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GEAR TEETH.. 385
When internal teeth are constructed according to this sys-
tem, the difference between the number of teeth in the internal
gear and its external pinion must never be less than 1 2 ; practically
it is better to limit the difference to 15 or 20 teeth.
As interchangeability is seldom required for internal gear-
ing, such gears and their mates are generally constructed together
and the designer chooses a generating circle of suitable size to
give the shape of tooth he considers best, and he may also vary
the size of the driving or the driven gear so as to reduce con-
tacts when the teeth are approaching each other, etc., according
to his own judgment and experience.
The difference in pitch diameter of the internal gear and its
pinion should never be less than the sum of the diameters of the
generating circles, and the diameter of the generating circle of
the flanks for the pinion should never be larger than half the
pitch diameter, but it should, preferably, be smaller.
As a rule, fillets at the bottom of the teeth are not used in
internal gears, but if used they should be very small.
In order that gears constructed with cycloid teeth should
/un smoothly, it is very important to have the distance between
centers correct, so that the pitch lines will exactly meet each
other. For this reason, there are many kinds of machinery
where cycloid gears should not be used : for instance, for change
gears on lathes involute teeth are far more suitable.
When making patterns, the shape of one tooth is usually
carefully drawn on a thin piece of sheet metal, either brass or
iron ; this is then filed out and used as a templet in tracing
the other teeth on the pattern. Sometimes a fly-cutter is made
according to this constructed tooth, and all the teeth in the pat-
tern are cut on an index machine or a gear cutting machine ; but
if such a machine is not available, the next best way is to set out
the pitch line of the gear on this templet and also the center line
of the tooth, radially towards the center, then draw the pitch line
on the pattern, space off each tooth carefully with a pair of
dividers and draw the center line on each tooth prolonged across
the rim radially in the direction of the center of the gear, then
lay the templet carefully on each of these spacings, making
the pitch line and the center line of tooth on the templet to
exactly match the pitch line and center line of the tooth
drawn on the pattern, then trace around the templet and get the
shape of one tooth ; then move the templet to the next spacing
and trace the next tooth, and so on for all the teeth on the gear.
For small patterns it is convenient to fasten the templet to
a strip of metal long enough to reach from the teeth to the cen-
ter of the gear wheel, placing a point in the center of the gear,
drilling a hole in the strip and letting it swing around this point,
then after all the teeth are spaced off on the pattern the tem-
plet is swung from one tooth to the other and all the teeth are
traced by the templet. This method has the advantage that
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