Fig. 94.—View of transmission gears in an automobile. 1, Drive gear; 2, High and intermediate gear; 3, Low and reverse gear; 4, 8, Reverse idler gears; 5, 6, 7, Countershaft gears. (Courtesy of the Automobile Journal.)
Fig. 95.—Reducing gear of a steam turbine.
Fig. 93 is a diagram showing that the wheel and axle acts like a lever. The axis D is the fulcrum, the effort is applied at F, at the extremity of a radius of the wheel and the resisting weight W at the extremity of a radius of the axle. Hence, if Df, the effort distance, is three times Dw, the weight distance, the weight that can be supported is three times the effort. Here as in the lever, f × Df = w × Dw, or w:f = Df:Dw, or the ratio of the weight to the effort equals the ratio of the radius of the wheel to the radius of the axle. This is therefore the mechanical advantage of the wheel and axle. Since the diameters or circumferences are in the same ratio as the radii these can be used instead of the radii. Sometimes, when increased speed instead of increased force is desired, the radius of the wheel or part to which power is applied is less than that of the axle. This is seen in the bicycle, buzzsaw, and blower. Sometimes geared wheels using the principle of the wheel and axle are used to reduce speed, as in the transmission of an automobile (see Fig. 94), or the reducing gear of a steam turbine. (See Figs. 95 and 293.)
A bevel gear is frequently used to change the direction of the force. (See Fig. 94.)
Fig. 96.—A single movable pulley.
Fig. 97.—Block and tackle.
Fig. 98.—The fixed pulley considered as a lever.
Fig. 99.—The movable pulley considered as a lever.
125. The Pulley.—The pulley consists of a wheel turning on an axis in a frame. The wheel is called a sheave and the frame a block. The rim may be smooth or grooved. The grooved rim is used to hold a cord or rope. One use of the pulley is to change the direction of the acting force as in Fig. 84, where pulley B changes a horizontal pull at H to a downward force and pulley A changes this into an upward force lifting the weight W. These pulleys are fixed and simply change the direction. Without considering the loss by friction, the pull at W will equal that at F. Sometimes, a pulley is attached to the weight and is lifted with it. It is then called a movable pulley. In Fig. 96 the movable pulley is at P, a fixed pulley is at F. When fixed pulleys are used, a single cord runs through from the weight to the effort, so that if a force of 100 lbs. is applied by the effort the same force is received at the weight. But with movable pulleys several sections of cord may extend upward from the weight each with the force of the effort upon it. By this arrangement, a weight several times larger than the effort can be lifted. Fig. 97 represents what is called a block and tackle. If a force of 50 lbs. is exerted at F, each section of the rope will have the same tension and hence the six sections of the rope will support 300 lbs. weight. The mechanical advantage of the pulley or the ratio of the weight to the effort, therefore, equals the number of sections of cord supporting the weight. The fixed pulley represents a lever, see Fig. 98, where the effort and weight are equal. In the movable pulley, the fulcrum (see Fig. 99) is at D; the weight, W, is applied at the center of the pulley and the effort at F. The weight distance, Dw, is the radius, and the effort distance, Df, is the diameter of the pulley. Since W/F = Df / Dw = 2 in a movable pulley, the weight is twice the effort, or its mechanical advantage is 2.
Important Topics
1. Wheel and Axle, Law of Wheel and Axle.
2. Pulley, Fixed and Movable, Block and Tackle, Law of Pulley.