear and a toroidal-form globoid worm. These gears mechanisms are characterized by their non-orthogonal axes of rotation, a departure from traditional designs where axes are typically perpendicular. This work focuses on developing a mathematical modeling approach that defines and studies the active tooth surfaces and the mesh region of the synthesized gear set. Special attention is given to studying the singularity of the meshed active tooth surfaces. The locations of the ordinary nodes and undercutting points and the orientation of the total circumferential velocity are determined. This modeling is essential for predicting and improving the hydrodynamic load capacity of the synthesized gear transmission. The results of this study provide valuable information into the operational advantages of the Wildhaber-type gear set, highlighting its potential as a high-power transmission application where precision and efficiency are essential.