Theory of Machine
In gears, interference takes place when

Pitch of the gears is not same
The tip of a tooth of a mating gear digs into the portion between base and root circles
Gears do not move smoothly in the absence of lubrication
Gear teeth are undercut

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Theory of Machine
The contact ratio is given by

(Length of path of recess)/(Circular pitch)
(Length of the arc of approach)/cosφ
(Length of the arc of contact)/(Circular pitch)
(Length of the path of approach)/(Circular pitch)

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Theory of Machine
Two pulleys of radii r₁ and r₂ and at distance x apart are connected by means of an open belt drive. The length of the belt is

π (r₁ + r₂) + (r₁ - r₂)²/x + 2x
π (r₁ - r₂) + (r₁ + r₂)²/x + 2x
π (r₁ - r₂) + (r₁ - r₂)²/x + 2x
π (r₁ + r₂) + (r₁ + r₂)²/x + 2x

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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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