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# Machine Dynamics MCQ – Analytical Synthesis for Slider Crank Mechanism

If the crank rotation angle varies from 45 degrees to 135 degrees, Using three precision points with chebyshev’s spacing, synthesize a slider crank mechanism where where displacement of slider is square of the crank rotation. From the above information calculate ‘a’ in mm.

a) 48.2

b) 58.2

c) 45.6

d) 42.2

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Answer: a

Explanation: From the above data θs=45° and θf=135°, assuming starting displacement and final displacement of slider as 100mm and 30mm respectively,

We calculate k1 = 96.4mm

k1 = 2a

Therefore a = 48.2mm.

If the crank rotation angle varies from 45 degrees to 135 degrees, Using three precision points with chebyshev’s spacing, synthesize a slider crank mechanism where where displacement of slider is square of the crank rotation. From the above information calculate ‘c’ in mm.

a) 148.2

b) 158.2

c) 135.7

d) 120.2

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Answer: c

Explanation: From the above data θs=45° and θf=135°, assuming starting displacement and final displacement of slider as 100mm and 30mm respectively,

We calculate k1 = 96.4mm

k1 = 2a

Therefore a = 48.2mm

Now k2 = 2.a.c = 13084

Therefore c = 135.7mm.

If the crank rotation angle varies from 45 degrees to 135 degrees, Using three precision points with chebyshev’s spacing, synthesize a slider crank mechanism where where displacement of slider is square of the crank rotation. From the above information calculate ‘b’ in mm.

a) 148.2

b) 158.2

c) 135.7

d) 120.2

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Answer: d

Explanation: From the above data θs=45° and θf=135°, assuming starting displacement and final displacement of slider as 100mm and 30mm respectively,

We calculate k1 = 96.4mm

k1 = 2a

Therefore a = 48.2mm

Now k2 = 2.a.c = 13084

Therefore c = 135.7mm

Now b2 = a2 + c2 – k3

Therefore b = 120.2mm.

What is the relation between displacement of slider and crank angle over an interval?

a) Quadratic

b) Directly proportional

c) Linear

d) Inversely proportional

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Answer: c

Explanation: The displacement of the slider depends on the crank angle in a linear mathematical relation. It also depends on the starting crank angle and starting point.

Which of the following is true regarding synthesis of mechanisms?

a) It determines the dimensions of the link

b) It determines the input and output angles of the links

c) It determines velocity of link

d) It determines acceleration of link

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Answer: a

Explanation: For computer aided synthesis of mechanism, determination of the dimensions of the given link is the main objective.

What is the unit of constant of proportionality C used in the relation between displacement of slider and crank angle?

a) m/rad

b) m/s-rad

c) m-s/rad

d) m/s2

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Answer: a

Explanation: The displacement of the slider is proportional to the crank angle hence a proportionality constant C is introduced; this has the units metre/radians. m/rad.

Synthesis of mechanism is used to determine the acceleration of the link.

a) True

b) False

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Answer: b

Explanation: Synthesis of mechanism is used to determine the dimensions of the link, acceleration of the link can be calculated by using methods of klein’s constructions.

Constant of proportionality is always positive.

a) True

b) False

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Answer: b

Explanation: The constant of proportionality used in the relation between slider displacement and the crank angle can take both positive and negative values.

From the given data calculate the constant of proportionality.

s = 10mm, Ss = 5mm θ=50 degrees and θs = 45 degrees.

a) 1

b) -1

c) 1/2

d) -1/2

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Answer: a

Explanation: We know that constant of proportionality is related by:

s – Ss = C(θ – θs)

substituting the values we get

C = 1.