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Right Handed Cartesian Rule-of-Thumb
Below is an rule-of-thumb method to determine the designation of the three primary linear axes in a right handed cartesian coordinate system.
The thumb, index finger and middle finger of the right hand are held so that they form three right angles, the thumb indicates X-Axis, the index finger Y-Axis, and the middle finger Z-Axis.
In the case of a three axis machine with a spindle, the spindle is commonly parallel to Z-Axis.
In that situation, point your middle finger parallel to the spindle and rotate your hand so that your thumb and index finger are parallel to the other two axes.
Align your thumb to the longer axis as X-Axis is usually longer that Y-Axis.
The three primary rotary axes are designated by their plane's being perpendicular to the linear axes.
That plane could be said to rotate around the axis.
A-Axis rotates around X-Axis, B-Axis rotates around Y-Axis, and C-Axis rotates around Z-Axis.
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