PULLEY

, one of the five mechanical powers; consisting of a little wheel, being a circular piece of wood or metal, turning on an axis, and having a channel around it, in its edge or circumference, in which a cord slides and so raises up weights.

The Latins call it Trochlea; and the seamen, when fitted with a rope, a Tackle. An assemblage of several Pulleys is called a System of Pulleys, or Polyspaston: some of which are in a block or case, which is fixed; and others in a block which is moveable, and rises with the weight. The wheel or rundle is called the Sheave or Shiver; the axis on which it turns, the Gudgeon; and the fixed piece of wood or iron, into which it is put, the Block.

Doctrine of the Pulley.—1. If the equal weights P and W hang by the cord BB upon the pulley A, whose block b is fixed to the beam HI, they will counterpoise each other, just in the same manner as if the cord were cut in the middle, and its two ends hung upon the hooks fixed in the Pulley at A and A, equally distant from the centre.

Hence, a single Pulley, if the lines of direction of the power and the weight be tangents to the periphery, neither assists nor impedes the power, but only changes its direction. The use of the Pulley therefore, is when the vertical direction of a power is to be changed into an horizontal one; or an ascending direction into a descending one; &c. This is found a good provision for the safety of the workmen employed in drawing with the Pulley. And this change of direction by means of a Pulley has this farther advantage; that if any power can exert more force in one direction than another, we are hence enabled to employ it with its greatest effect; as for the convenience of a horse to draw in a horizontal direction, or such like.

But the great use of the Pulley is in combining several of them together; thus forming what Vitruvius and others call Polyspasta; the advantages of which are, that the machine takes up but little room, is easily removed, and raises a very great weight with a moderate force.

2. When a weight W hangs at the lower end of the moveable block p of the Pulley D, and the chord GF goes under the Pulley, it is plain that the part G of the cord bears one half of the weight W, and the part F the other half of it; for they bear the whole between them; therefore whatever holds the upper end of either rope, sustains one half of the weight; and thus the power P, which draws the cord F by means of the cord E, passing over the fixed pulley C, will sustain the weight W when its intensity is only equal to the half of W; that is, in the case of one moveable Pulley, the power gained is as 2 to 1, or as the number of ropes G and F to the one rope E.

In like manner, in the case of two moveable Pulleys P and L, each of these also doubles the power, and produces a gain of 4 to 1, or as the number of the ropes Q, M, S, K, sustaining the weight W, to the 1 rope O sustaining the power T; that is, W is to T as 4 to 1. And so on, for any number of moveable Pulleys, viz, 3 such Pulleys producing an increase of power as 6 to 1; 4 Pulleys, as 8 to 1; &c; each power adding 2 to the number. Also the effect is the same, when the Pulleys are disposed as in the fixed block X, and the other two as in the moveable block Y; these in the lower block giving the same advantage to the power, when they rise all together in one block with the weight.

But if the lower Pulleys do not rise all together in one block with the weight, but act upon one another, having the weight only fastened to the lowest of them, the | force of the power is still more increased, each power doubling the former numbers, the gain of power in this case proceeding in the geometrical progression, 1, 2, 4, 8, 16, &c, according to the powers of 2; whereas in the former case, the gain was only in arithmetical progression, increasing by the addition of 2. Thus, a power whose intensity is equal to 8lb applied at a will, by means of the lower Pulley A, sustain 16lb; and a power equal to 4lb at b, by means of the Pulley, will sustain the power of 8lb acting at a, and consequently the weight of 16lb at W; also a third power equal to 2lb at c, by means of the Pulley C, will sustain the power of 4lb at b; and a 4th power of 1lb at d, by means of the Pulley D, will sustain the power 2 at c, and consequently the power 4 at B, and the power 8 at A, and the weight 16 at W.

3. It is to be noted however, that, in whatever proportion the power is gained, in that very same proportion is the length of time increased to produce the same effect. For when a power moves a weight by means of several Pulleys, the space passed over by the power is to the space passed over by the weight, as the weight is to the power. Hence, the smaller a force is that sustains a weight by means of Pulleys, the slower is the weight raised; so that what is saved or gained in force, is always spent or lost in time: which is the general property of all the mechanical powers.

The usual methods of arranging Pulleys in their blocks, may be reduced to two. The first consists in placing them one by the side of another, upon the same pin; the other, in placing them directly under one another, upon separate pins. Each of these methods however is liable to inconvenience; and Mr. Smeaton, to avoid the impediments to which these combinations are subject, proposes to combine these two methods in one. See the Philos. Trans. vol. 47, pa. 494.

Some instances of such combinations of Pulleys are exhibited in the following figures; beside which, there are also other varieties of forms.

A very considerable improvement in the construction of Pulleys has been made by Mr. James White, who has obtained a patent for his invention, and of which he gives the following description. The last of the three following figures shews the machine, consisting of two Pulleys Q and R, one fixed and the other moveable. Each of these has six concentric grooves, capable of having a line put round them, and thus acting like as many different Pulleys, having diameters equal to those of the grooves. Supposing then each of the grooves to be a distinct Pulley, and that all their diameters were equal, it is evident that if the weight 144 were to be raised by pulling at S till the Pulleys touch each other, the first Pulley must receive the length of line as many times as there are parts of the line hanging between it and the lower Pulley. In the present case, there are 12 lines, b, d, f, &c, hanging between the two pulleys, formed by its revolution about the six upper lower grooves. Hence as much line must pass over the uppermost Pulley as is equal to twelve times the distance of the two. But, from an inspection of the figure, it is plain, that the second Pulley cannot receive the full quantity of line by as much as is equal to the distance betwixt it and the first. In like manner, the third Pulley receives less than the first by as much as is the distance between the first and third; and so on to the last, which receives only one twelfth of the whole. For this receives its share of line n from a fixed point in the upper frame, which gives it nothing; while all the others in the same frame receives the line partly by turning to meet it, and partly by the line coming to meet them.

Supposing now these Pulleys to be equal in size, and to move freely as the line determines them, it appears evident, from the nature of the system, that the number of their revolutions, and consequently their velocities, must be in proportion to the number of suspending parts that are between the fixed point above mentioned and each Pulley respectively. Thus the outermost Pulley would go twelve times round in the time that the Pulley under which the part n of the line, if equal to it, would revolve only once; and the intermediate times and velocities would be a series of arithmetical proportionals, of which, if the first number were 1, the last would always be equal to the whole number of terms. Since then the revolutions of equal and distinct Pulleys are measured by their velocities, and that it is possible to find any proportion of velocity, on a single body running on a centre, viz, by finding proportionate distances from that centre; it follows, that if the diameters of certain grooves in the same substance be exactly adapted to the above series (the line itself being supposed inelastic, and of no magnitude) the necessity | of using several Pulleys in each frame will be obviated, and with that some of the inconveniencies to which the use of the Pulley is liable.

In the figure referred to, the coils of rope by which the weight is supported, are represented by the lines a, b, c &c; a is the line of traction, commonly called the fall, which passes over and under the proper grooves, until it is fastened to the upper frame just above n. In practice, however, the grooves are not arithmetical proportions, nor can they be so; for the diameter of the rope employed must in all cases be deducted from each term; without which the smaller grooves, to which the said diameter bears a larger proportion than to the larger ones, will tend to rise and fall faster than they, and thus introduce worse defects than those which they were intended to obviate.

The principal advantage of this kind of Pulley is, that it destroys lateral friction, and that kind of shaking motion which is so inconvenient in the common Pulley. And lest (says Mr. White) this circumstance should give the idea of weakness, I would observe, that to have pins for the pulleys to run on, is not the only nor perhaps the best method; but that I sometimes use centres fixed to the Pulleys, and revolving on a very short bearing in the side of the frame, by which strength is increased, and friction very much diminished; for to the last moment the motion of the Pulley is perfectly circular: and this very circumstance is the cause of its not wearing out in the centre as soon as it would, assisted by the ever increasing irregularities of a gullied bearing. These Pulleys, when well executed, apply to jacks and other machines of that nature with peculiar advantage, both as to the time of going and their own durability; and it is possible to produce a system of Pulleys of this kind of six or eight parts only, and adapted to the pockets, which, by means of a skain of sewing silk, or a clue of common thread, will raise upwards of an hundred weight.

As a system of Pulleys has no great weight, and lies in a small compass, it is easily carried about, and can be applied for raising weights in a great many cases, where other engines cannot be used. But they are subject to a great deal of friction, on the following accounts; viz, 1st, because the diameters of their axes bear a very considerable proportion to their own diameters; 2d, because in working they are apt to rub against one another, or against the sides of the block; 3dly, because of the stiffness of the rope that goes over and under them. See Ferguson's Mech. pa. 37, 4to.

But the friction of the Pulley is now reduced to nothing as it were, by the ingenious Mr. Garnett's patent friction rollers, which produce a great saving of labour and expence, as well as in the wear of the machine, both when applied to Pulleys and to the axles of wheel-carriages. His general principle is this; between the axle and nave, or centre pin and box, a hollow space is left, to be filled up by solid equal rollers nearly touching each other. These are furnished with axles inserted into a circular ring at each end, by which their relative distances are preserved; and they are kept parallel by means of wires fastened to the rings between the rollers, and which are rivetted to them.

The above contrivance is exhibited in the annexed figure; where ABCD represents a piece of metal to be inserted into the bo<*> or nave, of which E is the centrepin or axle, and 1, 1, 1, &c, rollers of metal having axes inserted in the brazen circle which passes through their centres; and both circles being rivetted together by means of bolts passing between the rollers from one side of the nave to the other; and thus they are always kept separate and parallel.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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PROTRACTING
PROTRACTOR
PSEUDO Stella
PTOLEMAIC
PTOLEMY
* PULLEY
PUMP
PUNCHEON
PUNCHINS
PURBACH (George)
PURLINES