Siemens SINUMERIK 840D sl Programming Manual page 308

Transformations
6.2 Three, four and five axis transformation (TRAORI)
In the examples shown here, you can see the arrangements as illustrated by the CA
machine kinematics with the Cardanic tool head!
Machine manufacturer
The axis sequence of the orientation axes and the orientation direction of the tool can be set
up using the machine data as appropriate for the machine kinematics.
In this example, A' lies below the angle φ to the X axis.
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Programming Manual, 03/2013, 6FC5398-2BP40-3BA1
Job Planning