Kinematic singularities

Kinematic singularities are specific axis positions of a kinematic.

In singular positions, the kinematic is unable to execute movements in certain Cartesian directions or rotations about specific spatial axes. A simple example is a fully extended robot arm which cannot move any further outwards (outside the work space).

Singularities have no impact on purely axis movements (e.g. with #PTP).

Singularities become critical if movements are executed in the vicinity of the programming coordinate system (PCS). Extremely fast axis movements may occur in these zones despite slow TCP movements.

However, since axis dynamics are limited, the TCP path velocity can be greatly reduced in the vicinity of a singularity.

It should be noted that these effects are a direct result of the physical kinematics. The controller can only minimise these effects or use alternative strategies, but they are not completely avoidable.

Robot singularities

See Singularities with a six-axis articulated robot kinematic

Singularity with complete five-axis kinematics

In complete kinematics, the tool orientation is mapped in angular notation in a tool direction vector which is then used to map the ACS axis angle. This is dependent on P-CHAN-00247.

On the other hand, with RTCP kinematics, the tool orientation is derived directly from the programmed ACS machine angles.

With complete kinematics, the controller can no longer map the unambiguous position of the tool direction vector to an unambiguous position of the ACS orientation axes. With a complete five-axis kinematic, there are either two or an infinite number of possible ACS angle pairs for a given tool direction vector. The latter is referred to as the kinematic singularity of the structure.

In standard CA kinematics, the singular tool direction vector is ori = (0.0, 0.0, 1.0) and the corresponding ACS angular position is A_ACS=0. The C_ACS angle can assume any value in the motion range of this axis without any change in tool orientation.

The singularity at A_ACS=0 separates the two ACS angle solutions discussed above. With a CA head, for example, these angles are at orientation vector ori = (0.0, -0.7071, 0.7071)

1. C_ACS=0, A_ACS=45
2. or C_ACS=180 A_ACS=-45.

When moving out of the singularity, the controller selects the angular solution using the shortest path strategy.

Enormous dynamic stresses can occur depending on the change in orientation in the vicinity of this singular axis position. This can lead to high axis speeds of rotary axes, although the TCP path velocity (relative velocity of the TCP between tool and workpiece) is relatively low at these positions.

For certain technologies, such as laser cutting, a sufficient distance to the critical area of the singularity of this structure can be achieved with alternative tool head structures.
For example, an AB tool head that has the singularity at tool direction vector ori = (0.0, 1.0, 0.0) and ori = (0.0, -1.0, 0.0). The critical range can be avoided by using the technically required restriction of the chamfer angle of the rotary axes, e.g. B_ACS=+-50°.

Optimum velocity curves are obtained for positioning movements in the singularity range using special CNC functions (e.g. #PTP).