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

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Theory of Machine
The primary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r (sin 2θ/n)
m.ω².r cosθ
m.ω².r (cos 2θ/n)
m.ω².r sinθ

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