A machining fixture controls position and orientation of datum references (used to define important functional features of the geometry of a mechanical part) relative the reference frame for an NC program. Inaccuracies in fixture’s location scheme result in a deviation of the work part from its nominal specified geometry. For a part to be acceptable this deviation must be within the limits allowed by the geometric tolerances specified. This paper addresses the problem of characterizing the acceptable level of inaccuracy in the location scheme so that the features machined on the part comply with the limits associated with its geometric tolerances. First we solve the “forward problem” that involves predicting the tolerance deviation resulting at a feature from a known set of errors on the locators. However, the paper concentrates on solving the “inverse” problem that involves establishing bounds on the errors of the locators to ensure that the limits specified by geometric tolerances at a feature are not violated.

1.
American Society of Mechanical Engineers, 1994, ASME Y14.5.1M-1994 Standard, Mathematical Definition of Dimensioning and Tolerancing Principles, American Society of Mechanical Engineers.
2.
American Society of Mechanical Engineers, 1994, ASME Y14.5M-1994 Standard, Dimensioning and Tolerancing, American Society of Mechanical Engineers.
3.
Laloum, M., and Weill, R., 1991, “The Influence of Fixture Positioning Errors on the Geometric Accuracy of Mechanical Parts,” Proceedings of CIRP Conference on PE & MS, 215–225.
4.
Asada
,
H.
, and
By
,
A. B.
,
1985
, “
Kinematic Analysis of Workpart Fixturing for Flexible Assembly With Automatically Reconfigurable Fixtures
,”
IEEE J. Rbo. Autom.
,
RA-1
(
2
), pp.
86
94
.
5.
Choudhuri
,
S. A.
, and
De Meter
,
E. M.
,
1999
, “
Tolerance Analysis of Machining Fixture Locators
,”
ASME J. Manuf. Sci. Eng.
,
121
, pp.
273
281
.
6.
Wang, M. Y., 1999, “Automated Fixture Layout Design for 3D Workpieces,” Proceedings of the 1999 IEEE Conference on Robotics and Automation, pp. 1577–1582.
7.
Marin
,
R.
, and
Ferreira
,
P.
,
2001
, “
Kinematic Analysis and Synthesis of Deterministic 3-2-1 Locator Schemes for Machining Fixtures
,”
ASME J. Manuf. Sci. Eng.
,
123
(
4
), pp.
708
719
.
8.
Marin
,
R.
, and
Ferreira
,
P.
,
2002
, “
Optimal Placement of Fixture Clamps: Minimizing the Maximum Clamping Forces
,”
ASME J. Manuf. Sci. Eng.
,
124
(
3
), pp.
686
694
.
9.
Marin
,
R.
, and
Ferreira
,
P.
,
2002
, “
Optimal Placement of Fixture Clamps: Maintaining Form Closure and Independent Regions of Form Closure
,”
ASME J. Manuf. Sci. Eng.
,
124
(
3
), pp.
676
685
.
10.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
11.
Bazaraa, M. S., Sherali, H. D., and Shetty, C. M., 1993, Nonlinear Programming. Theory and Algorithms, John Wiley & Sons, 2nd Edition.
You do not currently have access to this content.