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Consider, while building a new machine which has different elements in it. For instance, a machine having a driving assembly, main body, chassis, crucible etc. Then, how would I calculate the center of gravity and how would I know the calculated value is an exact value or Cg value gives a balanced system?

Should I calculate a center of gravity of each element or the whole system?

Suppose I need to calculate the center of gravity of each element, how would I calculate? What are the factors to be considered other than weight and distance from the reference plane?

Any suggestions would be appreciated.

Thank you in advance

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You have to know the mass and CG of each individual part.

Then once assembled you set your machine against a corner wall which you will use as xy axis. measure the Dx and Dy, the distance from CG of parts to corresponding X and Y walls.

Then you calculate CG_x as:

$$ CG_x = (\Sigma Mn. Dxn )/W $$ and CG_y as:$$ CG_y = (\Sigma Mn.Dyn)/ W $$ Then you can transfer this X and Y to a more convenient axis, such as one parallel with a prominent axis on your machine.

There are many CAD programs that can calculate CG by the specs and wire-mesh of the machine.

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  • $\begingroup$ Thank you all for your suggestions. But my Question is, consider a machine in an inclined plane has two main assemblies one at the bottom and another at the top. There is no connection between the two assemblies. Now I need to calculate the center of gravity of top assembly or I want Center of gravity of top assembly at a particular required point. How would I do that? Also, to get the center of gravity of the whole machine, I should also have to calculate the Cg for the bottom assembly and using Cg of both assemblies I can obtain the Cg of the entire system. Is that make sense? $\endgroup$
    – Ranjith
    Apr 2, 2018 at 20:31
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You can use the a finite element-like method like you're describing, chop up the object in box shaped pieces and combine their individual weight and gravity centre(the exact middle with boxes), but that's rather hard and time-consuming to do.

If you have the opbject at your disposal, you can determine it by just using a scale. If you take three or four points, the front, back and side, you know the weight distribution and location of the gravity centre in the horizontal plane. If you tilt the object at a known angle and measure one of the points again, you can calculate the height of the gravity centre with trigonometry.

If you're working with a vehicle or dynamic object, determining the rotational inertia may also be interesting.

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