Theory of Machine
Crowning on pulleys helps

For automatic adjustment of belt position so that belt runs centrally
In increasing velocity ratio
Increase belt and pulley life
In decreasing the slip of the belt

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Theory of Machine
The contact ratio is given by

(Length of the arc of contact)/(Circular pitch)
(Length of the arc of approach)/cosφ
(Length of the path of approach)/(Circular pitch)
(Length of path of recess)/(Circular pitch)

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