Coordinate systems

After the homing, the controller is at the machine zero point or in the machine coordinate system. If this is followed by inputs from the NC program (e.g. X100), the programmed coordinates (Index p) then coincide with the absolute coordinates (Index a):

 

xa = xp

ya = yp

 

Offsets occur due to the definition of workpiece coordinate systems. The spatial positions in the workpiece coordinate system differ from the coordinate systems that are defined by the physical machine axes. Here a distinction must be made between programmed, constant, translatory offsets in a single axis and dynamic offsets that result from kinematic (e.g. cylindrical ⇔ Cartesian) or geometric transformations (e.g. tool radius compensation, mirroring), which in general affect several axes.

For example, the zero point can be offset from machine zero point M to a freely selectable workpiece zero point W or a workpiece coordinate system by a zero offset (NPV-G54…G59). The absolute coordinates result from adding zero offsets (NPV) and programmed coordinates:

 

xa = xNPV + xp

ya = yNPV + yp

 

Irrespective of these NPVs specified by the zero offset data block, additional offset types can be explicitly programmed in the subroutine by using e.g. G92 X... Y ... Z ...

This reference point offset (BPV) is added to the preceding NPV. The absolute coordinates can then be determined as follows:

 

xa = xNPV + xBPV + xp

ya = yNPV + yBPV + yp

 

Defining a workpiece coordinate system using NPV and BPV (for legend, see below)
Defining a workpiece coordinate system using NPV and BPV (for legend, see below)

xa, ya

Absolute coordinates

xp, yp

Programmed coordinates

xNPV, yNPV

Zero offset

xBPV, yBPV

Reference point offset

M:

Machine zero point

W:

Workpiece zero point

B:

Reference point for coordinates

P:

Position

The coordinate display on the user interface shows active offsets by the remaining difference between the coordinates of physical machine axes (ACS) and workpiece coordinates (PCS). However, some offsets also result from manipulating machine and workpiece coordinates (e.g. tool radius compensation, mirroring) and therefore do not result in a coordinate difference.

The tables below provide an overview of the additional offset types in anticipation of the sections further below. The following conditions for the parameters are active:

activation and deactivation means the time when the offset is visible on the user interface because of coordinate differences or coordinate changes. However in general, an offset only becomes physically active at the earliest with the first motion that follows any activation or deactivation. For example, deactivation at program end leads to a compensating motion in the first motion of the following program.

Programmable offsets (linear, constant)

No.

Description

Definition

ACS PCS
Difference
if
active

activation

deactivation

Temporary
suppression

1

Reference point offset

NC program

Yes

NC block
G92 X.. Y..
G90/91 Consider
dependency

NC block “G92 X0 Y0“ or
NC program start

"#SUPPRESS
OFFSETS"

"#MCS ON"

2

Zero offset

List
NC prg.

Yes

NC block “G54...G59

NC block “G53“
or
NC program start

“#SUPPRESS
OFFSETS“

"#MCS ON"

3

Clamp position offset

List

Yes

Program paths
Not changeable
during program

NC program start
Not changeable during program

„#SUPPRESS
OFFSETS“

"#MCS ON"

4

Tool
offset

List
NC prg.
External

Yes

NC block “D..“

NC block “D0“
or
NC program start

“#SUPPRESS
OFFSETS“

"#MCS ON"

5

Position preset

NC program

Yes

NC block "#PSET.."

NC block
”#PRESET...“
or
program start

“#SUPPRESS
OFFSETS“

"#MCS ON"

6

CS
offset

NC program

Yes

NC block
#CS ON[vx,vy,vz,.."

NC block “#CS OFF“
or
NC program end

"#MCS ON"

7

ACS offset

NC program

Yes

NC block
#ACS ON[vx,vy,vz,..

NC block
”#ACS OFF“
or
NC program end

"#MCS ON"

Offsets caused by geometric transformation (linear, dynamic):

No.

Description

Definition

ACS PCS
Difference
if
active

activation

deactivation

Temporary
suppression

8

CS

NC program

Yes

NC block
”#CS ON[..,..,..]“

NC block “#CS OFF“
or
NC program end

"#MCS ON"

9

ACS

NC program

Yes

NC block
”#ACS ON[..,..,..]“

NC block “#ACS OFF“
or
NC program end

"#MCS ON"

10

Contour rotation

NC program

No

NC block
”#ROTATION
ON[ANGLE..]”

NC block
”#ROTATION OFF”

"#MCS ON"

11

Mirroring

NC program

No

NC motion block
after G21/22/23

NC motion block
after G20

Not
suppressible

12

Tool radius compensation

NC program

No

NC block G41/42

NC block G40

Not
suppressible

13

Kinematic
transformation

NC program

No

NC block
”#TRAFO ON
Automatic
program start

NC block
”# TRAFO OFF

"#MCS ON"

Offsets caused by special functions:

No.

Description

Definition

ACS PCS
Difference
if
active

activation

deactivation

Temporary
suppression

14

Offset
due to
manual operation
with
parallel interpolation

Handwheel
NC prg.

Yes

NC block "G201"

NC block "G202"

Not
suppressible

15

Offset
due to
measurement run

NC program

Yes

NC block "G101"

NC block "G102"

"#SUPPRESS OFFSETS"

"#MCS ON"

16

Offset
after
ho-
ming

NC program

No

NC block
“G74 X.. Y.. Z.. “

Not possible

Not
suppressible

The NC command #SUPPRESS OFFSETS only acts within an NC block

The NC command #MCS ON deactivates any offsets until command #MCS OFF is programmed.

Within every (A)CS the offset types 1, 2 and 5 are stored "locally”.

Overview of additional offsets and coordinate systems
Overview of additional offsets and coordinate systems