Theory of Machine
The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity ω₁ rad/s in the clockwise direction and the link OB turns with angular velocity ω₂ rad/s in the clockwise direction, then the rubbing velocity at the pin joint O is (where r = Radius of the pin at O)

(ω₁ + ω₂)r
(ω₁ - ω₂)r
ω₁.ω₂.r
(ω₁ - ω₂)2r

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Theory of Machine
The secondary 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 (sin 2θ/n)
m.ω².r sinθ

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