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** *** Chanin Sinlapeecheewa*** † ‡
Artifact Calibration of Coordinate Measuring Machine (2nd Report)
– Self Calibration of Redundant Coordinate Measuring Machine –
Kiyoshi TAKAMASU, Osamu SATO, Chanin SINLAPEECHEEWA, Ken SHIMOJIMA and Ryoshu FURUTANI
Traceable calibration methods for 3D mechanisms are necessary to use the mechanisms as coordinate measuring
machines. The calibration method of coordinate measuring machine using artifacts, artifact calibration method, is proposed
in taking account of traceability of the mechanism. Coordinate measuring machine which has multiple forward kinematics
for one measuring point call as “redundant coordinate measuring machine”. In this article, the self calibration method for
the two dimensional laser tracker system as the example of the redundant coordinate measuring machine is formulated
base on least squares method. Firstly, the calculation system which takes out the values of kinematic parameters using least
squares method is formulated. Secondly, the estimation value of uncertainty of measuring machine is calculated using
error propagation method. The self calibration method for the redundant coordinate measuring machine is applicable to
various types of 3D redundant mechanisms.
Key words: geometric calibration, kinematic calibration, coordinate measuring machine, laser tracker, redandunt
coordinate measuring machine, self caalibration
* 15 9 18
**
7-3-1
***
†
‡ 2-2
精密工学会誌 Vol.70,No.5,2004 711
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l3 + d3
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(a) 3 laser trackers measure coordinate of cat’s eye
Y
X
camera 1
(bx2, by2, u2)
t1
camera 2
(bx3, by3, u3)
t2
t3
(x, y)
laser
(0, 0, 0)
profile
(b) Laser scanner and 2 cameras measure profile
Y
X manipulator (0, 0)
t1 + d1
l1one point(x, y)
l2 l3
t2 + d2
t3 + d3
(c) 3DOF articulating measuring machine measure one point artifact
Fig. 1 Examples of coordinate measuring with redundancy in two
dimensional space
座標測定機のアーティファクト校正(第2 報)
712 精密工学会誌 Vol.70,No.5,2004
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座標測定機のアーティファクト校正(第2 報)
精密工学会誌 Vol.70,No.5,2004 713
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9
(a) Total error (b) from parameters (c) from laser trackers
Fig. 2 Error ellipse (size multiplied 2000) of position errors by total errors, from parameters and from laser trackers: no. of calibration points = 722
Table 1 Mean and max of standard deviations of parameters by no. of
calibration points 41 to 1058
pitch of points 10 mm 5 mm 2.5 mm 2 mm
no. of point 41 181 722 1058
mean ( m) 9.1 4.0 2.0 1.7
max ( m) 12.5 5.5 2.7 2.3
Table 2 Standard deviations ( m) and coefficient of correlations of 6
parameters; calibration points = 722
bx2 bx3 by3 d1 d2 d3
bx2
bx3
by3
d1
d2
d3
Fig. 3 Position errors after calibration: no. of calibration points = 722
10 m
m
座標測定機のアーティファクト校正(第2 報)
714 精密工学会誌 Vol.70,No.5,2004
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17) (1987)
18)
(1982)
(a) with variance and covariance (b) select small error from 3 points (c) simple average
Fig. 4 Comparisons of 3 averaging methods: no. of calibration points = 181
m
座標測定機のアーティファクト校正(第2 報)
精密工学会誌 Vol.70,No.5,2004 715