Home | ADCATS Info | Search | Site Map | Bulletin Board | Reports & Publications | Bibliography | Contact Us
Naval Report 1995
Home : Tolerancing Bibliography : Naval Report 1995  
Robust Geometric Calculations with Applications to Tolerancing

Table of Contents:

  1. Principal Investigator.
  2. Productivity Measures.
  3. Summary of Objectives and Approach.
  4. Detailed Summary of Technical Progress.
  5. Transitions and DOD Interactions.
  6. Software and Hardware Prototypes.
  7. List of Publications.
  8. Invited and Contributed Presentations.
  9. Honors, Prizes or Awards Received.
  10. Project personnel promotions obtained.
  11. Project Staff.
  12. Misc Hypermedia URL.
  13. Keywords.

Principal Investigator.

Productivity Measures.

Summary of Objectives and Approach.

  1. Click here to see the project summary.

Detailed Summary of Technical Progress.

  • Flexible Assembly Tolerancing. In working on tolerancing complex surfaces, it became obvious that flexibility of some of these surfaces was significant. We have developed a procedure to to combine linear tolerance analysis and linear finite element analysis to estimate the residual stresses in an assembly due to tolerance allocation.

  • Statistical Bezier Curves. A common mathematical method for describing tolerances involves offset curves/surfaces. The offset of a rational curve cannot in general be described as a rational curve. This complicates offset mathematimizations. We have developed a way to describe the statistical space occupied by a Bezier curve with a profile tolerance in terms of the statistical variation of the control points. This method avoids the calculation of an actual offset and describes the possible curves that may exist within a profile band. The interaction of two statistical Bezier curves can then be described terms of the variance and covariance terms associated with the control points. We utilize this to define continuous descriptions of the variations of a gap/interference in an assembly.

  • Tolerance Bibliography. We currently have a large bibliography on tolerance analysis. This bibliography is available on the network in HTML format. It has also been distributed to other researchers at Click here to go to the infobase.

  • 3-D Surface Implicitization. A paper was written and accepted on surface implicitization. Several referees hailed it as one of the most significant contributions of the decade in curves and surfaces. The paper describes a radically new approach for performing parametric to implicit conversion of surface equations.

  • Explicit Curve and Surface Modeling. A fast new technique for bounding parametric curves and surfaces with explicit (functional) curves and surface was devised. This concept also allows the construction of a family of curves or surfaces which are assured to not intersect.

  • Ray Tracing. Kris Klimaszewski completed a dissertation on ray tracing. He developed a ray tracer which is several times faster than previous algorithms on many scenes.

    Transitions and DOD Interactions.

  • We are currently negotiating with Boeing Aerospace and Lockheed to apply the flexible assembly modeling methodology to their applications.
  • We are working with a local company, Fibertek, to apply the flexible assembly modeling methodology to their product. They produce fiberglass passenger compartments for railway cars. Each compartment is composed of 9 fiberglass panels that are subject to shrinkage and warpage. We are recreating a finite element model of this passenger compartment and will provide estimates of the residual stresses and forces necessary to assemble this compartment based on the design tolerances associated with each panel.
  • Texas Instruments is currently marketing a 2-D version of the BYU Computer-Aided Tolerancing Software, CATS, as TI/TOL 3.0. The tolerance analysis software is fully integrated into the Pro/Engineer CAD system.

    Software and Hardware Prototypes.

    1. TI/TOL 3.0 2-D Computer-Aided Tolerance Analysis System for Pro/Engineer.

    List of Publications.

    1. K. W. Chase, Jinsong Gao, S.P. Magleby, "General 2-D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments", Journal of Design and Manufacture, v 5, n 2, 1995.
      Now Available on the Web: HTML | ACROBAT 3.0
    2. Jinsong Gao, K.W. Chase, S.P. Magleby, "General 3-D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments", Journal of Design and Manufacture (pending).
    3. Jinsong Gao, K.W. Chase, S.P. Magleby, "Including Geometric Feature Variations in Tolerance Analysis of Mechanical Assemblies", Journal of Design and Manufacture (To be published)
      Now Available on the Web: HTML | ACROBAT 3.0
    4. Jinsong Gao, K.W. Chase, S.P. Magleby, "Comparison of Assembly Tolerance Analysis by the Direct Linearization Method and Modified Monte Carlo Methods:, ASME Design Engineering Technical Conference, Boston, MA, Sept. 17-20, 1995.
      Now Available on the Web: HTML | ACROBAT 3.0
    5. S.E. Benzley, K.G. Merkley, T.D. Blacker, L. Schoof, "Pre- and Post-Processing for the Finite Element Method", Finite Elements in Analysis and Design, n 19, pp. 243-260, 1995.
    6. S.E. Benzley, E. Perry, K.G. Merkley, G. Sjaardema, "A Comparison of All Hexagonal and All Tetrahedral Finite Elements for Elastic and Elastic-Plastic Analysis", Sandia Meshing Conference, (to be published).
    7. Texas Instruments, TI/TOL 2D Multi-Dimensional Tolerance Management Tool User Reference Manual", Texas Instruments, Plano TX, 1994.
    8. Brown, C.T, "Statistical Models for Position and Profile Variation in Mechanical Assemblies", M.S. Thesis, Brigham Young University, 1995.
    9. Glancey, C., "A Second Order Method for Assembly Tolerance Analysis", M.S. Thesis, Brigham Young University, 1995.
    10. T. W. Sederberg and F. Chen, "Implicitization using moving curves and surfaces", Computer Graphics Annual Conference Series, 1995, 301-308.
    11. R. Farouki and T. W. Sederberg, "Analysis of the Offset to a Parabola", Computer Aided Geometric Design, 12, 639-645, 1995.
    12. T. Saito, G. Wang, and T. W. Sederberg, "Hodographs and normals of rational curves and surfaces", Computer Aided Geometric Design, 12, 417-430, 1995.
    13. T. W. Sederberg, "Point and tangent computation of tensor product rational Bezier surfaces", Computer Aided Geometric Design, 12, 103-106, 1995.
    14. T. W. Sederberg, T. Saito, D. Qi, and K. Klimaszewski, "Curve implicitization using moving lines," Computer Aided Geometric Design, 11, 687-706, 1994.
    15. T. W. Sederberg and T. Saito, "Rational ruled surfaces: Implicitization and section curves." Graphical Models and Image Processing, 57, 4, 334-342, July, 1995.
    16. G. Wang and T. W. Sederberg, "Computing areas bounded by rational Bezier curves," Computer Aided Design, Drafting, and Manufacturing, 4, 2, 1994, 18-27.

    Invited and Contributed Presentations.

    1. "Tolerance Analysis - a Quantitative Tool for Concurrent Engineering", 3rd International Applied Statistics Conference, Dallas TX, June, 1995.
    2. "Overview of Computer-Aided Tolerance Analysis", Colt Manufacturing, Hartford, CT, June 1995.
    3. "Comparison of Assembly Tolerance Analysis by the Direct Linearization Method and Modified Monte Carla Methods", ASME Design Technical Conference, Boston, Sept. 1995.
      Now Available on the Web: HTML | ACROBAT 3.0
    4. "Overview of Computer-Aided Tolerance Analysis", Boeing Assembly Modeling Interest Group, Seattle, April 1995.
    5. "Tolerance Analysis of Flexible Structures", Fibertek, Springville UT, July 1995.
    6. "Tolerance Analysis of Flexible Structures", Lockheed, Fort Worth TX, June, 1995.
    7. "NURBS in CAGD", Oct. 25 1994, Fukuyama University.
    8. "Recent Advances in Ray Tracing", Hiroshima Prefectural Technoplaza, Oct. 27 1994.
    9. "The SIGGRAPH papers selection process", Visual Computing '94 workshop, Tokyo, Oct. 29, 1994.
    10. "Efficient algorithms for curves and surfaces", GraphiCon, St. Petersburg, July 2, 1995
    11. "Real root finding of polynomials in Bernstein form", AMS-SIAM Conference on Applied Math, Park City, July 21, 1995.
    12. "Implicitization using moving curves and surfaces", SIGGRAPH, LA, Aug. 10, 1995.

    Honors, Prizes or Awards Received.

    Project Personnel Promotions Obtained.

    Project Staff.

    Misc Hypermedia.

    1. The ADCATS WWW Site.


      The goals of the WWW project are to establish a central site for the latest research and software in CAD-based assembly tolerancing tools, to provide a forum to facilitate communication of new technologies and to provide a bibliography with easy access to articles and reports that deal with tolerance analysis.

      Present Services

      Various service have already been implemented at the site. The site is still under construction with new options and improvements being added as Internet development tools become available. Currently, the site features the software and research of the ADCATS organization at BYU. An overview of the CADD application and theory is available and is followed by several 2-D and 3-D examples.

      To aid in tolerance research, technical articles, papers, bibliographies and abstracts can be reviewed, studied, and copied through an FTP service. Also, to stimulate communication between researchers in this field, an electronic listserver has been implemented. Researchers can now use the listserver at this site to ask questions, help others, and to keep up to date n tolerance research.

      The ADCATS web site runs on a QUADRA 950 and has 28 MB of RAM. The URL for ADCATS is "www.adcats.byu.edu".


      Various software packages are used to provide the services at the ADCATS site. A brief overview and breakdown of these applications will now be discussed.

      File Preparation

      The majority of the documents available at this site were created in Microsoft Word format. Microsoft Word has the capability of saving files in an "interchange format" known as RTF. This neutral format is then used by another application called RTFtoHTML which converts the Word files into browsable HTML documents (with embedded graphics included).

      Research Aids

      Files are made available for research with a powerful search engine called "Total Research - WWW." This application will use a key word to find ALL files with references to this word. This greatly speeds up the research process. Files are made accessible in two ways: FTP and binary files. FTPd is the application used for the server FTP capabilities and DropStuff compresses files into transferable binary files.

      Graphical Features

      Many graphics formats can be converted with "GraphicConverter." "MapServ" and "GifServ" are script applications which are in the process of being implemented for more esthetic presentations.


      The web server is also a mail server which enables listserver capabilities. Three applications work together to provide this service. "MailShare" makes the computer a mail server. "AutoShare" provides the listserver capabilities and "Listserv" interfaces with web browsers to provide an interactive interface.


      Various scripts are used to provide feedback forms which are coupled with the "Eudora" electronic mail package.

      Future Goals

      One future objective is the implementation of an interactive database interface at the web site. This will facilitate the research objectives of the project.


    1. Tolerance Analysis.
    2. Assembly Modeling.
    3. Computer-aided Tolerancing.
    4. Surface-surface intersection.

    The ADCATS site: Home | ADCATS Info | Search | Site Map | Bulletin Board | Reports & Publications | Bibliography | Contact Us