Inverse Kinematics

$14.$ 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.

$15.$ Repeat Problem $3-14$ for the three$-$link planar arm with prismatic joint of Figure $3\mathrm{.}36.$

$16.$ Solve the inverse position kinematics for the cylindrical manipulator of Figure $3\mathrm{.}37.$

$17.$ Solve the inverse position kinematics for the cartesian manipulator of Figure $3\mathrm{.}38.$

Fig. $3\mathrm{.}35$ Three$-$link planar robot with revolute joints.

Fig. $3\mathrm{.}36$ Three$-$link planar robot with prismatic joint