Interpretable interval constraint solvers in semantic tolerance analysis

Computer-Aided Design and Applications

Volumn 5, Issue 5, 2008, Pages 654-666

  Wang, Yan ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Generalized interval; Quantified interval constraint satisfaction; Tolerance analysis

Indexed keywords

APRIORI; GENERALIZED INTERVAL; INTERPRETABILITY; INTERVAL CONSTRAINT; INTERVAL CONSTRAINT SATISFACTION; NEW APPROACHES; NON-LINEAR CONSTRAINTS; NUMERICAL ESTIMATION; NUMERICAL RESULTS; POSTERIORI; SEMANTIC TOLERANCE MODELING; TOLERANCE ANALYSIS; TOLERANCING;

NUMERICAL ANALYSIS; NUMERICAL METHODS; SEMANTICS;

FITS AND TOLERANCES;

EID: 73349129986     PISSN: 16864360     EISSN: None     Source Type: Journal    
DOI: 10.3722/cadaps.2008.654-666     Document Type: Article

References (47)

1. Chase, K. W.; Gao, J.; Magleby, S. P.: General 2-D tolerance analysis of mechanical assemblies with small kinematic adjustments, J. of Design and Manufacturing, 5(4), 1995, 263-274.
2. Wang, Y.: Semantic tolerance modeling based on modal interval analysis, In Proc. 2006 NSF Workshop on Reliable Engineering Computing (REC'06), Georgia Institute of Technology, Savannah, GA, 2006, 293-318.
3. Wang, Y.: Semantic tolerance modeling, In Proc. 2006 ASME International Design Engineering Technical Conferences & The Computer and Information in Engineering Conference (IDETC2006), Philadelphia, PA, 2006, Paper No. DETC2006-99069.
4. Wang, Y.: Semantic tolerancing with generalized intervals, Computer-Aided Design & Applications, 4(1-4), 2007,257-266.
5. Hong, Y. S.; Chang, T.-C.: A comprehensive review of tolerancing research, Int. J. of Production Research, 40(11),2002, 2425-2459.
6. Zhang, H. C. (eds.): Advanced Tolerancing Techniques, John Wiley & Sons, New York, 1997.
7. Shah, J. J.; Ameta, G.; Shen, Z.; Davidson, J.: Navigating the tolerance analysis maze, Computer-Aided Design & Applications, 4(5), 2007, 705-718.
8. Wirtz, A.; Gachter, C.; Wipf, D.: From unambiguously defined geometry to the perfect quality control loop, Annals of the CIRP, 42(1), 1993, 615-618.
9. Martinsen, K.: Statistical process control using vectorial tolerancing, In CIRP/JSPE/ASME Proc. 4th CIRP Seminar on Computer Aided Tolerancing, University of Tokyo, Tokyo, Japan, 1995, 195-210.
10. Rivest, L.; Fortin, C.; Morel, C.: Tolerancing a solid model with a kinematic formulation, Computer-Aided Design, 26(6), 1994, 465-476.
11. Clément, A.; Valade, C.; Rivière, A.: The TTRSs: 13 oriented constraints for dimensioning, tolerancing and inspection, Advanced Mathematical Tools in Metrology III, 1996, 24-41.
12. th CIRP Seminar on Computer Aided Tolerancing, University of Tokyo, Tokyo, Japan, 1995, 143-154.
13. rd Seminars on Computer Aided Tolerancing, Cachan, France, 1993, 179-196.
14. th ASME Design Automation Conference, 1999, Paper No. DAC-8587.
15. Whitney, D. E.; Gilbert, O. L.; Jastrzebski, M.: Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies, Research in Engineering Design, 6, 1994, 191-210.
16. Desrochers, A.; Riviere, A.: A matrix approach to the representation of tolerance zones and clearances, Int. J. Advanced Manufacturing Technology, 13, 1997, 630-636.
17. Lafond, P.; Laperrière, L.: Jacobian-based modeling of dispersions affecting pre-defined functional requirements of mechanical assemblies, Proc. IEEE Int. Symp. Assembly & Task Planning, 1999, 20-25.
18. Descrochers, A.; Ghie, W.; Laperrière, L.: Application of a unified Jacobian-torsor model for tolerance analysis, ASME J. Comp. in Sci. Eng., 3(1), 2003, 2-14.
19. Chase, K. W.; Magleby, S. P.; Gao, J.; Sorensen, C. D.: Including geometric feature variations in tolerance analysis of mechanical assemblies, IIE Transactions, 28(10), 1996, 795-807.
20. Gao, J.; Chase, K. W.; Magleby, S. P.: Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments, IIE Transactions, 30(4), 1998, 367-377.
21. Sacks, E.; Joskowicz, L.: Parametric kinematic tolerance analysis of general planar systems, Computer-Aided Design, 30(9), 1998, 707-714.
22. Zou, Z.; Morse, E.P.: A gap-based approach to capture fitting conditions for mechanical assembly, Computer-Aided Design, 36(8), 2004, 691-700.
23. Zhang, G.: Simultaneous tolerancing for design and manufacturing, Intl J. Prod. Res., 34(12), 1996, 3361-3382.
24. Liu, S.; Hu, S.: Variation simulation for compliant sheet metal assemblies using finite element methods, ASME J. of Manufacturing Science & Engineering, 119(3), 1997, 368-374.
25. Chang, M.; Gossard, D. C.: Modeling the assembly of compliant, non-ideal parts, Computer-Aided Design, 29(10),1997, 701-708.
26. Long, Y.; Hu, S.: A unified model for variation simulation of sheet metal assemblies, In Geometric Design Tolerancing: Theories, Standards, and Applications, ed. by H.A. Elmaraghy, London: Chapman & Hall, 1998, pp.208-219
27. Shiu, B. W.; Ceglarek, D.; Shi, J.: Muilti-stations sheet metal assembly modeling and diagnostics, Trans. NAMRI, 24, 1996, 199-204.
28. Camelio, J.; Hu, S. J.; Ceglarek, D.: Modeling variation propagation of multi-station assembly systems with compliant parts, ASME J. of Mechanical Design, 125(4), 2003, 673-681.
29. Huang, W.; Lin, J.; Kong, Z.; Ceglarek, D.: Stream-of-variation (SOVA) modeling - Part II: A generic 3D variation model for rigid body assembly in multistation assembly processes, ASME J. Manu. Sci. & Eng., 129(4),2007, 832-842.
30. Gardenes, E.; Sainz, M. A.; Jorba, L.; Calm, R.; Estela, R.; Mielgo, H.; Trepat, A.: Modal intervals, Reliable Computing, 7(2), 2001, 77-111.
31. Dimitrova, N. S.; Markov, S. M.; Popova, E. D.: Extended interval arithmetics: new results and applications, in L. Atanassova; J. Herzberger (Eds.): Computer Arithmetic and Enclosure Methods, Elsevier, 1992, 225-232.
32. Shary, S. P.: A new technique in systems analysis under interval uncertainty and ambiguity, Reliable Computing, 8(2), 2002, 321-418.
33. Moore, R. E.: Interval Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1966.
34. Kaucher, E.: Interval analysis in the extended interval space IR, Computing Supplementum, 2, 1980, 33-49.
35. Hyvönen, E.: Constraint reasoning based on interval arithmetic: the tolerance propagation approach, Artificial Intelligence, 58, 1992, 71-112.
36. Benhamo, F.; McAllester, D.; Van Hentenryck, P.: CLP(Intervals) revisited, Proc. ILPS'94, 1994, pp.124-138.
37. Collins, G. E.: Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition, Lecture Notes in Computer Science, 33, 1975, 134-183.
38. Collins, G. E.; Hong, H.: Partial cylindrical algebraic decomposition for quantifier elimination, J. of Symbolic Computing, 12, 1991, 299-328.
39. Benhamou, F.; Goualard, F.: Universally quantified interval constraints, Proc. CP2000, Lecture Notes in Computer Science, 1894, 2000, 67-82.
40. Benhamou, F.; Goualard, F.; Languenou, E.; Christie, M.: Interval constraint solving for camera control and motion planning, ACM Trans. Computational Logic, 5(4), 2004, 732-767.
41. Shary, S. P.: Interval Gauss-Seidel method for generalized solution sets to interval linear systems, Reliable Computing, 7, 2001, 141-155.
42. Sainz, M. A.; Gardenes, E.; Jorba, L.: Formal solution to systems of interval linear or non-linear equations, Reliable Computing, 8(3), 2002, 189-211.
43. Ratschan, S.: Continuous first-order constraint satisfaction, In Artificial Intelligence, Automated Reasoning, and Symbolic Computation, ed. By J. Calmet, B. Benhamou, O. Caprotti, L. Henocque, and V. Sorge, Lecture Notes in Computer Science, 2385, 2002, 181-195.
44. Ratschan, S.: Efficient solving of quantified inequality constraints over the real numbers, ACM Trans. on Computational Logic, 7(4), 2006, 723-748.
45. Herrero, P.; Sainz, M. A.; Vehi, J.; Jaulin, L.: Quantified set inversion with applications to control, Reliable Computing, 11(5), 2005, 369-382.
46. Goldztejn, A.; Jaulin, L.: Inner and outer approximations of existentially quantified equality constraints, Proc. CP2006, Lecture Notes in Computer Science, 4204, 2006, 198-212.
47. Neumaier, A.: Interval Methods for Systems of Equations, University Press, Cambridge, 1990.