By this time you have seen that there are a couple themes that are present in all the lecture examples and homework problems in rigid body kinematics. One theme is that one needs to write a velocity/acceleration equation for each link in the mechanism. Another theme is that, although you might be asked to find only acceleration information (as in this problem), you must solve for velocities first (the acceleration equations involve angular velocity components). With these themes in mind, consider the following process for solving this problem:- Write down the velocity equation for link CB: v_B = v_C + omega_CB x r_B/C
- Write down the velocity equation for link OA: v_A = v_O + omega_OA x r_A/O
- Write down the velocity equation for link AB: v_A = v_B + omega_AB x r_A/B
- Substitute the expressions for v_A and v_B from steps 1. and 2. into the equation for step 3. Equate components on both sides of equation for both i and j. This gives you two equations in terms of two unknowns omega_CB and omega_OA. Solve these two equations.
- Repeat steps 1. through 4. above using acceleration equations to find alpha_BC and alpha_AO.
- Once you have found omega_BC and alpha_BC from above, you can now use the rigid body acceleration equation for link BC to find the acceleration of point D.
After a while, all of the problems begin to look alike! The only differences are in the "Given" and "Find" aspects as well as the trigonometry in finding angles.
7 comments:
Isn't #3 of 5/148 suppose to be : AB: v_B = v_A + omega_AB x r_B/A ?
It really doesn't matter what order you use on #3. Either v_A = v_B + omega_AB x r_A/B OR v_B = v_A + omega_AB x r_B/A will give you the same answer because both are on the same rigid body AB.
Question!
omega_bc = omega_bd
alpha_bc = alpha_bd
Are these true?
Jin, that's the only issue I'm running into. If we can make that assumption than the problem is easy to finish.
Is alpha_OA 0? All the math works out this way but I don't trust my answer.
Chris,
I did not get 0 for alpha_OA. Initially I did, but then saw that I had missed a negative when doing a cross product.
QUOTE:
Question!
omega_bc = omega_bd
alpha_bc = alpha_bd
Are these true?
YES, these is true because points B, C, and D all lie on the same member. For alpha_ao i got 0 and for alpha_bc i got a number around 2000. Can someone corroborate on this last value?
Those numbers are what I got as well dpinto. Hopefully this response is not too late for you.
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