$3.(1\mathrm{.}5$ points$)$ A three$-$segment planar model of a person passing UC

sitting to stand can be modeled as rigid bodies. It is assumed that the movement it occurs in a two$-$dimensional plane and that gravity acts in the $\backslash ($ y $\backslash )-$direction.

The model has three segments:

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

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

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

Each segment is connected through frictionless revoluta joints. And you can suppose that the foot is rigidly connected to the floor.

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

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

$-$ I$1,$ I$2,$ I$3$: Moment of inertia of each segment with respect to its center of mass in kgm $\backslash (\backslash$overline$\{2\}\backslash )$

$\backslash (\backslash$cdot r $1,$ r $2,$ r $3\backslash )$ : Distance from the corresponding joint to the center of mass of each segment in meters.

$-\backslash ($ g$=9\mathrm{.}81\backslash$mathrm$\{$mls$\}2\backslash ).$ Acceleration due to gravity. A$.$ Make the free$-$body diagram

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