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382 GEAR TEETH.
FIG. 1.
The shape of gear teeth is usually either Involute or Cycloid
( also frequently called Epicycloid ). The shape of a cycloid
tooth for a rack is four equal cycloid curves, which may be con-
structed, so to speak, by letting the generating circle a ( see
Fig. 1 ) roll along on the pitch line of the rack, both above and
below.
Cycloid gears „,
—
-^
have the curve out-
side the pitch circle
formed by an Epi-
cycloid (see Fig. 26,
page 191) and the
curve inside the
pitch circle by a
Hypocycloid.
The curves al-
ways meet on the
pitch line in both
gears and racks.
The theoretical
requirements for
correct form of Epi-
cycloid gear teeth
are that the face of
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the teeth of one gear and the flank of the teeth of the other gear
must be produced by generating circles of the same diameter.
The diameter of the generating circle is limited by the size
of the smallest gear or pinion in the series of gears which are con-
structed to run together, because if the generating circle is as
large in diameter as half the pitch diameter of the gear, the
hypocycloid will be a straight line ; thus, the flank of the tooth
will be a straight radial line. If the generating circle is
larger than half the pitch diameter of the gear, the result will be
a weak and poor tooth with under-cut flank.
When the same size of generating circle is used for gears of
different diameters but of the same pitch, all such gears will work
correctly together, and for this reason it is possible to construct
interchangeable gears having’ cycloid teeth. If the diameter of
the generating circle is equal to half the diameter of the
smallest gear in the set, this gear will have teeth with radial
flanks but all the other gears and the rack will have double-
curved teeth. Fig. 1 shows a rack drawn to >£-inch circular
pitch ; the generating circle is 0.98 inch diameter, which is equal
to half of the pitch diameter of a gear of 12 teeth and V
z inch
circular pitch.
All gears of the same pitch having 12 teeth or more, con-
structed by the same generating circle in the same manner as
the rack, will match and be interchangeable with the rack, and
will also match and be interchangeable with each other.
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