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Theory of Machine

Theory of Machine
Any point on a link connecting double slider crank chain will trace a

Straight line
Circle
Parabola
Ellipse

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Theory of Machine
In a reciprocating steam engine, when the crank has turned from inner dead centre through an angle θ, the angular velocity of the connecting rod is given by

ω sinθ/(n² - sin²θ)1/2
ω cosθ/(n² - cos²θ)1/2
ω cosθ/(n² - sin²θ)1/2
ω sinθ/(n² - cos²θ)1/2

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Theory of Machine
In an ideal machine, the output as compared to input is

More
Less
Equal
May be less or more depending on efficiency

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Theory of Machine
The two links OA and OB are connected by a pin joint at O. If the link OA turns with angular velocity ω₁ rad/s in the clockwise direction and the link OB turns with angular velocity ω₂ rad/s in the clockwise direction, then the rubbing velocity at the pin joint O is (where r = Radius of the pin at O)

(ω₁ - ω₂)2r
(ω₁ + ω₂)r
(ω₁ - ω₂)r
ω₁.ω₂.r

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Theory of Machine
In under damped vibrating system, the amplitude of vibration

Increases linearly with time
Increases exponentially with time
Decreases linearly with time
Decreases exponentially with time

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Theory of Machine
The efficiency of a screw jack is maximum, when (where α = Helix angle, and φ = Angle of friction)

α = 45° + φ/2
α = 90° - φ
α = 45° - φ/2
α = 90° + φ

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