Theory of Machine
The displacement of a flat faced follower when it has contact with the flank of a circular arc cam, is given by (where R = Radius of flank, r₁ = Minimum radius of the cam, and θ = Angle turned through by the cam)

(R - r₁) (1 - sinθ)
(R - r₁) (1 - cosθ)
R (1 - cosθ)
R (1 - sinθ)

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Theory of Machine
Pitch point on a cam is

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

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

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