The size of the pulley governs the speed of the machinery and this speed is determined by the relative movements of the pulleys and the ratios between their diameters and speeds. Pulleys are usually arranged in pairs, each with a different diameter and on a separate shaft. The mechanical principle involved in a pair of pulleys is that of the wheel and axle, the larger pulley being the wheel and the smaller one the axle. (See Chapter V (Pulleys, Inclined Planes, And Wedges. 37. Simple Form Of Pulley).) Since the belt running over the two pulleys always runs at the same speed as their rims, it is plain that the rims of both pulleys run at the same speed. The pulley running the smaller number of revolutions must be the larger of the two.
Fig. 144. - Split Iron Pulley. Pulleys are split to permit their being applied quickly to any shaft already in place.
Fig. 145. - Countershaft with Fast and Loose Pulley on Right. A shifting rod throws the belting from one pulley to the other.
Take, for example, a 16 in. driving pulley making 180 R. P. M. running with a pulley making 320 R. P. M. The rim of the 16 in. pulley will travel in one minute a distance equal to 180 times its circumference, or 180 X 16 X 3.1416, and the rim of the other pulley will travel, if we call D its diameter, 320 X D X 3.1416. Since the rims of the two pulleys will always travel at the same speed we can put these two expressions equal to each other, or
180 X 16 X 3.1416 = 320 X D X 3.1416 and solving this equation to find D, we will have
D = 180 X 16 X 3.1416 / 320 X3.1416 , or D = 9 in.
Now, according to the rule, we will have
16 X 180 = 9 X 320 or 2880 = 2880 which proves that the rule is correct.