Six Degrees of Freedom
These six degrees of freedom apply in particular to an CNC Machine linear axis.  As the saddle slides along it's quideway system it experiences motion from these degrees of freedom.

The six degrees of freedom for a horizontal linear axis are:

1. Pitch
2. Yaw
3. Roll
4. Linear positioning
5. Vertical straightness
6. Horizontal straightness

Six Degrees of Freedom Linear positioning represents the linear displacement for an axis.  In other words if an axis is commanded to move one inch, one inch is how much it has been displaced.  If the axis does not move one inch then the amount it is in error of one inch is called it's linear positioning error.

Straightness for an horizontal axis (X-Axis in the image) is represented in two directions, up and down (vertical), and side to side. (horizontal)  If an axis does not travel straight (or flat) along it's path, it has straightness errors.

Another way to describe the two directions of straightness would be relative to another axis direction because in the case of vertical axes both directions are horizontal. For example for Z-Axis in the image one direction would be relative to Y-Axis direction and the other X-Axis direction.

A CNC machine normally has more than one linear axis.  Generally the other axes are perpendicular or square to each other.  Once another axis is introduced we also add another degree of freedom for each axis, a squareness degree of freedom.  In the above picture there are three axes directions shown, X, Y, and Z so there are three squareness degrees of freedom, X/Y, X/Z, and Y/Z.  For this three axis example there are now 21 degrees of freedom.  The six degrees of freedom for each axis plus the three squareness degrees of freedom.  6 + 6 + 6 + 3 = 21.