Problems

$(6$ points$)$

Given the value of frame transformation ${?}^A{T}_B$ as follows:

$A{T}_B=\left[\begin{array}{cccc}{n}_x& o_x& a_x& P_x\\ n_y& o_y& a_y& P_y\\ n_z& o_z& a_z& P_z\\ 0& 0& 0& 1\end{array}\right]=\left[\begin{array}{cccc}0& -1& 0& 3\\ 1& 0& 0& 2\\ 0& 0& 1& 4\\ 0& 0& 0& 1\end{array}\right]$

a$)(3$ points$)$

Describe the values of position and orientation of the Frame $B$ relative to Frame $A.$

b$)3$ points$)$

Plot the orientation and position $($i$.$e$.$ origin$)$ of frame $B$ relative to frame $A.$

$(3$ points$)$

Provide the graphical representation of frame transformation ${?}^A{T}_B$ of frame B relative to frame A $.$

$(3$ points$)$

Given frame transformation ${?}^A{T}_B,$ provide the graphical representation of the inverse of

frame transformation i$.$e$.($:${(}_A^A{T}_B{)}^{-1}$