How can the degrees of freedom of a mechanism be obtained?

In summary, the degrees of freedom of a mechanism can be obtained by examining the number of independent variables and constraints present in the system. The degree of freedom is equal to the difference between the number of independent variables and the number of constraints. Additionally, the type of joints and connections between the links of the mechanism also play a role in determining the degrees of freedom. By understanding the structure and constraints of a mechanism, the degrees of freedom can be accurately determined.
  • #1
Alfredomaximun
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Thread moved from the technical forums to the schoolwork forums
Summary: ##M=3\left(n-1\right)-2j_1-j_2##

Hi, I'm trying to get the degrees of freedom of a can crusher.

1654270512452.png

So substituting I get

##
\begin{array}{l}M=3\left(n-1\right)-2j_1-j_2\\
n=5\\
j_1=5\\
M=3\left(5-1\right)-2\cdot 5-0\\
M=2\end{array}
##

And I would think it would be 1
 
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  • #2
Welcome to PF.

It's best to define all of your terms when posting equations. Assuming that this is a standard DoF problem, I think:

M = Mobility
n = Number of Links
j = Number of Joints

Is that correct? Also, did you generate the drawing of the can crusher on the right? If so, could you somehow show what corresponds to what on the picture on the left? I'm having trouble seeing how you came up with it.

I agree that I think this crusher "hinge" has basically 1 DoF, but it would be best to understand your drawing first to be sure. Thanks.

https://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)
 
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  • #3
berkeman said:
Bienvenido a PF .

Es mejor definir todos sus términos al publicar ecuaciones. Suponiendo que este es un problema estándar de DoF, creo:

M = movilidad
n = Número de enlaces
j = Número de articulaciones

Es eso correcto? Además, generó el dibujo de la trituradora de la lata a la derecha? Si es así, ¿podría mostrar de alguna manera qué corresponde a qué en la imagen de la izquierda?? Tengo problemas para ver cómo se te ocurrió.

Estoy de acuerdo en que creo que esta "bisagras" de la trituradora tiene básicamente 1 DoF, pero sería mejor entender su dibujo primero para estar seguro. Gracias.

https://en.wikipedia.org/wiki/Degrees_of_freedom_(mecánica)
Hi Berkeman, I changed the image and did it above but it doesn't seem to be correct

Imagen6.png


The original image was this
Imagen8.jpg
 

FAQ: How can the degrees of freedom of a mechanism be obtained?

What is the concept of degrees of freedom in a mechanism?

The concept of degrees of freedom in a mechanism refers to the number of independent parameters or variables that are required to fully describe the motion of the mechanism. It determines the complexity and range of motion of the mechanism.

How can the degrees of freedom of a mechanism be calculated?

The degrees of freedom of a mechanism can be calculated by using the Gruebler's equation, which takes into account the number of links, joints, and constraints in the mechanism. It is represented as F = 3(n-1) - 2j - h, where F is the degrees of freedom, n is the number of links, j is the number of joints, and h is the number of higher pairs or constraints.

What are the different types of degrees of freedom in a mechanism?

The different types of degrees of freedom in a mechanism are translational, rotational, and mixed. Translational degrees of freedom involve linear motion, rotational degrees of freedom involve rotational motion, and mixed degrees of freedom involve a combination of both linear and rotational motion.

How do the degrees of freedom affect the design of a mechanism?

The degrees of freedom play a crucial role in the design of a mechanism as they determine the range of motion and complexity of the mechanism. A higher number of degrees of freedom may result in a more complex and versatile mechanism, while a lower number of degrees of freedom may limit the range of motion and functionality of the mechanism.

Can the degrees of freedom of a mechanism be changed?

Yes, the degrees of freedom of a mechanism can be changed by altering the number of links, joints, or constraints in the mechanism. For example, adding or removing a link or joint can change the degrees of freedom. Additionally, using different types of joints or constraints can also affect the degrees of freedom of a mechanism.

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