Three cylindrical rollers of equal length and material are arranged as shown in end view below. Cylinders 2a and 2B have radius r and cylinder 1 has radius 4r. Their axes are parallel to each other and to that of the fixed concave cylindrical surface, of radius 6r, that supports them. They roll without slip. Assuming no damping and following the steps below, determine the frequency of small free rolling oscillations. For rotation 6, of the cylinder 1, determine the resulting rotation of the lower cylinders. [Hint: Does it look like an epicyclic gear train?] (a) When the upper roller rotates with velocity 6, determine the translational and rotational velocities of the centre of mass of the lower rollers. [Hint: In an epicyclic gear train the centres of these would be supported on the planet carrier.] (b)

Three cylindrical rollers of equal length and material are arranged as shown in end view below. Cylinders 2a and 2B have radius r and cylinder 1 has radius 4r. Their axes are parallel to each other and to that of the fixed concave cylindrical surface, of radius 6r, that supports them. They roll without slip. Assuming no damping and following the steps below, determine the frequency of small free rolling oscillations. For rotation 6, of the cylinder 1, determine the resulting rotation of the lower cylinders. [Hint: Does it look like an epicyclic gear train?] (a) When the upper roller rotates with velocity 6, determine the translational and rotational velocities of the centre of mass of the lower rollers. [Hint: In an epicyclic gear train the centres of these would be supported on the planet carrier.] (b)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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