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)
(r₁ + r₂) [(1 - cosθ)/cosθ]

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Theory of Machine
Angle of dwell of cam is defined as the angle

Moved by the cam from the instant the follower begins to rise, till it reaches its highest position
Of rotation of the cam for definite displacement of the follower
During which the follower returns to its initial position
Through which the cam rotates during the period in which the follower remains in the highest position

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

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