$3-23.$ Consider a two$-$link planar robot, with

positive orientations of ${}_1$ and ${}_2$ as

shown in Fig. P$3\mathrm{.}23.$Figure P$3\mathrm{.}23$ A two$-$link planar robot for

problem P$3-23.$

$($a$)$ Suppose $,{}_1=-\frac{5}{9}$rad,${}_2=$

$-\frac{13}{18}$rad,$l_1=5m,$ and $l_2=7m.$

Sketch the orientation of the robot

in the $x-y$ plane, and determine the

$x-y$ coordinates of point $P.$

$($b$)$ Suppose now that the same robot

is located in the second quadrant

and is oriented in the "elbow$-$down"

position as shown in Fig. P$3\mathrm{.}23.$

If the tip of the robot is located

at the point $P(x,y)=(-9,1),$ deter$-$

mine the values of ${}_1$ and ${}_2$