Theory of Machine
Crowning on pulleys helps

Increase belt and pulley life
In decreasing the slip of the belt
In increasing velocity ratio
For automatic adjustment of belt position so that belt runs centrally

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform pressure, is (where r₁ and r₂ = External and internal radii of collar respectively)

(1/2). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3). μ W (r₁ + r₂)
(1/2). μ W (r₁ + r₂)
(2/3). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]

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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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Theory of Machine
Two pulleys of radii r₁ and r₂ and at distance x apart are connected by means of a cross 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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