Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ω²r [sin θ + (sin 2θ/n)]
ωr [sin θ + (sin 2θ/n)]
ω²r [cos θ + (cos 2θ/n)]
ωr [cos θ + (cos 2θ/n)]

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Theory of Machine
Crowning on pulleys helps

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

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