Theory of Machine
Lower pairs are those which have

Two elements that permit relative motion
Elements of pairs not held together mechanically
Surface contact between the two elements when in motion
Point or line contact between the two elements when in motion

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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)

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

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Theory of Machine
Crowning on pulleys helps

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

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