Theory of Machine
Oldham's coupling is the

Second inversion of double slider crank chain
Third inversion of slider crank chain
Third inversion of double slider crank chain
Second inversion of single slider crank chain

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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 (cos 2θ/n)
m.ω².r cosθ
m.ω².r sinθ

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