Worksheet $4$: Inverse Dynamics

A subject has a mass of $75$ kg $.$ The foot and shank segment mass, lengths, and center of mass $\backslash ((\backslash$mathrm$\{$CoM$\})\backslash )$ locations are shown in the table. Positive moments are counter$-$clockwise.

The foot is parallel with the floor, and acceleration in both vertical $\backslash (($Z$)\backslash )$ and horizontal $(\backslash ($ y $\backslash ))$ directions is zero.

$-$ Vertical GRF $($GRFz$)\backslash (=810\backslash$mathrm$\{$~N$\}\backslash )$

$-$ Horizontal GRF $($GRFy$)\backslash (=90\backslash$mathrm$\{$~N$\}\backslash )$

The center of pressure is $19$ cm in front and $11$ cm below the ankle.

The center of mass is $8$ cm in front and $5$ cm below the ankle. $1.$ Calculate the joint reaction forces $(\backslash (\backslash$mathrm$\{$Rz$\},\backslash$mathrm$\{$Ry$\}\backslash ))$ at the ankle $(4$ points$)$

$2.$ Calculate the net muscle moment $($M$1)$ at the ankle. Is this in plantarflexion or dorsiflexion? $(7$ points$)$ The lower leg is $\backslash (80^\{\backslash$circ$\}\backslash )$ from the horizontal.

$3.$ Complete the free body diagram of the shank, to include forces and their distances from the center of mass $(4$ points$)$

$4.$ Calculate the location of the shank's center of mass. Specifically, find the horizontal and vertical distances to the center of mass from the ankle and knee. $(4$ points$)5.$ Calculate the joint reaction forces at the knee $(4$ points$)$

$6.$ Calculate the net muscle moment at the knee $(5$ points$)$