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

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Theory of Machine
Higher pairs are those which have

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

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