Theory of Machine
In a single slider crank chain

Two are turning pairs and two are sliding pairs
One is a turning pair and three are sliding pairs
Three are turning pairs and one is a sliding pair
Each of the four pairs is a turning pair

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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
Kinematic pairs are those which have

Point or line contact between the two elements when in motion
Surface contact between the two elements when in motion
Elements of pairs not held together mechanically
Two elements that permit relative motion

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Theory of Machine
Hammer blow

Is the maximum vertical unbalanced force caused by the mass added to balance the reciprocating masses
Is the maximum horizontal unbalanced force caused by the mass provided to balance the reciprocating masses.
Varies inversely with the square of the speed
Varies as the square root of the speed

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

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