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

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

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

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Theory of Machine
Pitch point on a cam is

The point on cam pitch curve having the maximum pressure angle
The point on cam pitch curve having the minimum pressure angle
Any point on pitch curve
Any point on pitch circle

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Theory of Machine
The displacement of the reciprocating roller follower, when it has contact with the straight flanks of the tangent cam, is given by (where r₁ = Minimum radius of the cam, r₂ = Radius of the roller follower, and θ = Angle turned by the cam from the beginning of the follower displacement)

(r₁ - r₂) (1 - cosθ)
(r₁ + r₂) (1 + cosθ)
(r₁ - r₂) [(1 - cosθ)/cosθ]
(r₁ + r₂) [(1 - cosθ)/cosθ]

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