Inertia questions

[Gary Lu]

Dear all, I have some questions about the inertia properties of the model in OpenSim and following are my questions.

1. I'm looking for the papers or the researches that the model arm26 used as references on setting its default mass center and inertia properties. Can anyone tell me where I can find them?
2. I'm wondering if OpenSim sets default shape for the body segments in the model? Take the 6 degrees of freedom between ground and pelvis for example, while using RRA tool, it has to balance six equations including three translational and three rotational equations, however, I suppose that not only OpenSim but others simulations software like Adams or Ansys don't really have equations of motion for any kinds of mechanism, in other words, the solutions are numerical instead of analytical one. So, when OpenSim need to reduce the residuals moment, it must need the inertia values of a segment to do this but it cannot just put those numbers into the equations so it set default shape to a body segment and just sum up the inertia effects from all the particles inside the shape w.r.t. the mass center to get the inertia properties, if so, it can also easily calculate the new inertia properties of an enlarged segment. If anyone can tell me how OpenSim deal with the inertia problems and also if my inspections are wrong or not?
3. Assumed that OpenSim do set default shape for body segments, here is my question. Under the assumption, I first think of an easy-accessed shape of cylinder that can be set as the default shape for both arms and legs. Below is a 2Kg cylinder with h=33cm and r=5cm, the coordinate are set as well, we can infer that the inertia of moment in y direction is 0.5*m*r*r which is nonrelated to the height, then the inertia of moment in x and z direction are the same as 1/12*m*(3*r*r+h*h). When I used scale tool to change the mass to 4Kg, the density and the h remain unchanged, as a result, the radius should be enlarged to 0.7 larger than the original one, then the inertia of moment in y direction should be four times as large as the original, but however, after scaling, the inertia just became twice as large as the original, so I traced back to the formula, I found that the only reason for the results must be that the density change to twice as large as the original and the radius remain unchanged, but this doesn't make any sense in a real human body. So I'm really confused about how OpenSim deal with the inertia of moments properties or OpenSim just doesn't care about them?

Thanks for reading this post and looking forward to someone that can explain these so I can sleep well at night!

[Thomas Uchida]

(a) The "Musculoskeletal Models" page in the documentation (https://simtk-confluence.stanford.edu:8 ... tal+Models) provides information about popular OpenSim models. As indicated in the first table, the "Arm26" model was derived from the "Stanford VA Upper Limb Model" (https://simtk.org/projects/up-ext-model). There are several papers listed on that page (on the About tab and the Documents tab).

[Gary Lu]

Thomas, thanks a lot for replying to my first question. Though I haven't found my answer through those documents. But I'll keep working on it anyway. Hope someone can answer my other two questions.