Homework H2.D - Fa22

Problem statement
Solution video



Animation of motion

Note that as link BD passes through the horizontal orientation, the velocity of B (as well as the angular velocity of AB) instantaneously goes to zero, yet the acceleration of B is not zero. In a couple days when we cover instant centers of zero velocity we will be able to predict when point B has zero velocity.

Solution plan

  1. Note that since D is traveling on a straight line with constant speed, the acceleration of D is zero. Therefore, we can write: a_B = a_D + alpha_BD x r_B/D - omega_BD^2*r_B/D = alpha_BD x r_B/D - omega_BD^2*r_B/D.
  2. Note that since A is a pin joint, the acceleration of A is zero. Therefore, we can write: a_B = a_A + alpha_AB x r_B/A - omega_AB^2*r_B/A = alpha_AB x r_B/A - omega_AB^2*r_B/A.
  3. Equate the expressions of a_B  from 1. and 2. above. This gives you two SCALAR equations in order to solve for two unknowns, alpha_AB and alpha_BD.

Note that you need to solve the velocity problem first. Follow the above procedure to do so. Here. the velocity of D is known as v_D = -v_D*j_hat.

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5 thoughts on “Homework H2.D - Fa22”

  1. Because Va = 0 and Vd is a known quantity, do we need to orient the relative motion equations so that we are solving for Vb on both sides? That's what I did, and I believe I got the correct answer, I'm just wondering if we could order the cross products / position vectors in the opposite way and get the answer if we did so consistently?

    1. Noah: For your two velocity vector equations, the velocity of B can appear on either side of the equations. As you suggest, moving v_B from one side of the equation to the other only requires switching the signs on position vectors.

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