Ah David, I don’t think the one in the headstock is going to do quite what you want. I did use a setup like this for the columns on my Leak based compound engine. (ME 1983). The technique is used there to allow turning an offset foot and head on an angled column. hard to describe in words, and I don’t have a photo handy, but picture a turned column to go between a bedplate and a cylinder block. The back columns are cast and support the crosshead slides, but the two columnts on the front just brace that side. Now, to make things prettier, we decide to angle the columns outwards a little. So the middle of the column is easily turned between centres, but the ends now have to be angled to match the flat faces on the two castings.
So the ends are done by using an offset centre at the headstock end . The turning is then done at the tailstock end, the end face and a short parallel section that blends into the main part of the column. This is also done at the other end by turning the whole job around. As well as the offset centre, you need a drive dog setup that prevents any movement, eg wire the dog to the drive pin.
I can see this needs a photo, so I will pop down and take one this afternoon.
Usual ways of turning a taper are:
1/Offset the topslide…OK but limited length
2/Offset the tailstock…hard to set accurately for the taper you want, even harder to get back parallel again. (Taper will vary with job length so all blanks must be identical.)
/3 Offset centre in tailstock, eg boring head with a centre. Fine provided the boring head does not move in the taper, same proviso regarding blanks.
4/ Many different sorts of taper turning attachments as made by lathe manufacturers and described by people like George Thomas . Probably the ideal way, if you happen to have one.
I guess CNC would be another way, but not likely to be relevant here.
The Unimat Sl also allowed angling the headstock
regards
John