Theory of Machine
The advantage of the piston valve over the slide valve is that in the former case

Both wear and power absorbed are low
Power absorbed is less
The pressure developed being high provides tight sealing
Wear is less

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

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