Which of the following defines a kinematic singularity in a robotic arm?

• A. A configuration where the end effector cannot be reached.
• B. The manipulator's joints all reach maximum speed.
• C. A pose where the end effector has infinite reach.
• D. A configuration where the Jacobian loses rank.

Answer: (D)

Kinematic singularities arise when the Jacobian that maps joint velocities to end-effector velocities loses rank. In that configuration, the rows (or columns) become dependent, so the manipulator can no longer move in certain Cartesian directions even though the joints can still rotate. This makes the motion locally ill-conditioned: small joint motions can cause large or unpredictable end-effector moves, and some end-effector velocities become unattainable.

That’s why the correct description is a configuration where the Jacobian loses rank. The other ideas describe things like simply not reaching a pose, exceeding joint speed limits, or an unphysical infinite reach, none of which capture the geometric/kinematic constraint signaled by a rank-deficient Jacobian.