Restrictions For Kinematics And Interpolation; Singularities Of Orientation - Siemens SINUMERIK 840D sl Function Manual

F2: Multi-axis transformations

1.8 Restrictions for kinematics and interpolation

1.8 Restrictions for kinematics and interpolation
For systems where there are less than six axes available for transformation, the following
restrictions must be taken into account.
5-axis kinematics
For 5-axis kinematics there are two degrees of freedom for orientation. The assignment of
orientation axes and tool vector direction must be selected so that there is no rotation around
the tool vector. As a result, only two orientation angles are required to describe the
orientation. If the axis is traversed using ORIVECT, the tool vector performs pure swiveling
motion.
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 Chapter "Polynomial interpolation of
orientation vectors [Page 109]".
1.8.1

Singularities of orientation

Description of problem
As described in Chapter "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.
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Function Manual, 09/2011, 6FC5397-2BP40-2BA0
Special Functions