A robot position is considered to be a singularity position when no unique value can be obtained by inverse transformation even for a given state and step sequence. Or when the smallest Cartesian change of the robot can also lead to a very large axis angle change, it is also called a robot singularity position. Singularities are not mechanical properties, but mathematical properties. For this reason, singularities only exist within the range of trajectory movement and not during axis movement. KUKA robots with 6 degrees of freedom have 3 different singularity positions: overhead singularity α1, extended position singularity α2, and hand axis singularity α3.
The singularity positions of a KUKA robot refer to specific configurations where the robot’s motion capabilities are restricted. At these points, the robot’s joints reach extreme angles or align in a way that causes a loss of degrees of freedom. This can lead to erratic behavior or difficulty in performing certain tasks. Understanding and avoiding these singularity positions is crucial for smooth and accurate robot operation.
1 Overhead singularity α1
Definition: For an overhead singularity, the wrist point (i.e. the intersection of axes A4, A5, A6) is perpendicular to the robot axis A1. In this case, the position of axis A1 cannot be determined unambiguously by inverse transformation and can be assigned any value.
System response: When the target point of a PTP motion statement is at an overhead singularity, the robot control system can react via the system variable $SING UL_POS[1]. The specific manifestation is that the angle of axis A1 is determined to be 0° (default setting) or the angle of axis A1 remains unchanged from the start point to the target point.
Impact: Overhead singularities may cause instability or loss of accuracy when the robot approaches or passes through this point.
2 Extended position singularity α2
Definition: For an extended position singularity, the wrist point is exactly on the extension of axes A2 and A3. At this time, the robot is at the edge of the working range. The inverse transformation can be used to obtain a unique axis angle, but a small Cartesian speed change will result in a large axis speed for axes A2 and A3.
System response: When the target point of a PTP motion statement is located on an extended position singularity, the robot control system can react via the system variable $SING UL_POS[2]. The specific manifestation is that the angle of axis A2 is determined to be 0° (default setting) or the angle of axis A2 remains unchanged from the start point to the target point.
Impact: Extended position singularities affect the smoothness of the movement because a small TCP speed change will result in a large axis speed change.
3 Hand axis singularity α3
Definition: For the hand axis singularity, axis A4 and axis A6 are parallel to each other and axis A5 is within ±0.01812°. At this point, the positions of the two axes cannot be clearly determined by the inverse transformation, because axis A4 is parallel to axis A6 and can have any number of possibilities, but the sum of their axis angles is the same.
System response: When the target point of the PTP motion statement is located on the hand axis singularity, the robot control system can react through the system variable $SING UL_POS[3]. Specifically, the angle of axis A4 is determined to be 0° (default setting) or the angle of axis A4 remains unchanged from the starting point to the target point.
Impact: The hand axis singularity is the most common situation in field commissioning, which requires the operator to have more precise adjustment capabilities for the robot control.
In general, the three singularity positions of KUKA robots each have their own specific definitions, system responses and operational impacts. Understanding the characteristics of these singularities is essential for effectively programming and operating KUKA robots to ensure that the robots can perform tasks safely and efficiently.