# How can I calculate the center of mass/gravity for vector objects?

I'm making a mobile (in the Calder sense) by laser-cutting from a vector file (Corel Draw). I have a set of outlines that will be the individual pieces.

Is there a way in Corel (or some other program) to calculate the center of mass so I place the holes to suspend the pieces?

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Inventor will do it, but it's probably overkill for your needs. Maybe the demo? – Sam May 1 '11 at 15:08
This sounds like math. We're just a bunch of graphic designers in here. ;) – DA01 May 2 '11 at 14:51

This answer may not count if you require a strictly programmatic solution, but I found it interesting so I thought I'd share. :)

The math way would be to break the shape into a collection of triangles and do a weighted average of their individual centers of gravity. I don't think any of the popular drawing programs will automate that for you. It can be done manually but it may not be worth your time.

This site has a breakdown of a physical approach that may be a faster yield on your time: http://www.scn.org/~bh162/center_of_mass.pdf

The basic premise is that objects with uniform thickness can be determined using 2-3 plumb lines from random points at or near the edges of your shape.

1. Print & cut out a copy of your shape.
2. Select 3 points somewhat close to different edges on your object.
3. Use a pin or nail to poke holes in your 3 points. The holes should end up slightly larger than the diameter of the implement so that the cutout can swing freely.
4. Hang your object using the pin through one of the holes.
5. While your object is hanging, use a string and weight to make a plumb line and trace the line.
6. Repeat the hang & plumb line for the other holes.
7. The point where all your lines intersect is the center of gravity for your shape.
8. If your lines are precise, you should be able to determine an accurate center with 2 lines and the 3rd line is just for additional verification.
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fabulous. we are so accustomed to having the software to do the job for us that sometimes (often) overlook the idea that the best solution is the simple physical one! – Lauren Ipsum May 3 '11 at 12:31
I agree: I was going to suggest cutting it out of foam core... – horatio May 3 '11 at 14:46

I export to a very large PNG file of 3000 pixels. Then I drag and drop into Algodoo (which is now free). Put the axle where you want and play the simulation and it will show you where it's off balance. You can then adjust your drawing until it's balanced where you want.

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