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 - sinθ)
(R - r₁) (1 - cosθ)

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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

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

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