how to accurately grind 60 degree lathe bits

Thought experiment for you:-

Set the sliding mitre to 30 degrees and the table to 0 degrees.

Grind the tool

You now have a tool with a 60 degree included angle.

Hold the tool against the sliding mitre and note that the cutting edge of the tool is parallel to the face of the wheel (It'd better be, you just ground it :-)

Now tilt the table up and down. Note that the cutting edge remains parallel to the face of the wheel. Thus the correct angle to set the mitre to is 30 deg (actually, it'd be 27.5 for a proper thread ;-)

Not too worried about the accuracy of the clearance angle. The included angle of the thread is the important one!

regards Mark Rand RTFM

Now I'm confused. I think it depends on whether the miter tilts with the work versus only the work tilting. Or whether you're north or south of the equator.

The mitre tilts with the work. The cutting edge (that you just ground in the thought experiment) is already parallel with the face of the wheel. When you tilt it, you are rotating it about an axis parallel to the face of the wheel. Therefore you aren't changing that particular angle when you tilt the table to give the relief.

It took me quite a lot of head scratching before I was happy with the concept for some 29 degree and 40 degree included angle bits for ACME turning and gear shaping...

regards Mark Rand (east of the Equator :-) RTFM

OK, I agree. I believe my calculation applies to a different case, when you have a work holder that applies the clearance angle by tilting the work up, while the miter stays in the horizontal plane perpendicular to the wheel.

I think I follow you. The test I use is to continue the change to an extreme and see if it still holds true. In this case, tilt the table almost vertical, so you grind an edge suitable for a wood chisel.

Yes, that would be useful for some things (3D mitres?), but a real pain for tool grinding...

regards Mark Rand RTFM