Vertically-articulated six-axis serial robots exhibit three types of singularities: wrist singularities, shoulder singularities, and elbow singularities. A wrist singularity occurs when axes 4 and 6 are coincident. A shoulder singularity occurs when the wrist center lies on a cylinder centered about axis 1 and with a radius equal to the distance between axes 1 and 4. Finally, an elbow singularity occurs when the wrist center lies in the same plane as axes 2 and 3.
When a robot is controlled in Cartesian mode and passes near a singularity, the speed of some joints becomes suddenly very large and the Cartesian velocity of the end-effector is significantly reduced. For this reason, trajectories that make the robot pass near singular configurations should be avoided.
The following video illustrates the three types of singularities:
An excellent reference on this topic is the following tutorial: What are singularities in a six-axis robot arm?
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