Figure $1($the next page$)$ shows a robot manipulator whose structure and geometry are supposed to be known.

$1.$ Set up $($with a proper explanation$)$ a coordinate system for each body of the manipulator based on the D$-$H notation $($do the work on the figure directly$).[20]$

$2.$ Fill in the first row $(\backslash (\backslash$mathrm$\{$i$\}=1\backslash ))$ in the following table. $[15]$

$3.$ Write out the transformation matrix $\backslash (\{\}\_\{1\}^\{0\}$ T $\backslash ).[10]$

$4.$ Write out the origin of the frame $1$ with respect to the frame $0.[15]$

The general transformation matrix is given below:

Figure $1$