inverse dynamics in combination with simm spline

[Florian Schellenberg]

Dear all,

For this example I used the gait2392_simbody model but set the mass of the whole foot and tibia of both legs to 0.
By applying a force directly on the center of rotation of the knee (basically on tibia [0 0 0]) and performing the inverse dynamics tool, the moment in the knee is surprisingly NOT equal 0. The values reaches from -1.2 Nm to -6.8 Nm, which represents a wrong moment arm of about .3 cm up to 1.7 cm (a force of 400N was applied). (See attached plot)

By changing the simm spline function to a constant function with the value 0 (no translation as e function of the knee angle) or by changing the values in the simm spline function to constant values in the osim-file, the resulting moment is, as one can expect, 0!

May anyone tell me how the center of rotation in the inverse dynamics tool using simm spline function is calculated?
I guess that there is a miscalculation in the ID-Tool. If this is the case, does anyone have an idea how I can change this?

If you need further documentations please let me know.

All the best and

[Michael Sherman]

Hi, Florian. If rotation and translation are coupled, then necessarily moment and force are coupled; they are flip sides of the same coin. So the results you are getting make sense from a technical perspective. Whether the knee actually couples rotation and translation is a biomechanical modeling question; I am not qualified to say but I understand that the knee is not well-modeled by a pure rotational joint.

Regards,
Sherm

[Florian Schellenberg]

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[Florian Schellenberg]

Dear Sherman,

Thanks for your reply, but I have to clarify myself.
I applied a force directly on the knee joint while changing the knee angle. But as a consequence of the translation and rotation of the knee joint as a function of the angle, I also changed the point where the force applies. That means, the force is always on the center of rotation of the knee joint and therefore, the acting moment should always be zero, but it is not (see attached file in my first post).
Therefore, my question is if the center of rotation of the joint is not the same in the model than it is used in the ID-Tool? And if this is the case: Which center of rotation is chosen in the ID-Tool?
So, actually it is not a biomechanical question. It is more a mechanical question or if there is a miscalculation in the software using ID in combination with a simm spline function.

If my concern is still not clear, I would upload a movie to show the problem.

Thank you and all the best for 2015,
Florian

[Michael Sherman]

Hi, Florian. The concept "center of rotation" is not needed for ID analysis so we do not need to calculate it to perform correct inverse dynamics. Rather, what we need is to know the partial derivatives of translation and rotation with respect to the joint coordinate (the joint Jacobian). The SimmSpline is defining that Jacobian.

My question would be how are you determining the center of rotation and why are you confident there should be no moment? Perhaps someone more familiar with how the center of rotation concept maps to the equations of motion can explain? It isn't obvious to me.

Regards,
Sherm

[Michael Sherman]

BTW, have you seen our paper describing how we model joints? It provides a good explanation of how the knee is modeled, including all the equations. I would be interested to see how the center of rotation is calculated in those terms and why the moment should be zero if you apply a force there. I suppose that implies that the force application point does not translate as a function of an infinitesimal change to the joint angle, i.e. the Jacobian there is zero. Is that right?

Sherm

[Florian Schellenberg]

Dear Sherm,
I wish you a happy new year and thank you for your answer and your paper. Corresponding your paper, I noticed, that my assumption (the center of rotation (CoR) of the knee is [0 0 0] on the tibia) is not usable due to the sliding fact of the tibia as a function of the knee angle.
Now, my issue to move on is to calculate the right CoR of the knee with respect to the femur as well as to the tibia. Do you have any idea how one can plot the CoR as a function of the knee angle in the x and y direction?
I'll keep you informed about my results as soon as possible.

Thank you and all the best,
Florian

[Michael Sherman]

Hi, Florian. Happy New Year! I have asked Ajay Seth to respond; he may know an easy way to squeeze CoR out of OpenSim. Regards, Sherm

[Florian Schellenberg]

Dear Sherm,

Thank you for your answer and for forwarding the question to Ajay Seth. Unfortunately, I have not received a response regarding the CoR of the knee.
It would be very helpful for my further research to get this information.

However, I tried to calculate the CoR of the knee by myself. To check the correctness of the calculated CoR in the knee, I applied a force (artificially made by myself, not a measurement one) acting in z direction and with its force application point direct on the CoR. So the resulting moment should be zero due to the fact that there is no lever arm. This should also answer your question why there should be no moment (torque).
For the defined translation in the knee (SimmSpline) I used the CubicSpline-funciton, however, this leads to small errors. I will try to reproduce the SimmSpline function to get the right results. Do you know where I can find this definition?

Are you interested in the results or in some plots to clarify my problems? If yes, I will provide them to you, if not, it's also fine for me.

Thank you and all the best. You helped me a lot.
Florian