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Dynamics problem - Kinematics of Rigid Bodies

  1. Nov 14, 2008 #1
    1. The problem statement, all variables and given/known data
    There is a slider-crank mechanism. Express the angular velocity omegaAB and angular acceleration alphaAB of the connecting rod AB in terms of the crank angle theta for a given constant crank speed omega naught. Take omegaAB and alphaAB to be positive counterclockwise.

    The structure is a point A free to slide laterally connected by a rigid rod of length l to point B. Point B is connected to another point O by a rod of length r. The crank angle theta between r and the horizontal is given, as is the crank speed omega naught. Take omegaAB and alphaAB to be positive counterclockwise.

    2. Relevant equations
    velocity = r * omega
    acceleration tangential = alpha * radius

    3. The attempt at a solution

    I first tried to define the horizontal distance between A and O. I found x to be r*cos(theta) + sqrt(l^2 - r^2*sin(theta)^2)
    At this point I took the derivative of x to be the velocity, and I divided the velocity by x.

    At this point I have an ungodly mess and I have no idea how to put omeganaught into the equation. I feel like I just need to understand the relationship between x or theta and omega naught to understand the equation, but I do not. I apologize for the lack of a graphical representation of the problem.
     
  2. jcsd
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