Problem $1.$ The following figure shows a $3-$DOF robotic arm. Given the dimensional

values, $a,b,c,$ and position of point $P,$ find the angle of all three motors for the case that

gripper head $($link with the length of $c)$ is along negative $x$ direction. $(30$ points$)$

$a=6in$

$b=8in$

$c=4in$

$P_x=-3in$

$P_y=9\mathrm{.}5in$

Rubric: $$

graphic model $(10$ points$)$

math model $(10$ points$)$

two possible solutions $(10)$