As to one kind of gears which is called the cylindrical ring and pinion gear, it is easier to understand that the involute profile provides a constant ratio and is insensitive to center distance displacement. The generating principle of an involute is derived from a straight rack with straight tooth profile. A particular gear, rolling in the rack with constant center distance to the rack, requires involute flank surfaces. A shaping tool with the shape of a rack can machine a gear with a perfect involute flank form.

To understand the bevel gear tooth geometry, you might first observe the case of straight bevel gears. If the generating rack used to derive the cylindrical gear involute is bent in a horizontal plane into a circular shape, it will result in a crown gear which is used to derive the flank form of bevel pinion and gear. In the case of straight bevel gears, the crown gear or generating gear can be placed between the pinion and gear assembly. Its center is located exactly at the intersection point of the pinion and gear shafts.

It is possible to use a bevel generating gear that is identical to the ring gear. The pinion is in that case generated by rolling with the bevel generating gear, and the gear is manufactured simply by plunging the cutter to full depth without rolling.

A straight tooth bevel gear set has contact lines that are parallel to the pitch line. The first contact between a generating gear tooth and a pinion tooth starts, for example, in the root and moves during the rotation of the two mating members along the path of contact straight up to the top. The contact lines represent the momentary contact between the two flanks in mesh.

With a spiral bevel gear set, the contact lines are inclined relative to the pitch line orientation. Unlike the contact lines of the straight ring gears set, the contact lines of the spiral bevel gear set have different lengths. The contact lines between pinion and generating gear are identical to the contact lines between cutter blades and pinion flanks.