Theory of Machine
In a reciprocating steam engine, when the crank has turned from inner dead centre through an angle θ, the angular velocity of the connecting rod is given by

ω sinθ/(n² - sin²θ)1/2
ω cosθ/(n² - cos²θ)1/2
ω sinθ/(n² - cos²θ)1/2
ω cosθ/(n² - sin²θ)1/2

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Theory of Machine
Crowning on pulleys helps

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

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