Belt length calculation for two pulleys

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A common problem in designing servo motor mounts for machinery is calculating the belt length needed to go around two pulleys of different diameters which are a certain distance apart. Given R1 = the radius of the large pulley, R2 = the radius of the small pulley, and D = the distance between their centers, the solution for L, the belt length is:

L = 2 R1 (pi - a + tan a) + 2 R2 (a - tan a), where a = acos ((R1-R2)/D)

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