A programmer says: put the gripper 40 cm in front of the base, 10 cm up, pointing down. The controller must find a set of shoulder, elbow and wrist angles that produce exactly that pose. That calculation is inverse kinematics, or IK.
Forward kinematics is easy and has one answer. IK is harder: there may be several valid solutions (elbow up or elbow down), none at all if the point is out of reach, or infinitely many on a redundant seven-joint arm. Near singularities, poses where two axes line up, a small tool movement demands a huge joint speed, and the robot slows down or faults.
Every teach pendant jog in Cartesian mode and every motion command in a pick-and-place program runs IK, usually hundreds or thousands of times per second.
