In a lathe properly adapted, screws to any degree of pitch, or number of threads in a given length, may be cut by means of a leading screw of any given pitch, accompanied with change wheels and pinions; coarse pitches being effected generally by means of one wheel and one pinion with a carrier, or intermediate wheel, which cause no variation or change of motion to take place. Hence the following.

Rule

Divide the number of threads in a given length of the screw which is to be cut by the number of threads in the same length of the leading screw attached to the lathe; and the quotient i- the ratio that the wheel on the end of the screw must bear to that on the end of the lathe spindle.

Example

Let it be required to cut a screw with 5 threads in an inch, the leading screw being of ½ inch pitch, or containing 2 threads in an inch ; what must be the ratio of wheels applied? 5 / 2 = 2.5, the ratio they must bear to each other.

Then suppose a pinion of 40 teeth be fixed upon for the spindle.

40 x 2.5 = 100 teeth for the wheel on the end of the screw.

But screws of a greater degree of fineness than about 8 threads in an inch are more conveniently cut by an additional wheel and pinion, because of the proper degree of velocity being more effectively attained; and these, on account of revolving upon a stud, are commonly designated the stud wheels, or stud-wheel and pinion; but the mode of calculation and ratio of screw are the same as in the preceding rule. Hence, all that is further necessary is to fix upon any three wheels at pleasure, as those for the spindle and stud-wheels; then multiply the number of teeth in the spindle-wheel by the ratio of the screw, and by the number of teeth in that wheel or pinion which is in contact with the wheel on the end of the screw; divide the product by the stud-wheel in contact with the spindle-wheel; and the quotient is the number of teeth required in the wheel on the end of the leading screw.

Example

Suppose a screw is required to be cut containing 25 threads in an inch, and the leading screw, as before, having two threads in an inch, and that a wheel of 60 teeth is fixed upon for the end of the spindle, 20 for the pinion in contact with the screw-wheel, and 100 for that in contact with the wheel on the end of the spindle; required the number of teeth in the wheel for the end of the leading screw.

25 / 2 = 12.5, and 60 X 12.5X20 / 100 = 150 teeth.

Or suppose the spindle and screw-wheels to be those fixed upon, also any one of the stud-wheels, to find the number of teeth in the other.

60 X 12.5 / 150 X 100 = 20 teeth, or 60 X 12.5 X 20 / 150 = 100 teeth.