Euler Interpretation

[Alessandro Navacchia]

Hi Michael,

I am modifying the splines in the Walker knee custom joint and I would like to be sure I'm doing it right. Are the three translations defined in the coordinate system after the Euler rotations are performed?
For example, if I have a transformation matrix that describes the position and orientation of the tibia coord sys (St) in the femur coord sys (Sf) (TF matrix - the matrix that trasforms a vector in St to Sf) I should simply use the translation vector of TF to define the splines?
Also, the order of the three translations does not matter, does it?

Thanks a lot!

Alessandro

[Michael Sherman]

Hi, Alessandro. You can see exactly what the custom joint is doing in the paper cited at the top of this thread, equation 18. It calculates the transform X_PB(q) giving the position and orientation of the child frame B in the parent frame P, expressed in the P frame, as a function of the generalized coordinates q. Thus the translation is independent of the rotation of B with respect to P.

However, while that is always true the specific meaning depends on how the modeler chose to make the joint. I don't know the details of the joint in the Walker model. First question, which body is the parent P? Typically it would be the femur but that is just a convention. Then, how are the three translation functions p1,p2,p3 defined? Together they must constitute a vector (p1,p2,p3) from the P origin to the B origin, expressed in the P frame. However, the joint designer is free to make them depend on any or all of the q coordinates, including rotational ones. I would suggest looking at the defining equation in the paper, and then looking in the actual model to see what the modeler did.

The most common choices would lead to the femur being the parent, and each of the three translational splines would give one of the coordinates in a frame fixed to the femur so that would be my guess. Someone here who is familiar with the Walker model could give you a definitive answer.

Regards,
Sherm

[Alessandro Navacchia]

Thank you Michael, it was very helpful. I think I figured it out.
I would like to ask you another question that is not related to Euler angles (I previously posted a similar question but I did not get any response): is it possible to obtain the dynamic equations of a model in the symbolic form from Simbody?

Thanks again for your help.

Alessandro

[Michael Sherman]

Equations are not available in symbolic form from OpenSim or Simbody. You can get them numerically though.