I didn't make it through the video, but emc supports probing with G38.2.
G38.2 probe does a straight movement and records the feedback position
at the time a digital input goes TRUE.  It then decelerates the axis
within machine constraints.  The resulting values are stored
in interpreter parameters and can be used e.g., with G10 L2 or G92 to
modify the coordinate system in effect.

The very old gcode reference
http://www.isd.mel.nist.gov/personnel/kramer/pubs/RS274NGC_3.web/RS274NGC_33a.html#1013622
includes gcode to find the center of a circle.  I don't think this
example has made it forward into the current emc documentation, but I
think it's fairly likely to still work.

Jeff

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