68 D.-M. Chen and W.D. Zhu Table 6.5 Comparison of measured and calculated rotation angles at location 2 Coordinate (mm) Measurement Calculation from Set 1 Calculation from Set 2 x y z ˛ (ı) ˇ(ı) ˛1 ( ı) ˇ1 ( ı) • ’1 (%) •ˇ1 (%) ˛2 ( ı) ˇ2 ( ı) • ’2 (%) •ˇ2 (%) 150 150 0 6.669 3.107 6.669 3.100 0.008 0.220 6.667 3.102 0.021 0.149 150 150 0 1.463 3.012 1.463 3.007 0.022 0.178 1.473 3.001 0.693 0.358 150 150 0 1.381 2.403 1.383 2.394 0.216 0.345 1.388 2.398 0.573 0.191 150 150 0 6.538 2.806 6.543 2.801 0.077 0.148 6.540 2.801 0.026 0.154 5 35 80 3.257 0.892 3.256 0.893 0.014 0.066 3.253 0.897 0.110 0.602 5 35 80 3.082 0.902 3.077 0.896 0.171 0.621 3.074 0.900 0.258 0.118 5 25 80 3.082 0.702 3.073 0.697 0.279 0.583 3.071 0.702 0.371 0.072 5 25 80 3.257 0.702 3.253 0.693 0.119 1.148 3.249 0.698 0.218 0.459 5 25 150 2.530 0.349 2.526 0.349 0.129 0.083 2.517 0.338 0.476 3.051 5 25 150 2.349 0.345 2.342 0.341 0.289 1.037 2.333 0.331 0.643 3.973 5 35 150 2.349 0.546 2.338 0.548 0.429 0.300 2.330 0.538 0.790 1.554 5 35 150 2.530 0.556 2.523 0.556 0.262 0.120 2.514 0.546 0.616 1.746 120 120 0 6.091 2.514 6.094 2.509 0.057 0.175 6.093 2.511 0.038 0.112 120 120 0 1.933 2.479 1.932 2.474 0.045 0.210 1.940 2.470 0.370 0.382 120 120 0 1.867 1.898 1.865 1.894 0.085 0.190 1.869 1.898 0.147 0.025 120 120 0 5.999 2.181 5.997 2.182 0.022 0.060 5.995 2.181 0.066 0.045 80 80 0 5.345 1.733 5.343 1.732 0.040 0.051 5.343 1.733 0.043 0.005 80 80 0 2.571 1.743 2.571 1.744 0.000 0.106 2.577 1.741 0.224 0.061 80 80 0 2.520 1.209 2.523 1.209 0.124 0.017 2.527 1.211 0.263 0.179 80 80 0 5.282 1.375 5.282 1.365 0.006 0.658 5.280 1.365 0.021 0.676 Table 6.6 Comparison of measured and calculated rotation angles at location 3 Coordinate (mm) Measurement Calculation from Set 1 Calculation from Set 2 x y z ˛ (ı) ˇ(ı) ˛1 ( ı) ˇ1 ( ı) • ’1 (%) •ˇ1 (%) ˛2 ( ı) ˇ2 ( ı) • ’2 (%) •ˇ2 (%) 150 150 0 2.844 5.132 2.843 5.126 0.040 0.125 2.844 5.121 0.014 0.209 150 150 0 7.786 5.059 7.802 5.062 0.211 0.058 7.792 5.050 0.081 0.172 150 150 0 7.551 0.502 7.567 0.505 0.214 0.656 7.558 0.494 0.095 1.549 150 150 0 2.765 0.019 2.760 0.012 0.153 36.667 2.764 0.025 0.023 30.408 5 35 80 4.355 3.015 4.348 3.015 0.140 0.013 4.352 3.010 0.066 0.159 5 35 80 4.523 3.000 4.517 3.007 0.128 0.263 4.520 3.002 0.065 0.083 5 25 80 4.520 2.822 4.512 2.820 0.156 0.067 4.515 2.815 0.091 0.232 5 25 80 4.355 2.828 4.344 2.828 0.245 0.008 4.347 2.824 0.169 0.150 5 25 150 3.653 1.793 3.634 1.811 0.513 0.991 3.644 1.806 0.254 0.731 5 25 150 3.825 1.784 3.807 1.799 0.466 0.854 3.816 1.794 0.229 0.582 5 35 150 3.825 1.587 3.802 1.604 0.576 1.089 3.812 1.600 0.336 0.835 5 35 150 3.650 1.609 3.630 1.617 0.541 0.497 3.640 1.613 0.279 0.256 120 120 0 3.292 4.618 3.289 4.607 0.070 0.249 3.290 4.603 0.061 0.324 120 120 0 7.230 4.523 7.245 4.519 0.203 0.080 7.236 4.510 0.086 0.278 120 120 0 7.059 0.095 7.070 0.094 0.164 0.891 7.063 0.103 0.059 8.369 120 120 0 3.219 0.479 3.212 0.473 0.188 1.222 3.215 0.484 0.111 0.996 80 80 0 3.891 3.901 3.894 3.897 0.072 0.089 3.893 3.895 0.061 0.144 80 80 0 6.510 3.812 6.520 3.806 0.164 0.148 6.514 3.801 0.066 0.291 80 80 0 6.408 0.883 6.416 0.883 0.120 0.111 6.410 0.890 0.033 0.794 80 80 0 3.841 1.108 3.833 1.105 0.200 0.253 3.834 1.112 0.177 0.440 2.642 mm in Set 2, which appear on the highest raised block. At location 2 the maximum Euclidean-norm differences are less than 1 mm in both sets. At location 3, the maximum Euclidean-norm differences are 1.323 mm in Set 1 and 0.897 mm in Set 2, which also appear on the highest raised block. For an engineering application of a SLDV, errors of measured velocities caused by these Euclidean-norm differences between exact and estimated coordinates can be neglected because the vibration of such small zones can be considered as purely translational. By scanning the 3D structure, the methodology for determining the orientation and position of a SLDV is validated. The rotation matrix and translation vector can map coordinates of a scan point from the SMCS to SCS with high accuracy.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==