# 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.

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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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This is a very interesting question from Analytical Synthesis for Slider Crank Mechanism topic in division Computer Aided Analysis and Synthesis of Mechanisms of Machine Dynamics

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Right choice is (d) 120.2

For explanation I would say: 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 b^2 = a^2 + c^2 – k3

Therefore b = 120.2mm.

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