479_Dynamics 11ed Manual

479_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 16 ⎛ 0 ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎛ −c ⎞ ⎜ ⎟ ⎜ 0 ⎟ × ⎜ a ⎟ + ⎜ 0 ⎟ × ⎜ −a − b ⎟ = ⎜ ⎟ ⎜⎟ ⎜⎟ ⎜ ⎝ ω ⎠ ⎝ 0 ⎠ ⎝ ωBC ⎟ ⎝ 0 ⎠ ⎠ Given ⎛e⎞ ⎜d⎟ 2 2⎜ ⎟ e + d ⎝0⎠ vC ⎡⎛ 0 ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ 0 ⎞⎤⎤ ⎢⎜ 0 ⎟ × ⎜ a ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ a ⎟⎥⎥ ... ⎢⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥⎥ ⎣⎝ α ⎠ ⎝ 0 ⎠ ⎝ ω ⎠ ⎣⎝ ω ⎠ ⎝ 0 ⎠⎦⎦ ⎛ 0 ⎟ ⎛ −c ⎞ ⎛ 0 ⎟ ⎡⎛ 0 ⎟ ⎛ −c ⎞⎤ ⎞ ⎞ ⎞ ⎜ ⎜ −a − b ⎟ + ⎜ 0 × ⎢⎜ 0 × ⎜ −a − b ⎟⎥ +⎜ 0 ⎟× ⎟ ⎢⎜ ⎟⎜ ⎜ ⎟⎜ ⎟⎥ ⎜ α BC ⎟ ⎝ 0 ⎠ ⎜ ωBC ⎟ ⎢⎜ ωBC ⎟ ⎝ 0 ⎠⎥ ⎝ ⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦ ⎛ ωBC ⎟ ⎞ ⎜ ⎜ α BC ⎟ ⎜ ⎟ = Find ( ωBC , α BC , vC , aC) vC ⎟ ⎜ ⎜ aC ⎟ ⎝ ⎠ ωBC = 1.13 vC = −9.38 rad s in s = ⎛e ⎞ ⎜d⎟ 2 2⎜ ⎟ e + d ⎝0⎠ aC α BC = −3.00 rad 2 s aC = −54.7 in 2 s Problem 16-122 At a given instant gears A and B have the angular motions shown. Determine the angular acceleration of gear C and the acceleration of its center point D at this instant. Note that the inner hub of gear C is in mesh with gear A and its outer rim is in mesh with gear B. Given: ωB = 1 rad αB = 6 rad s 2 ωA = 4 rad αA = 8 rad s rA = 5 in s 2 s rC = 10 in rD = 5 in Solution: Guesses Given ωC = 1 rad s αC = 1 rad 2 s −ωA rA = ωB( rA + rD + rC) − ωC( rC + rD) −α A rA = α B( rA + rD + rC) − α C( rC + rD) 477 ...
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