# V-belt

Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.

Result

l =  2.2 m

#### Solution:

$\ \\ r_1 = d_1/2 = 52.5 \ mm \ \\ r_2 = d_2/2 = 196.5 \ mm \ \\ \Delta r = r_2-r_1 = 144 \ mm \ \\ \alpha = arctg(\dfrac{\Delta r} {l}) = arctg(\dfrac{ 144 } { 697 }) = 11.67^\circ = 0.203733309106 \ \\ dr = \sqrt{ l^2-(\Delta r)^2 } = \sqrt{ 697 ^ 2-( 144 )^2 } = 681.96 \ mm \ \\ l_1 = r_1\cdot (\pi-2\cdot \alpha) = 143.54 \ mm \ \\ l_2 = r_2\cdot (\pi+2\cdot \alpha) = 697.39 \ mm \ \\ l = l_1+l_2 + 2 \cdot dr = \dfrac{ 143.54+697.39+2 \cdot 681.96 }{1000} = 2.2 \ \text{m} \ \\$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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