Hereís a link to a document showing how I make a powered tool sharpener. I free-hand sharpen them but a tool-rest could be easily fashioned to work with this.

My primary hobby is wood carving, but have taken up turning to augment them. Since I have sharpened carving tools since 1980, I thought learning to sharpen lathe tools would be easy. I quickly learned itís a whole different skill set. If you are a turner who may be considering carving as a way to augment your turnings, and looking for a device to sharpen your tools, you may find this of some interest.

https://shellknobwoodcarvers.weebly.com/projects.html

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