68 CNC Machining
There are a number of situations where triangles can be applied to
determine a cutter path. To plot a cutter path, the cutter radius is added or
subtracted from the part outline. The cutter path is the path in which the
centerline of the spindle moves along the plane, staying away from the part
by the amount of the tool radius. To cut a 90° corner, the cutter moves past
the edges of the part a distance equal to the cutter radius. See Figure 3-26.
To cut an acute (less than 90°) angle, the cutter moves past the corner of the
workpiece equal to the distances represented by the X dimension of the
shaded triangle in Figure 3-27. To cut an obtuse (greater than 90°) angle, as
shown in Figure 3-28, the same formula is used. Notice that the distance
the cutter has to travel beyond the end of the part is greater than the cutter
radius for acute angles and less than the cutter radius for obtuse angles.
R
R
Figure 3-26. The location of a cutter when it is about to make a 90°
move is shown. The radius of the cutter is used when determining
the cutter location from the corner of the workpiece.
X
Workpiece
Toolpath direction
Cutter
X
22.5°
45°
Workpiece
0.25″
Figure 3-27. Illustration showing the triangle that must be solved to calculate the position of a cutter
when cutting an acute angle on a workpiece.
Angle on workpiece is 45°
Cutter radius is 0.25″
tan 22.5° (half of 45°) =
0.25″
X
X =
0.25″
tan 22.5°
X = 0.25″
0.414
X = 0.604″
The cutter must travel 0.604″
past the end of the workpiece
to begin cutting the bottom-
left side.