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

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Theory of Machine
For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively, and M = Mass on the sleeve)

S₂/S₁ = r₁/r₂
S₁/S₂ = r₁/r₂
(m.g - S₁)/(m.g - S₂) = r₂/r₁
(m.g + S₁)/(m.g + S₂) = r₁/r₂

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Theory of Machine
In elliptical trammels

Three pairs turning and one pair sliding
Two pairs turning and two pairs sliding
One pair turning and three pairs sliding
All four pairs are turning

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