Fundamentals of coordinate definitions

You program a workpiece by defining the path contours and the target coordinates.

Depending on the dimensioning used in the technical drawing, you use Cartesian or polar coordinates with absolute or incremental values.

Cartesian coordinates

Application

A Cartesian coordinate system consists of two or three axes that are all mutually perpendicular. Cartesian coordinates are relative to the datum (origin) of the coordinate system, which is at the intersection of the axes.

With Cartesian coordinates you can uniquely specify a point in space by defining the three axis values.

Description of function

In the NC program you define the values in the linear axes X, Y, and Z, such as with a straight line L.

11 L X+60 Y+50 Z+20 RL F200

The programmed coordinates are modally effective. As long as the value of an axis remains the same, you do not need to program the value for further path contours.

Polar coordinates

Application

You define polar coordinates in one of the three planes of a Cartesian coordinate system.

Polar coordinates are relative to a previously defined pole. From this pole you define a point by its distance to the pole and the angle to the angle reference axis.

Description of function

Polar coordinates can be used in, for example, the following situations:

  • Points on circular paths
  • Workpiece drawings with angular information, such as bolt hole circles

You define the pole CC with Cartesian coordinates in two axes. These axes specify the plane and the angle reference axis.

The pole is modally effective within an NC program.

The angle reference axis is related to the plane as follows:

Plane

Angle reference axis

XY

+X

YZ

+Y

ZX

+Z

11 CC X+30 Y+10

The polar coordinate radius PR is relative to the pole. PR defines the distance of this point from the pole.

The polar coordinate angle PA defines the angle between the angle reference axis and this point.

11 LP PR+30 PA+10 RR F300

The programmed coordinates are modally effective. As long as the value of an axis remains the same, you do not need to program the value for further path contours.

Absolute input

Application

Absolute input always references an origin. For Cartesian coordinates, the origin is the datum, and for polar coordinates the origin is the pole and the angle reference axis.

Description of function

Absolute values define the target point for positioning.

11 L X+10 Y+10 RL F200 M3

; Position at point 1

12 L X+30 Y+20

; Position at point 2

13 L X+50 Y+30

; Position at point 3

11 CC X+45 Y+25

; Define the pole with two axes using Cartesian coordinates

12 LP PR+30 PA+0 RR F300 M3

; Position at point 1

13 LP PA+60

; Position at point 2

14 LP PA+120

; Position at point 3

15 LP PA+180

; Position at point 4

Incremental entries

Application

Incremental entries are always referenced to the previously programmed coordinates. For Cartesian coordinates those are the values in the axes X, Y, and Z, and for polar coordinates the value of the polar coordinate radius PR and the polar coordinate angle PA.

Description of function

Incremental entries define the value by which the control positions. The previously programmed coordinates serve as the respective datum of the coordinate system.

You define incremental coordinates with an I before each axis designation.

11 L X+10 Y+10 RL F200 M3

; Position to point 1 absolutely

12 L IX+20 IY+10

; Position to point 2 incrementally

13 L IX+20 IY+10

; Position to point 3 incrementally

11 CC X+45 Y+25

; Define the pole absolutely in two axes with Cartesian coordinates

12 LP PR+30 PA+0 RR F300 M3

; Position to point 1 absolutely

13 LP IPA+60

; Position to point 2 incrementally

14 LP IPA+60

; Position to point 3 incrementally

15 LP IPA+60

; Position to point 4 incrementally