Dynamics_Part64

Dynamics_Part64 - Problem Set 9: Problem 2. Problem: In the...

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Unformatted text preview: Problem Set 9: Problem 2. Problem: In the planetary-gear system shown, the radius of gears A, B, C and D is R and the radius of outer gear E is 3R. Gear E rotates counter clockwise with angular velocity and gear A rotates clockwise with angular velocity 5 . 4 (a) Determine the angular velocity of planetary gears B, C and D. (b) Determine the angular velocity of the spider (the three pronged object) connecting the planetary gears. Solution: To begin, we identify the point of contact between gear A and gear B as Point 1. Also, Point 2 is the center of gear B, while Point 3 is the point of contact between gear B and gear E. To solve, we first determine the three velocity vectors v1 , v2 and v3 relative to the center of gear A. We then compute velocity vector v2 relative to Point 1. Finally, we compute velocity vector v3 relative to Point 2. This provides sufficient information to compute the three velocity vectors and the angular velocities B and S . By symmetry, C and D are equal to B . . A. B . . . ... . . ... . .. . ..... . .. ....... ...... . . ... .... .......... .... ...... ........ .. ..... ....... . . .. .. ... ............... ....................... ...... ........................ ...... .. .. . .. ... .... ..... .. ..... . .... .... .. .............. .... . .. . .. .. ... ... ... .. . ... ... .. .. ... . . . .. . .. .. . .. . . .. ... ... ... ... ... ... .. ..... .... .. ..... .... .. ... 2 . .. .. .. . ... .. ... ... .. . ... ... ... ... ... .. . . . . . .. .. . .. .. ... .. . ... . ... ... .. ... . .. .. . .. . . . . . . ... ... .. ... S .... ... . ... . . .. . .. . . .. . . .. . . . . .... .. . ... .. . . ..... . ... . .. . . . . .. . . . . ....................... . . .... .............................................................. . ... . . ............................................................................................. . . ...... ... . . . ...... .. . ....... .. . . . ........................................................................................................................ .. . . ........................................ . ... . ... .. . .. . . . .. . . . ................................................................................................................................... . . ................................................................................................................... . . ........................................................................................... . . . . . . . .............................................................................................................................. ... . .. . . ..................................................... .. . . ................................................ . . . . . .. . . . . . .. . . . . . ... .. . ... .. . . . ... .. . . . . ... .. . . . . .. .. .. . . .. .. .. . . .. . . .. . .. . .. . .. .. . .. . .. .. . .. . ... . ... .. . ... .. . . ... . ... .. .. . ... .. . .. . ... . ... ... ... ... ... . ... ... . .... . . .... .... ... ... . .... ... ... . ...... . .. . .................... ................... . ................... . ............. . ... . ... . . .. . .. .. . . . . 1 . . . . . . v3.... . . . . v R R v 1 2 v 3 A B E v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . ... . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E (a) Focusing first on expressing velocity vectors v1 , v2 and v3 relative to the center of gear A, we have the following. v1 v2 v3 = vA + A r1/A = vA + S r2/A = vA + E r3/A Since gear A is not translating, clearly vA = 0. Gears A and E are rotating clockwise and counter clockwise, respectively. We are given the following. 5 A = - k 4 and E = k ...
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This note was uploaded on 05/12/2010 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

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