Abstract
This paper introduces the ‘maximum material part’ (MMP) in higher dimensions, extending the 1-D MMP introduced in [9]. Given a toleranced object, an MMP is an ‘in-tolerance’ part that contains (as in set containment) all other in-tolerance parts, under suitable rigid motions. We show how tolerances leading to MMPs may be defined and how these lead to elegant solutions for the analysis of ‘floating’ assemblies of rigid toleranced objects. MMPs are also useful in motion planning with toleranced objects.
We examine links between MMPs and geometric tolerancing, and propose extensions to tolerancing standards that would facilitate the definition of MMPs. We suggest future research that might extend our approach to broader classes of tolerance and assembly specifications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing (ASME Y14.5M-1994), ASME, New York, NY.
American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles (ASME Y14.5.1M-1994), ASME, New York, NY.
Boyer, M., Stewart, N. F., 1991, “Modeling spaces for toleranced objects,” The International Journal of Robotics Research, vol. 10, no. 5.
Boyer, M., Stewart, N. F., 1992, “Imperfect form tolerancing on manifold objects: a metric approach,” The International Journal of Robotics Research, vol. 11, no. 5.
Hoffman, C. M., 1989, Geometric and Solid Modeling: An Introduction, Morgan Kaufmann, San Mateo, CA.
Jayaraman, R., Srinivasan, V., 1989, “Geometric tolerancing: I. Virtual boundary requirements,” IBM J. of Research and Development, Vol. 33, No. 2, pp. 90–104.
Joskowicz, L., Sacks, E., Srinivasan, V., 1997, “Kinematic Tolerance Analysis,” Computer Aided Design, vol. 29, no. 2, pp. 147–157.
Lozano-Perez, T., 1983, “Spatial planning: a configuration space approach”, IEEE Transactions on Computers, vol. C-32, no. 2, pp. 108–120.
Parratt, S. W., May 1994, “A theory of one-dimensional tolerancing for assembly,” Ph.D. dissertation, Mechanical Engineering, Cornell University, Ithaca, NY.
Requicha, A. A. G., 1977, “Part and assembly description languages I: Dimensioning and tolerancing,” TM-19, Production Automation Project, Univ. of Rochester, Rochester, NY.
Requicha, A. A. G., 1977, “Mathematical models of rigid solid objects,” TM-28, Production Automation Project, Univ. of Rochester, Rochester, NY.
Requicha, A. A. G., Tilove, R. B., 1978, “Mathematical foundations of constructive solid geometry,” TM-27a, Production Automation Project, Univ. of Rochester, Rochester, NY.
Requicha, A. A. G., 1980, “Representations for rigid solids: theory, methods, and systems,” ACM Computing Surveys, vol. 12, no. 4, pp. 437–464.
Requicha, A. A. G., 1983, “Toward a theory of geometric tolerancing,” The International Journal of Robotics Research, vol. 2, no. 4, pp. 45–60.
Requicha, A. A. G., 1984, “Representations of tolerances in solid modeling: issues and alternative approaches,” in Solid Modeling by Computers, Pickett, M. S., and Boyse, J. W., eds., Plenum Publishing, New York, NY, pp. 3–22.
Requicha, A. A. G., Whalen, T. W., 1992 “Representations for assemblies,” Institute for Robotics and Intelligent Systems report #267, Univ. of S. Calif., Los Angeles, CA.
Robinson, D. M., 1997 (expected), “Geometric Tolerancing for Assembly,” Ph.D. dissertation, Mechanical Engineering, Cornell University, Ithaca, NY.
Rossignac, J. R., 1985, “Blending and offsetting solid models,” TM-54, Production Automation Project, Univ. of Rochester, Rochester, NY.
Srinivasan V., Jayaraman, R., 1989, “Geometric tolerancing: II. Conditional tolerances,” IBM J. of Research and Development, vol. 33, no. 2, pp. 105–124.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Robinson, D.M. (1998). Geometric Tolerancing for Assembly with Maximum Material Parts. In: ElMaraghy, H.A. (eds) Geometric Design Tolerancing: Theories, Standards and Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5797-5_19
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5797-5_19
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7656-9
Online ISBN: 978-1-4615-5797-5
eBook Packages: Springer Book Archive