Theory of Machine
In a band and block brake, the ratio of tensions on tight side and slack side of the band is (where μ = Coefficient of friction between the blocks and the drum, θ = Semi-angle of each block subtending at the center of drum, and n = Number of blocks)

T₁/T₂ = μ. θ. n
T₁/T₂ = [(1 - μ tanθ)/(1 + μ tanθ)]n
T₁/T₂ = (μ θ)n
T₁/T₂ = [(1 + μ tanθ)/(1 - μ tanθ)]n

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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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