Consider the RP planar manipulator shown below. Angle OAE is a right angle. The revolute

joint rotates about origin O $.$ The length of the first linkage is a constant parameter $OA=a_1.$

The length of the second linkage is a variable $AE=d_2.$

a$.(20$ points$)$ Obtain the forward kinematic equations relating the end$-$effecter position $x_E,$

$y_E$ and orientation ${}_E$ to the joint displacements ${}_1$ and $d_2.$

b$.(20$ points$)$ Given the end effector position $(x_E,y_E),$ derive the inverse kinematics. Your

answer should define $({}_1,d_2)$ as functions of the $(x_E,y_E)$ position.