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

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Theory of Machine
The magnitude of velocities of the points on a rigid link is

Directly proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center
Inversely proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Inversely proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center

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