Center of gravity

I have used an iteration process to determine the centre of gravity for really irregular shapes. It should work on a shape with defined arcs like a violin as well.

Method

subdivide the object into strips. rather big increments (1cm or more).

Calculate the length, area and mass of each strip.

take any point on the axis and calculate the momentum around that point. ( sum mass * x dimension)

Iterate for a minimum absolute value.

The specific strip can then divided into thinner strips and a new minimum point can be iterated in that strip. continue until accurate enough.

The same procedure should be done with the other axis.

I had an irregular z value as well. and used Simpson or somthing similar for that calculations.

Hi Kokkoplus; It's is digging back a tad for me but as I recall there is a feature in then, ( 12 years ago ), in Design CAD 3D that would allow you to display an image of the part in question as a cross sectional slice at any angle of view. If then you were to use the area feature to determine the area of that cross section. It got a bit manual at this one step, but divide the area by two and display half of the initial image. It will give you the X and Y at fixed Z of any point along the half cut line. Repeat the fore mentioned at at a differnt theta,(Z). It will again tell you the X and Y at that fixed Z. On comparing the data from the two different views, there will be only one set of X and Y coordinates that are the same. Do it agian at a different angle if you wish. That same matching set will appear. Keep in mind that you would have an object of equal density, or, one material to be able to take the area as a function of mass. ( Other note...I notice that there is a free trial version of some 3D CAD software as a pop-up on this CR4 site. It may have that function. Good luck! There may be a hollow object error there that I am forgeting about but I just can't remember the details of that software.

dear friend, you make a 3d model of it, in any 3d cad software give density to it, software will give u location of center of gravity.

You can calculate the CG of any object using a 3D modeling software, you can try AutoCAD or ProE which are available for Free Trial

It is much simpler than you think.

You don't need any software.

You must hang your 2D figure in at leat two different points of the edge by using a string. You continue each time the vertical line shown by te string on the surface of 2D figure. Their intersection is the center of gravity of the 2D figure.

contact me for more details

dragan_gdf@yahoo.com

Now I know why the picture of my in laws (outlaws) is always hanging skew.

Hendrik; Behave!! I guess you can rule out Christmas at the in-laws.

Actually the picture is straight. It's the room that is skewed.

Remember those fun houses that deceived you into thinking you were leaning although you felt like you were standing like you always have.

John

Ok, I am trying to do the same thing with a bird I am making that will sit in the yard. The bird is made of a rock wrapped in a metal saddle so you can weld the neck, head, and tail feather to the saddle. The legs are pipe and the pivot point by cutting a bit out of each side. Then a bolt it welded to each side of the saddle and the whole works sits on the cut out legs. This then can move back and forth in the wind or if you touch it it will rock just like a rocking chair. But I am having a time trying to get the balance point and I know it can't be something that difficult to do. The rolling it on a ball or pipe is too hard as this is pretty large item say 3 foot by 2 foot. Can you tell me a bit more about the string idea. Thanks so much Ralph

You basically use a plumb line for this, hang your object up & hang a plumb line from the same axis then mark this line on your object. Hang it again from a different point & mark another line, where your 2 lines cross is the C of G. You can repeat this a few more times to get a more accurate fix.

Thanks, I will try this.

If you actually have the physical object, as opposed to a drawing, then the string idea above would probably be the easiest and most accurate as it would factor in irregularities in density and thickness of the material. Another way, though sloppier, is to find a tank large enough to hold the object. Fill it with water most of the way and mark the water level. Immerse the object and mark the new water level, taking care not to include your hand any thing else that would displace the water. Then drop the object back into the water until it rises halfway between the two marks. The cq lies along the line coexistant with the water line. Mark the water line on the object. Reorient the object 90 degrees and do it again. Mark the water line on the object. The intersection point is the cg on the 2d surface, assuming the thickness is constant. It might be easier just to use the string trick. I've done it before and it works well. The theory there is that the center of mass in a gravitational force field will always align itself with the center of support. Take care to use a lightweight string. Something semirigid like wire can induce moments which will compromise the accuracy it the attachment point is not allowed to gimble.

Certainly any 3D software will do it & I think that 2D AutoCAD will find the centre of any area.

hi everybody

regardless of the thickness ın 2D calculations by assuming homogeneous material distribution you can calculate with a simple self made program . U will need only the data of the two coordinates (x,y) of each point on the surrounding polygon of the shape. Once you obtain these data referring to a fixed origin (theoretically this origin can be choosen inside or outside the polygon) by following a rotational direction connect succeeding points to the origin. Thus you have neighboring triangles. For each triangle (any two neighboring points on the polygon (x1,y1) and (x2,y2) ) you can have the area by a simple formula (x1.y2 - x2. y1)/2 . Which is actually the 2D vector product of the two neighboring location vectors. Simply by adding these areas you have the area of the whole polygon. The center of gravity for each triangle is the 2/3 of 1/2 of the two neighboring location vectors addition. Which is simply ((x1+x2)/3 , (y1+y2)/3 ) Again for each triangle Multiplate the area of the triangle by its coordinates of the c of gravity and add x and y seperately. Divide in the end the sum to the total area to obtain the coordinates of cog of the shape.

During this computation do not change the direction of the rotation. If you choose the other direction in the beginning it will result in the change of sign of the area. And keep your polygon always closed. It works also for concave or convex for any irregular shape.

The same idea can be applied for complex 3D figures by neighboring tetrahedrons on the surface. This time you can calculate volume , surface area, cog , and moments of inertia.

I hope this will help.

You'd have to be able to mathematically define the shape to get an accurate CG.

Solidworks allows you to determine the center of gravity in the mass properties of any model or assembly.

If you really do have a aluminum plate of irregular shape then making a 2d model would be a lot of work. Instead, lay the plate on a rod. Roll the plate to the balance point. Mark the intersection of the rod and plate on the plate. Turn the plate or rod through 90 degrees or so and repeat. The intersection of the two lines established by the 4 points marked on the plate will be the static balance point of the plate.

An alternative method would be to place the plate on a small steel ball. Roll until the balance point is found and smack it with a dead blow hammer to mark the center. (This method is fast and can be accurate but requires more skill than method one. You can mark both sides of the plate this way and test which is better and then use that one.)

If you have or wish to create a 2d or 3d solid model of the plate and find the center of mass Alibre is a good quality low cost software package.

Tony

Thank you all for the ideas. What I am trying to figure out is where the center of gravity is going to be before I actually produce the 3d object.

Ideally I should be able to import a 2d shape, change it slightly with a spline and calculate the center of gravity. The real object is going to be a violin plate which is not only arched but also anisotropic and that would certanly produce a difference between the balance point in the 2d model and the 3d real object. But I think the error should be neglegible or easy to correct.

Thanks again.

Hi Kokoplus,

If the plate is of homogeneous material, and perfectly flat, just cut a piece of the same exactly shape , useing any material to any convenient scale, put it on a tube on a perfectly horizontal surface, roll it sideways until it balances out. The exact CG (center of gravity) is where the plate touches the tube. it will be the same CG for any other material, provided it is of homogeneous SG.(specific gravity), and exactly the same shape. The good news are that you can easily find the CG for any angle along the chord line. NO complicated software required.

Wangito.

Hi Wangito.

I really need a software because in the designing stage I can draw several possible shapes and check if the CG falls in the right place. Then I can actually make the physical object.

I downloaded few trial versions of cad software but, so far, no luck. At first I though it would be a piece of cake to find such a program, especially because we are talking of 2D. But for some reason it is not so easy...

Kokkoplus