ME 242 Lecture 30 04.17

Example prob 7311 given cart mass mc rod mass ma

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Unformatted text preview: mc , Rod mass = ma rod length = 2L , inertia about O = IO Cart applies a moment Mk on rod at O Find: equations of motion for system d A mc g Ry FBD=IRD Rx F mc y FBD=IRD M O mc x Rx O b2 M N1 N2 F + Rx = mc x N + N - m g + R = m 1 2 c y cy b1 A Ry I ma g -Rx- (Ry + ma g) j = ma a A i a A = aO + k r A /O + k ( k r A /O ) ma aA y m a aA x -N1d + N 2 d - M = 0 = i + k Lb1 + k ( k Lb1 ) x 2 = i + Lb 2 - Lb1 x FBD=IRD M Choice of moment equations ma aA y ma aA x M Rx O A b2 b1 Rx O A b2 b1 ma aA y m a aA x -Rx i - (Ry + ma g) j = ma (i + Lb 2 - 2 Lb1 ) x Ry ma g I Ry ma g I -Rx = ma ( + L cos - 2 L sin ) x -Ry - ma g = ma (L sin + 2 L cos ) k M A = IA M O = IA k + r A /O ma a A M O = IO k + r A /O ma aO 2 Moment equation M 6 equations, 6 unknowns F + Rx = mc x N1 + N 2 - mc g + Ry = 0 -N1d + N 2 d - M = 0 -Rx = ma ( + L cos - 2 L sin ) x -Ry - ma g = ma (L sin + 2 L cos ) Rx O A b2 b1 ma aA y ma aA x Ry ma g I x Rx Ry N1 N2 M O IO k + r A /O ma aO = M k - ma gL sin k = IO k + Lb1 ma x i = IO k + Lma sin(90 - )k x = IO k + Lma cos k x M - ma gL sin = IO + Lm a cos x Equations of Motion M - ma gL sin = IO + Lm a cos x F = (ma + mc ) + ma (L cos - 2 L sin ) x A 3...
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This note was uploaded on 09/19/2009 for the course ME 242 taught by Professor Kam during the Spring '06 term at Nevada.

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