Kinematic Transformations 1 – front-face and peripheral surface transformation

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Sounds theoretical, but it is practical

It sounds very theoretical, but it has a daily practical use on the machine tool: Thanks to kinematic transformations, complex, non-rectangular machine coordinate systems are programmed, as usual, in a rectangular workpiece coordinate system. In other words: No matter how the machine realizes the machining, it is always possible to work with the workpiece coordinates from the drawing.

Kinematic transformations are thus important helpers in the background. This series of articles provides background knowledge on these powerful CNC functions and shows use cases you probably have not thought of yet.

Kinematic transformations for multitasking in milling and turning centers

Turning machining centers have long offered drilling and milling operations with driven tools. Modern milling machining centers, on the other hand, now also enable sophisticated turning operations. Such "multitasking" of turning and milling on one machine offers tangible advantages: The component spectrum of the machine is expanded and the elimination of reclamping operations significantly improves component accuracy.


Multitasking such as mill-turn and turn-mill are largely based on kinematic transformations. This series of articles introduces the important transformations for these two general-purpose technologies. This article is about the front-face and peripheral surface transformations.

Front-face Transformation


This kinematic transformation is used for machining with driven tools on turning centers that are not equipped with a real Y axis. Tool paths on the front-face of the turning workpieces are programmed in the G17 plane, i.e. in a rectangular workpiece coordinate system, as if there were a real Y axis. For SINUMERIK CNCs, the required kinematic transformation is activated with the CNC language command TRANSMIT.

The video shows how TRANSMIT converts the tool paths from the XY plane into a coordinated movement of the X axis and the C axis - i.e. the main spindle in position control.

Physical Limitation

However, a physical limitation of this transformation must be considered: If the tool path defined in the XY plane passes through the center of rotation of the component, the C axis would have to rotate infinitely fast in this pole position - and reverse at the same time. The speed of the main spindle is limited by the electrical energy required for this. However, by limiting the speed, the path feed rate also decreases, and the cutting conditions are therefore no longer optimal.

So if the focus of production is on components with machining near the rotation axis of the main spindle, it makes sense to invest in a machine with a real Y axis. But TRANSMIT is also used with such machines - namely when the Y axis does not cover the full diameter of a workpiece. In this case, a mixed operation with and without front-face transformation TRANSMIT exists.

Peripheral Surface Transformation


This transformation is used for machining on the peripheral surface of rotationally symmetrical workpieces. The tool paths are programmed in a rectangular workpiece coordinate system as if the cylindrical surface were flat, i.e. "unwound". If it is a turning machine, this is the G19 plane.

The CNC language command TRACYL activates the kinematic transformation. The video shows how the paths programmed in the ZY plane are now converted into a movement of the Z axis and the C axis (main spindle in position control).

TRACYL with curved pocket bottom

In drilling operations on the peripheral surface, the geometry of the machining operation is imprinted by the contour of the tool: A cylindrical drill produces a cylindrical borehole (with "parallel walls") whose bottom is imprinted by the contour of the drill cutting edge.


Milling on peripheral surfaces is different: If no Y-axis is in use, the cutter is always radially oriented. A flat-bottomed pocket programmed in the G19 plane has a curved bottom after milling on the peripheral surface - which means that the shoulders of the pocket are not parallel in the direction of unwinding.

A typical application for such pocket shapes is the production of the rollers for blister packaging machines, for example for medical tablets. Rolls milled in this way with TRACYL are also used in the production of hygiene articles.

Cylinder Transformation for Parallel Wall Grooves

TRACYL is also used when highly precise grooves are milled on peripheral surfaces - exactly when the cutter radius compensation is required to achieve the tolerance.


This type of TRACYL requires a real Y axis in the machine: as soon as the slot geometry has a portion along the axis of rotation of the workpiece, this third axis is required. Only if the grooves are purely radial does the third geometry axis (Y axis) not come into play.

The slot must be described forwards and backwards in one contour so that the tool path reverses at the end of the slot and the radius compensation becomes effective on both slot walls. The diameter of the cutter should be at least 90% of the slot, to avoid geometric distortions.


One application of this transformation is the manufacture of guide rollers for ultra-fast packaging machines. The speed profile of these machines is imprinted by grooves on the surface of rotating rollers. Minimum tolerances apply to these grooves - which can only be achieved by cutter radius correction.

TRACYL also on milling machines!

Rotationally symmetrical components are not just the domain of lathes. If the milling machine is equipped with a dividing head, for example with an A axis, TRACYL can be used there. The kinematics of 5-axis milling machining centers are in principle usable for the peripheral surface transformation.

ShopTurn and ShopMill: kinematic transformations in the background

The graphical work step programming ShopTurn and ShopMill also offers the front-face and peripheral surface transformation. What can be easily and quickly parameterized there via masks, also uses the CNC language commands TRANSMIT and TRACYL in the background to enable the kinematic transformations of the CNC.


In the next article, we will address the topic of 5-axis transformations with statically oriented tools.


Something to look forward to!

Author: Andreas Grözinger

(from CNC4you magazine 2022-2)

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