68 MECHA NICS 



The speed of a pulley or of a shaft is usually stated in revo- 

 lutions per minute, abbreviated R. P. M. 



Diameter and Speed of Driver. It often becomes necessary 

 to calculate the size or the speed of a pulley that drives or is 

 being driven by a machine. 



Let D = diameter of driving pulley, in inches; 

 d = diameter of driven pulley, in inches ; 

 N = number of R. P. M. of driving pulley; 

 = number of R. P. M. of driven pulley. 

 Then, if the diameter of the driven and the required speeds 

 of both pulleys are given, the diameter of the driver may be 

 found by the formula 



dn 

 D-- U> 



If the speed of the driver is to be found, it is necessary to 

 use the formula 



dn 

 X-- (2) 



EXAMPLE. A 12-in. pulley on a certain machine is to run 

 at 160 R. P. M. and is to be driven by belt from a pulley on 

 the shaft of an engine that makes 96 R. P. M. What must 

 be the diameter of the pulley on the engine shaft? 



SOLUTION. Substituting in formula 1, 



12X160 

 D = =20 in. 



Diameter and Speed of Driven. If the diameter of the 

 driving pulley and the desired speeds of both pulleys are 

 known, the required diameter of the driven pulley may be 

 found by the formula 



DN 



d= (1) 



n 



If the speed of the driven pulley is to be found, it is necessary 

 to use the formula 



DN 



n = -~ (2) 



a 



EXAMPLE 1. A 30-in. pulley on a line shaft running at 

 120 R. P. M. is to drive a pulley on a machine at 300 R. P. M. 

 What must be the diameter of the pulley on the machine? 



