Definition of custom intertia properties in SimMechanics

Dear support,

I want to define custom inertia properties in my SimMechanics-model. I am not quite sure if the terms "Moments of Inertia" and "Products of Inertia" are used in a correct way in the SimMechanics documentation. At least it is not explained clearly what the user is supposed to fill in the dialogue box.

From my CAD-modell I derived an inertia tensor in the form:

    [J_11 J_12 J_13
     J_12 J_22 J_23
     J_13 J_23 J_33]

I use exactly the same coordinate system in my SimMechanics-model to make the import of data easier. The coordinate systems of imported stl-file is taken as the reference frame in SimMechanics. It is neither a principal coordinate system nor the origin is located at the centre of mass.

In this post Arnaud Miege says that inertia is defined relative to the centre of mass:

"The key parameters for a SimMechanics Body block are its mass and inertia tensor relative to the centre of gravity of the body."

I doubt that. It makes more sense to me when the inertia properties are relative to the reference frame.

My question is: What am I expected to fill in for "Moments of Inertia" and "Products of Inertia"?

The documentation which can be found in the link below says the following:

Documentation: Inertia

Quote:

Moments of Inertia

Enter the principal moments of inertia as a 3-vector in the frame R of the solid. In the drop-down list, choose units. The default is kg*m^2 (kilograms-meters2).

Products of Inertia

Enter the products of inertia as a 3-vector in the frame R of the solid. In the drop-down list, choose units. The default is kg*m^2 (kilograms-meters2).

Principal moments are not equal to J_11, J_22, J_33 in the general case. Does this mean that I have to derive the principal moments of inertia from my inertia matrix (which are the eigenvalues)? If this is the case: In which order do I have to list the principal moments in the dialogue box (Can be found under the point "Custom Inertia" in the doc.).

I guess that the products of inertia are equal to J_12, J_13, J_23. Again: In which order do I have to put the values into the vector required in the dialogue box?

In that respect the documantation page I referred to says:

Quote:

"The products of inertia are (I23, I13, I12)."

Is this the right order?

I am a bit confused that there does not seem to be a simple way to get my inertia tensor directly into SimMechanics. It is a problem of conventions.

I hope you can help and clarify what I need to fill in the dialogue box.

I apologize for my limited English writing skills as I am not a native speaker.

Kind regards.

Jakub

Answer 1

[Pouya Jamali]

Diagonal elements of the inertia tensor are moments of inertia and the others are products of inertia. You should consider that this matrix is symmetrical so it just has 6 independent elements. If you have a CAD model it's better to use smlink to import the geometry automatically instead of fill in the inertia of the model parts manually.

Answer 2

[Jakub]

Thanks for your answer.

I know that the matrix is symmetric. I wrote the matrix down in Matlab Code at the beginning of my lengthy question. Here it is again:

     [J_11 J_12 J_13
     J_12 J_22 J_23
     J_13 J_23 J_33]

The questions remain: What am exactly I supposed to fill in into the fields when I have the inertia tensor relative the centre of mass of a body? And which is the coordinate system the filled in moments and products of inertia need to refer to? It is either a coordinate system located at the centre of mass or the reference frame I guess.

I need to fill in the inertia properties manually because the CAD model is not complete.