{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T11:51:16Z","timestamp":1762429876481},"reference-count":28,"publisher":"ASME International","issue":"1","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2003,3,1]]},"abstract":"<jats:p>This paper presents an optimization approach for the accurate evaluation of minimum-zone form tolerances from discrete coordinate measurement data. The approach minimizes the minimum-deviation objective function defined as the difference between the maximum and minimum distances of the measured coordinate data from the reference feature. The objective function is formulated as a function of rigid-body coordinate transformation parameters and involves fewer independent parameters than the existing tolerance evaluation algorithms. As a result, improved convergence efficiency and numerical stability are achieved. A standard direct search algorithm, the downhill simplex search algorithm, is employed to minimize the objective function. The least-squares estimates are employed as good initial conditions to facilitate convergence to the global solutions. A new method, named as the Median Technique, is implemented to well center the circularity measured data and well align the cylindricity measured data in order to provide valid least-squares estimates based on the Limacon approximation. Results from simulation and comparative studies have shown that the proposed method evaluates minimum-zone form tolerances with reliable accuracy.<\/jats:p>","DOI":"10.1115\/1.1565075","type":"journal-article","created":{"date-parts":[[2003,5,15]],"date-time":"2003-05-15T23:33:52Z","timestamp":1053041632000},"page":"31-38","update-policy":"http:\/\/dx.doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":17,"title":["Minimum-Zone Form Tolerance Evaluation Using Rigid-Body Coordinate Transformation"],"prefix":"10.1115","volume":"3","author":[{"given":"Dawit H.","family":"Endrias","sequence":"first","affiliation":[{"name":"Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada\u2009N6A\u20095B9"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hsi-Yung","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada\u2009N6A\u20095B9"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2003,5,15]]},"reference":[{"key":"2019100609481961000_r1","unstructured":"ASME Y14.5M-1994, Dimensioning and Tolerancing, The American Society of Mechanical Engineers, New York."},{"key":"2019100609481961000_r2","doi-asserted-by":"crossref","unstructured":"Murthy, T. S. R., and Abdin, S. Z., 1980, \u201cMinimum Zone Evaluation of Surfaces,\u201d Int. J. Mach. Tool Des. Res., 20, pp. 123\u2013136.","DOI":"10.1016\/0020-7357(80)90024-4"},{"key":"2019100609481961000_r3","doi-asserted-by":"crossref","unstructured":"Kanada, T., and Suzuki, S., 1993, \u201cEvaluation of Minimum Zone Flatness by Means of Nonlinear Optimization Techniques and its Verification,\u201d Precis. Eng., 15, pp. 93\u201399.","DOI":"10.1016\/0141-6359(93)90343-9"},{"key":"2019100609481961000_r4","unstructured":"Tsukada, T., and Kanada, T., 1985, \u201cMinimum Zone Evaluation of Cylindricity Deviation by Some Optimization Techniques,\u201d Bull. Jpn. Soc. Precis. Eng., 19, pp. 18\u201323."},{"key":"2019100609481961000_r5","doi-asserted-by":"crossref","unstructured":"Lai, H. Y., Jywe, W. Y., Chen, C. K., and Liu, C. H., 2000, \u201cPrecision Modeling of Form Errors for Cylindricity Evaluation Using Genetic Algorithms,\u201d Precis. Eng., 24, pp. 310\u2013319.","DOI":"10.1016\/S0141-6359(00)00041-6"},{"key":"2019100609481961000_r6","doi-asserted-by":"crossref","unstructured":"Carr, K., and Ferreira, P., 1995, \u201cVerification of Form Tolerances, Part I: Basic Issues, Flatness, and Straightness,\u201d Precis. Eng., 17, pp. 131\u2013143.","DOI":"10.1016\/0141-6359(94)00017-T"},{"key":"2019100609481961000_r7","doi-asserted-by":"crossref","unstructured":"Carr, K., and Ferreira, P., 1995, \u201cVerification of Form Tolerances, Part II: Cylindricity and Straightness of a Median Line,\u201d Precis. Eng., 17, pp. 144\u2013156.","DOI":"10.1016\/0141-6359(94)00018-U"},{"key":"2019100609481961000_r8","unstructured":"Wang, Y.\n          , 1992, \u201cMinimum Zone Evaluation of Form Tolerances,\u201d Manuf. Rev., 5, pp. 213\u2013220."},{"key":"2019100609481961000_r9","doi-asserted-by":"crossref","unstructured":"Sharma, R., Rajagopal, K., and Anand, S., 2000, \u201cA Genetic Algorithm Based Approach for Robust Evaluation of Form Tolerances,\u201d J. Manuf. Syst., 19, pp. 46\u201357.","DOI":"10.1016\/S0278-6125(00)88889-5"},{"key":"2019100609481961000_r10","doi-asserted-by":"crossref","unstructured":"Choi, W., and Kurfess, T. R., 1999, \u201cDimensional Measurement Data Analysis, Part 1: A Zone Fitting Algorithm,\u201d ASME J. Manuf. Sci. Eng., 121, pp. 238\u2013245.","DOI":"10.1115\/1.2831211"},{"key":"2019100609481961000_r11","doi-asserted-by":"crossref","unstructured":"Choi, W., and Kurfess, T. R., 1999, \u201cDimensional Measurement Data Analysis, Part 2: Minimum Zone Evaluation,\u201d ASME J. Manuf. Sci. Eng., 121, pp. 246\u2013250.","DOI":"10.1115\/1.2831212"},{"key":"2019100609481961000_r12","unstructured":"Traband, M. T., Joshi, S., Wysk, R. A., and Cavalier, T. M., 1989, \u201cEvaluation of Straightness and Flatness Tolerances Using the Minimum Zone,\u201d Manuf. Rev., 2, pp. 189\u2013195."},{"key":"2019100609481961000_r13","doi-asserted-by":"crossref","unstructured":"Huang, S. T., Fan, K. C., and Wu, J. H., 1993, \u201cA New Minimum Zone Method for Evaluating Straightness Errors,\u201d Precis. Eng., 15, pp. 158\u2013165.","DOI":"10.1016\/0141-6359(93)90003-S"},{"key":"2019100609481961000_r14","doi-asserted-by":"crossref","unstructured":"Huang, S. T., Fan, K. C., and Wu, J. H., 1993, \u201cA New Minimum Zone Method for Evaluating Flatness Errors,\u201d Precis. Eng., 15, pp. 25\u201332.","DOI":"10.1016\/0141-6359(93)90275-F"},{"key":"2019100609481961000_r15","doi-asserted-by":"crossref","unstructured":"Roy, U., and Zhang, X., 1992, \u201cEstablishment of a Pair of Concentric Circles with the Minimum Radial Separation for Assessing Roundness Error,\u201d Comput.-Aided Des., 24, pp. 161\u2013168.","DOI":"10.1016\/0010-4485(92)90035-9"},{"key":"2019100609481961000_r16","doi-asserted-by":"crossref","unstructured":"Roy, U., and Xu, Y., 1995, \u201cForm and Orientation Tolerance Analysis for Cylindrical Surfaces in Computer-Aided Inspection,\u201d Comp. Ind., 26, pp. 127\u2013134.","DOI":"10.1016\/0166-3615(94)00031-K"},{"key":"2019100609481961000_r17","doi-asserted-by":"crossref","unstructured":"Lai, J. Y., and Chen, I. H., 1996, \u201cMinimum Zone Evaluation of Circles and Cylinders,\u201d Int. J. Mach. Tools Manuf., 36, pp. 435\u2013451.","DOI":"10.1016\/0890-6955(95)00077-1"},{"key":"2019100609481961000_r18","doi-asserted-by":"crossref","unstructured":"Hodgson, T. J., Kay, M. G., Mittal, R. O., and Tang, S. Y., 1999, \u201cEvaluation of Cylindricity Using Combinatorics,\u201d IIE Trans., 31, pp. 39\u201347.","DOI":"10.1080\/07408179908969804"},{"key":"2019100609481961000_r19","unstructured":"Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed., Cambridge University Press, New York."},{"key":"2019100609481961000_r20","doi-asserted-by":"crossref","unstructured":"Shunmugam, M. S.\n          , 1987, \u201cNew Approach for Evaluating Form Errors of Engineering Surfaces,\u201d Comput.-Aided Des., 19, pp. 368\u2013374.","DOI":"10.1016\/0010-4485(87)90037-6"},{"key":"2019100609481961000_r21","doi-asserted-by":"crossref","unstructured":"Shunmugam, M. S.\n          , 1986, \u201cOn Assessment of Geometric Errors,\u201d Int. J. Prod. Res., 24, pp. 413\u2013425.","DOI":"10.1080\/00207548608919738"},{"key":"2019100609481961000_r22","doi-asserted-by":"crossref","unstructured":"Cheraghi, S. H., Lim, H. S., and Motavalli, S., 1996, \u201cStraightness and Flatness Tolerance Evaluation: An Optimization Approach,\u201d Precis. Eng., 18, pp. 30\u201337.","DOI":"10.1016\/0141-6359(95)00033-X"},{"key":"2019100609481961000_r23","doi-asserted-by":"crossref","unstructured":"Damodarasamy, S., and Anand, S., 1999, \u201cEvaluation of Minimum Zone for Flatness by Normal Plane Method and Simplex Search,\u201d IIE Trans., 31, pp. 617\u2013626.","DOI":"10.1080\/07408179908969863"},{"key":"2019100609481961000_r24","doi-asserted-by":"crossref","unstructured":"Samuel, G. L., and Shunmugam, M. S., 1999, \u201cEvaluation of Straightness and Flatness Error Using Computational Geometric Techniques,\u201d Comput.-Aided Des., 31, pp. 829\u2013843.","DOI":"10.1016\/S0010-4485(99)00071-8"},{"key":"2019100609481961000_r25","doi-asserted-by":"crossref","unstructured":"Samuel, G. L., and Shunmugam, M. S., 2000, \u201cEvaluation of Circularity from Coordinate and Form Data Using Computational Geometric Techniques,\u201d Precis. Eng., 24, pp. 251\u2013263.","DOI":"10.1016\/S0141-6359(00)00039-8"},{"key":"2019100609481961000_r26","doi-asserted-by":"crossref","unstructured":"Jywe, W. Y., Liu, C. H., and Chen, C. K., 1999, \u201cThe Min-Max Problem for Evaluating the Form Error of a Circle,\u201d Measurement, 26, pp. 273\u2013282.","DOI":"10.1016\/S0263-2241(99)00052-4"},{"key":"2019100609481961000_r27","doi-asserted-by":"crossref","unstructured":"Rajagopal, K., and Anand, S., 1999, \u201cAssessment of Circularity Error Using a Selective Data Partition Approach,\u201d Int. J. Prod. Res., 37, pp. 3959\u20133979.","DOI":"10.1080\/002075499189862"},{"key":"2019100609481961000_r28","doi-asserted-by":"crossref","unstructured":"Yau, H. T., and Menq, C. H., 1996, \u201cA Unified Least-Squares Approach to the Evaluation of Geometric Errors Using Discrete Measurement Data,\u201d Int. J. Mach. Tools Manuf., 36, pp. 1269\u20131290.","DOI":"10.1016\/0890-6955(95)00075-5"}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/3\/1\/31\/5626520\/31_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/3\/1\/31\/5626520\/31_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,6]],"date-time":"2019-10-06T13:48:30Z","timestamp":1570369710000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/3\/1\/31\/475185\/MinimumZone-Form-Tolerance-Evaluation-Using"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3,1]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,3,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.1565075","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,3,1]]}}}