All the four cases of design have t

All the four cases of design have the same pitch diameter, normal pressure angle, helical angle, and face width.Micro-geometry modifications were applied to the four cases of design to improve their meshing conditions.These micro-geometry modifications are listed in Table 3.For cases of design 1 and 2 corresponding to convex-to-concave and convex-to-plane type of meshing, a parabolic lead modification to the pinion as well as a tip relief to the rack were provided. For case 3 in which we have a convex-to-convex meshing type, only a small value of longitudinal crowning was provided.For Case 4 of design of a reference helical involute rack and pinion gear drive, the same lead modification that for Cases 1–3 was applied. In Case 4, a circular profile modification was used to provide a longitudinal direction of the contact path, similar to the contact paths achieved for pure rolling rack and pinion gear sets.