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Theory of Machine

Theory of Machine
The periodic time is given by (where ω = Angular velocity of the particle in rad/s)

ω/2π
π/ω
ω × 2π
2π/ω

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Theory of Machine
The natural frequency of free torsional vibrations of a shaft is equal to (where q = Torsional stiffness of the shaft, and I = Mass moment of inertia of the disc attached at the end of a shaft)

2π qI
(1/2π). √(q/I)
1/2π
2π. √(q/I)

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Theory of Machine
The transmissibility, for all values of damping factor, will be less than unity, if ω/ωn is

Equal to 1
Equal to 2
Less than 2
Greater than 2

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Theory of Machine
The Kutzbach criterion for determining the number of degrees of freedom (n) is (where l = number of links, j = number of joints and h = number of higher pairs)

n = 2(l - 1) - 3j - h
n = 2(l - 1) - 2j - h
n = 3(l - 1) - 2j - h
n = 3(l - 1) - 3j - h

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Theory of Machine
The example of spherical pair is

Bolt and nut
Lead screw of a lathe
Ball bearing and roller bearing
Ball and socket joint

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Theory of Machine
Length of arc of contact is given by

Arc of approach - Arc of recess
Arc of approach + Arc of recess
Arc of approach / Arc of recess
Arc of approach × Arc of recess

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