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Theory of Machine

Theory of Machine
Rectilinear motion of piston is converted into rotary by

Slider crank
Connecting rod
Cross head
Gudgeon pin

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Theory of Machine
The acceleration of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by

ω². (r₁ - r₂). (1 - sin² θ)
ω². (r₁ + r₂). (1 + cos² θ)
ω². (r₁ + r₂). [(2 - cos² θ)/cos³ θ]
ω². (r₁ r₂). (1 - cos² θ)

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Theory of Machine
The essential condition of placing the two masses, so that the system becomes dynamically equivalent, is (where l₁ and l₂ = Distance of two masses from the centre of gravity of the body, and kG = Radius of gyration of the body)

l₁l₂ = kG
l₁l₂ = kG²
l₂ = kG
l₁ = kG

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Theory of Machine
An eccentric sheave pivoted at one point rotates and transmits oscillatory motion to a link whose one end is pivoted and other end is connected to it. This mechanism has

3 links
4 links
5 links
2 links

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Theory of Machine
The displacement of a flat faced follower when it has contact with the flank of a circular arc cam, is given by (where R = Radius of flank, r₁ = Minimum radius of the cam, and θ = Angle turned through by the cam)

R (1 - cosθ)
(R - r₁) (1 - sinθ)
R (1 - sinθ)
(R - r₁) (1 - cosθ)

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Theory of Machine
In a system subjected to damped forced vibrations, the ratio of maximum displacement to the static deflection is known as

Damping factor
Logarithmic decrement
Critical damping ratio
Magnification factor

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