SCREW
, or Scrue, one of the six mechanical powers; chiefly used in pressing or squeezing bodies close, though sometimes also in raising weights.
The Screw is a spiral thread or groove cut round a cylinder, and everywhere making the same angle with the length of it. So that, if the surface of the cylinder, with this spiral thread upon it, were unfolded and stretched into a plane, the spiral thread would form a straight inclined plane, whose length would be to its height, as the circumference of the cylinder is to the distance between two threads of the Screw; as is evident by considering, that in making one round, the spiral rises along the cylinder the distance between the two threads.
Hence the threads of a Screw may be traced upon the smooth surface of a cylinder thus: Cut a sheet of paper into the form of a right-angled triangle, having its base to its height in the above proportion, viz, as the circumference of the cylinder of the Screw is to the intended distance between two threads; then wrap this paper triangle about the cylinder, and the hypothenuse of it will trace out the line of the spiral thread.
When the spiral thread is upon the outside of a cylinder, the Screw is said to be a male one. But if the thread be cut along the inner surface of a hollow cylinder, or a round perforation, it is said to be female. And this latter is also sometimes called the box or nut.
When motion is to be given to something, the male and female Screw are necessarily conjoined; that is, whenever the screw is to be used as a simple engine, or mechanical power. But when joined with an axis in peritrochio, there is no occasion for a female; but in that case it becomes part of a compound engine.
The Screw cannot properly be called a simple machine, because it is never used without the application of a lever, or winch, to assist in turning it.
1. The force of a power applied to turn a Screw round, is to the force with which it presses upwards or downwards, setting aside the friction, as the distance between two threads is to the circumference where the power is applied.
For, the Screw being only an inclined plane, or half wedge, whose height is the distance between two threads, and its base the said circumference; and the force in the horizontal direction being to that in the vertical one as the lines perpendicular to them, viz, as the height of the plane, or distance of the two threads, is to the base of the plane, or circumference at the place where the power is applied; therefore the power is to the pressure, as the distance of two threads, is to that circumference.
2. Hence, when the Screw is put in motion; then the power is to the weight which would keep it in equilibrio, as the velocity of the latter is to that of the former. And hence their two momenta are equal, which are produced by multiplying each weight or power by its own velocity. Two different forms of Screw presses, are as below.
3. Hence we can easily compute the force of any machine turned by a Screw. Let the annexed figure represent a press driven by a Screw, whose threads are each a quarter of an inch asunder; and let the Screw be turned by a handle of 4 feet long from C to D; then if the natural force of a man, by which he can lift, or | pull, or draw, be 150 pounds; and it be required to determine with what force the Screw will press on the board, when the man turns the handle at C and D with his whole force. The diameter CD of the power being 4 feet, or 48 inches, its circumference is 48 X 3.1416 or 1504 nearly; and the distance of the threads being 1/4 of an inch; therefore the power is to the pressure, as 1/4 to 150 4/5 or as 1 to 603 1/5: but the power is equal to 150lb; therefore as 1 : 603 1/5 :: 150 : 90,480; and consequently the pressure at the bottom of the Screw, is equal to a weight of 90,480 pounds, independent of friction.
But the power has to overcome, not only the weight, or other resistance, but also the friction of the Screw, which in this machine is very great, in some cases equal to the weight itself, since it is sometimes sufficient to fustain the weight, when the power is taken off.
Mr. Hunter has described a new method of applying the Screw with advantage in particular cases, in the Philos. Trans. vol. 71, pa. 58 &c.
The Endless Screw, or Perpetual Screw, is one which works in, and turns, a dented wheel DF, without a concave or female Screw; being so called because it may be turned for ever, without coming to an end. From the following schemes it is evident, that while the Screw turns once round, the wheel only advances the distance of one tooth.
1. If the power applied to the lever, or handle, of an endless Screw AB, be to the weight, in a ratio compounded of the periphery of the axis of the wheel EH, to the periphery described by the power in turning the handle, and of the revolutions of the wheel DF to the revolutions of the Screw CB, the power will balance the weight. Hence,
2. As the motion of the wheel is very slow, a small power may raise a very great weight, by means of an endless Screw. And therefore the chief use of such a Screw is, either where a great weight is to be raised through a little space; or where only a slow gentle motion is wanted. For which reason it is very useful in clocks and watches.
3. Having given the number of teeth, the distance of the power from the centre of the Screw B, the radius of the axis HE, and the power; to find the weight it will raise. Multiply the distance of the power from the centre of the Screw AB, by the number of the teeth, and the product will be the space passed through by the power, while the weight passes through a space equal to the periphery of the axis: then say, as the radius of the axis is to the space of the power just found, so is the power to a 4th proportional, which will be the weight the power is able to sustain. Thus, if AB = 3, the radius of the axis HE = 1, the power 150 pounds, and the number of teeth of the wheel DF 48; then the weight will be found = 21,600 = 3 X 150 X 48. Whence it appears that the endless Screw exceeds all others in increasing the force of a power.
4. A machine for shewing the power of the Screw may be contrived in the following manner. Let the wheel C (last fig.) have a Screw a b on its axis, working in the teeth of the wheel D, which suppose to be 48 in number. It is plain that for every revolution of the wheel C, and Screw ab, by the winch A, the wheel D will be moved one tooth by the Screw; and therefore in 48 revolutions of the winch, the wheel D will be turned once round. Then if the circumference of a circle, described by the handle of the winch, be equal to the circumference of a groove e round the wheel D, the velocity of the handle will be 48 times as great as the velocity of any given point in the groove. Consequently when a line G goes round the groove e, and has a weight of 48lb hung to it below the pedestal EF, a power equal to one pound at the handle will balance and support the weight.
Archimedes's Screw, is a spiral pump, being a machine for raising water, first invented by Archimedes.
Its structure and use will be understood by the following description of it.
ABCD (Pl. xxiii, fig. 6) is a wheel, which is turned round, according to the order of those letters, by the fall of water EF, which need not be more than 3 feet. The axis G of the wheel is raised so as to make an angle of about 44° with the horizon; and on the top of that axle is a wheel H, which turns such another wheel I of the same number of teeth; the axle K of this last wheel being parallel to the axle G of the two former wheels. The axle G is cut into a double threaded Screw, as in the annexed figure (fig. 7), exactly resembling the Screw on the axis of the fly of a common jack, which must be what is called a right-handed Screw; if the first wheel turns in the direction ABCD; but a left-handed Screw, if the stream turns the wheel the contrary way; and the Screw on the axle G must be cut in a contrary way to that on the axle K, because these axles turn in contrary directions. These Screws must be covered close over with boards, like these of a cylindrical cask; and then they will be spiral tubes. Or they may be made of tubes or pipes of lead, and wrapt round the axles in shallow grooves cut in it, like the figure 8. The lower end of the axle G turns constantly in the stream that turns the wheel, and the lower ends of the spiral tubes are open into the water. So that, as the wheel and axle are turned round, the water rises in the spiral tubes, and runs out at L through the holes M, N, as they come about below the axle. These holes, of which there may be any number, as 4 or 6, are in a broad close ring on the top of the axle, into which ring the water is delivered from the upper open ends of the Screw tubes, and falls into the open box N. The lower end of the axle K turns on a gudgeon in the water in N; and the spiral tubes in that axle take up the water from N, and deliver it into another such box under the top of K; on which there may be such another | wheel as I, to turn a third axle by such a wheel upon it. And in this manner may water be raised to any proposed height, when there is a stream sufficient for that purpose to act on the broad float boards of the first wheel. Archimedes's Screw, or a still simpler form of it, is also represented in fig. 9.
