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Mechanical Engineering QUESTION #2483
Question 1
The velocity of a node B of a driver link in rotational motion (angular velocity \(\omega = \dot{\phi}\), link length \(L_{AB}\)) is given by:
  • \(v_{Bx} = -L_{AB}\dot{\phi}\sin\phi,\quad v_{By} = L_{AB}\dot{\phi}\cos\phi\)✔️
  • \(v_{Bx} = L_{AB}\dot{\phi}\cos\phi,\quad v_{By} = L_{AB}\dot{\phi}\sin\phi\)
  • \(v_{Bx} = L_{AB}\dot{\phi}^2\cos\phi,\quad v_{By} = -L_{AB}\dot{\phi}^2\sin\phi\)
  • \(v_{Bx} = -L_{AB}\ddot{\phi}\cos\phi,\quad v_{By} = L_{AB}\ddot{\phi}\sin\phi\)
Correct Answer Explanation
Differentiating position equations \(x_B=x_A+L_{AB}\cos\phi\) and \(y_B=y_A+L_{AB}\sin\phi\) with respect to time: \(v_{Bx}=-L_{AB}\dot{\phi}\sin\phi\) and \(v_{By}=L_{AB}\dot{\phi}\cos\phi\).