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Figure 10: Surface of action connecting the gear and pinion base surfaces
The conclusion is that the first fundamental law of gearing:
ng • VS = 0
is well suited to govern the relationship of hypoid gears and can be employed
to develop a conjugate relationship between two hypoid members. This will be
further explained and demonstrated in the following section.
4.6 Conjugacy between Meshing Flanks
The term conjugate is used in mathematics for two or more surfaces that con-
tact each other along a line. Since the 1970’s the term conjugate has also
been employed in gear technology literature to define the “exact” gear pair
which presents a triple plurality of line contact between two gear flanks during
the meshing process [5].
Definition of the Conjugate Gear Pair
1. The flanks contact along a line (contact line), which is only limited by the
boundaries of the teeth i.e. the working area
2. The line contact between the flanks exists within the entire area of en-
gagement in every mesh position
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