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

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Theory of Machine
The contact ratio is given by

(Length of path of recess)/(Circular pitch)
(Length of the path of approach)/(Circular pitch)
(Length of the arc of contact)/(Circular pitch)
(Length of the arc of approach)/cosφ

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Theory of Machine
The relation l = (2/3).(j + 2) apply only to kinematic chains in which lower pairs are used. This may be used to kinematic chains in which higher pairs are used, but each higher pair may be taken as equivalent to

Two lower pairs and two additional links
Any one of these
Two lower pairs and one additional link
One lower pair and two additional links

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