What is a kinematic singularity, and how does it affect motion and control?

• A. A singularity occurs when the Jacobian loses rank, causing infinite joint velocity for finite end-effector velocity; movement can become difficult or control unstable.
• B. A singularity occurs when the robot reaches joint limits; there is no effect on velocity.
• C. Singularities increase the speed when moving near joints.
• D. It is when the end-effector exactly follows a straight line.

Answer: (D)

A kinematic singularity occurs when the manipulator’s Jacobian loses rank, so the map from joint velocities to end-effector velocities becomes ill-conditioned. At that configuration, moving the end-effector in some directions would require extremely large joint motions (in theory, infinite for a finite end-effector velocity), and in practice the controller becomes very sensitive or unstable. This reduces dexterity: some directions of motion become hard or impossible to achieve with reasonable joint speeds, and small disturbances can cause large, uncontrolled responses. That’s why planners and controllers try to avoid or slow down near singularities, or reconfigure the task to steer clear of them.

The other statements don’t capture what a singularity is. Reaching joint limits is a mechanical constraint, not the Jacobian-based loss of controllability. A general claim that singularities increase speed near joints isn’t accurate—the issue is poor or infinite joint-speed requirements in certain directions, not a universal speed boost. And a straight-line end-effector path by itself isn’t a definition of a singularity.