Theory of Machine
A Hartnell governor has its controlling force (Fc) given by Fc = ar + b, where r is the radius of rotation and a and b are constants. The governor becomes isochronous when

a is +ve and b is -ve
a is +ve and b = 0
a is +ve and b is also +ve
a = 0 and b is +ve

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Theory of Machine
In a circular arc cam with roller follower, the acceleration in any position of the lift will depend only upon

Radius of circular arc, cam speed, location of centre of circular arc and roller diameter
Total lift, total angle of lift, minimum radius of cam and cam speed
Mass of cam follower linkage, spring stiffness and cam speed
Total lift, centre of gravity of the cam and cam speed

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

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