# A Study on the Errors of 2D Circular Trajectories Generated on a 3D Printer
## 3 Experimental Results and Discussion
The effect of vibration suppression on \(\mathrm{TFR_{1}}\) or \(\mathrm{TFR_{1a}}\) shapes should be similar to the effect of a low pass numerical filtering of \(x_{e}\) and \(y_{e}\). Figure 19 presents the new shape of \(\mathrm{TFR_{1a}}\) (as \(\mathrm{TFR_{1 af}}\)) if \(x_{e}\) and \(y_{e}\) motions are filtered with a moving average numerical filter (with 1000 samples in the average). As expected, the size of the surface delimited by the \(\mathrm{TFR_{1 af}}\) is not significantly changed (17,399 \(\mathrm{\SIUnitSymbolMicro m}^{2}\) here by comparison with 17,711 \(\mathrm{\SIUnitSymbolMicro m}^{2}\) on \(\mathrm{TFR_{1a}}\) from Figure 15). The evolution of \(\mathrm{TFR_{1 af}}\) from Figure 19 is also useful when only the influence of the low frequency variable components from \(x_{e}\) and \(y_{e}\)-motions on P&A is investigated and used for errors compensation. The compensation is a feasible option with an appropriate control of stepper motors since they are operated using the microstepping drive technique [32]. If the accuracy describes how close the real trajectory is to a desired circle (or how close the shapes of \(\mathrm{TFR_{1}}\), \(\mathrm{TFR_{1a}}\) and \(\mathrm{TFR_{1 af}}\) by a point are), the precision describes the repeatability of real trajectories, each trajectory being generated using a complete cycle (period) of \(x\) and \(y\)-motions, partially described in Figure 9:6 The best way to compare these real trajectories is to use the comparison between trajectories fitting residuals related to a circle with a smaller radius than the radius of least square circle (defined similarly to \(\mathrm{TFR_{1a}}\)) but using low pass filtered \(x\) and \(y\)-motions (as \(\mathrm{TFR_{3 af}}\)). A perfect coincidence of real trajectories should produce a perfect coincidence of \(\mathrm{TFR_{3 af}}\) trajectories. Figure 20 presents the evolution of \(\mathrm{TFR_{3 af}}\) for five successive real trajectories (\(\mathrm{TFR_{3 af1}}\)\(\div\)\(\mathrm{TFR_{3 af5}}\)) and the evolution of \(\mathrm{TFR_{1a}}\). Figure 21 presents a zoomed in detail of Figure 20 in area B. As expected, there is not a perfect coincidence of \(\mathrm{TFR_{3 af}}\) trajectories, despite some certain shape similarities (except in area A on Figure 20 where the trajectory \(\mathrm{TFR_{3 af2}}\) is extremely different). It is obvious that the difference between trajectories is less than 10 \(\mathrm{\SIUnitSymbolMicro m}\) (except in area A). Without any improvement of the 3D printer structure and kinematics, this should also be the theoretical precision after an eventual compensation of the errors (using an appropriate control of the stepper motors). With ideal errors compensations, the trajectories \(\mathrm{TFR_{1f}}\) should be bordered outside by a circle with 10 \(\mathrm{\SIUnitSymbolMicro m}\) radius (or 35 \(\mathrm{\SIUnitSymbolMicro m}\) radius for the trajectories \(\mathrm{TFR_{3 af}}\)). A complete estimation of 3D printer P&A should consider specific trajectories (e.g., circles as in this study) placed in different positions in different 2D locations of the printing volume travelled with different speeds, clockwise and counter clockwise.