Mechanics, degree of freedom question

In summary, the DoF (mobility) of the system can be calculated using the equation M = 3(L-1) - 2J1 - J2, where L is the number of links, J1 is the number of full binary joints, and J2 is the number of half joints. In this system, there are 9 links and 1 half-joint, but the number of full joints is unclear due to uncertainty about the joints on the slider. It is possible that there are only two binary joints for each link, resulting in one ternary joint. Additionally, there may be only 1 DoF, which is the rotational movement of the circle attached to the top. The straight lines in the system
  • #1
yugeci
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Homework Statement



Calculate the DoF (mobility) of the following system:

3026041de8b9529d84160ec6964b3ec4.png


Homework Equations


[/B]
M = 3(L-1) - 2J1 - J2

(where L = number of links, J1 is the number of full binary joints and J2 is the number of half joints.

The Attempt at a Solution



I am very confident about there being 9 links, and 1 half-joint (the pin in the slot above the L link) but I am unsure about the number of full joints which I numbered here.

2b60e7e0a8424c6c6a8b32d4ec9c2d8a.png


I know from 1-7 should be correct, but I don't know about the joints on the slider. Should there only be two binary joints for each like I put there? Which is basically one ternary joint... 2 on the rigid link 'L' and on the link to which the slider is attached.

And if I am correct I take it there is only 1 DoF then, which is the rotational of the circle attached to the top?

Help would be appreciated here.
 
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  • #2
I presume the straight lines are strings. What happens when two straight lines meet at a little circle? Is it a pulley? Is it a post to which they are knotted? What about when three strings meet at a little circle? Can the little circles move?
 

What is the concept of mechanics in physics?

Mechanics is a branch of physics that deals with the study of motion and the forces that cause motion. It is concerned with how objects move and interact with each other in the physical world.

What are the fundamental principles of mechanics?

The fundamental principles of mechanics include Newton's laws of motion, the principle of conservation of energy, and the principle of conservation of momentum. These principles govern the behavior of objects in motion and are the basis for understanding mechanics.

What is meant by "degree of freedom" in mechanics?

In mechanics, degree of freedom refers to the number of independent parameters that are needed to describe the motion of a system. It is a measure of the complexity of a system and determines how many ways the system can move or change.

How is the degree of freedom calculated in a system?

The degree of freedom can be calculated by subtracting the number of constraints or restrictions in a system from the total number of parameters that describe the system. For example, a particle moving freely in space has three degrees of freedom (x, y, and z coordinates), while a particle constrained to move only in a straight line has one degree of freedom.

Why is understanding degree of freedom important in mechanics?

Understanding the degree of freedom in a system is important in mechanics because it helps us predict and analyze the behavior of objects in motion. It also allows us to determine the number of independent variables needed to fully describe a system and make accurate calculations.

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