Theory of Machine
The Kutzbach criterion for determining the number of degrees of freedom (n) is (where l = number of links, j = number of joints and h = number of higher pairs)

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

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Theory of Machine
The secondary 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 sinθ
m.ω².r (sin 2θ/n)
m.ω².r (cos 2θ/n)
m.ω².r cosθ

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