Homework H3.A - Sp23

Problem statement
Solution video

DISCUSSION THREAD

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Discussion and hints

Although the motion of B is made up of simple components (constant rotation rate for link OA, constant rotation rate for AB and constant extension of the telescoping link), the motion of B is quite complicated, as evidenced by the path of B and the velocity and acceleration of B shown above.

However, for an observer on link AD, the path of B is rather simple: that observer sees a straight-line path for B, moving only in the x-direction. This is shown in the above animation giving the view of this moving observer. Are you able to visualize this observed motion of B?

Clarification
The angles theta and phi are BOTH measured from fixed, horizontal lines. Therefore, the rotation rate of OA is theta_dot, and the rotation of AD is phi_dot; that is, the rotation rate of AD is independent of theta_dot.


 

14 thoughts on “Homework H3.A - Sp23”

    1. This is not intended to be a polar coordinates problem in kinematics. Instead, you should apply the moving reference frame kinematics equations to the problem. Place the observer on link AD. As shown in the animation above, the motion of P is a straight line in the x-direction.

    1. Yes, you can use length b. The right diagram is the position that you are supposed to solve at, while the left diagram I assume is there to give you a better understanding of what the given measurements are, such as which angles are theta and which angles are phi.

  1. Where does the angular velocity of link OA come in for the equation? Should the first term of the equation be : a_B = a_A...? and how would you find a_A? or would it be a_B = a_O .... where a_O is = ? I'm just having trouble conceptualizing the relationships into an equation.

  2. I want to make sure I am on the right path with this. Segment OA and AD are rigid links, meaning we can use the equations from chapter two. We can use a_A = a_O... where a_O = 0 and we can solve for a_A and ang. accel. Then, we can do a_B = a_A (with the solved a_A and angular acceleration = 0) using the equation from chapter 3. Is this somewhat on the right track?

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