PULLEY, a mechanical device for the duplication and reduplication of the intensity of a force. By its application the power exerted may overcome a resistance much greater than itself, through a sacrifice of velocity.
In its simplest form it consists of a wheel of wood or metal which turns on a smooth axle at tached to a supporting frame, usually in the form of a block. The rim of the wheel is grooved on its outer face so as to allow a rope, cord or chain to pass around it. Its principle of action was first enunciated by Steven, about 1610, based on the fact that the tension of a rope is the same at every point of its length.
Theoretically a fixed peg in the position of the axis of the pulley would serve the purposes defined just as well as a wheel. The latter is introduced for the specific purpose of reducing the friction.
the tension of the rope on both sides of the wheel is the same; tut, since the weight is sup ported by two upward forces each of which is equal to the force applied, the power is equal to one half the weight, the beam supporting the other half. In other words, the power that will lift a given weight by the use of a single fixed pulley will lift twice that weight by the employment of a free pulley.
Fixed and free pulleys may be combined in various ways to obtain a mechanical advantage. In the combination shown in Fig. 3, the tension on the beam at (a) is equal to the power ap plied, and at (b) it is equal to twice that power; but the relation of the power to the weight re mains the same as in case of the single free pulley.
If, however, the supporting cords pull at an angle (2 0), Fig. 4, the pulley is acted upon by three forces— the weight (w) acting ver In the single "fixed" pulley, Fig. 1, to satisfy the condition of static equilibrium, the tension of the rope must be the same on both sides of the wheel, therefore, the power applied is equal to the weight, and although no mechanical ad vantage is gained by its use, it serves to change the direction of the force applied. Incidentally, it loads the beam with twice the amount of that force.
In the single movable or "free') pulley with parallel cords, Fig. 2, as in the fixed pulley, tically downward, and two equal forces (p cos 0) acting upward. The resulting effect, 2p cos 0 = w, shows a mechanical disadvantage, since the power required increases with the an gle, and p= as shown by Figs. 2 and 3, only when = o , that is, when the strings are parallel. When —60°, the power is equal to the weight; and when 0=90°, or 2 4 =180°. an infinite amount of power would be required to draw the rope out horizontal.
Combinations of pulleys or compound pulleys are usually arranged according to one of the three systems represented by Figs. 5, 4 and 7,
which indicate the action of the supporting forces.
In the first system, Fig. 5, five independent pulleys are supported by an equal number of branches from the main cord. The mechan ical advantage stated in terms of weight (w) and power (p) is =32p ; or in general 2a p, when (n) represents the number of pulleys.
In the second system, Fig. 6, the weight is supported by the four forces, p + 2p + 2'p + 2'p -= 15p = (2'— 1)p, or in general, w.—(2n — 1)p.
the movable pulley. This is the form most fre quently used practically, its most extensive ap plication being the block and tackle devices of the running rigging of ships. See BLocx ; TACKLE.
The differential pulley is made up of two pulleys of slightly differing diameter, so fas tened together that they act as one. An endless chain passes around both, and in one of the bights is a movable pulley: the other bight is used to operate the pulley. As the chain is hauled down from the larger pulley it hoists the chain on the other side, but at the same time the nearer chain on the smaller pulley is un winding, so that the lifting bight is lessened in length very slowly. The closer the two fixed pulleys approximate the slower the lift, and the greater the power —usually 1 to 60.• The term pulley is used in quite a different sense when applied to the belt-wheels used in In the third system, Fig. 7, one continuous string is divided into six branches by six pul leys, and since the tension of each branch is equal to (p) the power applied, sents the mechanical advantage, or w = up, when (n) is the number of cords rising from power transmission (q.v.). The many formulas given for calculation of their dimensions vary indefinitely with the material of which the pul ley-wheel is made, the material and thickness of the belt, and the volume of power transmit ted. The width of face of such a wheel is from one-eighth to one-fourth wider than the belt, whose width is determined by the power. In the case of shifting belts the pulley-wheels have a flat face, but otherwise they are slightly crowned, from one-ninety-sixth of the width of the face to as much as one-tenth of such width —as advocated by different authorities. The relative speed of any two pulleys carrying a given belt is inversely as their diameters. To vary the speed at will astep') or "cone') pulleys are in use, the smallest wheel on the driving cone being opposite the largest wheel on the driven cone—and vice versa. Consult Collins, H. E., 'Shafting, Belting and Rope Transmis sion) (New York 1914) ; Goodeve, T. M., (Prin ciples of (London 1908) • Kent's 'Mechanical Engineer's Pocket Book' (New York 1915).