Page 53 - Gear Technology Solutions

the line of action. This principle implies that a tool, simply with straight cutting
edges as shown in Figure 4, can be used to form the complex involute profile.
Figure 4 also demonstrates the principle of profile shift, while maintaining the
first fundamental law of gearing.

Figure 4: Generating rack with straight profile forming involute profiles

The second fundamental law of gearing, which was proposed in 2017 [2], pln x
Vm + ng = 0 [1], is a redundant relationship to the first gearing law and it is lim-
ited to cylindrical gears with parallel axes and straight bevel gears without hy-
poid offset.

A third fundamental gearing law is proposed in [2] in two different notations.
The first notation covers only the special case of ratio = 1:

j b.g = j b.p = j b.op

The above notation applies only for cases with equal base pitch diameters be-
tween pinion and gear because the circular pitch and not the angular pitch has
to be equal between pinion, gear and the operating base pitch. The second
notation:
pb.g = pb.p = pb.op

is consistent with the requirement of equal circular pitch, which makes this no-
tation more relevant. However, it does not add additional substance to the first
law of gearing. As a conclusion it can be stated that the first law of gearing is
sufficient and applies without restrictions to all kinds of gearing.

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