Frames describing the base of a robot and an object are given relative to the Universe frame.
- Find a transformation ${ }^R T_H$ of the robot configuration if the hand of the robot is to be placed on the object.
- By inspection, show whether this robot can be a 3-axis spherical robot, and if so, find $\alpha, \beta, r$.
- Assuming that the robot is a six-axis robot with Cartesian and Euler coordinates, find $p_x$, $p_y, p_z, \phi, \theta, \psi$.
$$
{ }^U T_{a b j}=\left[\begin{array}{cccc}
1 & 0 & 0 & 2 \\
0 & 0 & -1 & 3 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1
\end{array}\right] \quad{ }^U T_R=\left[\begin{array}{cccc}
0 & -1 & 0 & -2 \\
1 & 0 & 0 & 5 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{array}\right]
$$