A kinematic singularity is a robot configuration in which the Jacobian matrix loses rank, causing the manipulator to lose one or more degrees of freedom in Cartesian space. At a singularity, certain end-effector motions become unachievable regardless of joint velocity magnitudes, and inverse kinematics solutions either vanish or require unbounded joint speeds. Singularity avoidance and singularity-robust inverse kinematics (via damped least-squares) are critical for safe, continuous robot motion, particularly near workspace boundaries and for wrist configurations of six-axis arms.