Question $5)(20$ points$)$ Using the coordinates of three markers in global space affixed to the upper arm, you create a

local coordinate system consisting of three, orthogonal unit vectors. The origin of the upper arm local coordinate system

defined in terms of the global coordinate system is located at $0\mathrm{.}3m,0\mathrm{.}65m$ and $-0\mathrm{.}42$ m in the $x,y$ and z directions,

respectively.

The unit vectors that you computed defining $x,Y,$ and $Z$ axes of the upper arm local coordinate system with respect to

global coordinate system are as follows:

vec$(x)=0\mathrm{.}4082$vec$()-0\mathrm{.}4082$vec$()+0\mathrm{.}8165$vec$(k)$

vec$(Y)=-0\mathrm{.}7428{}^{}+0\mathrm{.}5571{}^{}+0\mathrm{.}3714$vec$(k)$

vec$(Z)=0\mathrm{.}5345$vec$()-0\mathrm{.}8018{}^{}+0\mathrm{.}2673$vec$(k)$

Also, using the coordinates of three markers in global space affixed to the forearm, you create a local coordinate system

consisting of three, orthogonal unit vectors. The origin of the forearm local coordinate system defined in terms of the

global coordinate system is located at $-0\mathrm{.}4m,0\mathrm{.}05m$ and $-0\mathrm{.}91$ m in the $x,y$ and $z$ directions, respectively.

The unit vectors that you computed defining the forearm local coordinate system with respect to global are as follows:

vec$(x)=0\mathrm{.}6667{}^{}+0\mathrm{.}333$vec$()+0\mathrm{.}6667$vec$(k)$

vec$(Y)=0\mathrm{.}4286{}^{}+0\mathrm{.}8571{}^{}-0\mathrm{.}2857$vec$(k)$

vec$(Z)=0{}^{}-0\mathrm{.}5547{}^{}+0\mathrm{.}8321k^{}$

Given that an $x,Y,Z$ Cardan rotation sequence is used to define the elbow joint, compute the Cardan joint angles for

the elbow joint. What do these Cardan joint angles represent?