Formation surfaces of Monge by the kinematic method in AutoCAD environment

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Aims of research. Studying the possibility of forming Monge carved surfaces, defined by the method of their formation, creating an algorithm and program in the AutoLISP language to demonstrate the formation of surfaces in the AutoCAD environment in a dynamic mode. Methods. Monge carved surfaces are formed by a flat curve, located in the tangent plane to the fixed guide of the developable surface, when the plane and the curve roll along the guide surface without sliding. The described method of formation of these surfaces allows to perform their formation by the kinematic method in the AutoCAD environment using AutoLISP software. The article describes the construction of the Monge surfaces using cylindrical and conical surfaces as guides. A straight line and a sine wave are used as the forming lines. Results. An algorithm and a program in the AutoLISP language were created to form sets of compartments of several Monge surfaces and to visualize the formation of these surfaces in a dynamic mode by sequentially displaying the compartments on the monitor screen. The mini-film about formation of Monge surface by rolling a plane with a straight line along a circular cone is created. In the mini-film the drawings received by transformation of drawings of the AutoCAD environment are used.

About the authors

Viktoryna A Romanova

People’s Friendship University of Russia (RUDN University)

Author for correspondence.

Associate Professor, Peoples' Friendship University of Russia (RUDN University). Research interests: visualization of the design of mechanisms and the formation of analytical surfaces in the AutoCAD environment using programs in the language AutoLISP

6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation


  1. Monge G. (1936). Annex of the analysis to geometry. Мoscow: ONTY Publ., 699.
  2. Monge G. (1947). Nachertatel'naya geometriya [Descriptive geometry]. Moscow: AN SSSR Publ., 291.
  3. Krivoshapko S.N., Ivanov V.N. (2010). Enciklopediya analiticheskih poverhnostej [Encyclopedia of analytical surfaces]. Moscow: Librokom Publ., 560.
  4. Rizvan Muhammad. (2004). Geometriya, konstruirovanie i issledovanie napryazhenno-deformirovannogo sostoyaniya obolochek v forme reznyh poverhnostej Monzha obshchego vida [Geometry, design and study of stressstrain state of shells in the form of carved Monge surfaces of general form] (Cand. Diss.). Moscow, 218. (In Russ.)
  5. Fillipova J.R. (2014). K voprosu o geometrii reznyh obolochek Monzha [To a question of geometry of carved covers of Monge]. Strength, creep and destruction of building and engineering materials and constructions, 132-135. (In Russ.)
  6. V.N. Ivanov, Rizvan Muhammad. (2003). Reznye poverhnosti Monzha i konstruirovanie obolochek [Carved surfaces of Monge and designing of covers]. Theory and practice of engineering researches: materials of a scientific conference of graduate students, teachers and young scientists, April 22-25, 2002. Moscow: RUDN Publ., 233-234. (In Russ.)
  7. Fillipova J.R. (2016). Sravnitel'nyj analiz rezul'tatov rascheta tonkoj obolochki v forme reznoj poverhnosti Monzha po bezmomentnoj teorii i metodom konechnyh elementov [The comparative analysis of results of calculation of a thin cover in the form of a carved surface of Monge according to the momentless theory and a finite element method]. Structural Mechanics of Engineering Constructions and Buildings, (8), 8-13. (In Russ.)
  8. Fillipova J.R. (2015). Ob aktual'nosti primeneniya reznyh poverhnostej Monzha v arhitekture [On the relevance of the use of carved surfaces of Monge in architecture]. Construction and reconstruction, (6), 91-95. (In Russ.)
  9. Schroeder W., Martin K., Lorensen B. (2003). The Visualization Toolkit. Kitware, Inc.
  10. Haber R.B. (Jan. 1990). Vizualization Techniques for Engineering Mechanics. Computing Systems in Engineering, 1(1), 37-50.
  11. Dupac M., Popirlan C.-I. (April 1st 2010). Web Technologies for Modelling and Visualization in Mechanical Engineering. doi: 10.5772/9037
  12. Gallagher R.S., Press S. (1994). Computer Visualization: Graphics Techniques for Engineering and Scientific Analysis. CRC Press, 336.
  13. Caha J., Vondrakova A. (2017). Fuzzy surface visualization using HSL colour model. Electronic Journal, 2(2), 26-42.
  14. Chetverukhin N.F., Levitsky V.S., Pryanishnikov Z.I., Tevlin A.M., Fedotov G.I. (1936). Kurs nachertatel'noj geometrii [The course of descriptive geometry]. Moscow: State Publishing House of Technical and Theoretical Literature, 435. (In Russ.)
  15. Ivanov O.N., Chaykin A.A., Shevchenko V.N. (1992). Yazyk programmirovaniya AutoLISP Release 10, 11
  16. Kudryavtsev E.M. (1999). AutoLISP. Programmirovanie v FutoCAAD-14 [AutoLISP. Programming in AutoCAD-14]. Moscow: DM Publ. (In Russ.)
  17. Romanova V.A., Matveev V.M. (2016). Vizualizaciya dvizheniya tochki kontakta zub'ev v cilindricheskoj zubchatoj peredache [Visualization of the movement of a contact point in cylinder cog-transmission]. Structural Mechanics of Engineering Constructions and Buildings, (1), 26-29. (In Russ.)
  18. Heifetz A.L., Loginovsky A.N., Butorina I.V., Vasilyev V.N. (2013). Inzhenernaya 3D-komp'yuternaya grafika [Inzhenernaya 3D-computer graphics]. Мoscow: Yurayt Publ., 464. (In Russ.)
  19. Ivanov V.N., Romanova V.A. (2016). Konstrukcionnye formy prostranstvennyh konstrukcij. Vizualizaciya poverhnostej v sistemah MathCad, AutoCad [Constructive forms of space constructions. Visualization of the surfaces at systems MathCAD, AutoCAD]. Moscow: ASV Publ., 410. (In Russ.)
  20. Ivanov V.N., Krivoshapko S.N., Romanova VA. (2017). Osnovy razrabotki i vizualizacii ob"ektov analiticheskih poverhnostej i perspektivy ih ispol'zovaniya v arhitekture i stroitel'stve [Bases of development and visualization of objects of analytical surfaces and the prospect of their use in architecture and construction]. Geometry and graphics, 5(4), 3-14. (In Russ.)
  21. Romanova V.A. (2015). Vizualizaciya obrazovaniya poverhnostej zontichnogo tipa [Visualization of formation of umbrella-type and umbrella surfaces with radial damping waves in the central point]. Structural Mechanics of Engineering Constructions and Buildings, (3), 4-8. (In Russ.)
  22. Romanova V.A. (2016). Formirovanie ciklicheskih poverhnostej s obrazuyushchej okruzhnost'yu peremennogo radiusa v AVTOKADЕ [The formation of cyclic surfaces with variable radius of generatrix circles in AutoCAD. Structural Mechanics of Engineering Constructions and Building, (3), 20-24. (In Russ.)
  23. Romanova V.A. (2012). Osobennosti izobrazheniya processa obrazovaniya poverhnostej v sisteme AutoCAD [The features of the image formation surfaces in the CAD system AutoCAD]. Structural Mechanics of Engineering Constructions and Building, (4), 3-5. (In Russ.)

Copyright (c) 2019 Romanova V.A.

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