# 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:

$\ \\ r_1 = d_1/2 = 52.5 \ mm \ \\ r_2 = d_2/2 = 196.5 \ mm \ \\ \Delta r = r_2-r_1 = 144 \ mm \ \\ \alpha = arctg(\dfrac{\Delta r} {l}) = arctg(\dfrac{ 144 } { 697 }) = 11.67^\circ = 0.203733309106 \ \\ dr = \sqrt{ l^2-(\Delta r)^2 } = \sqrt{ 697 ^ 2-( 144 )^2 } = 681.96 \ mm \ \\ l_1 = r_1\cdot (\pi-2\cdot \alpha) = 143.54 \ mm \ \\ l_2 = r_2\cdot (\pi+2\cdot \alpha) = 697.39 \ mm \ \\ l = l_1+l_2 + 2 \cdot dr = \dfrac{ 143.54+697.39+2 \cdot 681.96 }{1000} = 2.2 \ \text{m} \ \\$

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