Theory of Machine
There are six gears A, B, C, D, E and F in a compound train. The numbers of teeth in the gears are 20, 60, 30, 80, 25 and 75 respectively. The ratio of angular speeds of the driven (F) to the driver (A) of the drive is

1/8
12
4/15
1/24

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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)
(r₁ + r₂) (1 + cosθ)
(r₁ - r₂) [(1 - cosθ)/cosθ]

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Theory of Machine
The contact ratio is given by

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

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