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408 WORMS AND WORM GEARS.
The width of the threading tool at the point is given in
Column b, Table No. 52 , as 0.2325 inch. The depth of the space
to be cut in the worm is given in Column Z>, as 0.515 inch. The
diameter of the worm at the bottom of the thread will be
:
4.977 — 2 X 0.515 = 3.947 inches.
The depth of the space to be cut in the hob is given in col-
umn h in Table No. 52 as 0.5525 inch.
The diameter of the hob at bottom of thread will be
:
5.052 — 2 X 0.5525 = 3.947 inches.
Thus the only difference in size between the hob and the
worm is in the outside diameter and in the depth of the cut.
Both may be finished by the same tool, as the diameter at the
bottom of the thread and the thickness of the teeth at the pitch
line should be the same for both hob and worm.
Elliptical Gear Wheels.
Elliptical gear wheels are sometimes used in order to change
a uniform rotary motion of one shaft to an alternately fast and
slow motion of the other. See Fix. 15.
The pitch line is constructed and calculated the same as
the circumference of an ellipse. (See page 189.) The gear is
constructed involute the same as for spur gears. If the differ-
ence between the minor and the major diameters is large it may
be necessary to construct the teeth of different shapes at differ-
ent places on the circumference; in other words, the whole cir-
cumference of the gear cannot be cut with the same cutter. A
cutter of the same pitch, of course, but corresponding to a larger
diameter of gear, must be used where the curve of the pitch line
is less sharp.
The centers of the shafts are in the foci of the ellipse. If
two elliptical gear wheels, made from the same pattern, or cut
together at the same time, on the same arbor, are to work together
they must have an uneven number of teeth so that a space will
be diametrically opposite a tooth, as will be seen from Fig. 15.
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