481_Dynamics 11ed Manual

481_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics αG = 1 rad 2 α AC = 1 s Given Chapter 16 rad 2 s ⎞ ⎞ ⎛ 0 ⎞ ⎛ −a ⎞ ⎛ 0 ⎟ ⎛ −r ⎞ ⎛ 0 ⎟ ⎛ b sin ( θ ) ⎞ ⎜ ⎟⎜⎟⎜ ⎜ 0 ⎟ + ⎜ 0 × ⎜ −b cos ( θ ) ⎟ = 0 ⎜ 0 ⎟×⎜ 0 ⎟+⎜ 0 ⎟×⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ −ωDE ⎟ ⎝ 0 ⎠ ⎜ −ωG ⎟ ⎝ 0 ⎠ ⎜ ωAC ⎟ ⎝ 0 ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎛ 0 ⎞ ⎛ −a ⎞ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ −a ⎞⎤ ⎛ 0 ⎞ ⎛ −r ⎞ ⎜ ⎟⎜⎟⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥ ⎜ ⎟ ⎜ ⎟ ⎜ 0 ⎟ × ⎜ 0 ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ 0 ⎟⎥ + ⎜ 0 ⎟ × ⎜ 0 ⎟ ... = 0 ⎜ −α DE ⎟ ⎝ 0 ⎠ ⎜ −ωDE ⎟ ⎢⎜ −ωDE ⎟ ⎝ 0 ⎠⎥ ⎜ α G ⎟ ⎝ 0 ⎠ ⎝ ⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦⎝ ⎠ ⎞ ⎢⎜ ⎞ ⎞ ⎛ 0 ⎟ ⎡⎛ 0 ⎟ ⎛ −r ⎞⎤ ⎛ 0 ⎟ ⎛ b sin ( θ ) ⎞ ⎜ ⎥⎜ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ 0 ⎟⎥ + ⎜ 0 ⎟ × ⎜ −b cos ( θ ) ⎟ ... ⎜⎟ ⎜ ⎟ ⎜ ωG ⎟ ⎢⎜ ωG ⎟ ⎝ 0 ⎠⎥ ⎜ α AC ⎟ ⎝ 0 ⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦⎝ ⎠ 0 ⎞ ⎛ 0 ⎞ ⎛ b sin ( θ ) ⎞ ⎛ ⎜ ⎟⎜ ⎟ + ⎜ 0 ⎟ × ⎜ 0 ⎟ × ⎜ −b cos ( θ ) ⎟ ⎜ ⎟ ⎜ ωAC ⎟ ⎜ ωAC ⎟ ⎝ 0 ⎠ ⎝ ⎠⎝ ⎠ ⎛ ωG ⎞ ⎜ ⎟ ⎜ ωAC ⎟ ⎜ ⎟ = Find ( ωG , ωAC , α G , α AC) αG ⎟ ⎜ ⎜ α AC ⎟ ⎝ ⎠ ωG = −5.33 rad α G = −2.07 rad s 2 ωAC = 0.00 rad s α AC = −28.7 rad 2 s s Now find the motion of gear F . ωAC b + ωG c = ωAC( b + c + d) − ωF d ωF = 479 ωAC( c + d) − ωG c d ωF = 10.67 rad s ...
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