# Inverse dynamics operation

Hi anybody’s team,

I’m using a model where there are:

• external forces F(t);
• muscles forces Fm(x,dx/dt)
• ligaments forces Fl=k*Dl + r * Ddl/Dt; (normal dumper-stiffness model)

does Anybody try to solve the following system equation during Inverse Dynamics?

M d/dt(dx/dt) = F(t) + Fm(x,dx/dt) + Fl(Dl,Ddl/Dt);

Why don’t I have accelerations and velocities of the system at the end of the simulation??

Is it possible that during Inverse Dynamics Anybody solve the following simplify equation??

0 = F(t) +Fm(x,dx/dt)+Fl (Dl).

Thanks,
Best regards,
Giovanni

Dear Giovanni,

I’m not sure how complex you model will be.
But you can do some test with the AnyForceMomentMeasure2 class.
Please look how to use this class in the reference manual.

In the reference manual, there is this following sentence:
"…Notice that including all forces on a segment or a system of segments should ideally give zero equivalent force and moment due to equilibrium, but this must indeed include all forces including reactions, forces of gravity, and inertia forces. "

Also there are some options for this class regarding gravity and inertial forces.

For easy test, I would recommend you to build a very simple model (for instance, simple 1-DOF arm with external force, muscle and ligament).

Best regards,
Moonki

dear moonki,

I have seen that the inertial moments are calculate, but why is the lin.Vel my ligament value set for all the inverse dynamics simulation (without particular movement as input, but only forces) equal to 0, while in the kinematics (with a particular movement as input) that value change step by step?

Best regards,
Giovanni

Dear Giovanni,

It sounds a little to me like you are running FDK and not normal inverse dynamic analysis. In FDK, AnyBody computes the static equilibrium in the directions you specify to be ForceDep in the drivers. So if your ligament is along one of those directions, its velocity and acceleration will be zero.

You could try running a normal inverse dynamic analysis (ForceDepOnOff = Off in your study), and then you should see the velocity and acceleration.

Best regards
Michael Skipper Andersen
Associate Professor
Aalborg University

Dear AnyBody’s team,

so, if I want to see the behavior of a system where act on it, muscle forces, external forces and ligament forces I have to use the FDK solver. Nevertheless this kind of solver allows to solve only static equilibrium, therefore I can not use a ligament force created with an AnyForce class and defined like: klin.Pos+rlin.Vel, otherwise I don’t see the contribution of the velocity.

Is what I have said right??

Best regards,
Giovanni

Hey Giovanni!

No, not completely. Let me explain.

In the FDK model, it typically does not make sense to set degrees-of-freedoms associated with large motions as ForceDep. For the knee model, a FDK model could include 5 FDK dofs and one normal dof. The 5 FDK dofs would be int/ext, abd/add, ant/post, med/lad and dist/comp whereas flexion/extention would not be set to FDK as it should be used to control the movement of the model. What this then means is that the velocities and accelerations of ligaments caused by the angular velocity and acceleration around the flexion/extension axis will be included in the model. The velocity and acceleration components originating from the movements in the FDK dofs will be neglected on the other hand.

So in short, in FDK model for the knee as outlined above, the ligament velocities and accelerations will be non-zero if the model moves and your viscoelastic model should make sense.

Secondly, the viscoelastic ligament model can also be used in a normal inverse dynamics model. The main difference between normal inverse dynamics and FDK is that the FDK model also computes some of the displacements you would otherwise have to provide as input in the inverse dynamics model.

Best regards
Michael Skipper Andersen
Associate Professor
Aalborg University

Dear Prof. Andersen,

I have a model with 4 FDK directions (abd/add; ext/int; medial/lateral; anterior/posterior) and fixed flexion for Tibia and I have a fixed patella. May I see the answer of the system (movements and ligaments tear) with a simple stiffness ligament model and external forces as input to the knee? Are in this case the inertial forces considered?

Best regards,
Giovanni

Hi Giovanni!

Yes, you may analyse the movement in that case with a simple stiffness model. Only the inertial forces occuring due to movements in the two non-FDK dofs will be included So, since you fixed flexion (and I assume you also fixed dist/comp), no movement in those dofs are present in your model.

Best regards
Michael

Dear Michael,