TouchDRO Coordinate System

Saturday, January 18, 2014
DRO Coordinate System

One of the aspects of the TouchDRO application that causes confusion is the coordinate system. Every once in a while I get questions like “Can I do hole circle/pattern/tool offset on a different plane because on my mill the spindle is X (or Y) axis?”, or something along these lines. This question really means that the DRO is not set up right and the user is trying to compensate for it by “customizing” the user interface. Obviously, this is your DRO and you are free to set it up whichever way you like it. TouchDRO is pretty flexible, and the basic DRO functionality will work just fine even if you have axes mixed up and backwards. After a while you will likely get accustomed to it, and use the DRO without second thoughts. Never the less following the conventions is a good idea in the long term.

First of all, once you get used to a “broken” DRO, using one that is set up right will be counter-intuitive and will increase the chance of mistakes. I learned this lesson a hard way with a lathe that had a right-hand cross feed screw. When I bought a good lathe, it took me months to get rid of the bad muscle memory and stop “retracting” the cutter into the part. Second, the functions in the application are implemented based on the standard axes. If your DRO is set up differently, many of the functions will be useless. For example, functions such as “Hole Circle”, “Hole Pattern”, “Tool Radius Offset”, etc. assume that the exis drilling the holes will be Z. Similarly, lathe tool offset function uses Z and X axes for the table and cross slide movement respectively.

The Coordinate System

TouchDRO uses the “right hand” Cartesian coordinate system that is commonly used in manual machining and in most, if not all, CAD/CAM packages. There is a mnemonic called the “right hand rule” that might help you remember it better: partially close your right hand so that your thumb, index finger and the middle finger form some resemblance right angles. Your index finger will then point in the positive “X” direction, middle finger will show the positive “Y” directions and your thumb will represent the positive “Z” direction.

Right hand coordinate system mnemonic

The convention in the trade is to assign the axis parallel to the spindle to be “Z”, with X and Y being used for the other two axes. Additionally, there are two sets of secondary* axes: angular and linear. Angular axes that rotate about X, Y, and Z are commonly designated A, B, and C respectively. They use the “right hand screw rule”: close your hand and point the thumb in the positive direction of the axis; your fingers will point in the positive direction of rotation. The linear axes U,V and W are often used for things like quill, etc.

Vertical Mill

Vertical Milling Machine Coordinate System

Vertical milling machine is probably the most intuitive when it comes to it’s coordinate system. As I mentioned earlier, the axis parallel to the spindle is Z. On a vertical mill this axis is, well, vertical, therefore table’s longitudinal travel will be “X” and cross travel will be “Y”, with the numbers increasing as it moves to the right and away from you. Moving the knee up will increase the Z value and vice versa. On a tabletop milling machines that don’t have a knee, moving the head and/or the quill down has the same effect as moving the knee up. If your setup includes a DRO on the knee/head and the quill, the application allows Z and W readouts to be combined, giving you a single Z position.

Horizontal Mill or Surface Grinder

Horizontal Mill Coordinate System

On a horizontal mill or a surface grinder the cross travel of the table becomes Z (because it’s parallel to the spindle’s axis), X then, is the longitudinal travel of the table and Y is vertical.


Lathe Coordinate System

Finally, on a lathe, the bed is parallel to spindle, therefore logically it becomes the Z axis, pointing away from the headstock. In other words moving the carriage away from the headstock increases the position and vice versa. The cross slide on a lathe is X, with the positive direction pointing away from you (towards the center of rotation). A milling attachment axis then becomes Y.

Special note should be made about the 3-in-1 combination machines that basically consist of a lathe with a tabletop milling machine attached to it. They have two spindles, so depending on which function you use, the axes change accordingly. For the purposes of the TouchDRO application I consider them to be two separate machines, otherwise some functions make no sense. In the new version of the app it’s easy to switch between machines, so this should not pose much inconvenience.


  1. Yuriy,
    are you sure its the right hand you have to hold out? If you hold out your right hand the middle finger points in the left, or negative direction (as far a milling goes). If you use your left hand then the middle finger points to the right, or positive direction. Unless I'm missing something here.

    1. Yes, I'm pretty sure. The picture is rotated 90 degrees from the milling table. Rotate it so the index finger points along the X axis and the middle finger will point away from you...
      Thank you

  2. Yuri thank you for taking the time to enlighten me