Problem $2[10+10$ Points$]$

Attach a spherical wrist to the three$-$link articulated manipulator as shown in Figure $2.$

$($a$)$ Derive the complete set of forward kinematic equations, by establishing appropriate DH

coordinate frames, constructing a table of link parameters, forming the A$-$matrices, etc.

$($b$)$ Write $T_0^6$ for the manipulator.

Figure $2$: Elbow Manipulator with spherical wrist