Articulated Arm Coordinate Measuring Machine Calibration by Laser Tracker Multilateration

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2"> </td><td align="center" rowspan="2">Offsets (mm)</td><td align="center" rowspan="2"> </td><td align="center" colspan="3">Origin coordinates (mm)</td></tr><tr class="thead"><td align="center"><span style="width: 23.237499px;"><svg height="11.825" id="M89" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 23.237499 11.825" width="23.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,9.9,12.713)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.012,-0,0,-.012,15.552,12.713)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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</svg></span></td><td align="center"><span style="width: 22.200001px;"><svg height="12.1625" id="M91" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 22.200001 12.1625" width="22.200001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,8.525,12.1)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.012,-0,0,-.012,14.177,12.1)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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</svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left">LT1</td><td align="center"><span style="width: 24.012501px;"><svg height="16.3125" id="M92" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 24.012501 16.3125" width="24.012501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,4.637,16.25)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.012,-0,0,-.012,10.278,16.25)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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<g transform="matrix(.012,-0,0,-.012,17.613,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></span></td><td align="center">1.51695</td><td align="center">0</td><td align="center">0</td><td align="center">0</td></tr><tr><td align="left">LT2</td><td align="center"><span style="width: 24.012501px;"><svg height="16.3125" id="M93" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 24.012501 16.3125" width="24.012501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M238 681l-124 -585q-7 -31 4 -31q10 0 37.5 18.5t49.5 41.5l16 -22q-40 -48 -89.5 -81.5t-76.5 -33.5q-42 0 -16 122l105 488q7 32 0 41t-39 9h-35l5 26q35 3 71 13t58 17.5t26 7.5q14 0 8 -31z" id="x1D459"></path></g>
<g transform="matrix(.012,-0,0,-.012,4.637,16.25)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.012,-0,0,-.012,10.278,16.25)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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</svg></span></td><td align="center">0.89275</td><td align="center">2262.33138</td><td align="center">0</td><td align="center">0</td></tr><tr><td align="left">LT3</td><td align="center"><span style="width: 24.012501px;"><svg height="16.450001" id="M94" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 24.012501 16.450001" width="24.012501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M238 681l-124 -585q-7 -31 4 -31q10 0 37.5 18.5t49.5 41.5l16 -22q-40 -48 -89.5 -81.5t-76.5 -33.5q-42 0 -16 122l105 488q7 32 0 41t-39 9h-35l5 26q35 3 71 13t58 17.5t26 7.5q14 0 8 -31z" id="x1D459"></path></g>
<g transform="matrix(.012,-0,0,-.012,4.637,16.25)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.012,-0,0,-.012,10.278,16.25)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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</svg></span></td><td align="center">0.18749</td><td align="center">1713.00335</td><td align="center">2098.93521</td><td align="center">0</td></tr><tr><td align="left">LT4</td><td align="center"><span style="width: 24.012501px;"><svg height="16.3125" id="M95" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 24.012501 16.3125" width="24.012501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,4.637,16.25)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.012,-0,0,-.012,10.278,16.25)"><path d="M592 498l-30 -3q-13 63 -31 89q-13 19 -33.5 25.5t-75.5 6.5h-70v-493q0 -60 16 -75.5t86 -19.5v-28h-286v28q68 4 83.5 19.5t15.5 75.5v493h-62q-60 0 -83 -7t-33 -24q-12 -17 -32 -90h-29q10 116 12 180h20q10 -16 21 -20.5t34 -4.5h395q19 0 28.5 5t21.5 20h21
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</svg></span></td><td align="center">2.13351</td><td align="center">1913.00558</td><td align="center">−343.41959</td><td align="center">3010.23578</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Multilaterated offsets and origin coordinates obtained in multilateration reference system. 2798 iterations and objective function value below 1 <i>μ</i>m.

The Scientific World Journal

tab2

Table 2

Table 2: Articulated Arm Coordinate Measuring Machine Calibration by Laser Tracker Multilateration 