Theory of Machine
The method of direct and reverse cranks is used in engines for

Balancing of forces and couples
Vibration analysis
Kinematic analysis
The control of speed fluctuations

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

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Theory of Machine
The inversion of a mechanism is

Turning its upside down
Obtained by fixing different links in a kinematic chain
Obtained by reversing the input and output motion
Changing of a higher pair to a lower pair

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