Theory of Machine
The velocity of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by (where ω = Angular velocity of the cam shaft)

ω (r₁ + r₂) sinθ sec2θ
ω (r₁ + r₂) cosθ cosec2θ
ω (r₁ r₂) sinθ
ω (r₁ r₂) cosθ

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Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ω²r [cos θ + (cos 2θ/n)]
ω²r [sin θ + (sin 2θ/n)]
ωr [sin θ + (sin 2θ/n)]
ωr [cos θ + (cos 2θ/n)]

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