My Agie works similarly to what MitsTech explains:
Very basically -- I create geometry for the profile at the bottom (typically, though not necessarily the large end) of the taper, and geometry for the upper end of the taper. I tell the machine how far above the zero reference plane the bottom profile is, and how tall the part is (distance between the 2 "profiles" I have created).
The machine "knows" where the bottom wire guide is (it's a fixed position that never changes), and knows where the top wire guide is by absolute position of the Z axis (upper support assembly).
Since the machine knows where both guides are relative to the Zero plane, and it also knows where the upper and lower profiles of the tapered part are relative to that same zero plane... the machine can "figure out" where to position the wire guides to correctly cut the taper.
A slight bit of an over-simplification, but hopefully that makes sense.
Bottom line: if the position of the bottom of the part and height of the part are precisely measured, I've found that size and position on a tapered cut are usually right on the money first shot. (easily within tenths).
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Just thought of something else that you might be asking: the way to reference
position of a tapered cut within the part? My above explanation was more about controlling size/geometry of the tapered cut... but not about positioning that tapered cut in X/Y within the part.
On my machine, there is an "entry point" that defines the beginning of the operation - (this is typically done in the CAM package where the program is created). That entry point may be on the part, or it may be out in space off the side of the part (or obviously it could be in space in the center of a cavity
within the part, or even more likely it could simply be in the center of a vertical "start hole" for threading the wire). That all depends on what the tapered cut looks like.
The entry point is nothing more than a start point for the cut where the wire is (can be) vertical. Once again... a bit of a "loose" explanation, but basically if the entire cut is tapered, then the entry point is off the cut somewhere and the machine begins moving the upper head immediately so that upon reaching the imaginary surface of the tapered geometry... the wire is at the correct angle.
Whew... that was a long sentence, but hope it makes sense.