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GEAR TEETH. 39
1
than 14J^ degrees, all these other proportions will also change.
Fig. 6 shows a pattern for gears and rack constructed with
necessary clearance as used for cast gears. All tooth parts are
of the same dimensions as used for cycloid gears as given on
page 375. Fig. 7 shows a cut gear and rack constructed in the
same manner. The advantages of the involute system of gears
are in the strength of teeth, and also that the gears will trans-
mit uniform motion and run satisfactorily, even if the distance
between centers should be slightly incorrect.
Internal Gears with involute teeth.
Internal gears with involute teeth are constructed by the
same method as external gears. It is shown by Fig. 5 that the
same circle will form the teeth for an internal gear as well as
for an external gear of the same pitch diameter. The only dif-
ference is that the teeth in the internal gear will be concave,
because what is space in the external gear will be tooth in the
internal gear.
When the difference between the number of teeth in the
internal gear and its external pinion is small, it is necessary to
round the point of the teeth in the internal gear in order to make
them run free without interference.
Frequently the teeth, both in the internal gear and its
pinion, are made shorter than standard teeth in order to avoid
interference.
Sometimes it may be advisable to not only shorten the teeth
but also to increase the pressure angle from 14^ degrees to 20
degrees in order to obtain smooth running internal gears.
CHORDAL PITCH.
The term chordal pitch is not used very much in gear cal-
culations, but it is of practical value sometimes in machine
work to be able to determine the length of the chord as well as
the length of the arc.
Fig. 8 shows two teeth in a gear of 18 teeth, 1^ circular
pitch and 8.59 in. pitch diameter. The distance from d to e
measured on the curved line is the circular pitch and is i\
inches. The distance from d to e measured on a straight line
is the chordal pitch of the gear. The chordal pitch is always
less than the circular pitch.
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