Due to the difficulty of modeling the manufacturing deviations reliably, the existing geometric models, to date, have only con sidered the exact description of parts and assemblies. Yet, the tolerance representation and propagation issues in assemblies are crucial to answer parallel design of product and process queries. Many formal and informal methods have been developed. However, most proved special cases of the ANSI Y14.5M-82 specification standard. Also, the descriptions provided in actual solid and feature based de sign modelers are inadequate to ascertain a clear taxonomy of tolerance specifications, neither do they help address the assembly toler ance analysis and/or synthesis issues.
The paper purposes to discuss the tolerance representation schemes as well as their underlying philosophies. Then, because toler ance analysis and tolerance synthesis in assemblies are required, among other tasks, to assign functional tolerances, measure the manufacturability and the interchangeability of parts in assemblies, ease tolerance inspection and evaluate costs of alternative assembly sequences, we shall assess deterministic and statistical methods.
Prasad, B., 1996. Concurrent Engineering Fundamental, Volune I, 1/e: Integrated Product and Process Organization, New Jersey : Upper Saddle River, Prentice Hall PTR.
2.
Reddy, R., Srinivas, K., Jagannathan, V. and Karinthi, R., 1993. "Computer support for concurrent engineering," Computer, 26: 4-12.
3.
Reidel, J. and Dewan, P., 1993. "Towards computer supported concurrent software engineering ," Computer, 26: 11-17.
4.
Clement, A. and Bourdet, P., 1998. "Modeling, representation and processing of tolerances, tolerance inspection: A survey of current hypothesis," Edit Elmaraghy, H. A., Geometric Design Tolerancing: Theories, Standards andApplications, Chapman & Hall, 1-33.
5.
Dimensioning and Tolerancing, 1982, ANSI Y 14.5M, ASME, USA.
6.
Dimensioning and Tolerancing, 1994, ASME Y14.5M, ASME, USA.
7.
Requicha, A.A.G. and Voelcker, H.B., 1983, "Solid modeling: current status and research directions," IEEE Comput. Graph & Applic., 7 (3), 25-37.
8.
Rossignac, J.R. and Requicha, A.A.G.,1986, "Offsetting operations in solid modeling," Computer-Aided Geom. Des., (3): 129-148.
9.
Voelcker, H.B., 1998. "Remarks on the Essential Elements of Tolerancing Schemes," edit Elmaraghy, H. A., Geometric Design Tolerancing: Theories, Standards and Applications, Chapman & Hall, 119-121.
10.
Roy, U. and Liu, C.R., 1988, "Feature based representational scheme of solid modeler for providing dimensioning and tolerancing information," Robot & Comput. Integr. Manuf., 3 (4), 335-345.
11.
Juster, N.P. , 1992, "Modeling and representation of dimensions and tolerances: a survey," Computer Aided Design , 1 (24), 3-17.
12.
Hillyard, R.C. and Braid, I.C., 1978, "Characterizing non ideal shapes in terms of dimensions and tolerances," Computer Graphique, 3 (12), 234-238.
13.
Gossard, D.C. , Zuffante, R.P. and Sakurai, H., 1988, "Representing dimensions, tolerances and features in MCAE system," IEEE Comput, Graph. & Applic., 2 (8), 51-59.
14.
Aldefeld, B. , 1988, "Variation of geometries based on a geometric reasoning method," Comput. Aided Design , 3 (20), 117-126.
15.
Hoffmann, P. , 1982, "Analysis of tolerances and process inaccuracies in discrete part manufacturing," Comput. Aided Design, 2 (14), 83-88.
16.
Bernstein, N.S. and Priess, K., 1989. Representation of tolerance information in solid models, In Ravani, B. (Ed.) Advances in Design Automation, Computer Aided and Computational DesignASME, 37-48, USA.
17.
Requicha, A.A.G. and Chan, S.C., 1986, "Representation of geometric features, tolerances and attributes in solid modelers based on constructive solid geometry," IEEE J. Robotics and Automation , 3 (2), 156-165.
18.
Turner, J.U. and Wozny, M.J., 1990, "The M-space theory of tolerances," Proceedings of the Advances in Design Automation, 1, 217-225, Chicago, Illinois.
19.
Guilford, J.D. , Turner, J.U. and Wozny, M.J., 1992, "Representing geometric tolerances in solid models," Computers in Engineering Journal , 1, 319-327.
20.
Turner, J.U. and Wozny, M.J., 1987, "Tolerance in computer aided geometric design," VisualComputer, 4 (3), 214-226.
21.
Gopin, A.M. and Gossard, D.C., 1979, "Symbolic dimensioning," Conf. Comput. Graphics in CAD/CAM, MIT, 268-281, USA.
22.
Fitzgerald, W.J., 1981, "Using axial dimensions to determine the proportions of line drawings in computer graphics," Comput. Aided Design, 6 (13), 377-382.
23.
Yu, Y.C. , Liu, C.R. and Kashyap, R.F., 1986, "A variational solid model for mechanical parts," ASME Winter Annual Meeting, PED, 21, 237-254.
24.
Fleming, A., 1987, "Analysis of uncertainties and geometric tolerances in assemblies of parts," PhD thesis, Univ. Edinburgh, U.K.
25.
Inui, M., Minura, M. and Kimura, F., 1995, "Relative positioning of assembled parts with small geometric deviations by using hierarchically approximated configuration space ," Proc. IEEE Int. Conf. Robot. Automat., 1605-1612.
26.
Suziki, H., Kimura, F. and Sata, T., 1985, "Treatment of dimensions on product modeling concept ," In Design and Synthesis, North Holland , 491-496.
27.
Todd, P., 1986, "An algorithm for determining consistency and manufacturability of dimensioned drawings," Knowledge Engineering and Computer Modeling in CAD, Butterworths, U.K, 36-41.
28.
Kondo, K., 1990, "PIGMOD: parametric and interactive geometric modeler for mechanical design," Comput. Aided Design, 10 (22), 633-644.
29.
Clement, A. and Riviere, A., 1993, "Tolerancing versus nominal modeling in the next generation of CAD/CAM systems," CIRP, Comput. Aided Tolerancing , 3rd seminar, Cachan, 97-114.
30.
Jayaraman, R. and Srinivasan, V., 1989, "Geometric tolerancing 1: virtually boundary requirements," IBM J. Res. & Develop. , 2 (33), 90-104.
31.
Bennich, P., 1998. "International standards for design tolerancing review and future perspective," Edit Elmaraghy, H. A., Geometric Design Tolerancing: Theories, Standards and Applications; Chapman & Hall , 37-51.
32.
Homem De Mello, L.S. and Sanderson , A.C., 1990, " AND/OR Graph representation of assembly plans," IEEE Trans., Robotics and Automation RA, 6 (2), 188-199.
Boothroyd, G. , 1991, Assembly Automation and Product Design, Marcel Dekker Inc.
35.
Bronsvoort, W.F. and Jansen, F.W., 1994. "Multi-view feature modeling for design and assembly," Advances in Feature Based Manufacturing , J. J. Shah, M. Mantyla and D. S. Nau (editors), Elsevier, 315-330.
36.
Danloy, J., Petit, F., Leroy, A., De Lit, P. and Rekiek, B., 1999, "A pragmatic approach for precedence graph generation ," Proc. of the 1999 IEEE International Symposium on Assembly and Task Planning (ISATP99),387-392.
37.
Baldwin, D.F., 1990, "Algorithmic method and software tools for the generation of mechanical assembly sequences," S.M. Thesis, Dept. of Mech. Eng., MIT, Cambridge, Massachusetts .
38.
van Emmerik, M. J. G. M. , 1990, "Interactive design of parameterized 3D models by direct manipulation," Ph.D. Thesis, Delft University of Technology, Delft University Press, Delft.
39.
De Fazio T. L., Edsall, A.C., Gustavson, R.E., Hernandez, J.A., Hutchins, P.M., Leung, H.W., Luby, S.C., Metzinger, R.W., Nevins, J.L., Tung, K.K., and Whitney, D.E., 1990, "A prototype for feature based design for assembly," CSDL-P-2917 , Charles Stark Draper Laboratory, Cambridge, Massachusetts.
40.
Sanderson, A.C., 1999, "Assemblability base on maximum likelihood configuration of tolerances," IEEE Transactions on Robotics and Automation, 3 (15), 568-572.
41.
Nevins, J.L. and Whitney, D.E., 1989. Concurrent Design for Products and Processes, McGraw-Hill, New York.
42.
Lee, S. and Yi, C., 1998, "An analytical approach to assemblability analysis ," Proc. of the 1998 IEEE International Conference on Robotics and Automation, 1484-1489.
43.
Whitney, D.E. , Gilbert, O.L. and Jastrzebski , M., 1994, " Representation of geometric variations using matrix transforms for statistical analysis on assemblies," Research. in Engineering Design, 6, 191-210.
44.
Jastrzebski, M., 1991, "Software for analysis of 3D statistical tolerance propagation in assemblies using closed form matrix transforms," S.M. Thesis , MIT, Dept. of Mechanical Engineering , Cambridge.
45.
Desrochers, A. and Delbart, O., 1998, "Determination of part position uncertainty within mechanical assembly using screw parameters," Edit Elmaraghy, H. A., Geometric Design Tolerancing: Theories, Standards and Applications, Chapman & Hall, 185-196.
46.
Hirukawa, H., Matsui, T. and Takase, K., 1991, "A general algorithm for derivation and analysis of constraints for motion of polyhedra in contact," Proc. of the Int. Workshop on Intelligent Robot Systems, 38-43.
47.
Srikanth, S. and Turner, J.U., 1990, "Toward a unified representation of mechanical assembly," Engineering with Computers, 6 (2), 103-112.
48.
Wang, N. and Oszoy, T.M., 1990, "Representation of assemblies for automatic tolerance chain generation," Engineering with Computers, 6 (2), 121-126.
49.
Mantripragada, R., Cunningham and Whitney, D.E., 1997, "Assembly oriented design: a new approach to designing assemblies," In M. J. Pratt, R. D. Sniram, and M. J. Wosny, editors, Product Modeling for Computer Integrated Design and Manufacture , 308-324, Chapman & Hall.
50.
Ashiagbor, A., Liu, H.C. and Nnaji, B.O., 1998, "Tolerance control and propagation for the product assembly modeler," Int. J. PROD. RES, 1 (36), 75-93.
51.
Liu, H.C., 1992, "Design with spatial relationships and tolerances specification and propagation for a product modeler," PhD thesis, Univ. of Massachusetts at Amherst.
52.
Bjorke, O., 1989. Computed Aided Tolerancing, 2nd edition, ASME Press, New York .
53.
Braun, P.R., Morse, E.P., and Voelcker, H.B., 1997, "Research in statistical tolerancing: Example of intrinsic non normalities and their effects," Proc. 5th CIRP Seminar on Computer Aided Tolerancing, edit Elmaraghy, H. A., University of Toronto, Canada, 1-12.
54.
Mansoor, E.M. , 1963, "The application of probability to tolerances used in engineering designs," Proc. Inst. ofMech. Eng., 1 (178), 29-51.
55.
Evan, D.H., 1975, "Statistical tolerancing: the state of the art. Part II, methods for estimating moments," J. Quality Tech ., 1 (7), 1-12.
56.
Parkinson, D.B., 1985, "Assessment and optimization of dimensional tolerances," ComputerAidedDesign, 17,191-199.
57.
Chase, K.W. , and Greenwood, W.H., 1988, "Design issue in mechanical tolerance analysis," Mfng. Review, 1 (1), 50-59.
58.
Nigam, S.D. and Turner, J.U., 1995, "Review of statistical approaches to tolerance analysis," Comput. Aided Design, 1 (27), 6-15.
59.
Kusiak, A., and Ferig, C.X., 1995, "Deterministic tolerance synthesis, a comparative study ," Computer Aided Design, 10 (27), 759-768.
60.
Skowronski, V.J., and Turner, J.U., 1997, "Using Monte Carlo variance reduction in statistical tolerance synthesis," Computer Aided Design, 1(29), 63-69.
61.
Rubinstein, Y.R. , 1981. Simulation and the Monte-Carlo Method, John Wiley & Sons Inc., New York.
62.
Martino, P.M. , and Gabriele, G.A., 1990, "Application of variational geometry to the analysis of mechanical tolerances," Proc. from ASME Advances in Design Automation Conference , 1, Montreal.
63.
Prasad, B., 1997. Concurrent Engineering Fundamental, Volume II, 1/e: Integrated Product Development, New Jersey: Upper Saddle River, Prentice Hall PTR.
64.
Varghese, P. , Braswell, R.N., Wang , B. and Zhang, C., 1996, " Statistical tolerance analysis using FRPDF and numerical convolution," Computer Aided Design, 9 (28), 723-732.
65.
Dong, Z., 1993, "Design for automated manufacturing," In Concurrent Engineering: Automation, Tools and Techniques, A. Kusiak (ed.), New York, Wiley.
66.
Kumar, S. and Raman, D., 1992, "Computer Aided Tolerancing, the past, the present and the future," In Journal of Design and Manufacturing, 2.
67.
Andrew Liou, Y.H., Lin, P.P., Lindeke , R.R. and Chiang, H.D., 1993, "Tolerance specification of robot kinematic parameters using an experimental design technique—the Taguchi method," Robotics & Computer Integrated Manufacturing , 3 (10), 199-207.
68.
Gadallah, M. and Elmaraghy, H., 1994, "The tolerance optimization problem using a system of experimental design," In Advances in Design Automation, ASME Publishers, N.Y., 69, 251-265.
69.
Iannuzzi, M.P. and Sandgren, E., 1995, "Tolerance optimization using genetic algorithms: Benchmarking with manual analysis," In CIRP Conference on Computer Aided Tolerancing, Paris.
70.
Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P.,1983, "Optimization by simulated annealing," Science, 220, 671-680.
71.
Zhang, C. and Wang, H., 1993, "The discrete tolerance optimization problem," Manufacturing Review, 6 (1), 60-71.
72.
Chase, K.W. , Gao, J., Magleby, S.P. and Sorenson, C.D., 1996, "Including geometric feature variations in tolerance analysis of mechanical assemblies," IIE Trans., 28, 795-807.
73.
Braun, P.R., Morse, E.P. and Voelcker, H.B., 1998, "Research in statistical tolerancing: examples of intrinsic non normalities, and their effects," edit Elmaraghy, H. A., Geometric Design Tolerancing: Theories, Standards and Applications, Chapman & Hall, 52-63.
74.
Trabelsi, A. and Delchambre, 2000, "Tolerance Synthesis using the worst case, the Taguchi, the Simulated Annealing and the Genetic Approaches: a comparative study," (paper in preparation).
