Modern Machine-Shop Practice, Volumes I and II

by Joshua Rose

In this case there are 36 turns of the feed screw a for one turn of the nut pinion g, the thread on sleeve b being 27, and that on the hub of c being 25 to the inch; hence, 36 turns of the feed screw gives an end motion to the sleeve b of ¹⁄₂₅ minus ¹⁄₂₇ = ²⁄₆₇₅, and ¹⁄₃₆ of that = ¹⁄₁₂₁₅₀ of an inch = the amount of sliding motion of the sleeve b, for each revolution of the lathe feed screw. By varying the proportions between the number of teeth in c′ and g and the pitches of the two threads in a proper and suitable ratio, the device enables the cutting of a true thread from any untrue one in which the variation is regular.

It is usual to fasten to the side of the lathe head stock a brass plate, giving a table of threads, and the wheels that will cut them, and obviously such tables vary according to the pitch of the lead screw, but a universal table may be constructed, such as the following table (prepared by the author) that will serve for any lathe.

At the top of the table is the number of teeth in wheels, advancing by four from 12 to 80 teeth, but it may be carried as much beyond 80 as desired. On the left hand of the table is a column of the same wheels. At the bottom of the scale are pitches of lead screw from 3 up to 20 threads per inch. Over each lead screw pitch are thread pitches, thus on lead screw pitch 4 we have 20, 19, 18, and so on.

NUMBERS OF TEETH FOR WHEEL TO GO ON LATHE SPINDLE, LATHE STUD, OR MANDRIL.

Lead Screw.	12	*16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
12	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3
16	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
20	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5
24	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6	6
28	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7	7
32	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8	8
36	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9	9
40	10	10	10	10	10	10	10	10	10	10	10	10	10	10	10	10	10	10
44	11	11	11	11	11	11	11	11	11	11	11	11	11	11	11	11	11	11
48	12	12	12	12	12	12	12	12	12	12	12	12	12	12	12	12	12	12
*52	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13	13
56	14	14	14	14	14	14	14	14	14	14	14	14	14	14	14	14	14	14
60	15	15	15	15	15	15	15	15	15	15	15	15	15	15	15	15	15	15
64	16	16	16	16	16	16	16	16	16	16	16	16	16	16	16	16	16	16
68	17	17	17	17	17	17	17	17	17	17	17	17	17	17	17	17	17	17
72	18	18	18	18	18	18	18	18	18	18	18	18	18	18	18	18	18	18
76	19	19	19	19	19	19	19	19	19	19	19	19	19	19	19	19	19	19
80	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20	20
	Lead Screw Pitch 3.	Lead Screw Pitch 4.	Lead Screw Pitch 5.	Lead Screw Pitch 6.	Lead Screw Pitch 7.	Lead Screw Pitch 8.	Lead Screw Pitch 9.	Lead Screw Pitch 10.	Lead Screw Pitch 11.	Lead Screw Pitch 12.	Lead Screw Pitch 13.	Lead Screw Pitch 14.	Lead Screw Pitch 15.	Lead Screw Pitch 16.	Lead Screw Pitch 17.	Lead Screw Pitch 18.	Lead Screw Pitch 19.	Lead Screw Pitch 20.

The use of the table is as follows:—

Find the pitch of the lead screw, and at the head of that column is the number of teeth for the lathe stud or mandril. Then find in that column the number of threads to be cut, and on the same line, but at the left hand, will be found the number of teeth for the lead screw.

Example.—The lead screw has a pitch of 4, and I require to cut 13 threads per inch. At the head of the column is 16, and on a line with the 13 of the column, but on the left is 52, each number being marked by a * hence the 16 and 52 are the wheels; if we have not those wheels, multiply both by 2 and 32, and 104 will answer.

If the pitch of the lead screw is 2 threads per inch, the wheels must advance by 6 teeth, as indicated below:—

NUMBERS OF TEETH FOR WHEEL TO GO ON LATHE
STUD, LATHE SPINDLE OR MANDRIL.