TY  - JOUR
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/875
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - MoNGeometrija 2016
EP  - 204
IS  - 2
SP  - 203
VL  - 45
UR  - https://hdl.handle.net/21.15107/rcub_grafar_875
ER  - 

@article{
author = "Obradović, Marija and Popkonstantinović, Branislav",
year = "2017",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "MoNGeometrija 2016",
pages = "204-203",
number = "2",
volume = "45",
url = "https://hdl.handle.net/21.15107/rcub_grafar_875"
}

Obradović, M.,& Popkonstantinović, B.. (2017). MoNGeometrija 2016. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 45(2), 203-204.
https://hdl.handle.net/21.15107/rcub_grafar_875

Obradović M, Popkonstantinović B. MoNGeometrija 2016. in FME Transactions. 2017;45(2):203-204.
https://hdl.handle.net/21.15107/rcub_grafar_875 .

Obradović, Marija, Popkonstantinović, Branislav, "MoNGeometrija 2016" in FME Transactions, 45, no. 2 (2017):203-204,
https://hdl.handle.net/21.15107/rcub_grafar_875 .

TY  - JOUR
AU  - Popkonstantinović, Branislav
AU  - Obradović, Ratko
AU  - Obradović, Marija
AU  - Jeli, Zorana
AU  - Stojicević, Miša
PY  - 2016
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/801
AB  - This paper analyzes the geometrical and mechanical characteristics of balance springs, which have the most important influence on the oscillation rate of the balance wheel and, consequently, the most decisive effects on the timekeeper's accuracy. These characteristics are obtained by a set of SolidWorks simulations of static structural studies based on the finite element model, which are performed and accomplished in a specific and original way. Our study demonstrates that the position of the balance spring center of mass and its momentum of inertia are not constant but depend on the angular displacement of the spring collet end. It also shows that the torque spring rate (the spring stiffness) varies as a function of angular displacement during the balanced spring twist. All results are presented numerically and graphically by a set of diagrams and can contribute to the better understanding of the balance spring geometrical and mechanical features and, therefore, be applied for improving a timepiece's accuracy. Moreover, the method of simulation study disclosed and explained in this paper provides general suggestions and guidance for similar studies. The accuracy of the presented results, as well as the validity of the complete simulation-based method, is proven by the experimentally determined relationship between balance spring restoring torque, stiffness, and spring angular displacement.
PB  - SAGE Publications Ltd
T2  - Simulation-Transactions of the Society for Modeling and Simulation International
T1  - Geometrical and mechanical characteristics of deformed balance spring obtained by simulation study
EP  - 997
IS  - 11
SP  - 981
VL  - 92
DO  - 10.1177/0037549716673453
ER  - 

@article{
author = "Popkonstantinović, Branislav and Obradović, Ratko and Obradović, Marija and Jeli, Zorana and Stojicević, Miša",
year = "2016",
abstract = "This paper analyzes the geometrical and mechanical characteristics of balance springs, which have the most important influence on the oscillation rate of the balance wheel and, consequently, the most decisive effects on the timekeeper's accuracy. These characteristics are obtained by a set of SolidWorks simulations of static structural studies based on the finite element model, which are performed and accomplished in a specific and original way. Our study demonstrates that the position of the balance spring center of mass and its momentum of inertia are not constant but depend on the angular displacement of the spring collet end. It also shows that the torque spring rate (the spring stiffness) varies as a function of angular displacement during the balanced spring twist. All results are presented numerically and graphically by a set of diagrams and can contribute to the better understanding of the balance spring geometrical and mechanical features and, therefore, be applied for improving a timepiece's accuracy. Moreover, the method of simulation study disclosed and explained in this paper provides general suggestions and guidance for similar studies. The accuracy of the presented results, as well as the validity of the complete simulation-based method, is proven by the experimentally determined relationship between balance spring restoring torque, stiffness, and spring angular displacement.",
publisher = "SAGE Publications Ltd",
journal = "Simulation-Transactions of the Society for Modeling and Simulation International",
title = "Geometrical and mechanical characteristics of deformed balance spring obtained by simulation study",
pages = "997-981",
number = "11",
volume = "92",
doi = "10.1177/0037549716673453"
}

Popkonstantinović, B., Obradović, R., Obradović, M., Jeli, Z.,& Stojicević, M.. (2016). Geometrical and mechanical characteristics of deformed balance spring obtained by simulation study. in Simulation-Transactions of the Society for Modeling and Simulation International
SAGE Publications Ltd., 92(11), 981-997.
https://doi.org/10.1177/0037549716673453

Popkonstantinović B, Obradović R, Obradović M, Jeli Z, Stojicević M. Geometrical and mechanical characteristics of deformed balance spring obtained by simulation study. in Simulation-Transactions of the Society for Modeling and Simulation International. 2016;92(11):981-997.
doi:10.1177/0037549716673453 .

Popkonstantinović, Branislav, Obradović, Ratko, Obradović, Marija, Jeli, Zorana, Stojicević, Miša, "Geometrical and mechanical characteristics of deformed balance spring obtained by simulation study" in Simulation-Transactions of the Society for Modeling and Simulation International, 92, no. 11 (2016):981-997,
https://doi.org/10.1177/0037549716673453 . .

TY  - JOUR
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Popkonstantinović, Branislav
PY  - 2015
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1930
AB  - Concave pyramids of second sort (CP II) are formed similarly to concave cupolae of second sort
(CC II) with a comparable logic of emergence to the regular-faced convex pyramids. They are formed by enclosing the space over a regular polygonal base by the lateral deltahedral wrapper consisting of equilateral triangles meeting in common apex. The plane net is composed of double row of equilateral triangles, so it is possible to form a regular faced pyramid even with bases greater than pentagonal, whereat the obtained polyhedron will be concave. In this paper we focus on a type of concave pyramids of second sort formed over the basic polygons with an even number of sides, type CP II-B which has half the number of lateral unit cells than the type CP II-A.
PB  - Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS
PB  - Brasov, Romania: University ‘Transilvania’ of Brasov
T2  - Journal of Industrial Design and Engineering Graphics (JIDEG)
T1  - Variations of Concave Pyramids of Second Sort with an Even Number of Base Sides
EP  - 50
IS  - 2
SP  - 45
VL  - 10
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1930
ER  - 

@article{
author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav",
year = "2015",
abstract = "Concave pyramids of second sort (CP II) are formed similarly to concave cupolae of second sort
(CC II) with a comparable logic of emergence to the regular-faced convex pyramids. They are formed by enclosing the space over a regular polygonal base by the lateral deltahedral wrapper consisting of equilateral triangles meeting in common apex. The plane net is composed of double row of equilateral triangles, so it is possible to form a regular faced pyramid even with bases greater than pentagonal, whereat the obtained polyhedron will be concave. In this paper we focus on a type of concave pyramids of second sort formed over the basic polygons with an even number of sides, type CP II-B which has half the number of lateral unit cells than the type CP II-A.",
publisher = "Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS, Brasov, Romania: University ‘Transilvania’ of Brasov",
journal = "Journal of Industrial Design and Engineering Graphics (JIDEG)",
title = "Variations of Concave Pyramids of Second Sort with an Even Number of Base Sides",
pages = "50-45",
number = "2",
volume = "10",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1930"
}

Obradović, M., Mišić, S.,& Popkonstantinović, B.. (2015). Variations of Concave Pyramids of Second Sort with an Even Number of Base Sides. in Journal of Industrial Design and Engineering Graphics (JIDEG)
Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS., 10(2), 45-50.
https://hdl.handle.net/21.15107/rcub_grafar_1930

Obradović M, Mišić S, Popkonstantinović B. Variations of Concave Pyramids of Second Sort with an Even Number of Base Sides. in Journal of Industrial Design and Engineering Graphics (JIDEG). 2015;10(2):45-50.
https://hdl.handle.net/21.15107/rcub_grafar_1930 .

Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, "Variations of Concave Pyramids of Second Sort with an Even Number of Base Sides" in Journal of Industrial Design and Engineering Graphics (JIDEG), 10, no. 2 (2015):45-50,
https://hdl.handle.net/21.15107/rcub_grafar_1930 .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Popkonstantinović, Branislav
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1252
AB  - Correspondingly to the method of generating the Concave Cupolae of second sort, the Concave Pyramids of second sort have the similar logic of origination, and their counterpart in regular faced convex pyramids (tetrahedron, Johnson's solids J1 and J2). The difference is that instead of onefold series of equilateral triangles in the lateral surface of the solid, there appear twofold series, forming deltahedral lateral surface with a common point, while bases are also regular polygons. This time, instead of the bases from n=3 to n=5, there are the basis from n=6 to n=9. The same lateral surface’s net can be folded and creased in two different ways, which produces the two types of Concave Pyramids of second sort: with a major and with a minor solid height. Combining and joining so obtained solids by the correspondent bases, the concave (ortho) bipyramids of second sort emerge, which then may be elongated, gyroelongated, and conca-elongated, creating a distinctive family of diverse concave polyhedral structures.
PB  - Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd
C3  - Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
T1  - Concave Pyramids of Second Sort -The Occurrence, Types, Variations
EP  - 168
SP  - 157
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1252
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav",
year = "2014",
abstract = "Correspondingly to the method of generating the Concave Cupolae of second sort, the Concave Pyramids of second sort have the similar logic of origination, and their counterpart in regular faced convex pyramids (tetrahedron, Johnson's solids J1 and J2). The difference is that instead of onefold series of equilateral triangles in the lateral surface of the solid, there appear twofold series, forming deltahedral lateral surface with a common point, while bases are also regular polygons. This time, instead of the bases from n=3 to n=5, there are the basis from n=6 to n=9. The same lateral surface’s net can be folded and creased in two different ways, which produces the two types of Concave Pyramids of second sort: with a major and with a minor solid height. Combining and joining so obtained solids by the correspondent bases, the concave (ortho) bipyramids of second sort emerge, which then may be elongated, gyroelongated, and conca-elongated, creating a distinctive family of diverse concave polyhedral structures.",
publisher = "Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd",
journal = "Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia",
title = "Concave Pyramids of Second Sort -The Occurrence, Types, Variations",
pages = "168-157",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1252"
}

Obradović, M., Mišić, S.,& Popkonstantinović, B.. (2014). Concave Pyramids of Second Sort -The Occurrence, Types, Variations. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd., 157-168.
https://hdl.handle.net/21.15107/rcub_grafar_1252

Obradović M, Mišić S, Popkonstantinović B. Concave Pyramids of Second Sort -The Occurrence, Types, Variations. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia. 2014;:157-168.
https://hdl.handle.net/21.15107/rcub_grafar_1252 .

Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, "Concave Pyramids of Second Sort -The Occurrence, Types, Variations" in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia (2014):157-168,
https://hdl.handle.net/21.15107/rcub_grafar_1252 .

TY  - CONF
AU  - Mišić, Slobodan
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1151
AB  - Concave Cupolae of fourth sort (CC IV) are polyhedra which lateral surface is created by folding a quadruple strip of equilateral triangles, while the bases are regular polygons. The unit cell that forms the deltahedral lateral surface by radial sequenceing around the axis of the solid is composed of two spatial hexahedrals. These unit cells are linked together in its upper zone by spatial quadrihedals, which consist of four equilateral triangles grouped around a common vertex. Over the same polygonal base, there can be formed four diverse Concave Cupolae of IV sort, using different variants of constructive procedure. In this paper, the application of the program for modeling the lateral surface of concave cupolae of IV sort, using the software package MATLAB, allows visual monitoring of the structural transformation of the concave cupolae of IV sort, for different polygonal bases and different variants of constructive procedure.
PB  - Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd
C3  - Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
T1  - The Structural Transformation of Concave Cupolae of Fourth Sort Using Different Variants of Constructive Procedure, 4th International Scientific Conference on Geometry and Graphics
EP  - 156
SP  - 147
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1151
ER  - 

@conference{
author = "Mišić, Slobodan and Obradović, Marija and Popkonstantinović, Branislav",
year = "2014",
abstract = "Concave Cupolae of fourth sort (CC IV) are polyhedra which lateral surface is created by folding a quadruple strip of equilateral triangles, while the bases are regular polygons. The unit cell that forms the deltahedral lateral surface by radial sequenceing around the axis of the solid is composed of two spatial hexahedrals. These unit cells are linked together in its upper zone by spatial quadrihedals, which consist of four equilateral triangles grouped around a common vertex. Over the same polygonal base, there can be formed four diverse Concave Cupolae of IV sort, using different variants of constructive procedure. In this paper, the application of the program for modeling the lateral surface of concave cupolae of IV sort, using the software package MATLAB, allows visual monitoring of the structural transformation of the concave cupolae of IV sort, for different polygonal bases and different variants of constructive procedure.",
publisher = "Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd",
journal = "Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia",
title = "The Structural Transformation of Concave Cupolae of Fourth Sort Using Different Variants of Constructive Procedure, 4th International Scientific Conference on Geometry and Graphics",
pages = "156-147",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1151"
}

Mišić, S., Obradović, M.,& Popkonstantinović, B.. (2014). The Structural Transformation of Concave Cupolae of Fourth Sort Using Different Variants of Constructive Procedure, 4th International Scientific Conference on Geometry and Graphics. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd., 147-156.
https://hdl.handle.net/21.15107/rcub_grafar_1151

Mišić S, Obradović M, Popkonstantinović B. The Structural Transformation of Concave Cupolae of Fourth Sort Using Different Variants of Constructive Procedure, 4th International Scientific Conference on Geometry and Graphics. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia. 2014;:147-156.
https://hdl.handle.net/21.15107/rcub_grafar_1151 .

Mišić, Slobodan, Obradović, Marija, Popkonstantinović, Branislav, "The Structural Transformation of Concave Cupolae of Fourth Sort Using Different Variants of Constructive Procedure, 4th International Scientific Conference on Geometry and Graphics" in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia (2014):147-156,
https://hdl.handle.net/21.15107/rcub_grafar_1151 .

TY  - JOUR
AU  - Malešević, Branko J.
AU  - Petrović, Maja
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1020
AB  - We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.
T2  - Mathematical Inequalities & Applications
T1  - On the extension of the Erdös-Mordell type inequalities
EP  - 281
IS  - 1
SP  - 269
VL  - 17
DO  - 10.7153/mia-17-22
ER  - 

@article{
author = "Malešević, Branko J. and Petrović, Maja and Obradović, Marija and Popkonstantinović, Branislav",
year = "2014",
abstract = "We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.",
journal = "Mathematical Inequalities & Applications",
title = "On the extension of the Erdös-Mordell type inequalities",
pages = "281-269",
number = "1",
volume = "17",
doi = "10.7153/mia-17-22"
}

Malešević, B. J., Petrović, M., Obradović, M.,& Popkonstantinović, B.. (2014). On the extension of the Erdös-Mordell type inequalities. in Mathematical Inequalities & Applications, 17(1), 269-281.
https://doi.org/10.7153/mia-17-22

Malešević BJ, Petrović M, Obradović M, Popkonstantinović B. On the extension of the Erdös-Mordell type inequalities. in Mathematical Inequalities & Applications. 2014;17(1):269-281.
doi:10.7153/mia-17-22 .

Malešević, Branko J., Petrović, Maja, Obradović, Marija, Popkonstantinović, Branislav, "On the extension of the Erdös-Mordell type inequalities" in Mathematical Inequalities & Applications, 17, no. 1 (2014):269-281,
https://doi.org/10.7153/mia-17-22 . .

TY  - CONF
AU  - Popkonstantinović, Branislav
AU  - Miladinović, Ljubomir
AU  - Obradović, Marija
AU  - Stojićević, Miša
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1220
AB  - This paper presents the geometrical properties of one special type of escapement mechanism – the grasshopper escapement, by which the first marine chronometers were equipped. The most important and distinguish mechanical feature of this escapement is also disclosed that contact surfaces between pallets and escapement teeth do not need lubrication. In addition, paper presents the escapement 3D solid model and explains briefly its operational cycle.
PB  - Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd
C3  - Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
T1  - Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism
EP  - 181
SP  - 173
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1220
ER  - 

@conference{
author = "Popkonstantinović, Branislav and Miladinović, Ljubomir and Obradović, Marija and Stojićević, Miša",
year = "2014",
abstract = "This paper presents the geometrical properties of one special type of escapement mechanism – the grasshopper escapement, by which the first marine chronometers were equipped. The most important and distinguish mechanical feature of this escapement is also disclosed that contact surfaces between pallets and escapement teeth do not need lubrication. In addition, paper presents the escapement 3D solid model and explains briefly its operational cycle.",
publisher = "Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd",
journal = "Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia",
title = "Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism",
pages = "181-173",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1220"
}

Popkonstantinović, B., Miladinović, L., Obradović, M.,& Stojićević, M.. (2014). Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism. in Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd., 173-181.
https://hdl.handle.net/21.15107/rcub_grafar_1220

Popkonstantinović B, Miladinović L, Obradović M, Stojićević M. Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism. in Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia. 2014;:173-181.
https://hdl.handle.net/21.15107/rcub_grafar_1220 .

Popkonstantinović, Branislav, Miladinović, Ljubomir, Obradović, Marija, Stojićević, Miša, "Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism" in Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia (2014):173-181,
https://hdl.handle.net/21.15107/rcub_grafar_1220 .

TY  - CONF
AU  - Mišić, Slobodan
AU  - Obradović, Marija
AU  - Lazović, Goran
AU  - Popkonstantinović, Branislav
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1977
AB  - The paper discusses the generation of a specific group of polyhedra, Concave Cupolae of Fourth Sort (CC IV) with regular polygonal bases, using constructive and analytical procedures. Beside determination of the parameters of these polyhedra, the paper deals with their visualization, by the application of graphical software MATLAB. We consider one of the four possible types of forming the lateral surfaces of the Concave Cupolae of fourth sort.
PB  - Timişoara: Editura Politehnica
C3  - Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics
T1  - Generating a Type of Concave Cupolae of Fourth Sort
EP  - 82
IS  - 1
SP  - 79
VL  - 58(72)
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1977
ER  - 

@conference{
author = "Mišić, Slobodan and Obradović, Marija and Lazović, Goran and Popkonstantinović, Branislav",
year = "2013",
abstract = "The paper discusses the generation of a specific group of polyhedra, Concave Cupolae of Fourth Sort (CC IV) with regular polygonal bases, using constructive and analytical procedures. Beside determination of the parameters of these polyhedra, the paper deals with their visualization, by the application of graphical software MATLAB. We consider one of the four possible types of forming the lateral surfaces of the Concave Cupolae of fourth sort.",
publisher = "Timişoara: Editura Politehnica",
journal = "Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics",
title = "Generating a Type of Concave Cupolae of Fourth Sort",
pages = "82-79",
number = "1",
volume = "58(72)",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1977"
}

Mišić, S., Obradović, M., Lazović, G.,& Popkonstantinović, B.. (2013). Generating a Type of Concave Cupolae of Fourth Sort. in Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics
Timişoara: Editura Politehnica., 58(72)(1), 79-82.
https://hdl.handle.net/21.15107/rcub_grafar_1977

Mišić S, Obradović M, Lazović G, Popkonstantinović B. Generating a Type of Concave Cupolae of Fourth Sort. in Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics. 2013;58(72)(1):79-82.
https://hdl.handle.net/21.15107/rcub_grafar_1977 .

Mišić, Slobodan, Obradović, Marija, Lazović, Goran, Popkonstantinović, Branislav, "Generating a Type of Concave Cupolae of Fourth Sort" in Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics, 58(72), no. 1 (2013):79-82,
https://hdl.handle.net/21.15107/rcub_grafar_1977 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Popkonstantinović, Branislav
AU  - Petrović, Maja
AU  - Malešević, Branko
AU  - Obradović, Ratko
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1928
AB  - Concave cupolae of second sort, combined with the other regular faced polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The
paper presents research on regular-faced polyhedral structures obtained by joining the bases of square concave cupolae of second sort, with the appropriate sides of Archimedean solid - truncated 
cube, and its application in architecture, based on geometric, structural, and functional analysis.
PB  - Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)
T2  - Technics Technologies Education Management
T1  - Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture
EP  - 1214
IS  - 3
SP  - 1198
VL  - 8
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1928
ER  - 

@article{
author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav and Petrović, Maja and Malešević, Branko and Obradović, Ratko",
year = "2013",
abstract = "Concave cupolae of second sort, combined with the other regular faced polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The
paper presents research on regular-faced polyhedral structures obtained by joining the bases of square concave cupolae of second sort, with the appropriate sides of Archimedean solid - truncated 
cube, and its application in architecture, based on geometric, structural, and functional analysis.",
publisher = "Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)",
journal = "Technics Technologies Education Management",
title = "Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture",
pages = "1214-1198",
number = "3",
volume = "8",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1928"
}

Obradović, M., Mišić, S., Popkonstantinović, B., Petrović, M., Malešević, B.,& Obradović, R.. (2013). Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture. in Technics Technologies Education Management
Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)., 8(3), 1198-1214.
https://hdl.handle.net/21.15107/rcub_grafar_1928

Obradović M, Mišić S, Popkonstantinović B, Petrović M, Malešević B, Obradović R. Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture. in Technics Technologies Education Management. 2013;8(3):1198-1214.
https://hdl.handle.net/21.15107/rcub_grafar_1928 .

Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, Petrović, Maja, Malešević, Branko, Obradović, Ratko, "Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture" in Technics Technologies Education Management, 8, no. 3 (2013):1198-1214,
https://hdl.handle.net/21.15107/rcub_grafar_1928 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
AU  - Mišić, Slobodan
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/487
AB  - The paper examines geometrical, static and dynamic properties of the polyhedral structures obtained by folding and creasing the two-rowed segment of equilateral triangular net. Bases of these concave polyhedra are regular, identical polygons in parallel planes, connected by the alternating series of triangles, as in the case of convex antiprisms. There are two ways of folding such a net, and therefore the two types of concave antiprisms of second sort. The paper discusses the methods of obtaining the accurate position of the vertices and other linear parameters of these polyhedra, with the use of mathematical algorithm. Structural analysis of a representative of these polyhedra is presented using the SolidWorks program applications.
AB  - Rad se bavi ispitivanjem geometrijskih, statičkih i dinamičkih osobina jedne poliedarske strukture nastale nabiranjem dvorednog segmenta mreže jednakostraničnih trouglova. Osnove ovih konkavnih poliedara su pravilni, identični poligoni u paralelnim ravnima, povezani nizom naizmeničnih trouglova, kao i u slučaju konveksnih antiprizmi. Postoje dve varijante savijanja ovakve mreže, pa samim tim i dva tipa konkavnih antiprizmi druge vrste (KA II) za svaku posmatranu osnovu od n=5, n=∞. U radu su razmotreni načini dobijanja tačnog položaja temena i drugih linearnih parametara ovih poliedara, uz primenu algoritma za njihovo matematičko izračunavanje. Strukturalna analiza jednog predstavnika ovih poliedara data je korišćenjem aplikacija programa SolidWorks, kako bi se ispitala mogućnost primene ovih oblika u inženjerstvu.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - On the properties of the concave antiprisms of second sort
T1  - O osobinama konkavnih antiprizmi druge vrste
EP  - 263
IS  - 3
SP  - 256
VL  - 41
UR  - https://hdl.handle.net/21.15107/rcub_grafar_487
ER  - 

@article{
author = "Obradović, Marija and Popkonstantinović, Branislav and Mišić, Slobodan",
year = "2013",
abstract = "The paper examines geometrical, static and dynamic properties of the polyhedral structures obtained by folding and creasing the two-rowed segment of equilateral triangular net. Bases of these concave polyhedra are regular, identical polygons in parallel planes, connected by the alternating series of triangles, as in the case of convex antiprisms. There are two ways of folding such a net, and therefore the two types of concave antiprisms of second sort. The paper discusses the methods of obtaining the accurate position of the vertices and other linear parameters of these polyhedra, with the use of mathematical algorithm. Structural analysis of a representative of these polyhedra is presented using the SolidWorks program applications., Rad se bavi ispitivanjem geometrijskih, statičkih i dinamičkih osobina jedne poliedarske strukture nastale nabiranjem dvorednog segmenta mreže jednakostraničnih trouglova. Osnove ovih konkavnih poliedara su pravilni, identični poligoni u paralelnim ravnima, povezani nizom naizmeničnih trouglova, kao i u slučaju konveksnih antiprizmi. Postoje dve varijante savijanja ovakve mreže, pa samim tim i dva tipa konkavnih antiprizmi druge vrste (KA II) za svaku posmatranu osnovu od n=5, n=∞. U radu su razmotreni načini dobijanja tačnog položaja temena i drugih linearnih parametara ovih poliedara, uz primenu algoritma za njihovo matematičko izračunavanje. Strukturalna analiza jednog predstavnika ovih poliedara data je korišćenjem aplikacija programa SolidWorks, kako bi se ispitala mogućnost primene ovih oblika u inženjerstvu.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "On the properties of the concave antiprisms of second sort, O osobinama konkavnih antiprizmi druge vrste",
pages = "263-256",
number = "3",
volume = "41",
url = "https://hdl.handle.net/21.15107/rcub_grafar_487"
}

Obradović, M., Popkonstantinović, B.,& Mišić, S.. (2013). On the properties of the concave antiprisms of second sort. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 41(3), 256-263.
https://hdl.handle.net/21.15107/rcub_grafar_487

Obradović M, Popkonstantinović B, Mišić S. On the properties of the concave antiprisms of second sort. in FME Transactions. 2013;41(3):256-263.
https://hdl.handle.net/21.15107/rcub_grafar_487 .

Obradović, Marija, Popkonstantinović, Branislav, Mišić, Slobodan, "On the properties of the concave antiprisms of second sort" in FME Transactions, 41, no. 3 (2013):256-263,
https://hdl.handle.net/21.15107/rcub_grafar_487 .

TY  - JOUR
AU  - Popkonstantinović, Branislav
AU  - Miladinović, Ljubomir
AU  - Obradović, Marija
AU  - Ostojić, Gordana
AU  - Stankovski, Stevan
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/534
AB  - The paper analyzes the effects of pendulum temperature dilatation on the timepiece running and accounts for the basic mathematical principles that neutralization of these detrimental effects are based upon. Both preliminary and detailed calculations are presented, as well as some design solutions leading to technically acceptable pendulum temperature dilatation. Explanation is given for the design of bimetal gridiron pendulum, wood pendulum with a lead weight, mercury pendulum, and pendulum with an Invar alloy rod.
T2  - Acta Polytechnica Hungarica
T1  - Mathematical Principles and Optimal Design Solutions to Compensation for the Pendulum Temperature Dilatation
EP  - 128
IS  - 8
SP  - 117
VL  - 10
UR  - https://hdl.handle.net/21.15107/rcub_grafar_534
ER  - 

@article{
author = "Popkonstantinović, Branislav and Miladinović, Ljubomir and Obradović, Marija and Ostojić, Gordana and Stankovski, Stevan",
year = "2013",
abstract = "The paper analyzes the effects of pendulum temperature dilatation on the timepiece running and accounts for the basic mathematical principles that neutralization of these detrimental effects are based upon. Both preliminary and detailed calculations are presented, as well as some design solutions leading to technically acceptable pendulum temperature dilatation. Explanation is given for the design of bimetal gridiron pendulum, wood pendulum with a lead weight, mercury pendulum, and pendulum with an Invar alloy rod.",
journal = "Acta Polytechnica Hungarica",
title = "Mathematical Principles and Optimal Design Solutions to Compensation for the Pendulum Temperature Dilatation",
pages = "128-117",
number = "8",
volume = "10",
url = "https://hdl.handle.net/21.15107/rcub_grafar_534"
}

Popkonstantinović, B., Miladinović, L., Obradović, M., Ostojić, G.,& Stankovski, S.. (2013). Mathematical Principles and Optimal Design Solutions to Compensation for the Pendulum Temperature Dilatation. in Acta Polytechnica Hungarica, 10(8), 117-128.
https://hdl.handle.net/21.15107/rcub_grafar_534

Popkonstantinović B, Miladinović L, Obradović M, Ostojić G, Stankovski S. Mathematical Principles and Optimal Design Solutions to Compensation for the Pendulum Temperature Dilatation. in Acta Polytechnica Hungarica. 2013;10(8):117-128.
https://hdl.handle.net/21.15107/rcub_grafar_534 .

Popkonstantinović, Branislav, Miladinović, Ljubomir, Obradović, Marija, Ostojić, Gordana, Stankovski, Stevan, "Mathematical Principles and Optimal Design Solutions to Compensation for the Pendulum Temperature Dilatation" in Acta Polytechnica Hungarica, 10, no. 8 (2013):117-128,
https://hdl.handle.net/21.15107/rcub_grafar_534 .

TY  - CONF
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
AU  - Mišić, Slobodan
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2033
AB  - The paper discusses determining the positions and spatial coordinates of the vertices of polyhedral structures - concave antiprisms of second sort. These polyhedra originate from folding the double row strip of equilateral triangles, closed by two identical regular polygons, the principle akin to the way of the concave cupolae of second sort formation. The paper considers constructive -geometrical solution, including the method of solving the problem using the mechanisms, by application of SolidWorks software package.
PB  - Novi Sad: Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
T1  - Concave Antiprisms of Second Sort with Regular Polygonal Bases
EP  - 143
SP  - 133
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2033
ER  - 

@conference{
author = "Obradović, Marija and Popkonstantinović, Branislav and Mišić, Slobodan",
year = "2012",
abstract = "The paper discusses determining the positions and spatial coordinates of the vertices of polyhedral structures - concave antiprisms of second sort. These polyhedra originate from folding the double row strip of equilateral triangles, closed by two identical regular polygons, the principle akin to the way of the concave cupolae of second sort formation. The paper considers constructive -geometrical solution, including the method of solving the problem using the mechanisms, by application of SolidWorks software package.",
publisher = "Novi Sad: Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012",
title = "Concave Antiprisms of Second Sort with Regular Polygonal Bases",
pages = "143-133",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2033"
}

Obradović, M., Popkonstantinović, B.,& Mišić, S.. (2012). Concave Antiprisms of Second Sort with Regular Polygonal Bases. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
Novi Sad: Faculty of Technical Sciences, University of Novi Sad., 133-143.
https://hdl.handle.net/21.15107/rcub_grafar_2033

Obradović M, Popkonstantinović B, Mišić S. Concave Antiprisms of Second Sort with Regular Polygonal Bases. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012. 2012;:133-143.
https://hdl.handle.net/21.15107/rcub_grafar_2033 .

Obradović, Marija, Popkonstantinović, Branislav, Mišić, Slobodan, "Concave Antiprisms of Second Sort with Regular Polygonal Bases" in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012 (2012):133-143,
https://hdl.handle.net/21.15107/rcub_grafar_2033 .

TY  - CONF
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Petrović, Maja
AU  - Popkonstantinović, Branislav
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2032
AB  - We discuss the spatial interpretation of the Erdös-Mordell inequality on the area of triangle ABC, and also consider the plane extension of this inequality.
PB  - Novi Sad: Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
T1  - One Application of the  Cone Surfaces on the Erdosh-Mordell inequality
EP  - 351
SP  - 335
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2032
ER  - 

@conference{
author = "Obradović, Marija and Malešević, Branko and Petrović, Maja and Popkonstantinović, Branislav",
year = "2012",
abstract = "We discuss the spatial interpretation of the Erdös-Mordell inequality on the area of triangle ABC, and also consider the plane extension of this inequality.",
publisher = "Novi Sad: Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012",
title = "One Application of the  Cone Surfaces on the Erdosh-Mordell inequality",
pages = "351-335",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2032"
}

Obradović, M., Malešević, B., Petrović, M.,& Popkonstantinović, B.. (2012). One Application of the  Cone Surfaces on the Erdosh-Mordell inequality. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
Novi Sad: Faculty of Technical Sciences, University of Novi Sad., 335-351.
https://hdl.handle.net/21.15107/rcub_grafar_2032

Obradović M, Malešević B, Petrović M, Popkonstantinović B. One Application of the  Cone Surfaces on the Erdosh-Mordell inequality. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012. 2012;:335-351.
https://hdl.handle.net/21.15107/rcub_grafar_2032 .

Obradović, Marija, Malešević, Branko, Petrović, Maja, Popkonstantinović, Branislav, "One Application of the  Cone Surfaces on the Erdosh-Mordell inequality" in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012 (2012):335-351,
https://hdl.handle.net/21.15107/rcub_grafar_2032 .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Popkonstantinović, Branislav
AU  - Petrović, Maja
PY  - 2011
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2030
AB  - In recent years, we are witnessing an increasing use of triangular modular building systems, which, especially in representative objects, almost push out the orthogonal system. Considering that deltahedra are assembled of equilateral triangles matching system, we investigated a possible application of such polyhedral forms in geometry of architectural edifices. Deltahedral concave cupola with a regular polygonal base is formed by connecting two concentric regular polygons: n-gon and 2n-gon by multiple series of equilateral triangles. Lateral surface of the cupola is obtained by folding a net of equilateral triangles to a concave polyhedral surface. The paper analyzes the prospect of such surfaces in architecture, not only in the geometry of roof structures, which is imposing as an obvious solution, but also as a structural skeleton of the whole building. The analysis includes several criteria for evaluating the suitability of these forms for practical application: their static properties, atmospheric effects, functional analysis, preferential use of certain constructive systems, and finally, aesthetic properties of these forms.
PB  - Iasi: The Gheorghe Asachi Technical University of Iasi
C3  - Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011
T1  - Possibilities of Deltahedral Concave Cupola Form Application in Architecture
EP  - 140
IS  - Fasc. 3
SP  - 123
VL  - Tomul LVII (LXI)
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2030
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav and Petrović, Maja",
year = "2011",
abstract = "In recent years, we are witnessing an increasing use of triangular modular building systems, which, especially in representative objects, almost push out the orthogonal system. Considering that deltahedra are assembled of equilateral triangles matching system, we investigated a possible application of such polyhedral forms in geometry of architectural edifices. Deltahedral concave cupola with a regular polygonal base is formed by connecting two concentric regular polygons: n-gon and 2n-gon by multiple series of equilateral triangles. Lateral surface of the cupola is obtained by folding a net of equilateral triangles to a concave polyhedral surface. The paper analyzes the prospect of such surfaces in architecture, not only in the geometry of roof structures, which is imposing as an obvious solution, but also as a structural skeleton of the whole building. The analysis includes several criteria for evaluating the suitability of these forms for practical application: their static properties, atmospheric effects, functional analysis, preferential use of certain constructive systems, and finally, aesthetic properties of these forms.",
publisher = "Iasi: The Gheorghe Asachi Technical University of Iasi",
journal = "Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011",
title = "Possibilities of Deltahedral Concave Cupola Form Application in Architecture",
pages = "140-123",
number = "Fasc. 3",
volume = "Tomul LVII (LXI)",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2030"
}

Obradović, M., Mišić, S., Popkonstantinović, B.,& Petrović, M.. (2011). Possibilities of Deltahedral Concave Cupola Form Application in Architecture. in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011
Iasi: The Gheorghe Asachi Technical University of Iasi., Tomul LVII (LXI)(Fasc. 3), 123-140.
https://hdl.handle.net/21.15107/rcub_grafar_2030

Obradović M, Mišić S, Popkonstantinović B, Petrović M. Possibilities of Deltahedral Concave Cupola Form Application in Architecture. in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011. 2011;Tomul LVII (LXI)(Fasc. 3):123-140.
https://hdl.handle.net/21.15107/rcub_grafar_2030 .

Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, Petrović, Maja, "Possibilities of Deltahedral Concave Cupola Form Application in Architecture" in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011, Tomul LVII (LXI), no. Fasc. 3 (2011):123-140,
https://hdl.handle.net/21.15107/rcub_grafar_2030 .

TY  - JOUR
AU  - Popkonstantinović, Branislav
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Jeli, Zorana
PY  - 2011
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2028
AB  - Theory of clock, watch and chronometer escapements is important
and interesting part of theory of mechanisms and kinematics. Despite the fact that chronometer escapements are invented in past times, from the viewpoint of kinematics and machine theory, these mechanisms represent the jewel treasuries of knowledge and engineering wisdom. This paper considers and discloses operational principles and constructive geometry of Thomas Earnshaw‟s chronometer detent escapement. Moreover, process of 3D solid modeling, and assembling of all escapement parts, as well as the motion study and simulation of escapement operational cycle are presented and explained. This analysis and considerations enlighten not just the kinematical properties and characteristic of one particular chronometer escapement type, but also clarify and illuminate the process of computer aided mechanism design, construction and motion analysis.
PB  - Iasi: "Gheorghe Asachi" Technical University of Iasi
T2  - Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011
T1  - Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism
EP  - 72
IS  - Fasc. 5
SP  - 55
VL  - Tomul LVII (LXI)
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2028
ER  - 

@article{
author = "Popkonstantinović, Branislav and Obradović, Marija and Malešević, Branko and Jeli, Zorana",
year = "2011",
abstract = "Theory of clock, watch and chronometer escapements is important
and interesting part of theory of mechanisms and kinematics. Despite the fact that chronometer escapements are invented in past times, from the viewpoint of kinematics and machine theory, these mechanisms represent the jewel treasuries of knowledge and engineering wisdom. This paper considers and discloses operational principles and constructive geometry of Thomas Earnshaw‟s chronometer detent escapement. Moreover, process of 3D solid modeling, and assembling of all escapement parts, as well as the motion study and simulation of escapement operational cycle are presented and explained. This analysis and considerations enlighten not just the kinematical properties and characteristic of one particular chronometer escapement type, but also clarify and illuminate the process of computer aided mechanism design, construction and motion analysis.",
publisher = "Iasi: "Gheorghe Asachi" Technical University of Iasi",
journal = "Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011",
title = "Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism",
pages = "72-55",
number = "Fasc. 5",
volume = "Tomul LVII (LXI)",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2028"
}

Popkonstantinović, B., Obradović, M., Malešević, B.,& Jeli, Z.. (2011). Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism. in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011
Iasi: "Gheorghe Asachi" Technical University of Iasi., Tomul LVII (LXI)(Fasc. 5), 55-72.
https://hdl.handle.net/21.15107/rcub_grafar_2028

Popkonstantinović B, Obradović M, Malešević B, Jeli Z. Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism. in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011. 2011;Tomul LVII (LXI)(Fasc. 5):55-72.
https://hdl.handle.net/21.15107/rcub_grafar_2028 .

Popkonstantinović, Branislav, Obradović, Marija, Malešević, Branko, Jeli, Zorana, "Solid Modeling and Motion Study of Chronometer Detent Escapement Mechanism" in Buletinul Institutului Politehnic din Iaşi, Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi - Proceedings of ICEGD Conference, Iasi 2011, Tomul LVII (LXI), no. Fasc. 5 (2011):55-72,
https://hdl.handle.net/21.15107/rcub_grafar_2028 .

TY  - JOUR
AU  - Popkonstantinović, Branislav
AU  - Čučaković, Aleksandar
PY  - 2006
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/122
AB  - In modern cartography, Mercator's conformal cylindrical map projection is mathematically described by equations which involve logarithmic and trigonometric functions. It is evident that calculus and di®erential geometry are necessary for the derivation of these equations. The very fact that Mercator's map was published in 1569, long before logarithms and calculus were invented, confirms that Mercator created his famous map projection somehow directly - by some simple and plain geometrical constructions. This paper exposes one possible constructive graphical method by which the direct geometrical synthesis of Mercator's conformal cylindrical map projection can be accomplished. We believe that the original inventive process used by Gerhard KREMER MERCATOR in creation of his famous world map was at least similar or compatible to the method exposed in this paper.
PB  - Heldermann Verlag
T2  - Journal for Geometry and Graphics
T1  - One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts
EP  - 71
IS  - 1
SP  - 63
VL  - 10
UR  - https://hdl.handle.net/21.15107/rcub_grafar_122
ER  - 

@article{
author = "Popkonstantinović, Branislav and Čučaković, Aleksandar",
year = "2006",
abstract = "In modern cartography, Mercator's conformal cylindrical map projection is mathematically described by equations which involve logarithmic and trigonometric functions. It is evident that calculus and di®erential geometry are necessary for the derivation of these equations. The very fact that Mercator's map was published in 1569, long before logarithms and calculus were invented, confirms that Mercator created his famous map projection somehow directly - by some simple and plain geometrical constructions. This paper exposes one possible constructive graphical method by which the direct geometrical synthesis of Mercator's conformal cylindrical map projection can be accomplished. We believe that the original inventive process used by Gerhard KREMER MERCATOR in creation of his famous world map was at least similar or compatible to the method exposed in this paper.",
publisher = "Heldermann Verlag",
journal = "Journal for Geometry and Graphics",
title = "One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts",
pages = "71-63",
number = "1",
volume = "10",
url = "https://hdl.handle.net/21.15107/rcub_grafar_122"
}

Popkonstantinović, B.,& Čučaković, A.. (2006). One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts. in Journal for Geometry and Graphics
Heldermann Verlag., 10(1), 63-71.
https://hdl.handle.net/21.15107/rcub_grafar_122

Popkonstantinović B, Čučaković A. One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts. in Journal for Geometry and Graphics. 2006;10(1):63-71.
https://hdl.handle.net/21.15107/rcub_grafar_122 .

Popkonstantinović, Branislav, Čučaković, Aleksandar, "One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts" in Journal for Geometry and Graphics, 10, no. 1 (2006):63-71,
https://hdl.handle.net/21.15107/rcub_grafar_122 .

TY  - CONF
AU  - Popkonstantinović, Branislav
AU  - Obradović, Marija
PY  - 1996
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2720
AB  - This paper discloses the proof, based on the space restitution, that geometrical loci of Laguerre's points of perspective elliptical involuted sets represent two circles. The exposed theorem is a contribution to the theory  of Projective geometry; moreover, it makes the constructive methods of an objects axial rotation in central projection more effective.
PB  - Cracow University of Technology, Cracow, 1996.
C3  - Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG)
T1  - The Geometrical Loci of Laguerre’s points of Perspective elliptical Involuted Sets
EP  - 131
SP  - 128
VL  - 1
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2720
ER  - 

@conference{
author = "Popkonstantinović, Branislav and Obradović, Marija",
year = "1996",
abstract = "This paper discloses the proof, based on the space restitution, that geometrical loci of Laguerre's points of perspective elliptical involuted sets represent two circles. The exposed theorem is a contribution to the theory  of Projective geometry; moreover, it makes the constructive methods of an objects axial rotation in central projection more effective.",
publisher = "Cracow University of Technology, Cracow, 1996.",
journal = "Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG)",
title = "The Geometrical Loci of Laguerre’s points of Perspective elliptical Involuted Sets",
pages = "131-128",
volume = "1",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2720"
}

Popkonstantinović, B.,& Obradović, M.. (1996). The Geometrical Loci of Laguerre’s points of Perspective elliptical Involuted Sets. in Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG)
Cracow University of Technology, Cracow, 1996.., 1, 128-131.
https://hdl.handle.net/21.15107/rcub_grafar_2720

Popkonstantinović B, Obradović M. The Geometrical Loci of Laguerre’s points of Perspective elliptical Involuted Sets. in Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG). 1996;1:128-131.
https://hdl.handle.net/21.15107/rcub_grafar_2720 .

Popkonstantinović, Branislav, Obradović, Marija, "The Geometrical Loci of Laguerre’s points of Perspective elliptical Involuted Sets" in Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG), 1 (1996):128-131,
https://hdl.handle.net/21.15107/rcub_grafar_2720 .

TY  - CONF
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
PY  - 1996
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2719
AB  - General collinear planes whose double straight line is at infinity are affine collinear planes.
Affine collinear planes whose double points of collocation on the infinitely distant double straight line are the absolute points or their real representatives, are the conform planes. The paper considers conform affine transformations: homothety, translation, rotation and axial symmetry, as well as their combinations by defining their types of collocation as: elliptic, hyperbolic, parabolic or perspectivelly collinear.
PB  - Cracow University of Technology, Cracow, 1996.
C3  - Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG)
T1  - Affine Conform Planes as the Special Cases of General Collinear Planes
EP  - 144
SP  - 141
VL  - 1
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2719
ER  - 

@conference{
author = "Obradović, Marija and Popkonstantinović, Branislav",
year = "1996",
abstract = "General collinear planes whose double straight line is at infinity are affine collinear planes.
Affine collinear planes whose double points of collocation on the infinitely distant double straight line are the absolute points or their real representatives, are the conform planes. The paper considers conform affine transformations: homothety, translation, rotation and axial symmetry, as well as their combinations by defining their types of collocation as: elliptic, hyperbolic, parabolic or perspectivelly collinear.",
publisher = "Cracow University of Technology, Cracow, 1996.",
journal = "Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG)",
title = "Affine Conform Planes as the Special Cases of General Collinear Planes",
pages = "144-141",
volume = "1",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2719"
}

Obradović, M.,& Popkonstantinović, B.. (1996). Affine Conform Planes as the Special Cases of General Collinear Planes. in Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG)
Cracow University of Technology, Cracow, 1996.., 1, 141-144.
https://hdl.handle.net/21.15107/rcub_grafar_2719

Obradović M, Popkonstantinović B. Affine Conform Planes as the Special Cases of General Collinear Planes. in Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG). 1996;1:141-144.
https://hdl.handle.net/21.15107/rcub_grafar_2719 .

Obradović, Marija, Popkonstantinović, Branislav, "Affine Conform Planes as the Special Cases of General Collinear Planes" in Proceedings of the 7th International Conference on Engineering Computer Graphic and Descriptive Geometry (ICECGDG), 1 (1996):141-144,
https://hdl.handle.net/21.15107/rcub_grafar_2719 .