The calculation of inverse dynamics

[Yuta Shimane]

Hi,

I have question regarding inverse dynamics tool.
First, I analyzed walking motion, and estimated joint moment from kinematics data and grand reaction force. The question is there is no difference between the result obtained by applying GRF to only the right foot and the result obtained by applying GRF to both feet, when the joint moment of the right foot is analyzed (see the figure below). In other words, when targeting the right foot, is it possible to perform an accurate analysis by applying GRF to only the right foot? Could you tell me whether the analysis of the right foot is not affected by the force from the left and is independent?

Second, I would like to know how OpenSim's Inverse dynamics tool is solved. As you know, a calculation method based on the Newton Euler equation is used for the calculation of inverse dynamics in a general link model.

Best regards!

System environment: OpenSim 3.3

figure1.png (456.18 KiB) Viewed 373 times

figure2.png (437.94 KiB) Viewed 373 times

[Nicos Haralabidis]

Hello Yuta,

The right lower-limb joint moments make sense to me that they are identical, when only applying right foot ground reaction force (GRF) and when applying both GRFs to each of the separate feet. I believe this can be explained due to how the GRFs are mapped from cartesian/spatial space to joint space (generalized coordinates), using the model's Jacobian Transpose (J^T times ExternalForcesCartesianSpaceVector). The Jacobian is a matrix which contains the derivatives of the functions describing cartesian space velocities of the body segments with respect to each of the generalized speeds. For example, the left lower-limb cartesian velocities are not dependent on the generalized speeds of the right lower-limb, thus those entries in the Jacobian are zero. When J^T times ExternalForcesCartesianSpaceVector is made with GRF applied to either both feet or one foot, the contribution on the joint moment opposite to the foot which GRF was applied is zero due to the matrix-vector multiplication, with elements of the Jacobian containing zero. I hope this makes sense...! Apologies if it's poorly worded! Perhaps someone with more expertise can comment on this and improve on my answer!

Cheers,

Nicos