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Old Aug 15th 2017, 08:56 AM   #1
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6 degrees of freedom manipulator

A movable panel is connected to two 6 degrees of freedom manipulators.

If the two manipulators move apart in x direction within the same force and the same distance, the forces applied to the point in the panel will be the opposite to each other and will be cancelled out. So then the panel will be stay where it was? But I feel like the panel will move downward when the two manipulators move apart though. I need theoretical explanation what will happen to the panel when two manipulators move apart in x direction. Any ideas?
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Old Aug 16th 2017, 09:27 AM   #2
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Think about how forces are transmitted into the object by the arms of the manipulators. There is an x- and z-component of force from each. The x-components cancel out, as you suggest, so the object experience 0 displacement in the x-direction. But the z-components of force do not cancel - they add. Hence there is vertical movement based on F=ma, where F is the sum of forces of the manipulator arms in the z-direction minus the object's weight.
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Old Aug 16th 2017, 01:54 PM   #3
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Originally Posted by ChipB View Post
Think about how forces are transmitted into the object by the arms of the manipulators. There is an x- and z-component of force from each. The x-components cancel out, as you suggest, so the object experience 0 displacement in the x-direction. But the z-components of force do not cancel - they add. Hence there is vertical movement based on F=ma, where F is the sum of forces of the manipulator arms in the z-direction minus the object's weight.
In addition please keep in mind that the center of mass of a closed system never changes. In this case the plate must move down so that the center of mass remains unchanged.
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Old Aug 16th 2017, 02:30 PM   #4
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Originally Posted by Pmb View Post
In addition please keep in mind that the center of mass of a closed system never changes. In this case the plate must move down so that the center of mass remains unchanged.
I'm not following you. Not sure what you mean by a "closed system" - do you mean in a thermodynamic sense (i.e. no transfer of energy to or from the outside)? Also note that the center of mass does change, as the object is lowered.
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Old Aug 16th 2017, 03:01 PM   #5
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Originally Posted by ChipB View Post
I'm not following you. Not sure what you mean by a "closed system" - do you mean in a thermodynamic sense (i.e. no transfer of energy to or from the outside)?
See the definition of it at: https://en.wikipedia.org/wiki/Closed_system

Originally Posted by ChipB View Post
Also note that the center of mass does change, as the object is lowered.
Why are you asserting that the center of mass does change? I'm referring to the center of mass of the entire system which includes the panel, the two manipulators and the connecting rods. The center of mass will definitely not change. The amount that the panel moves is determined by the conservation of the center of mass.

Are you saying that you've never heard the term "closed system" before? Einstein used a closed system when he wrote

The Principle of Conservation of the Center of Gravity and the Inertia of Energy, Albert Einstein, Annalen der Physik, 20 (1906): 626-633.

He also used the principle of the conservation of the center of mass. If you want details of his argument then see the webpage I created about it at:
Einstein?s Box
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Old Aug 16th 2017, 07:01 PM   #6
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Originally Posted by Pmb View Post
Are you saying that you've never heard the term "closed system" before?
Note: Chip. Please understand that just because I was surprised that you may never have heard that term before it doesn't mean that I consider you in anyway lacking in your understanding of physics. In fact I consider your knowledge of physics to be quite good in fact, perhaps even exceptional.

After I wrote the above question I took a look in a four of the many physics texts I have. It wasn't defined in three of them. It was only listed in the index of the basic physics text I have by Knight. I was quite surprised by that. Then again I may know the term as well as I do because it became an important part of the area of physics I chose to specialize in, i.e. relativity and relativistic mass. There the term becomes quite important because the expression E = mc^2 is true for a closed system and not for open systems. E.g. its not valid for a rod under compression or tension. This isn't a well known fact because almost all special relativity texts don't cover continuous mechanical mediums which is described by the stress-energy-momentum (SEM) tensor. The SEM tensor is only talked about in texts such as EM and GR texts, neither of which usually discuss continuous media. Older texts such as those by Rindler and Tolman cover it quite well. The theory of which being originally the work of Max von Laue.
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Old Aug 17th 2017, 11:25 AM   #7
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Can we assume that the links between the manipulators and the plate are of a fixed length?
Can we assume that the points where the links meet the manipulators and the points where the links meet the plate are free to rotate?

If so, doesn't this then become a simple geometric problem.
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Old Aug 17th 2017, 02:57 PM   #8
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Hi Pmb,

The only use of the term "closed system" that I have experience with is with regards to either thermodynamics (no transfer of energy from or to the outside of the system in question) and in fluid mechanics (conservation of mass). So thanks for the opportunity to learn something!

Regarding change of CM - I interpret from the OP's drawing that the manipulator sits on the ground. It can raise and lower an object, just as an elevator can raise and lower a mass, through transmittal of forces into the ground. The OP asked about movement relative to the ground, which for this purpose we can assume is immovable, and hence it's not a closed system. If we wanted to include the movement of the Earth, then I agree - it would then be a closed system and as the mass is lowered the Earth moves slightly upward in the direction of the mass, and the CM of the manipulators + object + Earth doesn't change.

Woody: I agree with you - it is a simple geometry exercise. However the OP asked about how movement occurs based on forces, which is why I tried to explain how forces in this example cancel or add, as the case may be.

Last edited by ChipB; Aug 17th 2017 at 03:02 PM.
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