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Representation and reasoning of geometric tolerances in design

Published online by Cambridge University Press:  27 February 2009

Jhy-Cherng Tsai
Affiliation:
Mechanical Engineering Department, National Chung-Hsing University, Taichung, Taiwan 40227, ROC
Mark R. Cutkosky
Affiliation:
Mechanical Engineering Department, Stanford University, Stanford, CA 94305, USA

Abstract

The geometric dimensioning and tolerancing (GD&T) specifications of a design are directly associated with its performance and functional requirements. They also govern the manufacturing and quality control processes needed to achieve those requirements. This paper reviews recent work in geometric tolerance representation and reasoning and presents a generic and uniform graph-based representation scheme, called the Tolerance Network, to represent GD&T specifications across a part or assembly. The network can accommodate GD&T specifications related to the function, behavior, manufacturing, and inspection requirements embedded in design specifications and supports the use of different types of tolerances. The network also accommodates common design practices such as the specification of overconstrained features and parts. The necessary properties of such a network are discussed that allow under- and overconstrained design specifications to be detected and analyzed.

Type
Articles
Copyright
Copyright © Cambridge University Press 1997

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References

REFERENCES

Akella, P., Siegwart, R., & Cutkosky, M. R. (1991). Manipulaing with soft fingers: Contact force control. Proc. of the 1991 IEEE Int. Conf. on Robotics and Automation, 652657.CrossRefGoogle Scholar
ANSI Y14.5M (1994). Geometric dimensioning and tolerancing.Google Scholar
ASME Y14.5.1 (1994). Mathematical definition of dimensioning and tolerancing principles.Google Scholar
Berstein, N. S., & Preiss, K. (1989). Representstion of tolerance information in solid modles. Proc. of the 1989 AMSE Design Techinical Conf., 3748.Google Scholar
Binford, T., Frants, L., Cutkosky, M.R., & Tsai, J.-C. (1990). Representation and propagation of tolerances for CAD/CAM systems. Proc. of the 1FIP WG5.2 Workshop on Geometric Modeling.Google Scholar
Bjorke, O. (1989). Computer-Aided Tolerancing, 2nd ed.ASME Press, New York.Google Scholar
Cutkosky, M.R., Tenenbaum, J.M., & Muller, D. (1988). Features in process-based design. Proc. of the 1988 ASME Int. Computer in Engineering Conf., 557562.Google Scholar
DeFazio, 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., & Whitney, D.E. (1990). Prototype of feature-based design for assembly. Proc. of the 1990 ASME Design Technical Conf., 916.CrossRefGoogle Scholar
Evans, D.H. (1974). Statistical tolerancing: The state of the art part I: Background. J. Quality Technol. 6(4), 188195.CrossRefGoogle Scholar
Faux, I.D. (1990). Modelling of components and assemblies in terms of shape primitives based on standard dimensioning and tolerancing surface features. In Geometric Modeling for Product Engineering, pp. 259275. Elsevier Science, Amsterdam, North-Holland.Google Scholar
Fleming, A. (1988). Geometric relationships between toleranced features. Artif. Intell. 37(1–3), 403412.CrossRefGoogle Scholar
Gossard, D.C., Zuffante, R.P., & Sakurai, H. (1988). Representing dimensions, tolerances, and features in MACE systems. Comput. Graphics and Applications 8(2), 5159.CrossRefGoogle Scholar
Gossard, D.C., Light, R.A., & Lin, V.C. (1980). The use of symbolic dimensioning in computer aided design. Annals of the CIRP 29, 567569.CrossRefGoogle Scholar
Harary, F. (1969). Graph theory. Addison-Wesley, Reading, MA.CrossRefGoogle Scholar
Hillyard, R.C., & Braid, I.C. (1978). Analysis of dimensions and tolerances in computer-aided mechanical design. Computer-Aided Design 10(3), 161166.CrossRefGoogle Scholar
Hutchinson, S.A., & Kak, A.C. (1990). Spar: A planner that satisfies operational and geometric goals in uncertain environments. AI Magazine 11(1), 3161.Google Scholar
ISO (1992). Product Data Representation and Exchange (STEP) Part 1: Overview and fundamental principles.Google Scholar
ISO-1101 (1983). Geometric tolerancing: Toleranced characteristics and symbols—examples of indication and interpretation.Google Scholar
Kimura, F., Suzuki, H., Ando, H., Sata, T., & Kinosada, A. (1987). Variational geometry based logical constraints and its application to product modelling. Annals of CIRP 36(1), 6568.CrossRefGoogle Scholar
Kimura, F., Suzuki, H., & Wingard, L. (1986). A uniform approach to dimensioning and tolerancing in product modeling. Proc. of CAPE'86, 165178.Google Scholar
Kirchner, H.O.K., Gurumoorthy, B., &; Prinz, F.B. (1987). A perturbation approach to robot calibration. Int. J. Robotics Res. 6(4), 4759.CrossRefGoogle Scholar
Konkar, R. (1993). Incremental kinematic analysis and symbolic kinematic synthesis of mechanism. PhD Dissertation. Stanford University.Google Scholar
Konkar, R., Cutkosky, M.R., & Tenenbaum, J.M. (1990). Toward an assembly editor for concurrent product and process design. Proc. of the IF1P WG5.2 Workshop on Geometric Modeling.Google Scholar
Lee, K., & Gossard, D.C. (1985). A hierarchical data structure for representing assemblies: Part 1. Computer-Aided Design 17(1), 1519.CrossRefGoogle Scholar
Light, R., & Gossard, D.C. (1982). Modification of geometry models through variational geometry. Computer-Aided Design 14(4), 209214.CrossRefGoogle Scholar
Lin, V.C, Gossard, D.C, & Light, R.A. (1981). Variational geometry in computer aided design. Comput. Graphics 15(3), 171177.CrossRefGoogle Scholar
Martino, P. (1992). Simplification of feature based models for tolerance analysis. Proc. of 1992 ASME Int. Computer in Engineering Conf.CrossRefGoogle Scholar
Requicha, A.A. (1983). Toward a theory of geometric tolerancing. Int. J. Robotics Res. 2(4), 437464.CrossRefGoogle Scholar
Requicha, A.A. (1993). Mathematical definition of tolerance specifications. Manufact. Rev. 6(4), 269275.Google Scholar
Requicha, A.A., & Chan, S.C. (1986). Representation of geometric features, tolerances, and attributes in solid modelers based on constructive geometry. J. Robotics and Automation RA- 2(3), 156166.Google Scholar
Requicha, A.A., & Whalen, T.W. (1991). Representations for assemblies. In Computer-Aided Mechanical Assembly Planning (de Mello, L.S.H. and Lee, S., Eds.), Chap. 2, pp. 1539. Kluwer Academic, Boston.CrossRefGoogle Scholar
Roy, U., Banerjee, P., & Liu, C.R. (1989). Design of an automated assembly environment. Computer-Aided Design 21(9), 567569.CrossRefGoogle Scholar
Roy, U., & Liu, C.R. (1988). Feature-based representational scheme of a solid modeler for providing dimensioning and tolerancing information. Robotics Computer-Integrated Manufact. 4(3/4), 335345.CrossRefGoogle Scholar
Sata, T., Kimura, F., & Fujita, T. (1985). Designing machine assembly structure using geometric constraints in product modelling. Annals of CIRP 34(1), 169172.CrossRefGoogle Scholar
Shah, J., & Yan, Y. (1996). Representation and mapping of geometric dimensions from design to manufacturing. Proc. of the 1996 ASME Design Engineering Technical Conf., 96-DETC/DAC-1481.CrossRefGoogle Scholar
Slocum, A.H. (1992). Precision machine design. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Sowa, J.F. (1992). Semantic networks. In Encyclopedia of Al (Shapiro, S., Ed.), Vol. 2, 2nd ed., pp. 14931511. John Wiley & Sons, New York.Google Scholar
Thomas, F. (1991). Graphs of Kinematic constraints. In Computer-Aided Mechanical Assembly Planning (de Mello, L.S.H. and Lee, S., Eds.), Chap. 4. pp. 81110. Kluwer Academic, Boston.CrossRefGoogle Scholar
Tsai, J.-C. (1993). Tolerance reasoning for concurrent CAD/CAM systems. PhD Dissertation. Stanford University.Google Scholar
Tsai, J.-C. (1996). Geometric tolerance analysis for mechanism design. Proc. of the 1996 ASME Design Engineering Technical Conf., 96-DETC/DAC-1053.CrossRefGoogle Scholar
Tsai, J.-C., & Cutkosky, M.R. (1992). Tolerance reasoning for concurrent design. Proc. of the 2nd Int. Conf. on Automation Technol., 4147.Google Scholar
Tsai, J.-C., Guo, D.-N., & Cheng, K.-D. (1995). Variational kinematic models for geometric tolerances and fittings. Proc. of the 4th Nat. Applied Mechanisms and Robotics Conf., AMR 95107.Google Scholar
Tsai, J.-C., Konkar, R., & Cutkosky, M.R. (1992). Issues in incremental analysis of assemblies for concurrent design. In Artificial Intelligence in Design '92 (Gero, J., Ed.), pp. 617635. Kluwer Academic, Dordrecht, The Netherlands.Google Scholar
Turner, J.U. (1987). Tolerances in computer-aided geometric design. PhD Dissertation. Rensselaer Polytechnic Institute.CrossRefGoogle Scholar
Turner, J.U. (1990). Relative positioning of parts in assembly using mathematical programming. Computer-Aided Design 22(7), 394400.CrossRefGoogle Scholar
Wang, N., & Ozsoy, T.M. (1991). A scheme to represent features, dimensions, and tolerances in geometric modeling. J. Manufact. Sys. 10(3), 233240.CrossRefGoogle Scholar
Wilson, R.H. (1992). On geometric assembly planning. PhD dissertation. Stanford University.Google Scholar
Yu, Y.C., Liu, C.R., & Kashyap, R.L. (1988). A variational solid model for mechanical parts. Proc. of the USA-Japan Symp. Advances in Flexible Automation and Robotics, 237244.Google Scholar
Ziegert, J.C., Olson, D.G., & Datseris, P. (1992). Description of machine tool errors using screw coordinates. J. Machine Design 114, 531535.CrossRefGoogle Scholar