Shaping apparatus for finishing surfaces

An apparatus for finishing a zone on the surface of a bladed article of manufacture, said surface comprising a plurality of adjacent and contiguous zones, comprising:

• a support for a rigid abrasive surface, the support including at least two blocks configured to include one or more of the channels, wherein one block is configured to be positioned below the article and the other block is configured to be positioned above the article;
• one or more channels supported on the support, each of the channels having a cross-sectional profile including at least one finishing area to finish an operative zone of the article;
• wherein:
• the finishing area includes a contacting area and a non-contacting area, wherein the contacting area includes at least one rigid abrasive surface, and
• an angle θ of each finishing area of the cross-sectional profile is substantively the same as a clearance angle β of the article, the clearance angle β calculated as at least one of:
• clearance angle β=90°−γ;
• clearance angle β=90°−γ−α;
• and
• clearance angle β=90°−(γ−α)=90°−γ+α;
• where α is rake angle and γ is blade angle.