Basics of coordinate systems

Types of coordinate systems

For coordinates to be unambiguous they must define one point in all axes of the coordinate system:

Axes

Function

One

In a one-dimensional coordinate system, one coordinate defines one point on a number line.

Example: on a machine tool, a linear encoder represents a number line.

Two

In a two-dimensional coordinate system, two coordinates define one point in a plane.

Three

In a three-dimensional coordinate system, three coordinates define one point in space.

If the axes are arranged perpendicularly to each other, they create a Cartesian coordinate system.

Using the right-hand rule you can recreate a three-dimensional Cartesian coordinate system. The fingertips point in the positive directions of the three axes.

Origin of the coordinate system

Unambiguous coordinates require a defined reference point to which the values refer, starting from zero. This point is the coordinate origin, which lies at the intersection of the axes for all three-dimensional Cartesian coordinate systems of the control. The coordinate origin has the coordinates X+0, Y+0, and Z+0.