70 CNC Machining
Pythagorean theorem: C2 = A2 + B2
52 = A2 + 32
25 = A2 + 9
25 – 9 = A2
√16 = √A2
4 = A
Figure 3-29. Cutter locations when cutting a 90° radius corner on a workpiece.
Center of
workpiece
radius
Workpiece
Toolpath direction
Cutter
position 1
X
Workpiece
1.25
″
Y
Cutter
position 2
Cutter
position 3 The distance from the
center of the workpiece
radius to the center of
the cutter at Position 1
is 1.25″ (workpiece
radius + cutter radius).
Therefore, the formula
to find the X dimension
for each change in Y is
X2 + Y2 = 1.252.
X2 + Y2 = 1.252
X2 = 1.252 – Y2
X = √1.252 – Y2
If the cutter travels
in the Y direction
0.5″, the X position
can be calculated by
substituting 0.5″ for Y.
X = √1.252 – 0.52
X = √1.3125
X = 1.146
Figure 3-30. This illustration shows how to use the Pythagorean theorem to calculate the cutter position
as it creates a corner radius.
To start, we need to calculate the position of the cutter in Position 2
based on the center of the workpiece radius. We know that Y = 1.00″ and
H = 2.25. Therefore, X can be calculated using Pythagorean’s theorem.
X2 + 12 = 2.252
X2 = 2.252 – 12
X = √2.252 – 12
X = √5.0625 – 1
X = 2.0156