Theory of Machine
The Whitworth quick return motion mechanism is formed in a slider crank chain when the

Coupler link is fixed
Longest link is a fixed link
Slider is a fixed link
Smallest link is a fixed link

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Theory of Machine
The displacement of the reciprocating roller follower, when it has contact with the straight flanks of the tangent cam, is given by (where r₁ = Minimum radius of the cam, r₂ = Radius of the roller follower, and θ = Angle turned by the cam from the beginning of the follower displacement)

(r₁ - r₂) (1 - cosθ)
(r₁ + r₂) [(1 - cosθ)/cosθ]
(r₁ - r₂) [(1 - cosθ)/cosθ]
(r₁ + r₂) (1 + cosθ)

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Theory of Machine
In a cam drive with uniform velocity follower, the sharp corners of the displacement diagram are rounded off at the beginning and at the end of each stroke. This is done

Because of loose contact of follower with cam surface
Because of difficulty in manufacturing cam profile
Because the uniform velocity motion is a partial parabolic motion
In order to have acceleration in beginning and retardation at the end of stroke within the finite limits

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