If a belt drive has pulleys of 10.125" and 6.625", and the center distance is 12.375", what is the accurate belt length?

To determine the accurate belt length for a belt drive system, you can use the formula for calculating the length of a belt on two pulleys, which is given by:

[ L = 2C + \frac{\pi}{2}(D_1 + D_2) + \frac{(D_1 - D_2)^2}{4C} ]

where:

• ( L ) is the belt length,

• ( C ) is the center distance between the pulleys,

• ( D_1 ) and ( D_2 ) are the diameters of the larger and smaller pulleys, respectively.

For the given problem:

• The diameter of the larger pulley (( D_1 )) = 10.125 inches

• The diameter of the smaller pulley (( D_2 )) = 6.625 inches

• The center distance (( C )) = 12.375 inches

Now, plug these values into the formula:

1. Calculate ( 2C ):

( 2 \times 12.375 = 24.75 )

2. Calculate ( \frac{\pi}{2}(D_1 + D_2) ):