$(16$ Points$)$ A FANUC robot is required to perform operations at point $1$ through point $51$ that have equal intervals on the part surface as shomn in the Figure below.

Please answer the following questions that relate to the development of a FANUC robot TP program for this robot task

$(1)2$ points$)$ Describe how to set up an accurate user frame UF$[1]$ on the part surface as shown in the Figure above?

$(2)(2$ points$)$ Describe how to teach and record robot point $P[1]$ at point $1$ that is defined as the frame transformation of user tool frame UT$[2]$ relative to user frame UF$[1]?$

$(3)(2$ points$)$ Given that point $!$ through point $51$ have equal intervals on the part surface as shown in the Figure above. Find offset values of $x$ in $x-$axis and $y$ in $y-$axis of user frame UF$[1]$ between two consecutive points.

$(4)(10$ points$)$ Develop a FANUC robot TP program through using "OFFSET, PR$[$j$]"$ motion option in motion instructions so that the robot is able to move the robot's tool from only taught point $P[1]$ at point $1$ to each of other untaught points $($i$.$e$.$ point $2$ through point $51)$ sequestially.

Explain the function of each instruction of your robot program