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In this paper the consideration related to formation of ruled surfaces with a single method for their set up that was proposed in the first part of the work, is continued. In the first part of the work were considered more than twenty variants for set up of ruled surfaces, including four set ups by guide lines, overall known in the literature, for example, in the books of S.A. Frolov, A.V. Bubennikov, M.Ya. Gromov. However, the set up of ruled surfaces with the help of guide lines was proposed in a new aspect – as a constituent of a single method for setting absolutely all ruled surfaces, taking place in science and industry, and with additional variants. Besides, have been proposed equation systems, which solution leads to generation of equation for the given ruled surface. New set ups of ruled surfaces have included eighteen examples, which is the main material of the work’s first part. Also was proposed a table in which have been put all possible variants for set up of geometric figures’ guiding lines to obtain ruled surfaces. Of course, the proposed variants of guiding lines’ combination were presented in the enlarged form. In the proposed paper have been considered new, not presented before, variants for set up of ruled surfaces. Have been presented 19 examples, including the ones with one or two guiding planes, as well as when the guiding line belongs to one of guiding surfaces. Such surfaces can be considered as ruled surfaces of smooth transition. As in the first part of the work, the equation systems leading to the equation of the set ruled surface are proposed.
surfaces, ruled surfaces, geometry, descriptive geometry, surface formation.
1. Bubennikov A.V., Gromov M.Ya. Nachertatel`naya geometriya [Descriptive geometry]. Moscow: Vy`sshaya shkola Publ., 1973. 416 p. (in Russian)
2. Gershman I.P. Konstruirovanie poverkhnostey putem vydeleniya ikh nepreryvnykh lineychatykh karkasov iz mnogoparametricheskikh mnozhestv liniy [Design surfaces by highlighting their non-continuous bar frames from a multivariate sets of lines]. Trudy UDN im. P. Lumumby [Works UDN them. P. Lumumba]. Moscow, 1967, V. 26, I. 3, pp. 33-47. (in Russian)
3. Dimentberg F.M. Teoriya vintov i eyo prilozheniya [The theory of screws and its applications]. Moscow, Nauka Publ., 1978. 328 p. (in Russian)
4. Ivanov V.N., Krivoshapko S.N., Romanova V.A. Osnovy` razrabotki i vizualizacii ob``ektov analiticheskih poverhnostej i perspektivy` ih ispol`zovaniya v arxitekture i stroitel`stve [Bases of development and visualization of objects of analytical surfaces and prospects of their use in architecture and construction]. Geometriya i grafika [Geometry and Graphics]. 2017, V. 5, I. 4, pp. 3-14. DOI:https://doi.org/10.12737/article_5a17f-590be3f51.37534061. (in Russian)
5. Kalashnikov S.N. Zubchatie kolesa i ih izgotovlenie [The gears and their manufacture]. Moscow. Mashinostroenie Publ. 1983. 264 p. (in Russian)
6. Kamalov A. Konstruirovanie lineychatykh poverkhnostey karkasno-parametricheskim metodom i ikh primenenie. Kand. Diss. [The design of the ruled surfaces of frame-parametric method and their application. Cand. Diss.]. Samarkand, 1980. (in Russian)
7. Karacharovskii V.YU., Riazanov S.A. Vizualizatsionnaya otsenka geometricheskikh kharakteristik kontaktiruyushchey poverkhnosti v chervyachnykh peredachakh na osnove primeneniya metodov 3D komp'yuternoy grafiki [Application of 3D computer graphics and solid modeling in the design processes gear cutting]. Vestnik Saratovskogo gosudarstvennogo tehnicheskogo universiteta [Bulletin of the Saratov State Technical University]. Saratov, SGTU Publ. 2010, I. 4, pp. 55-60. (in Russian)
8. Kislookiy V.N., Sedletskaya N.I., Kharchenko A.I. Avtomatizatsiya predstavleniya geometrii diskretnykh modeley v zadachakh prochnostnykh raschetov lopatok parovykh turbin [Automation before presentation of the geometry of discrete models in problems of stress analysis of steam turbine blades]. Prikladnaya geometriya i inzheneznaya grafika [Applied Geometry and Engineering Graphics]. Kiev, Budivel'nik Publ., 1979, I. 28, pp. 19-23. (in Russian)
9. Koznevski E`. Karkasy` kry`sh i derev`ya teorii grafov [Frames of the roofs and trees of graph theory]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 1, pp. 12-20. DOI:https://doi.org/10.12737/18054. (in Russian)
10. 10. Kokareva Ya.A. Sintez uravnenij linejchaty`x poverxnostej s dvumya krivolinejny`mi i odnoj pryamolinejnoj napravlyayushhimi [Synthesis of the equations of the ruled surfaces with two curvilinear and one rectilinear guide]. Geometriya i grafika [Geometry and Graphics]. 2018, V. 6, I. 3, pp. 3-12. DOI:https://doi.org/10.12737/article_5bc454948a7d90.80979486. (in Russian)
11. Miloserdov E.P. Raschet parametrov konstruktsii i razrabotka algoritmov realizatsii analemmaticheskikh solnechnykh chasov [Calculation of the design parameters and the development of the implementation of algorithms analemmaticheskih sundial]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 3, pp. 14-16. DOI:https://doi.org/10.12737/2076. (in Russian)
12. Nitejskij A.S. Konstruirovanie torsovoj poverhnosti metodom podvizhnogo trekhgrannika Frene [Construction of a torso surface by the method of a movable triaxial Frenet]. Omskij nauchnyj vestnik [Omsk Scientific Herald]. 2013, I. 2 (120), pp. 151-153. (in Russian)
13. Panchuk K.L., Lyashkov A.A., Varepo L.G. Kinematicheskaya geometriya krivoj linii i ee prilozhenie k geometricheskomu modelirovaniyu ploskogo zubchatogo zacepleniya [Kinematicheskaya geometriya krivoj linii i ee prilozhenie k geometricheskomu modelirovaniyu ploskogo zubchatogo zacepleniya]. Geometriya i grafika [Geometry and Graphics]. 2018, V. 6, I. 3, pp. 3-12. DOI:https://doi.org/10.12737/article_5bc454948a7d90.80979486. (in Russian)
14. Peredachi spiroidny`e s cilindricheskimi chervyakami. Raschet geometrii: metodicheskie ukazaniya [Transfers spiroid with cylindrical worms. Geometry calculation: methodical instructions]. Moscow: Rotaprint VNIINMASh Publ., 1977. 66 p. (in Russian)
15. Podgornyj A.L. Konstruirovanie poverxnostej obolochek po zadanny`m usloviyam na osnove vy`deleniya ix iz kongruencij pryamy`h [The construction of shell surfaces with given conditions on the basis of their separation from congruences of straight lines]. Prikladnaya geometriya i inzhenernaya grafika [Applied Geometry and Engineering Graphics]. Kiev, Budіvel`nik Publ., 1969, V. VIII, pp. 17-28. (in Russian)
16. Pilipaka S.F., Mukvich N.N. Konstruirovanie linejchatyh poverhnostej obshchego vida v sisteme soprovoditel'nogo trekhgrannika napravlyayushchej prostranstvennoj krivoj [Construction of ruled surfaces of general form in the system of the accompanying trihedron of the directional spatial curve]. Trudy Tavricheskoj gosudarstvennoj agrotekhnicheskoj akademii [Proceedings of the Taurian State Agrotechnical Academy]. Melitopol: TDATU Publ., 2007, I. 4. (in Russian)
17. Rachkovskaya G.S. Geometricheskoe modelirovanie i grafika kinematicheskih linejchatyh poverhnostej na osnove triady kontaktiruyushchih aksoidov [Geometric modeling and graph of kinematic ruled surfaces based on the triad of contacting axoids]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 3, pp. 46-52. DOI:https://doi.org/10.12737/21533 (in Russian)
18. Ryzhov N.N. Matematicheskoe modelirovanie proezzhey chasti avtomobil'nykh dorog [Mathematical modeling carriageway roads]. Moscow, MADI Publ., 1988. (in Russian)
19. Sal'kov N.A. Geometricheskoe modelirovanie i nachertatel'naya geometriya [Geometric modeling and descriptive geometry]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 4, pp. 31-61. (in Russian)
20. Sal`kov N.A. Geometricheskaya sostavlyayushhaya texnicheskix innovacij [Geometric component of technical innovations]. Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 2, pp. 85-94. DOI:https://doi.org/10.12737/article_5b55a-5163fa053.07622109. (in Russian)
21. Sal'kov N.A. Geometricheskie parametry grokhota [Geometric parameters of the screen]. Prikladnaya geometriya i inzhenernaya grafika [Applied Geometry and Engineering Graphics]. Kiev, Budivel'nik Publ., 1987, I. 43, pp. 69-71. (in Russian)
22. Sal'kov N.A. Matematicheskoe modelirovanie lineynykh i poverkhnostnykh form avtomobil'nykh dorog na podkhodakh k mostam [Mathematical modeling of linear and surface-forms of roads on the approaches to bridges]. Trudy MADI: Prikladnye teoreticheskie voprosy proektirovaniya perekhodov cherez vodotoki [Proceedings MADI: Applied theoretical design issues crossing streams]. Moscow, 1989, pp. 60-66. (in Russian)
23. Sal`kov N.A. Metody` parametricheskoj geometrii v modelirovanii avtomobil`ny`h dorog [Methods of parametric geometry modelling of roads]. Zhurnal estestvenno-nauchny`h issledovanij [Journal of Natural Sciences]. 2016, V. 1, I. 4, pp. 1-1. DOI:https://doi.org/10.12737/22143. (in Russian)
24. Sal'kov N.A. Modelirovanie avtomobil'nykh dorog [Modeling roads]. Moscow, INFRA-M Publ., 2012, 120 p. (in Russian)
25. Sal`kov N.A. Modelirovanie geometricheskih form avtomobil`ny`h dorog [Modeling of geometric shapes of roads: monograph]. Moscow: INFRA-M Publ., 2019. 162 p. (in Russian)
26. Sal'kov N.A. Nachertatel'naya geometriya: bazovyy kurs [Descriptive geometry: Basic course]. Moscow, INFRA-M Publ., 2013. 184 p. (in Russian)
27. Salkov N.A. Nachertatel'naja geometrija: Osnovnoj kurs [Descriptive geometry. The main course]. Moscow, INFRA-M Publ., 2014. 235 p. (in Russian)
28. Sal`kov N.A. Obshhie principy` zadaniya linejchaty`h poverhnostej [General principles of setting ruled surfaces]. Geometriya i grafika [Geometry and Graphics]. 2018, V. 6, I. 4, rr. 20-31. DOI:https://doi.org/10.12737/article_5c-21f4a06dbb74.56415078. (in Russian)
29. Sal'kov N.A. Parametricheskaya geometriya v geometricheskom modelirovanii [Parametric geometry in the geometric modeling]. Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 3, pp. 7-13. DOI:https://doi.org/10.12737/6519. (in Russian)
30. Sal`kov N.A. Formirovanie poverhnostej otkosov nasy`pej i vy`emok [The formation of the surfaces of slopes of embankments and excavations]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 1, pp. 55-63. DOI:https://doi.org/10.12737/18058. (in Russian)
31. Sal`kov N.A. Formirovanie poverxnostej pri kineticheskom otobrazhenii [The formation of surfaces at a kinetic display]. Geometriya i grafika [Geometry and Graphics]. 2018, V. 6, I. 1, pp. 20-33. DOI:https://doi.org/10.12737/article_5ad094a0380725.32164760. (in Russian)
32. Sal'kov N.A. Formirovanie tsiklicheskikh poverkhnostey v kineticheskoy geometrii [Formation of cyclic surfaces in kinetic geometry]. Geometriya i grafika [Geometry and graphics]. 2017, V. 5, I. 4, pp. 24-36. (in Russian)
33. Shvidenko Yu.Z. Sopryazheniya lineychatymi povrekhnostyami i ikh primenenie dlya konstruirovaniya obolochek. Kand. Diss. [Mate bar poverhnosti and their use of for constructing shells.Cand. Diss.]. Kiev, 1966. (in Russian)
34. Kheyfets A.L., Loginovskij A.N. 3D-modeli linejchaty`h poverhnostej s tremya pryamolinejny`mi napravlyayushhimi [3D-Models of ruled surfaces with three rectilinear guides]. Vestnik YuUrGU. Seriya «Stroitel`stvo i arhitektura» [Bulletin of SUSU. Series «Construction Engineering and Architecture»]. 2008, I. 25, pp. 51-56. (in Russian)
35. Frolov S.A. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, Mashinostroenie Publ., 1978. 240 p. (in Russian)
