Tool Radius Compensation
Digital Manufacturing
Updated: 19/10/2026
Tool radius compensation
- TRC offsets the tool center path (programmed points) according to
G41/G42 - New target points are calculated for each block on the basis of the offset intersection with the next block (arc or line)
- Disabled for rapid motions
Line-Line case
We need to calculate the point \(D\):
- Given the line equation \(y = ax + b\), we need to calculate the equation of the offset line(s)
- Calculate \(D\) as intercept between the two offset lines
Line-Line case
- Given \(y = ax + b\), the equation of the offset line is \(y = ax + b - v\)
- Being \(a = u/r\), it follows that: \(v = \sqrt{u^2 + r^2} = r\sqrt{a^2 + 1}\)
- So, \(y = ax + b \pm r\sqrt{a^2 + 1}\)
- The sign depends on G41/G42 and on the path direction
Line-Line case
Intersection \(D\) between
\(y = a_1 x + b_1 - v_1 = a_1 x + b_{o,1}\)
and
\(y = a_2 x + b_2 - v_2 = a_2 x + b_{o,2}\)
has coordinates:
\[(x_i, y_i) = \left(\frac{b_{o,2} - b_{o,1}}{a_1 - a_2}, \frac{b_{o,1}a_2 - b_{o,2}a_1}{a_2 - a_1}\right)\]
Line-Arc (or Arc-Line)
Similar to line-line case, but with a caveat:
- Line-circle intersection gives two points, \(G\) and \(B_r\): you have to select the intersection that is closer to the node to be offset (\(B\) in figure)
Line-Arc (or Arc-Line)
Similar to line-line case, but with a caveat:
- Line-circle intersection gives two points, \(G\) and \(B_r\): you have to select the intersection that is closer to the node to be offset (\(B\) in figure)
