神兜兜和他的朋友们

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40 A. Caballero-Ruiz et al. / Mechatronics 17 (2007) 231–243
* from the 51st generation to the 75th generation, the repeated 10,000 times and deviations presented in the cen-
mutation range was between18.8 and 18.8 lm; ter calculations were Ex < ±1.88 lm, Ey < ±1.88 lm y
* finally, from the 76th generation to the 100th genera- Ez < ±1.88 lm (see Fig. 12b). If each experimental data
tion, the mutation range was between1.8 and 1.8 lm. group is independently analyzed, it is easy to observe the
deviations with respect to the theoretical data (Fig. 13).
Fig. 12a shows the results of the GA implementation for These deviations are directly related to the MMT errors.
one of B2 position; the plot represents a correlation The algorithm was tested too for 14 position of B2 when
between the experimental data and the theoretical circles this ball was placed 17 mm from the MMT spindle to
that correspond to the experimental measurements. For establish the MMT error characteristics. The correspond-
this experimental data, the calculated center for B2 was ing points for the center of B2 and the characteristics for
X= 12831 lm, Y= 30168.3 lm and Z =11370.2 lm with each B2 position are presented in Fig. 14 and Table 1. This
a quadratic error of 448,069 motor steps, which is equiva- is a part of the final position set that will be analyzed in the
lent to an MMT error of 82 lm for that point. To deter- MMT evaluation. The maximum error was 85.9lmand
mine the robustness of the algorithm, the experiment was averageerror was35.68 lm.Thisresultissimilartothecal-
Fig. 12. (a) The experimental data and the theoretical points of the ball perimeter corresponding to the measurements and (b) deviations of the centers.
Fig. 13. MMT errors: (a) Measurements with Z axis constant; (b) Measurements with Y axis constant and (c) Measurements with X axis constant.