Singular Configuration (Kinematic Singularity)

An arm posture where the Jacobian matrix loses rank, so the end effector can't move in certain directions.

A singular configuration is a special class of arm posture. The Jacobian matrix — which converts joint velocities into end-effector velocity — has full rank across most postures, but at a singular configuration it loses rank, and the end effector becomes unable to move in some direction no matter how the joints turn. Two common types: a boundary singularity happens when the arm is fully extended, with the end effector at the very edge of the workspace; a wrist singularity happens on a 6-axis arm when the two wrist joint axes line up, effectively losing one degree of freedom. Near a singularity, moving the end effector a short distance in a straight line can demand extremely fast rotation from some joints, and numerical inverse-kinematics solutions also tend to become unstable there. This is why trajectory planning tries to avoid singularities, why numerical IK commonly uses damped least squares to keep joint speeds from exploding, and why manipulability is used to measure how far a posture is from becoming singular.

ExampleWhen a planar two-link arm is fully extended, the end effector can only move perpendicular to the arm — no combination of joint speeds produces any velocity continuing straight outward along the arm's own direction. In that posture, an external force pulling along the arm's direction is carried directly by the structure, with no torque needed from the joints.

Also called

Kinematic Singularity, Singularity, Wrist Singularity, Boundary Singularity

Related

Jacobian Matrix · Manipulability · Damped Least Squares · Jacobian Pseudoinverse · Spherical Wrist · Workspace

Sources

Modern Robotics 5.3: Singularities (Northwestern)
Modern Robotics 6.2: Numerical Inverse Kinematics (Part 1 of 2)