Mechanic Powers are those simple machines or elements that enter into the construction of the various parts of machinery: they are usually considered to be six in number; viz. the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. It may be easily shewn, however, that these are capable of being reduced to greater simplicity. Thus the wheel and axle is only a succession of levers, and the wedge and screw are merely modifications of the inclined plane; hence all the varieties of machinery are reduced to these three simple elements:
1. The lever.
2. The pulley.
3. The inclined plane.
In treating of the use of simple machines, it is usual to consider all bars as perfectly inflexible, cords as perfectly flexible, and surfaces to move on each other without friction, and afterwards to make allowances for these disturbing forces to the weight raised, as 1 to 2. In the diagram, a e b is the movable pulley supporting the weight at e; eaebp is a cord passing under the movable pulley, and over the fixed pulley at d. Now, as the whole weight is supported by the two portions of the cord c a and d b, each of them sustains one half, and as the passage of the cord over the fixed pulley makes no difference in the proportion, it is clear that the power p is equal to half the weight
When the cords are not parallel, as in the annexed diagram, the angle made by the cords with the perpendicular must be noticed. Thus the force acting in the direction f c must be resolved into two others, one pulling in the direction e c, and the other in f e. Now the force in e c does not all act in supporting the weight, which is wholly sustained by that infe: hence the power is to the weight as c f is to twice e f; and as c f is greater than e f, the power must be greater than one-half the weight, and, consequently, there is a loss of power by the obliquity of the cords. Sometimes the lower or movable pulley consists of a block containing several small wheels or sheaves, in which case the apparatus is termed a block and fall. The power with such a pulley is easily calculated, by observing the number of cords by which the lower block or fall is supported. If the fall be suspended by six ropes, of course each will sustain one-sixth of the weight, and the power will be to the weight as 1 to 6. In every combination of this kind, therefore, the power is to the weight as 1 to the number of cords supporting the lower block, or as 1 to twice the number of sheaves in the fall.
A modification of this arrangement is seen in the following diagram (Fig.1). of White's pulley: it consists of a number of concentric grooves, formed in a solid mass of brass, etc, the diameters of the grooves being regulated by the quantity of cord that has to pass over each. As these all move on a single axis, considerable reduction of friction is obtained; but the great difficulties attending the construction of this apparatus seem insuperable obstacles to its extensive employment. The power is calculated as in the last example. In the different arrangements hitherto mentioned, a single cord is employed passing round all the pulleys; and if attention be given to the spaces passed over by the part attached to the power and that affixed to the weight, it will be seen that the same law obtains as in the other mechanic powers, - the space passed over by the power exceeding that passed over by the weight, as much as the weight exceeds the power.
In this arrangement different cords are employed (as in Fig. 2 in the preceding page), one to each pulley; there being three movable pulleys, the power is to the weight as 1 to 8: thus suppose the power to be 1 lb., the cords a b and c l will each support l lb.; hence the cords supporting the pulley ef will each sustain 2 lbs., and the cords supporting h i will each bear 4 lbs. Or, suppose the weight to be sustained by the cord kih, each will support one-half; the cord gfe will support one-fourth, and clb will sustain one-eighth. In movable pulleys, then, with separate cords to each pulley, the power is to the weight as the number 2 raised to a power equivalent to the number of pulleys employed. If the number of pulleys had been four, the power gained would have been 2X2x2X2= 16.
Another combination, somewhat similar, is seen in the next figure (Fig. 1), in which the several cords are attached to the weight; this makes a little difference in the amount of power gained. A power p of 1 lb. will sustain a part of the weight equal to 1 lb. This power of 2 lbs. acting at d, will support an equal portion of the weight, which, again acting with double force at g, will sustain 4 lbs.; hence the quantity supported is l+2 + 4 = 7 times the power.
Another somewhat different arrangement is shown In Fig. 2, in which the one cord passes over a fixed, and the other, over one of the movable pulleys. A power of' 1 lb. at p would support a weight of 2 lbs. at w, and an equal advantage is gained by the attachment of the cord passing over the fixed pulley a; the power is therefore one-fourth of the weight. Other combinations sometimes occur, the nature of which will, it is presumed, be understood by reference to those above explained.