I make jewellery and make many of the required tools myself. I often have to make collets for holding gemstones of various sizes. Making a tapered mandrel for truing collets for round stones is a trivial lathe turning exercise, but a mandrel for oval collets is not so simple.

Commercially produced tapered, oval mandrels, are machined on an eccentric turning lathe (or grinder) , but the product has a severe problem: the difference along the mandrel between the major and minor dimensions is maintained instead of the ratio. At the large end, the dimensions are12.5x11mm, but at the small end they are 4.5×3, which means that the ratio varies between 1.14 and 1.5.

Oval gemstones typically have a ratio of around 1.4:1, so, to be able to make various sizes of oval collets, a tapered mandrel is needed that maintains the ratio of about 1.4:1. This was an interesting challenge.

Here is a photo of the small end of the finished mandrel: it is 2.6×1.86mm, and the large end is 8.5×6.1mm. Yes, I know the large end is not as big as the commercial product, but its big enough for my needs; it maintains a ratio of about 1.4:1 all along.

Here are photos of the wide and narrow sides.

So, here's the challenge. How would you make it?