WITH many amateurs it is a source of much perplexity how to manipulate the change wheels and leading screw of a screw-cutting lathe, in order to produce a screw of any desired thread, or "pitch."

It is therefore proposed in this short chapter to present the matter in a very plain and simple manner, which will elucidate the whole mystery.

What we have to do is to traverse the tool along the work revolving between the lathe centres, at such a ratio to the speed of the revolution as shall produce a screw of the desired fineness or coarseness, which is called the "pitch," and usually expressed as of so many threads to the inch in length of screw.

Now it will be obvious that if equal-sized wheels be used to connect the spindle of headstock and the leading screw which traverses the saddle, and with it the cutting tool, along the lathe bed, the speed of the revolution of the spindle (and with it the work driven by it) will be the same as that of the leading screw, and the screw produced will be precisely a counterpart in pitch to the leading screw; and as this may be often required, every set of change wheels is supplied with one pair of equal wheels, usually forty or sixty teeth, and to vary this ratio of speed the other twenty wheels are required.

Our object now is to see how to adjust these various wheels, so as to traverse the tool in such a relative speed to the speed of the revolution of the headstock spindle as shall cut our desired pitch.

A modern screw-cutting lathe is usually provided with a fixed pinion on the tail end of the spindle, and a second precisely similar pinion on a fixed stud screwed into the head-stock below it; and these are geared together by a third and intermediate wheel of the same or any convenient size; while a fourth wheel, precisely a counterpart of the third, is fixed to gear into it, and is running idly so long as the third is being used, but may be brought into gear with the head pinion by disengaging the third, and will thus reverse the motion of the second pinion. These three wheels, which we have called the second, third, and fourth, are fixed on a plate, swivelling on the stud of the second for a centre, and are called the reversing gear, and are used for the purpose of causing the leading screw to revolve in one direction or the other, to traverse the saddle from right to left, or vice versa, and thus to cut screws either right or left handed.

Now, as the pinion on the end of the spindle, and that (the second) on the fixed stud below it, are precisely the same, it follows that they will revolve at the same speed, and we may treat them as the same, and the sleeve connected to pinion on stud of reversing gear is now a correct substitute for the spindle of headstock, and in all our subsequent arrangements we shall treat it as the latter, and speak of it as the "spindle."

This sleeve, fixed to and revolving with the second pinion, is prepared with a key to receive the change wheels; and when we say we put such a change wheel on the spindle, we intend putting it on this sleeve.

Now, we have at our disposal for change wheels the "spindle," and the end of the leading screw, similarly prepared with a key for the wheels, and which we will more briefly speak of as the " screw."

But as these two revolve on fixed centres, we must have some adjustable means of connecting them by gearing, and this gearing, we have seen, must vary greatly to produce the results we desire; hence the use of the swing frame, or quadrant plate, which swivels at the end of the screw, and is provided with one or two slots, having a stud and sleeve long enough to admit of two wheels side by side, and adjustable along this slot. By this means, and the swivelling motion of the swing frame, it will be found that any gearing may be arranged to connect the spindle and the screw.

The sleeve revolving on the sliding stud of swing frame is called the "stud," and the driven wheel on it is called the stud wheel; and should there be occasion to use a second wheel on this sleeve, it would be called the "pinion." So we now have-

Spindle Stud Pinion Screw or, as they are frequently called-

Driver Driven Driver Driven

"We have now to consider the changing of the wheels on these three centres, to give the requisite ratio of speed between spindle and screw.

For simple pitches below twelve threads per inch, a single train of wheels - that is, three - only is needed, viz., one driver, on the spindle; one driven, on the screw; and one intermediate wheel, on the stud. Let it always be borne in mind that a mere idle or intermediate wheel, simply conveying motion, does not affect the ratio. Now the size of the change wheels, that is, the number of teeth, must always bear the same ratio as does the screw to be cut to the leading screw of the lathe; hence we will adopt the following:

Rule 1. - Place the pitch of the leading screw as numerator, and the pitch of the screw to be cut as denominator, in the form of a simple vulgar fraction; multiply both by 5 or 10, and the products will be the wheels required, the numerator being the spindle wheel, or driver, and the denominator the screw wheel, or driven.

Example. - To cut a screw of seven threads per inch with a leading screw of four threads per inch.

To cut a screw of twelve threads per inch, with a leading screw of two threads per inch:

2/12 x 10 = 20/120 = wheels required.

Or, if the pitch required be fractional, all we have to do is to reduce the fraction or mixed number to a whole number for a simple denominator, and proceed as before.

Example. - To cut a screw of four and three-quarter threads per inch, with a leading screw of four threads per inch:

4/4 3/2 (denominator of fraction) == 16/19 x 5 = 80/95 wheels required.

Pitches above twelve per inch may require, for convenience of gearing or bringing the sizes within the compass of the wheels usually supplied, that a double train (four wheels) be used - usually termed compounding; to effect which we will adopt