12 I Operating Instructions
I – 1 Fundamentals of Positioning
I – 1 Fundamentals of Positioning
Coordinate Systems
In order to define positions on a surface, a reference system is
required.
For example, positions on the earth's surface can be defined
absolutely by their geographic coordinates of longitude and latitude. In
contrast to the relative definition of a position that is referenced to a
known location, the network of horizontal and vertical lines on the
globe constitute an absolute reference system. See Fig. I.1.
On a milling machine, workpieces are normally machined according to
a workpiece-based Cartesian coordinate system (a rectangular
coordinate system named after the French mathematician and
philosopher Renatus Cartesius, who lived from 1596 to 1650). The
Cartesian coordinate system is based on three coordinate axes
designated X, Y and Z which are parallel to the machine guideways.
The figure to the right (Fig. I.2) illustrates the right-hand rule for
remembering the three axis directions: the middle finger is pointing in
the positive direction of the tool axis from the workpiece toward the
tool (the Z axis), the thumb is pointing in the positive X direction, and
the index finger in the positive Y direction.
You can skip over this chapter if you are familiar with the
concepts of coordinate systems, incremental and absolute
dimensions, nominal and actual positions, and distance-to-
go.
Fig. I.1 The geographic coordinate system is an
absolute reference system
Fig. I.2 Designations and directions of the axes on a
milling machine
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