## 3 Results
### Maximal Contour Error--Dependence on CNC Parameters  
Another parameter investigated was the maximum contour error. It was measured as the maximum absolute value of the contour error relative to the ideal final surface (see Section 2.4.). It should be noted here that the maximal contour error was attained in corner neighborhoods as a rule. This is not surprising, as the iTNC interpolator is able to interpolate line segments exactly. Therefore, the only areas where significant contour deviations can occur are precisely the corner neighborhoods (see Figure 11).  
The maximal contour error does, in general, depend on the parameters of contour tolerance, limit frequency, corner jerk, and angle size. Interestingly, the axial jerk limits did not affect the maximal contour error values. When both values of contour tolerance and limit frequency are fixed, the dependence of maximal error on corner jerk for individual angle sizes has the following character: for lower values (up to a certain threshold) of the corner jerk, the dependence is linear, while for higher values of corner jerk, the dependence is constant. Thus, given values of contour tolerance, limit frequency, and angle size, there exists a corner jerk threshold value such that an additional increase in the corner jerk parameter beyond this value does not have an additional effect on the maximal contour error. For an example of this type of dependence, see Figure 12.  
Based on the results obtained from the tests performed on the Fan toolpath, the maximal contour error can significantly exceed the prescribed contour tolerance. In fact, the contour tolerance limit can be exceeded by as much as 85% (see Figure 12). Thus, based on the regression models obtained from the experimental results, the maximal corner jerk values for which the contour tolerance is satisfied for all measured angle sizes (depending on the limit frequency and contour error settings) were calculated. These results are summarized in Table 3.  
The results obtained from the performed tests show that the overshoots at corners can exceed the prescribed tolerances significantly depending on the limit frequency and the value of the corner jerk limit.  
Figure 12: Dependence of maximum error on corner jerk for contour tolerance of 20 μm (horizontal dotted line) and limit frequency of 30 Hz. The results for individual angle sizes are distinguished by their color. The regression models are shown as full lines. The test result data are displayed as colored dots.  
As can be seen in Table 3, the range of corner jerk values for which the tolerance limit is satisfied increases with both the contour tolerance limit and the frequency limit. The impact of angle size on the dependence of maximal error on corner jerk is not readily discernible. It can be assumed that this influence is a result of the interaction between the selected filter type, the limit frequency, and the angle size. This interaction is difficult to model because the technical details of the iTNC interpolator implementation are not known.  
Despite this difficulty, the results show that practical information about the behavior of the interpolator system can still be obtained. The corner jerk limits presented in Table 3 refer to the worst-case scenarios and can thus be applied to general toolpaths to ensure that the programmed contour tolerance limit is satisfied at corners.  
This approach was also verified on the Valley toolpath. The results agreed with the predictions (i.e., contour tolerance was satisfied for tested corner jerk values below the respective thresholds and maximal errors exceeded contour tolerance for corner jerk values above the thresholds).