A belt drive has pulleys of 9.6875" and 6.255". The center distance is 28.375". What is the accurate belt length?

To find the accurate belt length for a belt drive system, we can utilize a specific formula that accounts for the diameters of the pulleys and the center distance between them. The formula to estimate the belt length (L) in a two-pulley system is:

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

In this situation, D1 and D2 represent the diameters of the two pulleys, and C is the center distance.

1. Find the average diameter:

• D1 = 9.6875 inches and D2 = 6.255 inches.

• The average diameter is calculated as ( (D1 + D2) / 2 = (9.6875 + 6.255) / 2 = 7.97125 ) inches.

2. Calculate the belt length using the formula:

• Substitute the given values into the formula:

• ( L = \pi \times 7.97125 + 2 \times 28.375 + \frac{