Geometrical resolvability of three-dimensional scenes

The formalization of problems on geometrical resolvability of three-dimensional scenes is discussed. This widespread problem facing the specialists in different fields of technology is considered by an example of assembling of technical systems. A theoretically-gaming model is offered which makes it possible to reduce laboriousness of checking the test configurations of details for geometric resolvability. A posteriori data on the element disposition can be used for increasing the efficiency of geometrical analysis of three-dimensional scenes. A depth of the element nesting is an index of difficulty of the geometrical situation. A topological model called the deformation retract can be a carrier of data on the nesting hierarchy.

References

[1] Kapustin N.M., Pavlov V.V., Kozlov L.A. Dialogovoe proektirovanie tekhnologicheskikh protsessov [Dialog design of technological processes]. Moscow, Mashinostroenie Publ., 1988. 255 p.

[2] Pavlov V.V. Matematicheskoe obespechenie SAPR v proizvodstve letatel’nykh apparatov [CAD software in aircraft production]. Moscow, MFTI Publ., 1978. 68 p.

[3] De Fazio T.L., Whitney D.E. Simplified generation of all mechanical assembly sequences. IEEE J. Rob. Autom., 1987, vol. 3, no. 6, pp. 640-658.

[4] Baldwin D.F., Abell, T.E., Lui M.M., De Fazio T.L., Whitney D.E. An integrated computer aid for generating and evaluating assembly sequences for mechanical products. IEEE Trans. Rob. Autom., 1991, vol. 7, no. 1, pp. 78-94.

[5] Whitney D.E. Mechanical assemblies: their design, manufacture, and role in product development. Oxford Univ. Press, 2004. 518 p.

[6] Dini G., Failli F., Lazzerini B., Marcelloni F. Generation of optimized assembly sequences using genetic algorithms. Annals of the CIRP, 1999, vol. 48, pp. 17-20.

[7] Antonsson E.K., Cagan J. Formal engineering design synthesis. Cambridge Univ. Press, 2005. 500 p.

[8] Lee Y.Q., Kumara S.R.T. Individual and group disassembly sequence generation through freedom and interference spaces. J. Des. Manuf., 1992, no. 2, pp. 143-154.

[9] Penev K., Ron A.J. Determination of a disassembly strategy. Int. J. Prod. Res., 1996, vol. 34, pp. 507-523.

[10] Bozhko A.N. Game modeling of a geometrical access. Nauka Obraz. MGTU im. N.E. Baumana. Elektron. Zh. [Sci. Educ. Bauman Moscow State Tech. Univ. Electron. J.], 2009, no. 12 (in Russ.).

[11] Bozhko A.N., Muammer S., Rogova O.B. Simulation of geometrical constraints in partitioning products on assembly units. Nauka Obraz. MGTU im. N.E. Baumana. Elektron. Zh. [Sci. Educ. Bauman Moscow State Tech. Univ. Electron. J.], 2012, no. 5 (in Russ.).

[12] Chernorutskiy I.G. Metody prinyatiya resheniy [Methods for decision making]. St. Petersburg, BKhV-Peterburg Publ., 2005. 408 p.

[13] Boltyanskiy V.G., Efremovich V.A. Naglyadnaya topologiya [Graphical topology]. Moscow, Nauka Publ., 1982. 149 p.