Cartesian coordinates

To describe a point in space with Cartesian coordinates it is necessary to project the point to the three axes of the coordinate system.

The coordinates x, y, z give the distance of the point to the point of origin.

This type of coordinate system is an often used system in engineering especially for translational movements in space. Cartesian coordinates are very useful for gantry cranes.

Coordinate description: P (x, y, z)

Cylindrical coordinates

This coordinate system is a combination of polar and Cartesian coordinates. They are preferred for robots with a cylindrical work space.

Radius and angle are given in polar coordinates.

The zero point of the radius lies in the point of origin. The height of the point is given by the z-axis in Cartesian coordinates.

Coordinate description: P (φ, r, z)

Spherical coordinates

Robots with spherical work spaces, like e.g. universal robots can operate polar with spherical coordinates.

It is defined by two angles and one straight line, which specify the distance of the point to the point of origin (radius). The basis is the coordinate system.

The pin angle φ (phi) includes the radius and the z- axis. The second angle (Meridian) includes the projection of the radius into the xy-plane with the x-axis.

Coordinate description: P ( φ, Meridian, r)