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

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Theory of Machine
Oldham's coupling is the

Second inversion of single slider crank chain
Second inversion of double slider crank chain
Third inversion of slider crank chain
Third inversion of double slider crank chain

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