A three$-$segment planar model of $$a person going from sitting to $$standing can be $$modeled as $$rigid bodies. It$$is $$assumed that the motion occurs in $$a two$-$dimensional plane and that gravity acts in $$the $-$y $$direction$.$

The model has three segments:

$-$Segment $1$: The leg $($from $$knee to $$ankle$)$

$-$Segment $2$: The thigh $($from $$hip to $$knee$)$

$-$Segment $3$: The trunk $($from $$the hip to $$the head$)$

Each segment is $$connected through frictionless revolute joints. And you can assume that the foot is $$rigidly connected to $$the floor.

For each of $$the segments $($leg$,$thigh and trunk$)$the following information is $$known$,$ according to $$the diagram.

$-$m$1,$m$2,$m$3$: Mass of $$each segment in $$kilograms

$-$l$1,$l$2,$l$3$: Moment of $$inertia of $$each segment with respect to $$its center of $$mass in$$kg$*$m$^2$

$-$r$1,$r$2,$r$3$: Distance from the corresponding joint to $$the center of $$mass of $$each segment in $$meters$.$

g$=9\mathrm{.}81$m$/$s$^2.$Acceleration due to $$gravity$.$

A$)$ Make the free body diagram.

B$)$ Formulate the Newton $-$ Euler equations for each of the segments.