Kinematic modelling of a mechanism (General Crank)

In summary: Based on what you have studied, could you please clarify the meaning of the following terms shown in your assigned problem?Topology of the mechanism (Topología del mecanismo)Equations of restriction (Ecuaciones de restricción)Problem of position (Problema de posición)Equations of movement in augmented formulation (Ecuaciones del movimiento en formulación aumentada)Problem of start-up (Problema de arranque)The topology of the mechanism is the layout of the parts of the mechanism. The equations of restriction are the equations that need to be solved to determine the position, velocity, and acceleration of
  • #1
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.
Mecanismos.png
 

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  • #2
Are you then after everything as a function of ##\theta_1##, ##\dot \theta_1##?
 
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  • #3
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...
 

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  • #4
Are you trying to find the output of point D as a pure function of the input ##\theta_1##?
 
  • #5
jogarta6 said:
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.
 
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  • #6
erobz said:
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
 
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  • #7
jogarta6 said:
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.

1684590714438.png
Please take a moment to learn how to use Latex
 
  • #8
erobz said:
##\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.
 

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  • #9
jogarta6 said:
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.
 
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  • #10
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.
 

FAQ: Kinematic modelling of a mechanism (General Crank)

What is kinematic modeling of a mechanism?

Kinematic modeling of a mechanism involves the mathematical description of the motion of the parts of a mechanism without considering the forces that cause this motion. It focuses on parameters such as position, velocity, and acceleration of each component in the system.

What is a general crank mechanism?

A general crank mechanism typically refers to a system where a crank converts rotational motion into linear motion or vice versa. It usually consists of components like a crank, connecting rod, and slider. This type of mechanism is commonly found in engines and pumps.

How do you derive the equations of motion for a crank mechanism?

Deriving the equations of motion for a crank mechanism involves setting up the geometric relationships between the different components. Using trigonometric relationships and differentiating with respect to time, one can obtain expressions for position, velocity, and acceleration of each part of the mechanism.

What are the common applications of crank mechanisms?

Crank mechanisms are widely used in various applications, including internal combustion engines, reciprocating pumps, and manual winches. They are essential in converting between rotational and linear motion, which is crucial in many mechanical systems.

What software tools are commonly used for kinematic modeling of mechanisms?

Several software tools are commonly used for kinematic modeling of mechanisms, including MATLAB, Simulink, SolidWorks, and ADAMS (Automatic Dynamic Analysis of Mechanical Systems). These tools help in simulating and analyzing the motion of mechanical systems.

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