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GEAR TEETH. 377
Example.
What will be the diameter of the gears to connect two shafts
when the distance between centers is 82 inches, and one shaft
is to make 135 revolutions and the other 105 revolutions per
minute ?
Solution
:
_, 2 X 32 X 135 nn . .
D = —-7-
—
. . ...— = 36 inches diameter.
13o -\~ lOo
, 2 X 32 X 105 aa . ,
a= —iOK 1 1A_— = 28 inches diameter.
13o -j- lOo
After the diameter of each gear is calculated, the pitch is
decided upon according to the power the gears have to transmit.
Frequently the pitch will have to be altered somewhat, and
such gears sometimes have teeth of very odd pitch, in order to
obtain the right number of teeth to give the required ratio of
speed. The ratio between the number of teeth in the gears may
always be seen from the ratio of speed between the two shafts.
For instance, in the above example, the ratio of speed between
the shafts is 135
Ao5, which, reduced to its lowest terms, is 9
/r,
therefore, the number of teeth in the two gears may be any
multiple of 9 and 7, respectively.
For instance, 8 X 9 = 72 teeth for the large gear, and 8 X
7 = 56 teeth for the small gear ; or, 10 X 9 = 90 teeth for the
large gear, and 10 X 7 = 70 teeth for the small gear, etc.
The dimensions of teeth may be calculated according to
rules given on page 375.
Diametral Pitch.
The dia?netral pitch of a gear is the number of teeth
to each inch of its pitch diameter. In cut gearing it is always
customary to calculate the gears according to diametral pitch.
When gears are calculated according to circular pitch the corre-
sponding circumference of the pitch circle is usually an even
number, but the diameter will generally be a number having
cumbersome fractions, and therefore the distance between the
centers of the gears will be a number having fractions which
may be very inconvenient to measure with common scales.
This is because the circumference of a circle divided by
3.1416 is equal to its diameter and the diameter multi-
plied by 3.1416 is equal to the circumference. When
gearing is calculated according to diametral pitch this trouble
is entirely avoided, as this directly expresses the number of
teeth on the circumference of the gear according to its pitch
diameter. For instance, "six diametral pitch" means that
there are six teeth on the circumference of the gear for each
inch of pitch diameter. Thus, a gear of six diametral pitch and
forty-eight teeth will be eight inches pitch diameter. A gear of
" eight diametral pitch " means that the gear has eight teeth per
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