Singularities Of Orientation - Siemens SINUMERIK 840D sl Function Manual

3-and 4-axis kinematics
For 3- and 4-axis kinematics, only one degree of freedom is available for orientation. The
respective transformation determines the relevant orientation angle. In this case, it only makes
sense to traverse the orientation axis using ORIAXES. In this case, the orientation axis is
directly and linearly interpolated.
Interpolation of the tool orientation over several blocks by means of orientation vectors
If the orientation of a tool is programmed over several consecutive part program blocks by
directly entering the appropriate rotary axis positions, then undesirable discontinuous changes
of the orientation vector are obtained at the block transitions. This results in discontinuous
velocity and acceleration changes of the rotary axes. This means that no continuous velocity
and acceleration of the orientation axes over several blocks can be achieved using large circle
interpolation.
Continuous block transitions
As long as only linear blocks (G1) are programmed, then the orientation axes also behave just
like linear axes. In this case, motion with continuous acceleration is achieved through
polynomial interpolation. Significantly better results can be achieved by programming the
orientation in space using orientation vectors (see Section "Polynomial interpolation of
orientation vectors (Page 110)").
2.8.1

Singularities of orientation

Description of problem
As described in Section "Singularities and how to treat them", singularities (poles) are
constellations in which the tool is orientated becomes parallel to the first rotary axis. If the
orientation is changed when the tool is in or close to a singularity (as is the case with large-
circle interpolation ORIWKS ), the rotary axis positions must change by large amounts to
achieve small changes in orientation. In extreme cases, a jump in the rotary axis position would
be needed.
Such a situation would be treated as follows:
There is only one relevant machine data, which circles the pole as usual:
MD24540 $MC_TRAFO5_POLE_LIMIT_1 (closing angle tolerance for interpolation by pole for
5-axis transformation)
or
MD24640 $MC_TRAFO5_POLE_LIMIT_2 (closing angle tolerance for interpolation by pole for
5-xis transformation)
For further information about the handling of singular positions, see:
References:
Programming Manual, Job Planning, Transformations; Section: Cartesian PTP travel
Special functions
Function Manual, 01/2015, 6FC5397-2BP40-5BA2
F2: Multi-axis transformations
2.8 Restrictions for kinematics and interpolation
83