$=(10,5),$ determme

${}_2.$ Assume $l_1=6in.$ and $l_2=8in.$

$3-21.$ Consider a two$-$link planar robot, with

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

shown in Fig. P$3\mathrm{.}18.$

$($a$)$ Suppose ${}_1=-30,{}_2=120,l_1=$

$5$ in $.,$ and $l_2=3in.$ Sketch the orien$-$

tation 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 fourth quadrant and

is oriented in the "elbow$-$up$"$ posi$-$

tion $($i$.$e$.,$ with a positive value of ${}_2).$

If the tip of the robot is located

point at $P(x,y)=(6,-4),$ determine

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