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

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Theory of Machine
The contact ratio is given by

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

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