Geometric Variations: Analysis, Optimization and Control

This paper is concerned with the design and manufacturing of 2D and 3D components in the context of process modeling and inspection. A methodology is proposed that models manufacturing processes and learns shape deformations that are the result of out-of-tolerance components. Then during inspection, a deformed shape is analyzed and the process parameter values determined. The key aspect of this approach is that the mapping between process parameters and shape is determined which is not possible using standard process modeling approaches such as finite element analysis. This is different to the traditional approach to tolerancing which is very much as additional procedure to design and doesn't consider process parameter variation, just shape variation. A review of tolerancing is presented as well as a description of techniques for process modeling.

[1]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Geoffrey D. Sullivan,et al.  A Finite Element Method for Deformable Models , 1989, Alvey Vision Conference.

[3]  I. S. Doltsinis.  Numerical analysis and design of industrial superplastic forming , 1993 .

[4]  C. Taylor,et al.  Active shape models - 'Smart Snakes'. , 1992 .

[5]  Aaron Heller,et al.  An object-oriented approach to template guided visual inspection , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[6]  Christopher J. Taylor,et al.  Model-Based Interpretation of 3D Medical Images , 1993, BMVC.

[7]  Laurent D. Cohen,et al.  A finite element method applied to new active contour models and 3D reconstruction from cross sections , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[8]  R. E. Kalman,et al.  Optimum Seeking Methods. , 1964 .

[9]  Aristides A. G. Requicha,et al.  Representation of geometric features, tolerances, and attributes in solid modelers based on constructive geometry , 1986, IEEE J. Robotics Autom..

[10]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

[11]  Joseph L. Mundy,et al.  Template Guided Visual Inspection , 1992, ECCV.

[12]  Geoff A. W. West,et al.  Segmenting curves into elliptic arcs and straight lines , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[13]  Joshua U. Turner.  Relative positioning of parts in assemblies using mathematical programming , 1990, Comput. Aided Des..

[14]  Geoffrey D. Sullivan,et al.  Active Contours using Finite Elements to Control Local Scale , 1992 .

[15]  R. Light,et al.  Modification of geometric models through variational geometry , 1982 .

[16]  H. Hotelling.  The Generalization of Student’s Ratio , 1931 .

[17]  David C. Hogg,et al.  Learning Flexible Models from Image Sequences , 1994, ECCV.

[18]  Geoffrey D. Sullivan,et al.  Parabolic and hermite cubic finite elements: a flexible technique for deformable models , 1990, BMVC.

[19]  Aristides A. G. Requicha,et al.  Toward a Theory of Geometric Tolerancing , 1983 .