The arm with $3$ DoF shown below has joints $1$ and $2$ perpendicular and joints $2$ and $3$ parallel, and all joints are at their zero location. Note that the positive sense of the joint angle is indicated. The link frames $\{0\}$ through $\{3\}$ for the arm is assigned as below.

Find the DH$-$parameters for it by filling in the table. $(8$ Points$)$

Show the solution steps in details. $(4$ Points$)$