Method of virtual displacement

In summary, the conversation is about a question regarding the calculation of moment needed to hold a mechanism in equilibrium state using the "Method of Virtual Displacements" or "Method of Virtual Works". The person asking the question is having trouble using the formula and concepts from their textbook and is seeking other methods to verify their answer. They also mention a diagram showing two links connected by three pinned joints and a moment applied at one of the joints. They provide an equation they have derived but are stuck on differentiating it. They also clarify that the mechanism is similar to a crank mechanism and the moment at point "M" is needed for selecting a motor to drive the mechanism.
  • #1
ham_revilo
5
0
http://img267.imageshack.us/img267/9636/qw5e64a2d1sda54.png

Hi guys. i have a question that needs verification. Referring to the above diagram,

Please determine the Moment, M (Nm) needed in order to hold the mechanism in equilibrium state as shown above by using "Method of Virtual Displacements" or also known as "Method of Virtual works".

I'm referring to this book, Engineering Mechanics:statics. i can't seem to use its formula and concept to apply into my question because I am not really good in that particular chapter.

FYI, i already tried using free body diagram ("Total Moment=0" concept) to resolve it but I need some other method to verify my answer. The only other method i found is Virtual Works. if you have any method to calculated it, do comment.

Thanks :)
 
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  • #2
God, morning, Ham

i can't seem to use its formula and concept to apply into my question because I am not really good in that particular chapter.

The rules here need you to show/explain some working even if wrong before obtaining help.

One thing puzzles me.

Your diagram appears to show two links connected by three pinned joints to each other, to a roller at the right hand end, and to a fixed support at the left hand end.

It also shows a moment M applied at the pinned joint between the fixed support and the first link.
Please explain this.
 
  • #3
Studiot said:
God, morning, Ham
The rules here need you to show/explain some working even if wrong before obtaining help.

One thing puzzles me.

Your diagram appears to show two links connected by three pinned joints to each other, to a roller at the right hand end, and to a fixed support at the left hand end.

It also shows a moment M applied at the pinned joint between the fixed support and the first link.
Please explain this.
so sorry. didnt notice there are rules like that here. my intention was getting new ideas or ways to look at this thing and calculate it. anyhow, following the book, i manage to come out with a equation but I am kinda stuck now.
http://img16.imageshack.us/img16/2465/1231245794.png
can anyone here differentiate x and θ. a, B, H are constant. i need to derive it into δx in respect of δθ

about your question, I am not sure if i understand you correctly, but this mechanism is very similar to the crank mechanism. the first link on the left which is fix to the support is the crank. and the link bar on the right is the linkage. so, yes, there will be a moment in between both bar.

i need to calculate the moment at point "M" is because there will be a motor mounting on point M to drive the whole mechanism. Hence, i need to know the moment/torque in order to select and buy a correct motor.
 
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What is the "Method of virtual displacement"?

The Method of virtual displacement is a mathematical technique used in mechanics to analyze the behavior of a system based on the principle of virtual work. It involves considering small, hypothetical displacements of a system and calculating the corresponding virtual work, which can then be used to determine the system's equilibrium and motion.

How is the Method of virtual displacement used in scientific research?

The Method of virtual displacement is used in a wide range of scientific research fields, including engineering, physics, and biomechanics. It is particularly useful in analyzing the behavior of complex systems, such as structures, machines, and biological systems, and can be applied to both static and dynamic systems.

What are the advantages of using the Method of virtual displacement?

The Method of virtual displacement offers several advantages over other analytical techniques. It allows for the calculation of equilibrium conditions and motion of a system without the need for complex mathematical equations. It also provides a clear visualization of the forces and displacements within a system, making it easier to understand and analyze.

Are there any limitations to using the Method of virtual displacement?

While the Method of virtual displacement is a powerful tool, it does have some limitations. It is based on the assumption that a system is in equilibrium, so it may not be accurate for highly dynamic systems. Additionally, it does not take into account certain factors, such as friction and plastic deformation, which may affect the behavior of a system.

How can the Method of virtual displacement be applied in real-world situations?

The Method of virtual displacement has many practical applications, such as designing and analyzing structures and machines, predicting the behavior of materials under different loading conditions, and understanding the movement and stability of biological systems. It is also commonly used in the development of new technologies, such as robotics and prosthetics.

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