Page 85 - Gear Technology Solutions

development of an involute by unrolling a cord from a disk. The disk holds here
the place of the base circle, and several geometric laws can be demonstrated
with an involute development. It appears logical that the chalk which is used to
draw the involute cannot draw anything below the base circle. In other words,
no part of the involute exists below the base circle (or inside of the disk). This
is because of the definition of the involute function and the resulting restrictions
in the mechanics of drawing an involute.

Figure 2: Involute development

The drawing in Figure 2 also shows that the unrolling of the cord can be
continued into infinity. If a particular gear design has a pressure angle of 20°
for example, then the point where the tangent to the involute includes an angle
of 20° to the line which connects this point with the center of the base circle is
the pitch point. A larger pressure angle is realized merely by unrolling the cord
further. The nominal pressure angle of a gear per definition is recorded at the
pitch circle. However, the effective pressure angle below the pitch circle
decreases as the distance to the base circle becomes smaller. Finally, at the
base circle, the effective pressure angle is zero degree. The critical area is
therefore at the beginning of the involute at the base circle. If the pressure
angle is chosen very small, for example 15°, then the risk occurs that the
dedendum (the distance from the pitch point to the root) reaches the base
circle or even extends below the base circle.

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