Theory of Machine
The velocity of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by (where ω = Angular velocity of the cam shaft)

ω (r₁ r₂) sinθ
ω (r₁ + r₂) sinθ sec2θ
ω (r₁ + r₂) cosθ cosec2θ
ω (r₁ r₂) cosθ

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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 sinθ
m.ω².r cosθ
m.ω².r (cos 2θ/n)

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