PRINCIPLES & PRACTICAL APPLICATIONS OF MECHANIC POWERS. MECHANIC Powers, or the Elements of Machinery, are certain simple mechanical arrangements whereby weights may be raised or resistances overcome with the exertion of less power or strength than is necessary without them. They are usually accounted six in number, viz., the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw; but properly two of these comprise the whole, namely, the lever and inclined plane, the wheel and axle being only a lever of the first kind, and the pulley a lever of the second,— the wedge and the screw being also similarly allied to that of the inclined plane: however, although such seems to be the case in these respects, yet they each require, on account of their various modifications, a peculiar rule of estimation adapted expressly to the different circumstances in which they are individually required to act. 1. THE LEVER. Levers, according to mode of application, as the following, are distinguished as being of the first, second, or third kind; and although levers of equal lengths produce different effects, the general principles of estimation in all are the same; namely, the power is to the weight or resistance, as the distance of the one end to the fulcrum is to the distance of the other end to the same point. In the first kind, the power is to the resistance, as the distance A B is to the distance B C. In the second, the power is to the resistance, as the distance A B is to that of AC; and, In the third, the resistance is to the power, as the distance A B is to that of A C. Rule, first kind.-Divide the longer by the shorter end of the lever from the fulcrum, and the quotient is the effective force that the power applied is equal to. Ex. 1. Let the handle of a pump equal 65 inches in length, and 10 inches from the shortest end to centre of motion; what is the amount of effective leverage thereby obtained? Ex. 2. Required the situation of the fulcrum on which to rest a lever of 15 feet, so that 21 cwt. placed at one end may equipoise 30 cwt. at the other, the weight of the lever not being taken into account. 15 x 2.5 is to be placed. =1.154 feet from the end on which the 30 cwt. The common steelyard, or Roman balance, as represented in fig. 1, Plate D, is a lever of the first kind, and so divided that one weight W, moved to or from the axis of motion, will equipoise and there indicate the weight of any article required to be known. It is by the second kind of lever, that the greatest effect is obtained from any given amount of power; hence the propriety of the application of this principle to the working of force pumps, and shearing of iron, as by the lever of a punching-press, &c. Rule, second kind.-Divide the whole length of lever, or distance from power to fulcrum, by the distance from fulcrum to weight, and the quotient is the proportion of effect that the power is to the weight or resistance to be overcome. Ex. Required the amount of effect or force produced by a power of 50 tbs. on the ram of a Bramah's pump, the length of the lever being 3 feet, and distance from ram to fulcrum 4 inches. 3 feet 36 inches, and =8, or the power and resistance 36 4.5 are to each other as 8 to 1; hence 50 × 8=400 lbs. force upon the ram. The lever on the safety valve of a steam boiler is of the third kind, the action of the steam being the power, and the weight or spring-balance attached the resistance; but in such application the action of the lever's weight must also be taken into account, and may be simply ascertained by such means as represented in fig. 2, Plate D, where A is a Salter's balance attached to the lever by a light line, immediately at the point of pressure on the valve, and which, raised by hand or otherwise, will indicate the lever's action at that point. This is perhaps the most frequent application of the third kind of lever to mechanical advantage, and that in which great nicety is required in estimation of effect: hence observe, as in other levers, there are three distinct points that require to be particularly attended to; namely, the weight, fulcrum, and re MECHANIC POWERS. 103 sistance, as shown in the annexed diagram to illustrate this particular case. Thus, suppose the weight to be placed on any one of the divisions, it is still the same weight, or 1; but because of the principle of the lever, the resistance is increased equal to the number of times the weight is distant from the fulcrum; consequently the action of the lever tends to press down the valve equal the sum of the weight and resistance, or the number of times the weight is distant from the resistance. 2. THE WHEEL AND PINION, OR CRANE. The mechanical advantage of the wheel and axle, or crane, is as the velocity of the weight to the velocity of the power; and being only a modification of the first kind of lever, it of course partakes of the same principles. 1. To determine the amount of effective power produced from a given power by means of a crane with known peculiarities. Rule.-Multiply together the diameter of the circle described by the winch, or handle, and the number of revolutions of the pinion to 1 of the wheel; divide the product by the barrel's diameter in equal terms of dimensions, and the quotient is the effective power to 1 of exertive force. Ex. Let there be a crane the winch of which describes a circle of 30 inches in diameter; the pinion makes 8 revolutions for 1 of the wheel, and the barrel is 11 inches in diameter; required the effective power in principle, also the weight that 36 tbs. would raise, friction not being taken into account. 30 x 8 11 =21.8 to 1 of exertive force; and 21.8 × 36=784.8 lbs. 2. Given any two parts of a crane to find the third that shall produce any required proportion of mechanical effect. Rule.-Multiply the two given parts together, and divide the product by the required proportion of effect; the quotient is the dimensions of the other parts in equal terms of unity. Ex. Suppose that a crane is required, the ratio of power to effect being as 40 to 1, and that a wheel and pinion 11 to 1 is unavoidably compelled to be employed, also the throw of each handle to be 16 inches; what must be the barrel's diameter on which the rope or chain must coil? 16 × 2=32 inches diameter described by the handle. The principle of the pulley, or more practically the block and tackle, is the distribution of weight on various points of support; the mechanical advantage derived depending entirely upon the flexibility and tension of the rope, and the number of pulleys or sheives in the lower or rising block: hence, by blocks and tackle of the usual kind, as shown in fig. 3, Pl. D, |