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)2r
ω₁.ω₂.r
(ω₁ + ω₂)r

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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 (sin 2θ/n)
m.ω².r sinθ
m.ω².r cosθ

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Theory of Machine
The maximum fluctuation of speed is the

Difference of the maximum and minimum speeds
Variations of speed above and below the mean resisting torque line
Difference of minimum fluctuation of speed and the mean speed
Sum of maximum and minimum speeds

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