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)

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

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Theory of Machine
Two pulleys of radii r₁ and r₂ and at distance x apart are connected by means of an open belt drive. The length of the belt is

π (r₁ + r₂) + (r₁ - r₂)²/x + 2x
π (r₁ - r₂) + (r₁ - r₂)²/x + 2x
π (r₁ - r₂) + (r₁ + r₂)²/x + 2x
π (r₁ + r₂) + (r₁ + r₂)²/x + 2x

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Theory of Machine
In a single slider crank chain

Three are turning pairs and one is a sliding pair
Each of the four pairs is a turning pair
One is a turning pair and three are sliding pairs
Two are turning pairs and two are sliding pairs

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