The main purpose of locating schemes are to position parts. The locating scheme utilizes tooling elements, referred to as locators, to introduce geometric constraints. A rigid part is uniquely positioned when it is brought into contact with the locators. By using kinematic analysis we derive a quadratic sensitivity equation that relates position error in locators with the resulting displacement of the part held by the locating scheme. The sensitivity equation which depends on the locator positions and the workpiece geometry around the contact points can be used for locating scheme evaluation, robust fixture design, tolerancing and diagnosis. The quadratic sensitivity equation derived in this paper is novel by adequate dealing with locator contact at nonprismatic surfaces, nonsmall errors, locator error interaction effects and locator errors in arbitrary directions. Theory for comparing the relative gain in precision by using the quadratic sensitivity equation instead of the linear is developed. The practical relevance of the quadratic sensitivity equation is tested through numerical experiments.

1.
Hu
,
S.
, and
Wu
,
S. M.
,
1992
, “
Identifying Root Causes of Variation in Automobile Body Assembly Using Principal Component Analysis
,”
Transactions of NAMRI
,
XX
, pp.
311
316
.
2.
Ceglarek
,
D.
,
Shi
,
J.
, and
Wu
,
S. M.
,
1993
, “
A Knowledge-based Diagnostic Approach for the Launch of Autobody Assembly Process
,”
ASME J. Eng. Ind.
,
116
, pp.
491
499
.
3.
Ceglarek
,
D.
, and
Shi
,
J.
,
1996
, “
Fixture Failure Diagnosis for Autobody Assembly Using Patter Recognition
,”
ASME J. Eng. Ind.
,
118
, pp.
55
66
.
4.
Hu
,
S. J.
,
1997
, “
Stream-of-variation Theory for Automotive Body Assembly
,”
CIRP Ann.
,
46
, No.
1
, pp.
1
6
.
5.
Apley
,
D. W.
, and
Shi
,
J.
,
1998
, “
Diagnosis of Multiple Fixture Faults in Panel Assembly
,”
ASME J. Manuf. Sci. Eng.
,
120
, No.
4
, pp.
793
801
.
6.
Carlson, J. S., 1999, “Root Cause Analysis for Fixtures and Locating Schemes Using Variation Data,” Proceedings of the 6th CIRP International Seminar on Computer-Aided Tolerancing, pp. 111–120.
7.
Ceglarek
,
D.
,
1998
, “
Multivariate Analysis and Evaluation of Adaptive Sheet Metal Assembly Systems
,”
CIRP Ann.
,
47
, No.
1
, pp.
17
22
.
8.
Nee, A. Y. C., Whybrew, K., and Senthil, Kumar A., 1995, Advanced Fixture Design For FMS, Springer-Verlag.
9.
Asada
,
H.
, and
By
,
A.
,
1985
, “
Kinematic Analysis of Workpart Fixturing for Flexible Assembly with Automatically Reconfigurable Fixtures
,”
IEEE Trans. Rob. Autom.
,
RA-1
, No.
2
, pp.
86
94
.
10.
Chou
,
Y-C.
,
Chandru
,
V.
, and
Barash
,
M. M.
,
1989
, “
A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis
,”
ASME J. Eng. Ind.
,
111
, No.
4
, pp.
299
306
.
11.
Menassa
,
R. J.
, and
Devries
,
W. R.
,
1989
, “
Locating Point Synthesis in Fixture Design
,”
CIRP Ann.
,
38
, No.
1
, pp.
165
169
.
12.
Trappey
,
J. C.
, and
Liu
,
C. R.
,
1990
, “
A Literature Survey of Fixture Design Automation
,”
The International Journal of Advanced Manufacturing Technology
,
5
, No.
4
, pp.
240
255
.
13.
Sayeed
,
Q. A.
, and
De Meter
,
E. C.
,
1994
, “
Machining Fixture Design and Analysis Software
,”
Int. J. Prod. Res.
,
32
, No.
7
, pp.
1655
1674
.
14.
Brost
,
R. C.
, and
Goldberg
,
K. Y.
,
1996
, “
A Complete Algorithm for Designing Planar Fixtures Using Modular Components
,”
IEEE Trans. Rob. Autom.
,
12
, No.
1
, pp.
31
46
.
15.
Menassa
,
R. J.
, and
DeVries
,
W. R.
,
1991
, “
Optimization Methods Applied to Selecting Support Positions in Fixture Design
,”
Trans. ASME
,
113
, pp.
412
418
.
16.
Cai
,
W.
,
Hu
,
S. J.
, and
Yuan
,
J. X.
,
1996
, “
Deformable Sheet Metal Fixturing: Principles, Algorithms and Simulations
,”
ASME J. Manuf. Sci. Eng.
,
118
, No.
4
, pp.
318
324
.
17.
Cai
,
Wayne
,
Hu
,
S. Jack
, and
Yuan
,
J. X.
,
1997
, “
Variational Method of Robust Fixture Configuration Design for 3-d Workpieces
,”
ASME J. Manuf. Sci. Eng.
,
119
, No.
4
, pp.
593
602
.
18.
Wang, M. Y., 1999, “Precision Workpiece Fixturing and Localization,” International Conference on Advanced Manufacturing Technology, Xi’an, China, June–1999.
19.
So¨derberg, R., and Carlson, J. S., 1999, “Locating Scheme Analysis for Robust Assemble and Fixture Design,” Proceedings of the 1999 ASME Design Engineering Technical Conference.
20.
Choudhuri
,
S. A.
, and
De Meter
,
E. C.
,
1999
, “
Tolerance Analysis of Machining Fixture Locators
,”
ASME J. Eng. Ind.
,
121
, No.
4
, pp.
273
281
.
21.
Carlson, J. S., and Ahlmark, T., 1997, Production Quality Improvements Using Statistical and Geometrical Analysis of Car Body Measurements, PhD thesis, Chalmers University of Technology Gothenburg Sweden.
22.
Weill, R., Darel, I., and Laloum, M., 1991, “The Influence of Fixture Positioning Errors on the Geometric Accuracy of Mechanical Parts,” Proceedings of CIRP Conference on PE and Ms, pp. 215–225.
23.
Rong, Y., Li, W., and Bai, Y., 1995, “Locating Error Analysis for Computer-aided Fixture Design and Verification,” Proceedings of the Computers in Engineering Conference and the Engineering Database Symposium ASME, pp. 825–832.
24.
Apostol, T., 1974, Mathematical Analysis, Addison Wesley.
25.
Mardia, K. V., Kent, J. T., and Bibby, J. M. 1982, Multivariate Analysis, Academic Press.
26.
Angeles, J., and Kecskemethy, A., 1995, Kinematic and Dynamics of Multi-Body System, Springer-Verlag.
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