Machining tools having concave cutting surfaces for precision machining and methods of manufacturing such

A machining tool with a cutting surface adapted to provide a variable projected machining width during machining, the machining tool comprising:

• the cutting surface, which includes a first cutting edge and a second cutting edge positioned at an angle relative to each other and that extend to a tip of the machining tool;
• and
• a back surface that forms a first acute angle with the cutting surface at the first cutting edge and a second acute angle with the cutting surface at the second cutting edge;
• wherein:
• a cross section of the cutting surface of the machining tool normal to a centerline of the machining tool is concave between the first cutting edge and the second cutting edge;
• and
• a cross section of the back surface of the machining tool normal to the centerline of the machining tool is convex between the first cutting edge and the second cutting edge.