Machinery's Handbook, 31st Edition
Pulley Speeds and Belt Lengths 2565 The values 12 and 13 in the numerator represent the diameters of the driven pulleys, B and D , and the values 24 and 18 in the denominator represent the diameters of the driving pulleys, A and C , as shown in the illustration. Speed of Driven Pulley in Compound Drive.— If diameters of pulleys A , B , C , and D (see illustration above), and speed of pulley A are known, the speed of the driven pulley D is found from:
driven pulley diameter driving pulley diameter
driven pulley diameter driving pulley diameter
speed of first driving pulley
#
#
Example 8: If the diameters of driving pulleys A and C are 18 and 24 inches, diameters of driven pulleys B and D are 12 and 13 inches, and the speed of driving pulley A is 260 rpm, speed of driven pulley D 12 13 18 24 260 720 rpm # # # = = Length of Belt Traversing Three Pulleys.— The length L of a belt traversing three pul leys, as shown in the diagram below, and touching them on one side only, can be found by the following formula. Pulley 2, Radius R 2 = 2 2 = 36.87, or 0.6435 rad.
C 23 = 8
C 12 = 10
1 = 53.13, or 0.9273 rad.
3 = 90, or 1.5708 rad.
Pulley 1, Radius R 1 = 1
Pulley 3, Radius R 3 = 4
C 13 = 6
Flat Belt Traversing Three Pulleys Referring to the diagram, R 1 , R 2 , and R 3 are the radii of the three pulleys; C 12 , C 13 , and C 23 are the center distances; and α 1 , α 2 , and α 3 are the angles, in radians, of the triangle formed by the center distances. Then: L C C C C R R C R R C R R R R R R R R 2 1 12 13 23 12 2 1 2 13 3 1 2 23 3 2 2 1 2 3 1 1 2 2 3 3 π α α α = + + + − + − + − + + + − + + ^ ^ ^ ^ ^ h h h h h < F Example 9: Assume R 1 = 1, R 2 = 2, R 3 = 4, C 12 = 10, C 13 = 6, C 23 = 8, α 1 = 53.13 degrees or 0.9273 radian, α 2 = 36.87 degrees or 0.6435 radian, and α 3 = 90 degrees or 1.5708 radi ans. Then:
. 8 4 2 1 2 4 09273 1 06435 2 15708 4 24 1 05 21 9911 8 4975 38 5436 2 2 2 # # # π = + + + − + − + − + + + + + + = + + − = ^ ^ ^ ^ ^ h h h h h ; E . . . . . . L 10 6 8 2 1 10 2 1 6 4 1
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