Fig. 1239.
Here we have two wheels having each 36 teeth; hence we may place one of them on the lathe spindle and one on the lead screw, as in [Fig. 1239]; and putting down the pitch of the lead screw, expressed in sixteenths as before, and beneath it the thread to cut also in sixteenths, we have:
| 4 | × | 6 | = | 24 | = | wheel | to be driven by lathe spindle, |
| 11 | × | 6 | 66 | = | „ | to drive lead screw wheel; |
the arrangement of the wheels being shown in [Fig. 1239].
We may prove the correctness of this arrangement as follows: The 36 teeth on the lathe spindle will in a revolution cause the 24 wheel to make 11⁄2 revolutions, because there are one and a half times as many teeth in the one wheel as there are in the other; thus: 36 ÷ 24 = 11⁄2. Now, while the 24 wheel makes 11⁄2, the 66 will also make 11⁄2, because they are both on the same sleeve and revolve together. In revolving 11⁄2 times the 66 will cause the 36 on the lead screw to make 23⁄4 turns, because 99 ÷ 36 = 23⁄4 (or expressed in decimals 2.75), and it thus appears that while the lathe spindle makes one turn, the lead screw will make 23⁄4 turns.
Now, the proportion between 1 and 23⁄4 is the same as that existing between the pitch of the lead screw and the pitch of the thread we want to cut, both being expressed in sixteenths; thus:
| Pitch | of lead screw in sixteenths | 4 | , and 11 ÷ 4 = 23⁄4; |
| „ | to be cut in sixteenths | 11 |
that is to say, 11 is 23⁄4 times 4.
Suppose it is required, however, to find what thread a set of gears already on the lathe will cut, and we have the following rule:
Rule.—Take either of the driven wheels and divide its number of teeth by the number of teeth in the wheel that drives it, then multiply by the number of teeth in the other driving wheel, and divide by the teeth in the last driven wheel. Then multiply by the pitch of the lead screw.