Accurate and consistent transformations between design and manufacturing coordinate systems are essential for high quality part production. Fixturing and coordinate measurement are common coordinate referencing techniques which are used to locate points or measurement points on workpiece reference surfaces to establish these coordinate transformations. However, uncertainty sources such as geometric form deviations in workpiece surfaces, tolerances on fixture locators, and errors in coordinate measurements exist. A result is that coordinate transformations established using the locating and measurement points are in herently uncertain. An uncertainty analysis method for coordinate referencing is presented in this paper. The uncertainty interval concept is used to describe essential characteristics of uncertainty sources in coordinate referencing and coordinate transformation relationships. The method is applied to estimating uncertainties in simple and compound coordinate transformation obtained using coordinate referencing in an experimental mold manufacturing system. Results of Monte Carlo simulations are used to show that the uncertainty analysis method gives a consistent and high percentage of coverage in evaluating coordinate referencing in the examples studied.

1.
Groover, M., and Zimmers, E. Jr., 1984, CAD/CAM: Computer-Aided Design and Manufacturing, Prentice-Hall, New Jersey.
2.
Boyes, W. E., 1989, Handbook of Jig and Fixture Design, Second Edition, Society of Manufacturing Engineers, Michigan.
3.
Hocken, R., et al., Technology of Machine Tools, Vol. 5, Machine Tool Accuracy, UCRL-52960-5.
4.
Cogun
C.
,
1992
, “
The Importance of the Application Sequence of Clamping Forces on Workpiece Accuracy
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
114
, pp.
539
543
.
5.
Bai, Y., and Rong, Y., 1993, “Machining Accuracy Analysis for Computer-Aided Fixture Designs,” Proceedings of ASME Winter Annual Meeting: PED-Vol. 64, New Orleans, LA, pp. 507–512.
6.
Rong, Y., Zhu, J., and Li, S., 1993, “Fixturing Feature Analysis for Computer-Aided Fixture Design,” Proceedings of ASME Winter Annual Meeting: PED-Vol. 64, New Orleans, LA, pp. 267–271.
7.
Phillips, S. D., Borchart, B., and Caskey, G., 1993, “Measurement Uncertainty Considerations for Coordinate Measuring Machines,” NISTIR 5170, National Institute of Standards and Technology, Gaithersburg, MD.
8.
Shen
Y.
, and
Duffie
N.
,
1991
, “
Uncertainties in the Acquisition and Utilization of Coordinate Frames in Manufacturing Systems
,”
Annals of the CIRP
, Vol.
40
, No.
1
, pp.
527
530
.
9.
ANSI/ASME PTC 19.1-1985 Part 1, 1985, Measurement Uncertainty, ASME, New York.
10.
CIRP STC ‘Me’ Working Party on 3DU
,
1978
, “
A Proposal for Defining and Specifying the Dimensional Uncertainty of Multi-axis Measuring Machines
,”
Annals of the CIRP
, Vol.
27
, No.
2
, pp.
623
630
.
11.
ISO 5168, 1978, “Measurement of Fluid Flow—Estimation of Uncertainty of a Flow-rate Measurement,” International Organization for Standardization, Geneva, Switzerland.
12.
Kline
S. J.
, and
McClintock
F. A.
,
1953
, “
Describing Uncertainty in Single-Sample Experiments
,”
Mechanical Engineering
, Vol.
75
, pp.
3
8
.
13.
Smith
R.
, and
Cheeseman
P.
,
1986
, “
On the Representation and Estimation of Spatial Uncertainty
,”
The International Journal of Robotic Research
, Vol.
5
, No.
4
, pp.
56
68
.
14.
Smith, R., et al., 1988, “Estimating Uncertain Spatial Relationships in Robotics,” Uncertainty in Artificial Intelligence 2, Elsevier Science Publishers B. V., pp. 435–461, North Holland.
15.
Donmez
M. A.
,
Blomquist
D. S.
,
Hocken
R. J.
,
Liu
C. R.
, and
Barash
M. M.
,
1986
, “
A General Methodology for Machine Tool Accuracy Enhancement by Error Compensation
,”
Precision Engineering
, Vol.
8
, No.
4
, pp.
187
196
.
16.
Treib
T. W.
,
1987
, “
Error Budgeting—Applied to the Calculation and Optimization of the Volumetric Error Field of Multiaxis Systems—
Annals of the CIRP
, Vol.
36
, No.
1
, pp.
365
368
.
17.
Siddall, J. N., 1982, Optimal Engineering Design, Marcel Dekker, Inc., New York.
18.
Coleman, H. W., and Glenn Steele, Jr., W., 1989, Experimentation and Uncertainty Analysis for Engineers, John Wiley & Sons, New York.
19.
Duffie
N.
,
Feng
S.
, and
Kann
J.
,
1988
, “
CAD-Directed Inspection, Error Analysis, and Manufacturing Process Compensation Using Tricubic Solid Databases
,”
Annals of the CIRP
, Vol.
37
, No.
1
, pp.
149
152
.
20.
Molnar, M., 1988, “Design and Implementation of a High Performance Material Handling System for Flexible Manufacturing,” M.S. Thesis, University of Wisconsin-Madison.
21.
Mandel
K.
, and
Duffie
N. A.
,
1987
, “
On-Line Compensation of Mobile Robot Docking Errors
,”
IEEE J. of Robotics and Automation
, Vol.
RA-3
, No.
6
, pp.
591
598
.
22.
Craig, J. J., 1989, Introduction to Robotics: Mechanics and Control, Second Edition, Addison-Wesley, New York.
23.
Wolfram, S., 1988, Mathematica: A System for Doing Mathematics by Computer, Addison-Wesley, California.
24.
Morgan, M. G., and Henrion, M., 1990, Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge Press, New York.
25.
Kalos, M. H., and Whitlock, P. A., 1986, Monte Carlo Methods, Volume I: Basics, John Wiley & Sons, New York.
26.
Press, W. H., et al., 1989, Numerical Recipes in Pascal, Cambridge Press.
27.
Paul, R. P., 1981, Robot Manipulators: Mathematics, Programming, and Control, MIT press.
28.
Hocken, R., 1991, “Sampling Techniques for Coordinate Measuring Machines,” Proc. of CIRP Intl. Sem. on Comp.-Aided Tolerancing, Penn State University.
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