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

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Theory of Machine
The Klein's method of construction for reciprocating engine mechanism

Utilizes a quadrilateral similar to the diagram of mechanism for reciprocating engine
Is based on acceleration diagram
Enables determination of Cariole’s component
Is a simplified form of instantaneous center method

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Theory of Machine
Cam angle is defined as the angle

Moved by the cam from the instant the follower begins to rise, till it reaches its highest position
Of rotation of the cam for a definite displacement of the follower
Through which, the cam rotates during the period in which the follower remains in the highest position
During which the follower returns to its initial position

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Theory of Machine
The static balancing is satisfactory for low speed rotors but with increasing speeds, dynamic balancing becomes necessary. This is because, the

Effects of unbalances are proportional to the square of the speed
Unbalanced couples are caused only at higher speeds
Effects of unbalances are directly proportional to the speed
Unbalanced forces are not dangerous at higher speeds

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