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: 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 o