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

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Theory of Machine
In a mechanism, the fixed instantaneous centers are those centers which

Remain in the same place for all configurations of the mechanism
None of the listed here
Vary with the configuration of the mechanism
Moves as the mechanism moves, but joints are of permanent nature

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Theory of Machine
In a four bar chain or quadric cycle chain

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

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