Figure Q$1$a shows a robotic system with $3$ elements A$,$ B$,$ C$,$ and withthe end effector $($G$)$ attached to member C and situated in its $$home$$position of $[0,0,0].($The coordinate system is as shown with the x$-$axisemerging from the paper.$)$Elements B and C may be rotated through angles $\backslash$theta AB and $\backslash$theta BCrespectively whilst A may rotate about its own axis as shown. Thejoints between elements are referred to as JAB and JBC$.$The lengths of elements A$,$ B$,$ C are $0\mathrm{.}35$m$,0\mathrm{.}4$m and $0\mathrm{.}25$mrespectively.$($i$)$ Find the coordinates of the home position with the origin shiftedto JAB.Calculate the final position of the end effector in terms of an origin atJAB after the following movements.$($ii$)$ Element B is rotated counter$-$clockwise through $30$O$,$ withelement C then rotated correspondingly back into a verticalalignment. Find the new position of the gripper again withrespect to JAB.$($iii$)$ Finally the entire assembly is rotated $90$Oabout element A intothe paper. What is the final position with respect to the homeposition.