The Analysis of Measurement Systems for the Construction of Geometrical Models of the Product

A. Brailov

doi:doi:10.12737/18056

The Analysis of Measurement Systems for the Construction of Geometrical Models of the Product

Published в Geometry & Graphics · Volume 4, Issue 1, 2016 · Pages 34–43 · Rubrics: Methodical questions of teaching

DOI 10.12737/18056

Received: 02.03.2016 Accepted: 17.03.2016 Published: 17.03.2016 Language of publication: RUS

Authors

A. Brailov

ABSTRACT

In the present work, on the basis of the analysis of existing systems of measurement for geometrical modeling, their components are defined. The system of measurement for geometrical modeling consists of three mutually perpendicular planes H-П1, F-П2, P-П3 and connected with them right three-dimensional system of coordinates OXYZ. The major features of such system related to ways of formation of the two-dimensional complex drawing of a geometrical image on the basis of laws of projective connections are revealed. As the first feature of systems of measurement for geometrical modeling it is possible to allocate a way of orientation (binding) of the right three-dimensional system of co-ordinates OXYZ concerning the set planes of projections H-П1, F-П2, P-П3. The second feature of systems of measurement for geometrical modeling is the way of conditional division of space on a part (semi spaces, quadrants, and octants). The third feature of systems of measurement for geometrical modeling is the way of numbering of the allocated parts of space (semi spaces, quadrants, and octants). Interrelations of elements of different systems of measurement with different projections of a geometrical image are defined. The relative location of projections of a geometrical image into the constructed two-dimensional complex drawings for various systems of measurement is determined. For the American system of measurement in the two-dimensional complex drawing of a geometrical image the horizontal projection is located above a frontal projection, and the profile projection is located to the right of a frontal projection. For the European system of measurement in the two-dimensional complex drawing of a geometrical image the horizontal projection is located below a frontal projection, and the profile projection is located to the right of a frontal projection. The logic behind a particular arrangement of views in the projective drawing of a product in the analyzed systems of measurement is explained. For the realized way of construction of the complex drawing in the American system of measurement the horizontal projection is the bottom view, and the profile projection is the left-side view. For the realized way of construction of the complex drawing in the European system of measurement the horizontal projection is the top view, and the profile projection is the left-side view.

KEYWORDS

descriptive geometry measurement system geometrical modeling the complex drawing of an image the projective drawing of a product.

Information References

Authors:

Type:

Article

Pages:

from 34 to 43

Status:

Published

Language:

Russian

Keywords:

descriptive geometry, measurement system, geometrical modeling, the complex drawing of an image, the projective drawing of a product.

References

1. Avtomatizacija proektirovanija i podgotovki proizvodstva. T-FLEX Parametric CAD [Automation of the designing and preparation production. T-FLEX Parametric CAD]. Moscow, Тоp Systems Publ., 2002, 41 p. (in Russian).

2. Brailov A.Yu. Komp´juternaja inzhenernaja grafika v srede T-FLEX: preobrazovanija dvuhmernyh i trehmernyh modelej izdelij [Computer engineering graphics in the environment of Т-FLEX: Transformations of two-dimensional and threedimensional models of products]. Kiev, Caravella Publ., 2007, 176 p. (in Russian)

3. Brailov A.Yu. Obshhij algoritm reshenija tipovyh geometricheskih zadach [The general algorithm of the solution of typical geometrical problems]. Prykladna geometrija ta inzhenerna grafika [Applied geometry and the engineering graphics]. Kiev, KNUBА Publ., 2013, I. 91, pp. 32-45. (in Russian)

4. Brailov A.Yu. Inzhenernaja geometrija [Engineering Geometry]. Kiev: Caravella Publ., 2013, 456 p. (in Russian).

5. Bronstein I.Н., Semendjaev K.A. Spravochnik po matematike dlja inzhenerov i uchashhihsja vtuzov [Handbook on the mathematician for engineers and pupils of technical colleges]. Moscow, Science Publ., 1986, 544 p. (in Russian).

6. Bubennikov A.V., Gromov М.Ya. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Vishaya shkola Publ., 1973, 416p. (in Russian).

7. Vanin V.V., Bliok А.V., Gnitecka G. О. Oformlennja konstruktors´koi´ dokumentacii [Appearance of design documentation]. Kiev, Caravella Publ., 2003, 160 p. (in Ukrainian).

8. Glazunov Е.А., Chetverukhin N.F. Aksonometrija [Axonometry]. Moscow, 1953, 291 p. (in Russian).

9. Ivanov G.S. Konstruirovanie tehnicheskih poverhnostej (matematicheskoe modelirovanie na osnove nelinejnyh preobrazovanij) [Design of engineering surfaces]. Moscow, Mashinostroenie Publ., 1987, 192 p. (in Russian).

10. Ivanov G.S. Nachertatel´naja geometrija [Descriptive Geometry]. Moscow, Mashinostroenie Publ., 1995, 223 p. (in Russian).

11. Ivanov G.S. Teoreticheskie osnovy nachertatel´noj geometrii [Theoretical foundations of Descriptive Geometry]. Moscow, Mashinostroenie Publ., 1998, 158 p. (in Russian).

12. Ivanov Yu.N., Podkoritov А.N., Strigo Yu.S. Nachertatel´naja geometrija [Descriptive Geometry]. Omsk, Omskаya Pravda Publ., 1962, 232 p. (in Russian).

13. Mihajlenko V.Е., Kovalyev S.N., Sedleckaya N.I. Inzhenernaja geometrija s jelementami teorii parametrizacii [Engineering Geometry with element of the theories of parameterization]. Kiev, UМК VО Publ., 1989, 83 p. (in Russian).

14. Korn G., Korn T. Spravochnik po matematike dlja nauchnyh rabotnikov i inzhenerov [Mathematical handbook for scientists and engineers]. Moscow, Science Publ., 1978, 832 p. (in Russian).

15. Kotov I.I., Polozov V.S., Shirokova L.V. Algoritmy mashinnoj grafiki [Algorithms of computer graphics]. Moscow, Mashinostroenie Publ., 1977, 231 p. (in Russian).

16. Kolotov S.М., Dolski Е.Е., Mihajlenko V.Е. Kurs nachertatel´noj geometrii [Course of Descriptive Geometry]. Kiev, Gosstrojizdat USSR Publ., 1961, 314 p. (in Russian).

17. Tevlin А.М. Kurs nachertatel´noj geometrii na baze JeVM [Course of Descriptive Geometry on the ground of computer]. Moscow, Vishaya shkola Publ., 1983, 175 p. (in Russian).

18. Levicki V.S. Mashinostroitel´noe cherchenie [Machine-building drawing]. Moscow, Vishaya shkola Publ., 1988, 351 p. (in Russian).

19. Mihajlenko V.E., Vanin V.V., Kovalyev S.N. Inzhenernaja i komp´juternaja grafika [Engineering and computer graphics: Handbook]. Kiev, Karavella Publ., 2013, 328 p. (in Russian).

20. Mihajlenko V.E. Inzhenerna ta komp´juterna grafika [Engineering and computer graphics]. Kiyv, Vishcha shkola Publ., 2001, 350 p. (in Ukrainian).

21. Mihajlenko V.E. Zbirnyk zadach z inzhenernoi´ ta komp´juternoi´ grafiky [Problems in the engineering and computer graphics]. Kiyv, Vishcha Shkola Publ., 2002, 159 p. (in Ukrainian).

22. Podkorytov A.N., Galzman E.G., Perevalov V.F. Konspekt lekcij po inzhenernoj grafike (so strukturno-logicheskimi shemami i s algoritmami graficheskih postroenij pri reshenii tipovyh zadach) dlja studentov nemehanicheskih special´nostej [Lectures on engineering graphics (with structurally logic schemes and algorithms of graphic constructions in solving typical problems) for students of non-mechanical specialties]. Odessa, ОSPU Publ., 1993, 83 p. (in Russian).

23. Romanicheva E.Т., Sokolova Т.Yu., Shandurina G.F. Inzhenernaja i komp´juternaja grafika [Engineering and computer graphics]. Moscow, DМК Press Publ., 2001, 592 p. (in Russian).

24. Rossijskij kompleks programm T-FLEX CAD/CAM/CAE/PDM [Russian complex of the programs T-FLEX CAD/CAM/CAE/PDM]. Moscow, Тоp Systems Publ., 2005, 52 p. (in Russian).

25. Rizhov N.N. Glavnye pozicionnye zadachi. Metodicheskie ukazanija [Main positional problems]. Moscow, МАDI Publ., 1983, 38 p. (in Russian).

26. Rizhov N.N. Parametricheskaja geometrija [Parametric geometry]. Moscow, МАDI Publ., 1988, 63 p. (in Russian)

27. Frolov S.А. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Mashinostroenie Publ., 1978, 240 p. (in Russian).

28. Brailov A.Yu. The Exclusion Method of Interference in Conjugated Helicoids. Proceedings of the Eighth International Conference on Engineering Design Graphics and Descriptive Geometry (Austin, Texas, USA). ISGG, 1998, V. 2, pp. 443-445.

29. Brailov A.Yu. Physical Constraints in the Control of Chip Breakability. ASME Journal of Manufacturing Science and Engineering, 1999 MED, V. 10, pp. 389-396 (Nashville, Tennessee, USA).

30. Brailov A.Yu., Tigaryev V.M. Graphic Method of Determination of Ranges of a Modification of Parameters of Complicated Movements. Proceedings of the Ninth International Conference on Engineering Design Graphics and Descriptive Geometry (Johannesburg, South Africa). ISGG, 2000, V. 2, pp. 412-416.

31. Brailov A.Yu. Interference in design. Proceedings of the Tenth International Conference on Geometry and Graphics (Kiev, Ukraine). ISGG, 2002, V. 1, pp. 84-88.

32. Brailov A.Yu. Designing using T-FLEX CAD. Proceedings of the Eleventh International Conference on Geometry and Graphics (Guangzhow, China). ISGG, 2004, pp. 397-402.

33. Brailov A.Yu. Development of a parametrical three-dimensional model of a product. Proceedings of the Twelfth International Conference on Geometry and Graphics (Salvador, Brazil). ISGG, 2006, P. # A19.

34. Brailov A.Yu. A theoretical approach to transformations of two-dimensional and three-dimensional models of the product. Proceedings of the Thirteenth International Conference on Geometry and Graphics (Dresden, Germany). ISGG, 2008, pp. 58-59.

35. Brailov A.Yu. Fundamental principles of design and technological development of an engineering product. Proceedings of the Fourteenth International Conference on Geometry and Graphics (Kyoto, Japan). ISGG, 2010, pp. 324-325.

36. Brailov A.Yu. Principles of product development. Engineering Graphics BALTGRAF11. Proceedings of the Eleventh International Conference (Tallinn, Estonia). IAB: Tallinn University of Technology Publ., 2011, pp. 95-104.

37. Brailov A.Yu. Laws of projective connections. Proceedings of the Fifteenth International Conference on Geometry and Graphics (Montreal, Canada). ISGG, 2012, pp. 121-122.

38. Brailov A.Yu. Principles of Design and Technological Development of Product. International Journal of Advances in Machining and Forming Operations. International Science Press, ISP, 2011, V. 3, I. 1, pp. 11-17 (Detroit, Michigan, USA).

39. Brailov A.Yu. The general approach to the solution of typical engineering geometrical problems. Proceedings of the Sixteenth International Conference on Geometry and Graphics (Innsbruck, Austria). ISGG, Innsbruck University Press Publ., 2014, pp. 444-458.

40. Cardone V., Iannizzaro V., Barba S., Messina B. Computer Aided Descriptive Geometry. Proceedings of the Fifteenth International Conference on Geometry and Graphics, (Montreal, Canada). ISGG, 2012, pp. 100-109.

41. Cervantes-Sanchez J.J., Zsombor-Murray P. Kinematics of a Mobile Overconstrained RRRCR Loop. Proceedings of the 16th International Conference on Geometry and Graphics, (Innsbruck, Austria), 2014, pp. 726-731.

42. Cucakovic A.A., Teofilovic N.K., Jovic B.S. Descriptive Geometry Education by Using Multimedia Tools. Proceedings of the 16th International Conference on Geometry and Graphics, (Innsbruck, Austria), 2014, pp. 262-265.

43. Honma I. A trial with teaching materials on descriptive geometry by using CAD for students with hearing impairments. Proceedings of the Fifteenth International Conference on Geometry and Graphics, (Montreal, Canada). ISGG, 2012, pp. 296-301.

44. Monge G. Application de l’Analyse à la Géométrie, Bachalier, Paris, 1850.

45. Ryan D.L. CAD/CAE descriptive geometry. Daniel L. Ryan. Boca Raton: CRC Press, 1992, 209 p.

46. Schmitt F. Descriptive geometry and 3D-CAD. Proceedings of the Eleventh International Conference on Geometry and Graphics (Guangzhow, China). ISGG, 2004, pp. 257-262.

47. Stachel H. Descriptive Geometry meets Computer Vision - the Geometry of Multiple Images. Proceedings of the Twelfth International Conference on Geometry and Graphics (Salvador, Brazil). ISGG, 2006, Paper #T30.

48. Suzuki K. Traditional Descriptive Geometry Education in 3D-CAD/CG Era. Journal for Geometry and Graphics. 2014. V. 18. I. 2, pp. 249-258.

49. Volkov V.Ya., Yurkov V.Yu., Panchuk K., Ilyasova O., Kaygorodtseva N., Yakovenko K. The innovative paradigm of teaching in descriptive geometry. Proceedings of the Fifteenth International Conference on Geometry and Graphics, (Montreal, Canada). ISGG, 2012, pp. 778-787.

50. Weiss G. Is advanced elementary geometry on the way to regain scientific terrain? Proceedings of the Fifteenth International Conference on Geometry and Graphics, (Montreal, Canada). ISGG, 2012, pp. 793-804.

51. Wu H., Suzuki K. Development of spatial ability of students during elementary-, junior high-, and senior high-schools. Proceedings of the Fifteenth International Conference on Geometry and Graphics, (Montreal, Canada). ISGG, 2012, pp. 815-823.

Доступ и загрузка

🗂 JATS XML ❝ To cite 📎 Citations

—

Views

—

Downloads

Citations

Индексируется в

RI RINC Indexing database

Indexing and databases

RINC →

The Analysis of Measurement Systems for the Construction of Geometrical Models of the Product

Confirmation

Регистрация