Abstract: Focusing on the meshing process between the pinion and rack, this paper analyzes the interference between the top of teeth of the pinion and the bottom of teeth of the rack, as well as between the bottom of teeth of the pinion and the top of teeth of the rack. Discriminant formulas were derived to prevent interference between the pinion top of teeth and rack bottom of teeth, between the fillet of the rack and the pinion tooth surface, between the pinion tooth root and the rack top of teeth, and between the transition curve of the pinion and the rack tooth surface. In addition, the starting radius of the helical pinion's involute and the discriminant condition for avoiding undercut were derived. Finally, a numerical example was conducted for verification, and a 3D model of the pinion-rack assembly was established in SolidWorks to validate the correctness of the formulas. The proposed discriminant expressions provide an important theoretical basis for the design and verification of pinion-rack mechanical products.