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
In a single slider crank chain

Each of the four pairs is a turning pair
One is a turning pair and three are sliding pairs
Three are turning pairs and one is a sliding pair
Two are turning pairs and two are sliding pairs

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Theory of Machine
Higher pairs are those which have

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

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