the change gears for cutting English threads with a
metric lead-screw, place 127 in the numerator and the threads per inch
to be cut, multiplied by the metric screw constant multiplied by 5, in
the denominator; 127 is the number of teeth on the spindle-stud gear and
the product of the numbers in the denominator equals the number of teeth
in the lead-screw gear._

=Quick Change-gear Type of Lathe.=--A type of lathe that is much used at
the present time is shown in Fig. 30. This is known as the quick
change-gear type, because it has a system of gearing which makes it
unnecessary to remove the change gears and replace them with different
sizes for cutting threads of various pitches. Changes of feed are also
obtained by the same mechanism, but the feeding movement is transmitted
to the carriage by the rod _R_, whereas the screw _S_{1}_ is used for
screw cutting. As previously explained, the idea of using the screw
exclusively for threading is to prevent it from being worn excessively,
as it would be if continually used in place of rod _R_, for feeding the
carriage when turning.

[Illustration: Fig. 30. Lathe having Quick Change-gear Mechanism]

[Illustration: Fig. 31. End and Side Views of Quick Change-gear
Mechanism]

The general construction of this quick change gear mechanism and the
way the changes are made for cutting threads of different pitch, will be
explained in connection with Figs. 30, 31 and 32, which are marked with
the same reference letters for corresponding parts. Referring to Fig.
30, the movement is transmitted from gear _s_ on the spindle stud
through idler gear _I_, which can be moved sidewise to mesh with either
of the three gears _a_, _b_ or _c_, Fig. 31. This cone of three gears
engages gears _d_, _e_ and _f_, any one of which can be locked with
shaft _T_ (Fig. 32) by changing the position of knob _K_. On shaft _T_
there is a gear _S_ which can be moved along the shaft by hand lever _L_
and, owing to the spline or key _t_, both the sliding gear and shaft
rotate together. Shaft _T_, carrying gears _d_, _e_ and _f_ and the
sliding gear _S_, is mounted in a yoke _Y_, which can be turned about
shaft _N_, thus making it possible to lower sliding gear _S_ into mesh
with any one of a cone of eight gears _C_, Fig. 31. The shaft on which
the eight gears are mounted has at the end a small gear _m_ meshing with
gear _n_ on the feed-rod, and the latter, in turn, drives the
lead-screw, unless gear _o_ is shift