MACHINERY. Compound machines are formed from two or more simple machines. Tools are the simplest implements of art; these when they become complicated in their structure become machines, and machines when they act with great power, take the name, generally speaking, of engines. The advantage that man has gained by pressing into his service the great forces of nature, instead of depending on his own feeble arm, is evinced by the fact that aided by the steam engine one man can now accomplish as much labor as 27,000 Egyptians, working at the rate at which they built the pyramids (Dapin). The mechanical powers will now be separately considered, it being remembered that none of them create force, but that they only modify and direct it, acting by certain great laws, established by the supreme Creator and generous Giver of the original sources, of both the Primary and Mechanical causes. He will labor most effectively and happily who studies these laws and acts in accordance with their principles, which are those laid down and explained in detail in books relating to NATURAL PHILOSOPHY. THE LEVER. The lever is an inflexible bar or rod, some point of which being supported, the rod itself is movable freely about that point as a center of motion. This center of motion is called the FULCRUM or PROP. In the lever three points are to be considered, viz.: the fulcrum or point about which the bar turns, the point where the force is applied, and the point where the weight is applied. There are three varieties of the lever, according as the fulcrum, the weight or the power is placed between the other two, but the action in every case is reducible to the same principle and the same general rule applies to them all. NOTE. When two forces act on each other by means of any machine, that which gives it motion is called THE POWER, that which receives it THE WEIGHT, hence, In the diagrams the letter P is used to denote the point of application of the forces; the letter F denotes the fulcrum, or prop, and W the weight. 1st. When the fulcrum (F) is between the force (P) and the weight (W). Fig. 1. 2d. When the weight (W) is between the fulcrum (F) and 2. the force (P). Fig. 2 THE LEVER. W Fig. 3. Lever 3rd kind. 3rd. When the force (P) is between the fulcrum (F) and the weight (W). Fig. 3. GENERAL RULE. The force (P) multiplied by its distance from the fulcrum (F) is equal to the weight (W) multiplied by its distance from the fulcrum, In the following examples the distances are figured in inches and the weight in pounds, the unit of distance in mechanics being one inch, and the unit of weight being one pound. NOTE. The following calculations are made on the supposition that the action of the mechanical powers is not impeded by their own weight, or by friction and resistance. Thus, in each calculation, in figuring the problems relating to the safety-valve, the weight of the valve, spindle and lever have to be taken into the estimate. A special rule (with illustrations) will be given in its proper place to show how these are to be provided for. EXAMPLE. What force applied at three feet from the fulcrum will balance a weight of 112 lbs. applied at 6 inches from the fulcrum (observe diagram of 1st form of lever). Here the leverages are 86 and 6 inches. That is, 18 lbs. applied at the end of a 3 foot bar with a fulcrum 6 inches from the point, will lift a box weighing 112 lbs. EXAMPLE. If 80 lbs. be applied at the extreme end of a 5 foot lever (with prop 1 foot from the point), what force is needed to balance the 80 lbs. The two leverages being 48 inches and 12 inches. Now, multiply the force (P) 80 lbs., by the distance from the fulcrum (F) 48 inches and divide by 12 inches. 48 inches. 12 in.)3840 PROOF. 48 x 80 lbs. 3840 320 lbs. This is an example worked from the lever of the second kind. THE LEVER. Under the general rule given, it will be seen that under all circumstances the force multiplied by its distance from the fulcrum, is equal to—or balanced by, the weight multiplied by its distance from the fulcrum; 4 sub-rules are added which will cover all problems where only three of the numbers are known. To find the power (P) on any lever, when the weight (W) and wo distances from the fulcrum (b)are given. SUB-RULE 1. Multiply the weight (W) by its distance from the fulcrum (b) and divide by the distance from P, to b. The quotient is the power. EXAMPLE. How much to balance 200 lbs., 18 inches from the fulcrum (b) to the end of the lever at (P). The whole length of the lever being 36 inches. 18 in. 36 in.)3600(100 lbs. Answer. The cxample given to illustrate the general rule is similar to this. |