Inverse Kinematics

Q$1.$ Given a desired position of the end$-$effector, how many solutions are there to the inverse kinematics of the three$-$link planar arm shown in Figure $3\mathrm{.}35?$ If the orientation of the end$-$effector is also specified, how many solutions are there?

Use the geometric approach to find them.

Q$2.$ Repeat ProbleM in quistion $1$ for the three$-$link planar arm with prismatic joint of Figure $3\mathrm{.}36.$

Q$3.$ Solve the inverse position kinematics for the cylindrical manipulator of Figure $3\mathrm{.}37.$

Q$4.$ Solve the inverse position kinematics for the cartesian manipulator of Figure $3\mathrm{.}38.$