Understanding the four bar linkage DOF

In summary, the conversation discusses the concept of degrees of freedom (DOF) in mechanisms, specifically using the example of a four bar linkage. It is determined that the DOF for this mechanism is 1, despite the fact that it appears to have 2 DOF due to the movement of two links. This is because the movement of one link is dependent on the movement of the other, and they are not independent. The concept is further explained using the example of a 5-bar linkage, which has 2 DOF. The conversation ends with a clarification of the understanding of DOF in relation to the movement and final position of a link.
  • #1
Sanchayan Ghosh
11
0
Hello guys,

I have a doubt with understanding DOFs. I have taken the example of the four bar linkage. According to Grueblr's condition, the DOF of this mechanism is 1.
[tex]\mbox{DOF} = 3(l-1) + 2j_1 + 2j_2\\l=4\ j_1=4\ j_2=0\\\mbox{DOF} = 1[/tex]
220px-4_bar_linkage_animated.gif

In the above figure, the links next to the ground link rotate. So it should be 2 DOFs. Then, the ternary link rotates, so it should be 1 more DOF. However, it is not so. This is a really fundamental place I am going wrong in. May anyone please explain this, as due to this I have difficulty understanding isomers in mechanisms.

Thank You
 
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  • #2
This is a very good question to have, but fortunately isn't too hard to answer.

Let's look at link AD. Point D definitely moves in a way that changes its x- and y-coordinates. But you could also express the angle of the link as theta (one degree of freedom), and then x=rAD cos(theta), and y=rAD sin(theta). Since x and y are both dependent on one variable, theta, they are not independent, and do not constitute two degrees of freedom. It is a form of parametric equations.

Another way to look at it is that you could replace the link AD by making the circle it creates into a slot in a piece of metal, insert a pin at point D, and place the pin in the slot. Point D would still follow the same path, its position described by its displacement along that path.

Taking that a little further, it doesn't matter whether a slot is 1) straight and oriented along the x-axis, 2) straight but angled (so that x and y change with motion), 3) curved in a circle, or 4) a more complex curve like your point E moves in - in every case motion along it is only one (independent) degree of freedom.
 
  • #3
It has 1 DOF for the mechanism. Meaning that if you move one link, all other links can be at only one already predetermined position.

In the following 5-bar linkage, you have 2 DOF. Meaning if you know the position of 2 links, you know the position of all links. If you know the position of only one link, there is a multitude of possible positions for the other links.

 
  • #4
Sirs,
Thank you for the answers. I think I have understood. However, I would like to articulate my understanding.

So, as jack said, for every movement of say one link, the other links if they move in only one way and end up in only one position, the two links are counted as moving together in a relation and the dof is 1 for it. So if two links are moving, 1 dof is if I move one link the other one moves and can only possesses one position for a predetermined motion of the link which I moved. However, if the dependent link, say translates and reached a position or rotates about an axis and reached its position, then it is called as having 2 dof and similarly based on the movement and final position , it can have more dof. Please do tell me if I am being right. Here.Thanks a lot.
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FAQ: Understanding the four bar linkage DOF

1. What is a four bar linkage DOF?

A four bar linkage DOF (degree of freedom) is a mechanism made up of four rigid links connected by four joints, allowing for rotational or translational movement. It is commonly used in engineering and science to create motion in machines.

2. How does a four bar linkage DOF work?

A four bar linkage DOF works by using the principle of rigid body kinematics, where the links are connected by joints that allow for movement. The links can be arranged in various configurations to create different types of motion, such as rotary, oscillatory, or translational.

3. What are the applications of a four bar linkage DOF?

A four bar linkage DOF has a wide range of applications in various fields, including robotics, automotive engineering, and biomechanics. It is commonly used in mechanisms that require controlled motion, such as car suspensions, prosthetic limbs, and robotic arms.

4. How is the DOF of a four bar linkage calculated?

The DOF of a four bar linkage can be calculated using the Gruebler's equation, which takes into account the number of links, joints, and constraints in the mechanism. The DOF can also be determined by analyzing the kinematic chain and identifying the number of independent motions.

5. What are the advantages of using a four bar linkage DOF?

One of the main advantages of a four bar linkage DOF is its simplicity and versatility. It can be easily designed and implemented in various systems, and its motion can be controlled precisely. It also has a compact size and is relatively low-cost compared to other mechanisms.

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