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6.4 How the Trochoid Removes Part of the Involute

While the involute generation creates the flank surface points from the top of
the tooth to the root, the trochoid generation works the opposite way. Figure 4
shows this generation in four steps. The green generating rack profile (equal to
one cutting edge of the hob cutter) forms the upper involute section in position
1. A line which begins at the generated flank point and is perpendicular to the
green generating line ends tangentially at the base circle (upper blue line). As
the generating process progresses, the cutting-edge profile takes the position
2. The length of the green line towards the left side of the drawing is given by
the center distance between the hob cutter and the gear blank. Already in
position 2 it can be observed that the left end of the cutting edge penetrates
below the base circle. From this point on, the blade tip begins to form a
trochoidal root function, while in the same position the cutting edge towards
the right side still forms the involute.

Figure 4: Generation of involute and trochoid

Cutting positions 3 and 4 show how the blade tip cuts deeper below the base
circle and begins after position 4 to create undercut. Due to the length of the
dedendum section of the blade, the undercut begins below the base circle
(green root fillet undercut) and continues above the base circle (red section) by
removing a considerable part of the already generated involute above the root
fillet section.

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