cutting edge;
therefore the top should slope back from this part of the edge.
Obviously, a tool ground in this way will have both a back and a side
slope.

When most of the work is done on the point or nose of the tool, as, for
example, with the lathe finishing tool _C_ which takes light cuts, the
slope should be straight back from the point or cutting edge _a--b_. As
the side tool shown in Fig. 10 does its cutting along the edge _a--b_,
the top is given a slope back from this edge as shown in the end view.
This point should be remembered, for when the top slopes in the right
direction, less power is required for cutting. Tools for certain classes
of work, such as thread tools, or those for turning brass or chilled
iron, are ground flat on top, that is, without back or side slope.

=Clearance for the Cutting Edge.=--In order that the cutting edge may
work without interference, it must have clearance; that is, the flank
_f_ (Fig. 10) must be ground to a certain angle [alpha] so that it will
not rub against the work and prevent the cutting edge from entering the
metal. This clearance should be just enough to permit the tool to cut
freely. A clearance angle of eight or ten degrees is about right for
lathe turning tools.

The back slope of a tool is measured from a line _A--B_ which is
parallel to the shank, and the clearance angle, from a line _A--C_ at
right angles to line _A--B_. These lines do not, however, always occupy
this position with relation to the tool shank when the tool is in use.
As shown to the left in Fig. 12, the base line _A--B_ for a turning
tool in use intersects with the point of the tool and center of the
work, while the line _A--C_ remains at right angles to the first. It
will be seen, then, that by raising the tool, as shown to the right, the
_effective_ clearance angle [alpha] will be diminished, whereas lowering
it, as shown by the dotted lines, will have the opposite effect.

A turning tool for brass or other soft metal, particularly where
considerable hand manipulation is required, could advantageously have a
clearance of twelve or fourteen degrees, as it would then be easier to
feed the tool into the metal; but, generally speaking, the clearance for
turning tools should be just enough to permit them to cut freely.
Excessive clearance weakens the cutting edge and may cause it to crumble
under the pressure of the cut.

[Illustration: Fig. 12. Illustrations showing how Effective Angles of
Sl