Volume centroid used when scalling?

[saintgeorges]

Hi,

I have a solid body (of a material of uniform density, for example steel), and I want to scale it by 2 times. As a center of scaling, I have always been using volume centroid, as its the same one as the center of the mass. Here is the preview of the body and its volume centroid:

"VC" - Volume Centroid

My colleague is now suggesting that I should rather take the volume centroid of the box that covers the mentioned body:

"BVC" - Box Volume Centroid

Here is the difference between objects once 2x scaling is applied:

"ScaledVC" (light red colored) is the 2x scaled object with VC(Volume Centroid) taken as the center of scaling.
"ScaledBVC" (blue edges colored) is the 2x scaled object with BVC(Box Volume Centroid) taken as the center of scaling


Both volume's of the scaled bodies are the same, but they do not have the same position.

Which one is correct?

Thank you.

 

[saintgeorges]

The Photos did not appear in the upper initial post. I apologize for that.
Here are the there photos that should have appeared up:

http://files.engineering.com/getfile.aspx?folder=64801518-d4fe-46cb-a6a8-268c513a5d47&file=1.jpg

http://files.engineering.com/getfile.aspx?folder=092dee81-a2e7-45fe-acc5-aec464b46478&file=2.jpg

http://files.engineering.com/getfile.aspx?folder=164a07f9-ac3e-4761-aa08-8820be08500c&file=3.jpg

 

[Lomarandil]

I suppose it depends on the intended purpose of the scaling, which I don't understand.

 

[JStephen]

So you scale it and move it to wherever it needs to be?

 

[saintgeorges]

By scaling it, the bottom surface beneath the body also moves, with the new scaled object.

 

[rb1957]

scaling a volume doesn't place a constraint on where it is (in space).

if the centroid of the scaled volume is critical it should be defined.

another day in paradise, or is paradise one day closer ?

 

[saintgeorges]

Hi rb1957,

I am not sure I understood you.
By scaling a volume its support surface underneath moves also.

 

[rb1957]

well, it could. scaling a volume only means you're making it bigger. what stays constant (if anything) it arbitrary; you could say that the base stay on the same plane, you could say the centroid doesn't move, you could say that the centroid on an equivalent box stays the same, you could say that one vertex stays the same, ...

another day in paradise, or is paradise one day closer ?

 

[saintgeorges]

I am afraid I do not understand you.

Yes, when scaling this body, the center of the scaling should remain fixed. The problem is that up until now I have been using volume centroid as the center of the scaling.
Now, it looks like volume centroid of the box that covers this body could be used too.

 

[jayrod12]

What he has been trying to tell you is that it doesn't matter where you scale from unless there are other constraints to be satisfied.

The size of the solid will still be changed appropriately (ie the scale factor) however depending on where you scale from the objects location in space will change accordingly.

 

[BAretired]

If you want to keep the volume centroid of the scaled object in the same location as that of the original object, then you should use the VC as your origin.

The BVC is an arbitrary choice. You could just as easily use any point on or off the object as origin. Then the x, y and z dimensions to each point on the scaled object would be precisely 2 times the x, y and z dimensions to the same point on the original object.

BA

 

[saintgeorges]

Thank you for all your replies, and help.