Woodturning Reference and Information Site 

PULLEYS AND BELTS

Rules for calculating Diameters and Speeds of Pulleys

Speed of Driven Pulley Required. Diameter and speed of driving pulley, and diameter of driven pulley are known. Rule-: Multiply the diameter of the driving pulley by its speed in revolutions per minute, and divide the product by the diameter of the driven pulley.
Example-: If the diameter of the driving pulley is 15 inches and its speed, 180 revolutions per minute, and the diameter of the driven pulley, 9 inches, then the speed of the driven pulley =  15x180/9= 300 revolutions per minute.
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Diameter of the Driven Pulley Required. Diameter and speed of driving pulley, and revolutions per minute of the driven pulley are known. Rule-: Multiply the diameter of the driving pulley by its speed in revolutions per minute, and divide the product by the required speed of the driven pulley. Example-: If the diameter of the driving pulley is 24 inches and its speed, 100 revolutions per minute, and the driven pulley is to rotate 600 revolutions per minute, then the diameter of the driven pulley = 24x100/600 = 4 inches. 
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Diameter of Driving Pulley Required. Diameter and speed of the driven pulley, and speed of the driving pulley are known. Rule-: Multiply the diameter of the driven pulley by its speed in revolutions per minute, and divide the product by the speed of the driving pulley. Example-: If the diameter of the driven pulley is 36 inches and its required speed 150 revolutions per minute, and the speed of the driving pulley is 600 revolutions per minute, then the diameter of the driving pulley  =36x150/600 = 9inches.
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Speed of Driving Pulley Required. Diameters of driving and driven pulleys, and speed of driven pulley are known. Rule-: Multiply the diameter of the driven pulley by its speed, and divide the product by the diameter of the driving pulley.
Example-: If the diameter of the driven pulley is 4 inches, its required speed, 800 revolutions per minute, and the diameter of the driver, 26 inches, then the required speed of the driver = 4x800/26 = 123 revolutions per minute approximately.
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Speed of Driven Pulley in Compound Drive Required. Diameters of pulleys A, B, C and D (see illustration), and speed of pulley A are known; find the speed of pulley D.

Rule-: Divide product of diameters of driving pulleys by the product of diameters of driven pulleys, and multiply quotient by speed of first driving pulley.
Example-: If the diameters of the driving pulleys A and C are 18 and 24 inches; the diameters of the driven pulleys B and D, 12 and 13 inches; and the speed of the driver A, 260 revolutions per minute; then the speed of the driven pulley D =18x24/12x13 x 260 = 720 revolutions per minute .                           

 Pulley Diameters in Compound Drive Required. Speeds of driving and driven pulleys are known; find diameters of the four pulleys A, B, C and D.  Rule-: Place the speed of the driving pulley as the numerator of a fraction, and the speed of the driven pulley as the denominator, and reduce this fraction to its lowest term, then resolve both the numerator and denominator into two factors, and multiply each pair of factors (a pair being one factor in the numerator and one in the denominator) by a trial number which will give pulleys of suitable diameters.
Example-:  If the speed of pulley A is 260 revolutions per minute, and the required speed of the pulley D is 720 revolutions per minute, find the diameters of the pulleys. The fraction 260/720 reduced to its lowest terms is 13/36, which represents the required speed ratio. Resolve 13/36 into two factors; 13/36 = 1x13/2x18. Multiply by trial numbers 12 and 1: (1x12)x(13x1)/(2x12)x(18x1) = 12x13/24x18 The values 12 and 13 in the numerator represent the diameters of the driven pulleys B and D and values 24 and 18 in the denominator, the diameters of the driving pulleys.