# Pulley

## weight, inches, power, inch, cord, movable and ascends

PULLEY. In mechanics, one of the six simple machines, or mechanical pow ers. It consists of a wheel, movable about an axis, and having a groove out in its circumference, over which a cord passes. The axle is supported by a box or sheave, called the black, which may either be movable, or fixed to a firm support.

A single pulley serves merely to change the direction of motion ; but several of them may be combined in va rious ways, by which a me chanical advantage or purchase is gained, greater or less, se conding to their number and the mode of combination. The purchase gained by any com bination is readily computed by comparing time celerity of the weight raised with that of the moving power, according to the principle of virtual ve locities, which is alike appli cable to all machines of what ever kind. In fig. 1, which represents a system where the several portions of the cord are parallel to each other, suppose the weight W to rise one inch, the two blocks would approach each other by that quantity, and consequently, the length of cord connecting a single pair of pulleys would be shortened by 2 inches, so that the power P would descend 2 inches. Let the number of pulleys in each block be es; then, while the weight ascends 1 inch, the power descends 2 n inches, and, y, is equilibrium, the power IS to the weight as 1 to 2 es.

In the combination represented in fig.

2, the purchase is much greater. Here the pulleys are all movable, and each is supported by a separate cord, having one end fastened to a fixed obstacle and the other attached to the succeeding pulley, excepting the upper block, which is fixed. It is evident that, for every inch the weight on the first pul ley a ascends, the second, b, ascends two ; the third, c, ascends four, and so on 3 the velocity being doubled by each additional pulley. The purchase finally obtained is, therefore, =2. ; or the power is to the weight as 1 : 2n.

The third combination, fig. 3, has still greater efficacy. In this system, each cord is fastened. to the weight, i and', pass ing over a pulley, s attached to another pulley, excepting the last, which supports the power. While the weight W rises 1 inch, the first movable pulley, f, will sink 1 inch, which allows the cord applied to it to slacken 2 inches, and this join ed to the inch which the weight ascends allows the second mo vable pulley g, to descend 3 inches.

This allows the next pulley in succession to descend 6 inches, which, joined to the 1 inch which the weight ascends, gives 7 inches for the descent of the third pulley. In like manner, it is found that the de scent of the fourth pulley is 15 inches. Hence, one movable pulley allows the weight to descend 2 X 1 + 1= 3 inches ; two such pulleys, 2 X 3 + 1 7 inches ; 8 2 X 7 1 = 15 inches ; four pulleys, 2 X 15 + 1 = 81 inches, and so on ; so that the purchase obtained by f/, movable pulleys, is 2. + or the Rower is to the weight as 1 to 2. + 1 —1. The theoretical advantage thus computed is, however, in all the cases, greatly di minished by friction, and the rigidity of the rope.

The two last combinations are of little, if any, use in practice, but various modi fications of the first are common. Senea ton' s pulley, or Snneaten's tack, as it is usu ally called, contains two rows of wheels, one under the other, in each block, and a single cord is made to pass over them in such a manner that the power and the weight both net in the same line with the centres of the two blocks, so that there is no tendency to twist. But this ingenious arrangement is open to several objections, and particularly the great amount of later al friction of so many independent wheels. In White's pulley (see fig. 1.) the wheels in each block turn on the same axis, and, consequently, revolve in the same time ; and they arc of different sizes, their di mensions being so proportioned that a point on the circumference of any wheel moves with the velocity of the rope on that wheel. To effect this the diameter of the wheels in the upper block must be as the numbers, 1, 3, 5, &c., and in the lower as 2, 4, 6, &c. Instead of separate wheels, the upper and lower blocks are cut in grooves in the above proportions, whereby the friction is reduced to that of one wheel in each block.