Theory of Machine
The Grubler's criterion for determining the degrees of freedom (n) of a mechanism having plane motion is (where l = Number of links, and j = Number of binary joints)

n = 2(l - 1) - 2j
n = (l -1) - j
n = 4(l - 1) - 3j
n = 3(l - 1) - 2j

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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)

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

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