Form Error Evaluation: An Iterative Reweighted Least Squares Algorithm*

[+] Author and Article Information
Xiangyang Zhu, Han Ding

School of Mechanical Engineering, Shanghai Jiaotong University, Huashan Road, Shanghai, China

Michael Y. Wang

Department of Automation & Computer-Aided Engineering, Chinese University of Hong Kong, Shatin, New Territory, Hong Konge-mail: yuwang@acae.cuhk.edu.hk

J. Manuf. Sci. Eng 126(3), 535-541 (Sep 07, 2004) (7 pages) doi:10.1115/1.1765144 History: Received December 02, 2002; Revised January 14, 2004; Online September 07, 2004
Copyright © 2004 by ASME
Topics: Algorithms , Errors
Your Session has timed out. Please sign back in to continue.


Shunmugam,  M. S., 1986, “On Assessment of Geometric Errors,” Int. J. Prod. Res., 24(2), pp. 413–425.
ANSI Standard Y14.5. Dimensioning and Tolerancing. New York: The American Society of Mechanical Engineers, 1982.
Technical Drawings-Geometrical Tolerancing. ISO/R1101, 1983-12-01.
Murthy,  T. S. R., and Abdin,  S. Z., 1980, “Minimum Zone Evaluation of Surfaces,” Int. J. Mach. Tool Des. Res., 20, pp. 123–136.
Fukuda, M., and Shimokohbe, A., 1984, “Algorithms for Form Error Evaluation-Methods of Minimum Zone and the Least Squares,” Proceedings of the International Symposium on Metrology and Quality Control in Production, pp. 197–202.
Shunmugam,  M. S., 1991, “Criteria for Computer-Aided Form Evaluation,” ASME J. Eng. Ind., 113, pp. 233–238.
Carr,  K., and Ferreira,  P., 1995, “Verification of Form Tolerance-Part I: Basic Issues, Flatness and Straightness,” Precis. Eng., 17(2), pp. 131–143.
Cheraghi,  S. H., Lim,  H. S., and Motavalli,  S., 1996, “Straightness and Flatness Tolerance Evaluation: An Optimization Approach,” Precis. Eng., 18(1), pp. 30–37.
Wang,  Y., 1992, “Minimum Zone Evaluation of Form Tolerances,” Manufacturing Review, 5(3), pp. 213–220.
Kanada,  T., and Suzuki,  S., 1993, “Evaluation of Minimum Zone Flatness by Means of Non-linear Optimization Technique and Its Verification,” Precis. Eng., 15(2), pp. 93–99.
Chetwynd,  D. G., 1985, “Application of Linear Programming to Engineering Metrology,” Proc. Inst. Mech. Eng., 199(B2), pp. 93–100.
Huang,  S. T., Fan,  K. C., and Wu,  J. H., 1993, “A New Minimum Zone Method for Evaluating Flatness Errors,” Precis. Eng., 15(1), pp. 25–32.
Lai,  H.-Y., Jywe,  W.-Y., Chen,  C.-K., and Liu,  C.-H., 2000, “Precision Modeling of Form Errors for Cylindericity Evaluation Using Genetic Algorithms,” Precis. Eng., 24, pp. 310–319.
Zhu,  L.-M., and Ding,  H., 2003, “Application of Kinematic Geometry to Computational Metrology: Distance Function Based Hierarchical Algorithms for Cylindericity Evaluation,” Int. J. Mach. Tools Manuf., 43(2), pp. 203–215.
Traband,  M. T., Joshi,  S., Wysk,  R. A., and Cavalier,  T. M., 1989, “Evaluation of Straightness and Flatness Tolerances Using the Minimum Zone,” Manufacturing Review, 2(3), pp. 189–195.
Samuel,  G. L., and Shunmugam,  M. S., 1999, “Evaluation of Straightness and Flatness Using Computational Geometric Techniques,” Comput.-Aided Des., 31, pp. 829–843.
Lee,  M. K., 1997, “A New Convex-hull Based Approach to Evaluating Flatness Tolerance,” Comput.-Aided Des., 29(12), pp. 861–868.
Zhu,  X. Y., and Ding,  H., 2002, “Flatness Tolerance Evaluation: An Approximate Minimum Zone Solution,” Comput.-Aided Des., 34, pp. 655–664.
Huang,  J., 1999, “An Exact Solution for the Roundness Evaluation Problems,” Precis. Eng., 23, pp. 2–8.
Huang,  J., 1999, “An Exact Minimum Zone Solution for Sphericity Evaluation,” Comput.-Aided Des., 31, pp. 845–853.
Samuel,  G. L., and Shunmugam,  M. S., 2000, “Evaluation of Circularity Form Coordinate and Form Data Using Computational Geometric Techniques,” Precis. Eng., 24, pp. 251–263.
Huang,  J., 1999, “An Exact Minimum Zone Solution for Three-dimensional Straightness Evaluation Problems,” Precis. Eng., 23, pp. 204–208.
Liu, J., and Wang, X. M., 1996, Saddle Point Programming and Geometric Error Evaluation, The Press of Dalian University of Technology.
Fan,  K.-C., and Lee,  J.-C., 1999, “Analysis of Minimum Zone Sphericity Error Using Minimum Potential Energy Theory,” Precis. Eng., 23, pp. 65–72.
Zhang,  Q., Fan,  K. C., and Li,  Z., 1999, “Evaluation Method for Spatial Straightness Errors Based on Minimum Zone Condition,” Precis. Eng., 23, pp. 264–272.
Murray, R. M., Li, Z. X., and Sastry, S. S., 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press.


Grahic Jump Location
The IRLS algorithm for form error evaluation
Grahic Jump Location
The IRLS algorithm with LBC for cylindericity evaluation
Grahic Jump Location
The IRLS algorithm for spatial straightness evaluation
Grahic Jump Location
The evolution of the maximum error in Example 2
Grahic Jump Location
The evolution of the maximum error in Example 3
Grahic Jump Location
The maximum error vs the number of iterations in Example 4




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In