Theory of Machine
When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by (where r = Pitch circle radius of pinion, R = Pitch circle radius of wheel, and φ = Pressure angle)

[(r² + R²) cosφ]/2
[(r + R) sinφ]/2
[(r + R) cosφ]/2
[(r² + R²) sinφ]/2

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Theory of Machine
Angle of action of cam is defined as the angle

Through which the cam rotates during the period in which the follower remains in the highest position
Moved by the cam from the instant the follower begins to rise, till it reaches its highest position
Of rotation of the cam for a definite displacement of the follower
Moved by the cam from beginning of ascent to the termination of descent

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

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