Subscribe to:
Post Comments (Atom)
skip to main |
skip to sidebar
Fall 2008 -- Purdue University -- West Lafayette, IN
Blog Post LABELS
- Blog Challenge Questions (9)
- Chapter 2 (2)
- Chapter 3 (19)
- Chapter 5 (11)
- Chapter 6 (23)
- Chapter 7 (7)
- Chapter 8 (9)
- Exam 1 (5)
- Exam 2 (4)
- Exam 3 (17)
- Exams (2)
- Final Exam (7)
- General (6)
- Gravity (2)
- Homework (2)
- in class (1)
- Lectures (1)
- Quizzes (2)
- Spring 2008 Archive (87)
- Spring-Mass Simulator (1)
- Student-Generated Solutions (1)
- Summer 2008 Archive (72)
10 comments:
I suggest that you start out with individual FBD's of the arm and block.
For the arm:
* Choose a rotational coordinate (like theta) representing the rotation of the arm.
* Draw forces acting on the arm: the dashpot force, the reaction forces at O and the force on the arm at A.
* The direction of the dashpot force depends on which direction that you chose for positive theta. Imagine the arm with a positive rotation rate (theta_dot > 0): in which direction does the dashpot force act?
For the block you will have the force acting on it by the arm and by the spring.
For kinematics, you need to relate the rotational coordinate theta that you chose to the coordinate x.
I have a few questions about some assumptions I have made in this problem.
1) Would it be correct to assume that the rotational equivalent of c*x_dot is c*theta_dot*b (where be is the distance from point B to the instant center of the crank).
2) Also, is it correct to assume that since the crank is massless it has zero inertia.
3) Finally, in the equation for zeta, is the numerator generally the coefficient in front of x_dot, and not simply c?
Thank you
--to Vincent--
1) Yes, your result is correct; the force of the dashpot on the arm is given by c*b*theta_dot. However, this is not really an assumption as it comes directly from kinematics.
2) Yes, massless necessarily means that the mass moment of inertia is to be zero.
3) Derive the EOM in the usual way. Divide through the EOM by the coefficient in front of x_dot_dot. The resulting coefficient in front of x_dot after this division is defined to be 2*zeta*omega_n. [omega_n^2 is the coefficient in from on theta after this division.] So, yes, zeta is dictated not just by "c" but the coefficient in front of theta_dot.
Let me know if I misunderstood any of your questions.
I'm having a really hard time relating the theta to the x coordinate. I'm assuming that it should almost be a linear relationship, but not sure how to go about getting it.
Are we assuming that the amplitude is relatively small, and therefore, we can assume that the movement of the mass m is only in the x-direction? Otherwise, wouldn't it follow the arc-path of the arm in a sense?
Yes, you are to assume small rotations of the arm. For this motion the mass moves only in the x-direction.
Is the force on the top of the block cx_dot? If not, how do we find it?
i am having trouble with the kinematics. i am relating xdot to ydot but i don't believe my final answer is correct.
Johnny, could you describe what you have chosen as your y coordinate?
As for myself, I chose to do a rigid body velocity equation relating points a and o (o is fixed). In this I was able to solve for x_dot in terms of theta_dot, does that help?
I used a force F as being applied to top of block pulling up on it, the same force F is applying the moment about O in the negative k dir,
after deriving Newton-Euler equations and F = m*x_dot_dot + k*x, plug F into moment equation for the arm. I used +x = +Theta*a to get a single EOM in terms of x, not sure if this is correct but think it is :]
Post a Comment