Endless Screw and Worm-Wheel.* When a screw is rotated between fixed bearings so that it cannot move longitudinally, it is called an endless screw, because the threads of the screw seem to travel onwards without ending.† When suck a screw gears with a toothed wheel, having its teeth set obliquely at the same angle as the threads of the screw so as to bear evenly thereon, the wheel is termed a worm-wheel. The endless screw is sometimes called the worm, no doubt from its resemblance to that well-known humble animal which, when coiled up for rest, would not turn upon any one unless trod upon.

By this arrangement, motion may be transmitted from one shaft to another at right angles to each other, without any possibility of the machine overhauling; for although the velocity ratio is very great, the efficiency is comparatively small-considerably under 50 per cent. with single-threaded screws-owing to the friction between the worm and the wheel.‡

It is most important for the student to comprehend that if the screw be a single-threaded one, it must make as many turns as there are teeth on the wheel, for every revolution of the latter. If the screw is a double-threaded one, then for each revolution thereof it drives the wheel through a distance equal to the distance between two teeth on the pitch circle, and if treble-threaded through the pitches of three teeth. Thus, if N equal the number of teeth in the worm-wheel, then, with a single-threaded screw, for every turn of the same, the wheel will move a distance of

2

I

N ;

with a

double-threaded worm and with a treble-threaded one N'

and so on.

3

Ñ

The endless screw and worm-wheel is used in a very great variety of circumstances, from the turning of a big marine engine when in port, to the delicate movements in a telescope or a microscope.

Combined Pulley, Worm, Worm-wheel and Winch Drum.—This combination is shown by the accompanying end and side views drawn from an experimental piece of apparatus in

* Refer to the next figure.

The term perpetual screw would express more exactly its action, for when in motion, it continually screws the worm-wheel round.

The greater the diameter of the screw and the smaller its pitch is, the better will be its bearing on the teeth of the wheel, but then the efficiency will be so small that there will be no chance of overhauling. This is the condition to be observed when the screw is intended to drive the wheel. If, however, it should be required to drive the screw by the wheel, or necessary that overhauling should take place, then the screw must be small in diameter, its pitch very great, and either double or treble threaded.

the Author's Laboratory, which is used by the students for ascertaining the efficiency of the machine, and for finding the co-efficient of friction between the endless screw and worm-wheel.

PULLEY, WORM, WORM-WHEEL AND WINCH DRUM.

By the Principle of Work (neglecting friction), if the drum, D, makes one turn, and if the worm be a single-threaded screw,

* It will be evident to the student that, given any four of these five values, he can change this formula so as to find the fifth one; and, that he can experiment with this machine in precisely the same way as has been already explained in the case of the wheel and axle, block and tackle, Weston's pulley block and screw, &c., to ascertain its working advantage, co-efficient of friction and efficiency.

Worm-wheel Lifting Gear. The accompanying figure shows a practical application of the endless screw and wormwheel for the same purpose as the Weston's differential block is used-viz., the lifting of weights without fear of the tackle over

WORM-WHEEL LIFTING GEAR. (By Holt & Willets.)

worm

hauling. A light-driving endless chain passes
over a V-grooved pulley having ridges or teeth
on the inner sides of the grooves, so as to fit
the pitch of the links of the chain. This
pulley is keyed to the outer end of a worm
spindle, whose screw gears with a
wheel fixed to or cast along with a second
V-grooved ridged pulley or drum, over which
is passed the movable end of a heavier lifting
chain after it has been reeved under a snatch-
block pulley. In fact, it is simply the previous
experimental apparatus in a handy and com-
pact form.

EXAMPLE IV.-If in lifting tackle of the above description the driving pulley has a radius R=5", the number of teeth in the worm-wheel N = 20, and the driven pulley a radius r=5"; what weight suspended from the snatch-block hook could be lifted by a force of 10 lbs. applied to the forward side of the light chain-(1) Neglecting friction, (2) if the modulus or efficiency of the whole appa

ratus were only 25?

ANSWER. (1) Applying the previous formula, and taking account of the fact that the lifting chain is combined with a snatch-block, we have

(2) Owing to friction, weight of chain and snatch-block, the actual result obtainable is only 25, or 25 per cent. of this theoretical value; consequently

LECTURE XV.-QUESTIONS.

I. A horizontal screw, of 1 inch pitch, is fitted to a sliding nut which is pulled horizontally by a cord passing over a fixed pulley, and having a weight, W, attached to it. To the free end of the screw there is fixed a pulley of 20 inches diameter, from the circumference of which a weight, ?, hangs by a cord. Find the ratio of P to W. Ans. I: 62.8.

=

2. In a set of combined lever, screw, and pulley gear, like that illustrated before Example I. in this Lecture, R 6", P = = 2 lbs., W: = 50 lbs., and the pitch of the screw is such that there are 2 threads to the inch; find (1) velocity ratio, (2) theoretical advantage, (3) working advantage, (4) work put in to lift W I ft., (5) work got out, (6) percentage efficiency. Ans. (1) 75°4 : 1; (2) 75'4 : I ; (3) 25: 1; (4) 150·8 ft.-lbs.; (5) 50 ft.-lbs.; (6) 33°1 per cent. 3. Describe, with sketches, the construction of an ordinary lifting jack in which the weight is lifted by means of a screw and nut. If the screw be 1 inch pitch, the lever 20 inches long, and the pressure applied at the end of the lever be 30 lbs. ; what weight can be lifted (neglecting friction)? (Take π = 31416.) (S. and A. Exam. 1890.) Ans. 3770 lbs.

4. In a screw-jack, where a worm-wheel is used, the pitch of the screw is inch, the number of teeth on the worm-wheel is 16, and the length of the lever is 10 inches; find the gain in pressure. Ans. P: W::I: 1069.

5. What practical objection is there to the use of screw gear of any description for obtaining great pressure? Take for example the case of the screw-lifting jack. Sketch in vertical section and plan, and describe, a traversing one to lift say 20 tons. Explain how the screw of the jack is raised and lowered without being turned round.

6. Sketch and describe the construction and action of a screw press for pressing goods so as to make them into bales for transport. What force must be applied at the end of a screw press lever 8' 4" in length, in order to exert on the goods a total pressure of 22,000 lbs. when the pitch of the screw is I"? If 60 per cent. be lost in friction, what pressure would result from the application of this force on the lever? Ans. 35 lbs.; 8800 lbs.

7. Sketch an ordinary bench vice. Apply the principle of work to find the gripping force obtained when a man exerts a pressure of 15 lbs. at the end of a lever 15 inches long, the screw having 5 threads per inch, the length from the hinge to the screw being 12 inches, and the length from the hinge to the jaws being 16 inches. Ans. 5303.6 lbs.

8. Explain, with a sketch, the manner in which the principle of work is applied in determining the relation of P to W in the case of the endless screw and worm-wheel. The lever handle which works the screw being 14" long, the number of teeth in the worm-wheel 20, and the load being a weight of 1000 lbs. hanging upon a drum 12" diameter on the worm-wheel shaft, find the force to be applied at the end of the lever handle in order to support the weight. (S. and A. Exam. 1887.) Ans. 21:43 lbs.

9. Explain the mechanical advantage resulting from the employment of an endless screw and worm-wheel. The lever handle which turns an endless screw is 14" long, the worm, which has 32 teeth, and a weight, W, hangs by a rope from a drum 6" diameter, whose axis coincides with that of the worm-wheel. If a pressure P be applied to the lever handle, find the ratio of P to W. (S. and A. Exam. 1883.) Ans. P: W:: 3:448. If in this question the worm be changed to (1) a double, and (2) a treblethreaded screw, what will be the respective ratios of P to W? (1) 1:74·6; (2) I: 49.7.

Ans.

LECTURE XVI.

CONTENTS.-General Idea of the Mechanism in a Screw-cutting LatheMotions of the Saddle and Slide Rest-Velocity Ratio of the Change Wheels-Rules for Calculating the Required Number of Teeth in Change Wheels-Examples I. II.-Movable Headstock for a Common Lathe-Description of the Screw-cutting Lathe in the Author's Electrical Engineering Workshop, with a complete set of Detail Drawings -Questions.

General Idea of the Mechanism in a Screw-cutting Lathe. We will devote this Lecture to giving a general idea of the mechanism by which screws are cut in lathes, and the velocity ratio of the screw to be cut to the leading screw, together with a description of a complete set of illustrations prepared from working drawings of a new self-acting screw-cutting lathe.

Referring to the following figure, and to the general view of the 6-inch centre screw-cutting lathe (further on), it will be seen that the round metal bar on which the screw is to be cut is placed between the steel centres of the fixed and movable headstocks of the lathe. This bar has an eye-catch on its end next to the fixed headstock, which engages with a driving-stud connected to the face-plate. In order to obtain the necessary force to cut the screw, and to reduce the speed of the workshop motion shafts (in the case of a power lathe, or of the treadle shaft in the case of a foot lathe) to the required velocity, the fixed headstock is supplied with back motion gearing. The back wheels may be put into or out of gear with the lathe spindle wheels at pleasure, by a simple eccentric motion (in the case of the lathes herein illustrated), or, as is sometimes effected, by sliding the back shaft forward, so that its wheels clear those on the lathe spindle, and then fixing it there, by a tapered pin fitting through a hole in the framing and a groove cut in the shaft. But, when the back motion is required for the purpose of making a slow heavy cut, the follower F, is thrown out of gear with the stepped cone pulley, so that the driver D, (which is keyed to the cone) may turn the follower F1; and the driver D, (which is keyed to the same spindle as F,) rotate the follower F, (which is keyed to the lathe spindle), and hence revolve the face-plate and the bar, out of which the screw is to be formed.

2