What are the singularities of a typical collaborative robot (cobot)

They might be collaborative and easy to use, but the robot arms manufactured by Universal Robots (all 37,000 of them) have singularities like any other 6R manipulator. However, because of the particular geometric design of the UR3, UR5 and UR10 cobots, their singularities are quite different from the singularities of so-called PUMA-style manipulators.

Most 6-axis industrial robots are of PUMA-style, meaning that the axes of joints 2 and 3 are orthogonal to the axes of joints 1 and 4, the axis of joint 5 is orthogonal to the axes of joints 4 and 6, and the axes of the last three joints are concurrent. The three types of singularities of PUMA-style robot arms are illustrated in this tutorial: https://mecademic.com/resources/Singularities/Robot-singularities

A UR robot has slightly different singularities. The most troublesome of them is the wrist singularity. It happens when the axes of joints 4 and 6 are parallel, i.e., when θ5° = 0, θ5 = ±180°, or θ5 = ±360°. Of course, problems occur even when these two axes are close to parallel, as you can see in the video, but when the axes are parallel, the robot can move indefinitely without displacing its end-effector.

The second type of singularity present in UR robots is the shoulder singularity. It occurs when the intersection point of the axes of joints 5 and 6 lie in one plane with the axes of joints 1 and 2. This singularity is relatively easy to prevent. It must, however, be considered in every risk assessment for a cobot installation, due to the sudden rapid motion produced by joint 1, when passing close to a shoulder singularity.

The last type of singularity present in UR robots is the elbow singularity. This singularity is quite obvious and occurs when the arm is fully stretched. (Theoretically, this singularity can also occur when the arm is fully folded, but even though joint 3 can rotate ±360°, the robot links collide each other well before reaching the fully folded configuration.) More precisely, the elbow singularity occurs when the axes of joints 2, 3 and 4 are coplanar, i.e., when θ3 = 0°. This singularity is by far the least problematic one, unless of course it makes you realize that your robot is not long enough...

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