Transformations

Speaking of GST-Transformations we refer e.g. to rotations or to zero-point-shifts.

The relation between the MCS (machine coordinate system) and the PCS (program coordinate system) is defined by the effective transformation T. T is the concatenation of the transformations T_Z, T_U and T_T (T = T_Z * T_U * T_T). Note that the order of concatenation is significant for the transformations do not commute in general. The transformation T_Z represents a (historical) zero offset shift, the transformation T_U represents a user defined transformation and the transformation T_T represents a tool transformation. They are described in detail later.

Figure “TransformationsTzTuTt” visualizes the relation between the MCS (machine coordinate system) and the PCS (program coordinate system):

T_Z is defined to be a translation by [20,20,0],
T_U is a combination of the translation [30,-10,0], followed by a rotation by 45 degree around the Z-axis,
T_T is a translation by [0,-10,0].

Figure “TransformationsTzTuTt”.

Further Information