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Motor, irregular rigid body of Different materials Forming a single robotic.

For example, Industrial robot, every geometric shape of the link is very complex. But we can find inertia matrix form CAD software, how these software tools calculate the inertia matrix of a single robotic arm? Is this inertia matrix accurate or equivalent?

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It is approximate and very accurate as long as the material properties are well defined. Many methods are combined to get it. Moment of inertia, parallel axes, mass distribution, etc etc. Simplification methods are implemented to make the computations efficient. All the bodies are simplified as well using triangles to make them convex.

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CAD software knows everything about your parts...(assuming you tell the things it doesn't know...as mentioned, material properties) After doing this, calculating multibody C.O.G or even inertias of complex bodies is 'trivial' (of course, it wasn't for the programmers).

These things can be very accurate, or can be made very accurate, however they can and usually will be off by a certain tolerance. How much one is willing to accept for an error is up to the user.

They can also be wrong simply because something as trivial as the electronics and wires within your body weren't modelled correctly, or given the correct initial data, on top of that, no material is perfectly homogenous, which CAD software always assumes. This may not even account for even 1% error and not matter for something small, but is extremely important when dealing with large heavy loads.

Because of this, it's almost always a good idea to experimentally verify such data yourself, using trifilar pendulums as an example or other equipment and methods

I generally use CAD data as a good lower boundary for initial guesses with empirical verification.

Of course, this again will only be as accurate as your measurements and is an entire branch on it's own.

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