Theory of Machine
The displacement of a flat faced follower when it has contact with the flank of a circular arc cam, is given by (where R = Radius of flank, r₁ = Minimum radius of the cam, and θ = Angle turned through by the cam)

R (1 - cosθ)
R (1 - sinθ)
(R - r₁) (1 - cosθ)
(R - r₁) (1 - 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)

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

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