Engineering Kinematic modelling of a mechanism (General Crank)

[member 736285]

Homework Statement

Kinematics of mechanisms

Relevant Equations

Constraint equations

Hi, I was wondering if you could help me with a job at the university that consists of the kinematic modeling of mechanism number 3 in the image attached to this message.

I have to set up the constraint equations and then solve the position, velocity and acceleration problem. For now I would like to know if the equations that I have raised are correct, especially the prismatic pair, I do not know if I have done it correctly. The exercise is done in Spanish, which is my language.

 

[erobz]

Are you then after everything as a function of $\theta_1$, $\dot \theta_1$?

 

[member 736285]

Sorry, I had a couple of errors in Pair R and in Pair P of point C. I'll send it to you again, let's see what you think...

 

[erobz]

Are you trying to find the output of point D as a pure function of the input $\theta_1$?

 

[berkeman]

I'll send it to you again,

In the future, please learn to use LaTeX to post your math equations directly into the forum. We generally don't allow attachments or images with math in them; they are too hard to quote, and often are very hard to read (yours are legible, fortunately). There is a link to the "LaTeX Guide" below the Edit window. Thank you.

 

[member 736285]

Are you trying to find the output of point D as a pure function of the input $\theta_1$?

Yes, I would like the independent variable to always be theta-1.

On the pair P, the angle restriction is that theta3 is always 90º. And then, I have made a simplification, that X3 is 0, since our teacher allows us to simplify the mechanism at our convenience

 

[erobz]

Yes, I would like the independent variable to always be theta-1.

On the pair P, the angle restriction is that theta3 is always 90º. And then, I have made a simplification, that X3 is 0, since our teacher allows us to simplify the mechanism at our convenience

$\theta_3 \equiv 90°$ doesn't make sense to me. You said you are after the position, velocity, acceleration of point D? If the angle I have labeled as $\varphi$ is $90°$, the system is fixed.

Please take a moment to learn how to use Latex

 

[member 736285]

$\theta_3 \equiv 90°$ doesn't make sense to me. You said you are after the position, velocity, acceleration of point D? If the angle I have labeled as $\varphi$ is $90°$, the system is fixed.

View attachment 326819Please take a moment to learn how to use Latex

The truth is that I am not very clear about what I have to do... I think I have to obtain the position, velocity and acceleration at all points of the mechanism. I am attaching the work guide to see if you can give me a hand.

Regarding the theta-3 angle, you may find it more meaningful considering that the slider does not have an eccentricity.

 

[erobz]

The truth is that I am not very clear about what I have to do... I think I have to obtain the position, velocity and acceleration at all points of the mechanism. I am attaching the work guide to see if you can give me a hand.

Regarding the theta-3 angle, you may find it more meaningful considering that the slider does not have an eccentricity.

Sorry, I don't speak Spanish. If you don't know what you are supposed to accomplish I don't think I will be able to help much.

I'm imagining the link I have labeled $r$ is spinning with constant angular velocity $\dot \theta = \rm{const.}$, I find what is the output of point $D$ given $\dot \theta$ to be of interest, but also very messy and much trig\calculus will ensue to get there. Perhaps that is because my methods are unsophisticated. I was going to solve for the $x,y$ coordinates of point $D$ as an explicit function of ($\theta, \dot \theta$), but maybe that is not necessary.

 

[Lnewqban]

Welcome, José!

Based on what you have studied, could you please clarify the meaning of the following terms shown in your assigned problem?

1. Topology of the mechanism (Topología del mecanismo)
2. Equations of restriction (Ecuaciones de restricción)
3. Problem of position (Problema de posición)
4. Equations of movement in augmented formulation (Ecuaciones del movimiento en formulación aumentada)
5. Problem of start-up (Problema de arranque)

Thank you.