Шпак DESCRIPTIVE GEOMETRY COURSE OF LECTURES НАЧЕРТАТЕЛЬНАЯ ГЕОМЕТРИЯ КУРС ЛЕКЦИЙ for international students in oil and gas engineering taught the program 131000.62 – Oil and Gas Engineering Stavropol 2014 1 УДК 514.18 (075.8) ББК 22. 151. 3 я73 Б 87 Published according to the Resolution of Educational Commission of North-Caucasus Federal University Reviewers: Sergey Babenishev – Professor of Mechanical Engineering and Technological Equipment Department at North-Caucasus Federal University, Dr. <...> Descriptive Geometry: course of lectures / authors: Andrey Bratsikhin, Maria Shpak. – Stavropol: Рublisher NCFU, 2014. – 73 p. <...> УДК 514.18 (075.8) ББК 22. 151. 3 я73 Authors: Andrey Bratsikhin – Head of Mechanical Engineering and Technological Equipment Department NCFU, Dr. <...> Eng. Maria Shpak – Docent of Mechanical Engineering and Technological Equipment Department NCFU, PhD. © North-Caucasus Federal University, 2014 2 TABLE OF CONTENTS LECTURE 1. <...> Descriptive geometry defined Descriptive geometry is essentially the technique of accurately representing objects by means of drawings and of solving graphically all problems related to their form and position. <...> Methods of projection There are two basic methods of the objects projection: central and parallel. <...> The natural triangular ABC is projected on the plane H by passing the lines through the center of projection (point S) and the main points of triangular – A,B C. The points of intersections these lines with plane H is the ABC-central projection of triangular on the plane H – AHBHCH. <...> In descriptive geometry is used method of parallel projection (Fig.1.2). <...> For ABC projection the parallel lines in a direction of vector S are passed through points ABC. 4 The triangular AHBHCH produced by intersection of parallel lines and plane H is a parallel projection of ABC. <...> Parallel projection The parallel projections can be orthogonal and oblique. <...> If the angles of projection are not perpendicular to plane that method is named “oblique projection”. <...> If a straight line is passed through any point of space and perpendicular to a plane, the point of space is said to be projected orthogonally on the plane at the point where the perpendicular intersects the plane. <...> The plane is the projection plane and is represented by the drawing paper (Figure <...>
Начертательная_геометрия._Курс_лекций.pdf
УДК 514.18 (075.8)
ББК 22. 151. 3 я73
Б 87
Published according to the Resolution
of Educational Commission
of North-Caucasus Federal University
Reviewers:
Sergey Babenishev – Professor of Mechanical Engineering and Technological
Equipment Department at North-Caucasus Federal University, Dr.Eng.
Vladimir Samoylenko – Senior Lecturer of Automatic, Electronic Engineering,
and Metrology Department at Stavropol State Agrarian University, PhD.
Descriptive Geometry: course of lectures / authors: Andrey Bratsikhin, Maria Shpak. –
Stavropol: Рublisher NCFU, 2014. – 73 p.
Брацихин А.А., Шпак М.А.
Б 87 Начертательная геометрия. Курс лекций: учебное пособие. – Ставрополь: Издво
СКФУ, 2014. – 73 с.
Course lectures is generated according to the requirements of Federal State Standard for
Higher Education for Bachelor’s Degree students.
Established on meeting of Mechanical Engineering and Technological Equipment Department
(Minute №3 at the 07th of October, 2014) for students taught the program 131000.62 – Oil
and Gas Engineering.
УДК 514.18 (075.8)
ББК 22. 151. 3 я73
Authors:
Andrey Bratsikhin – Head of Mechanical Engineering
and Technological Equipment Department NCFU, Dr.Eng.
Maria Shpak – Docent of Mechanical Engineering
and Technological Equipment Department NCFU, PhD.
© North-Caucasus Federal University, 2014
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TABLE OF CONTENTS
LECTURE 1. PRINCIPLE CONSIDERATION……………………………………………….
1.1. Descriptive geometry defined ………………………………………………………...
1.2. Methods of projection ………………………………………………………………...
1.3. Correspondence ………………………………………………………………………
1.4. The point in space …………………………………………………………………….
Control test ………………………………………………………………………………...
LECTURE 2. LINE PROJECTIONS ……………………………………………………………
2.1. Line projecting on the three projection planes ……………………………………..
2.2. Position of a line to the planes of projection ……………………………………….
2.3. Traces of a line ……………………………………………………………………….
2.4. True length of line definition …………………………………………………………
2.5. Position of lines in space …………………………………………………………….
2.6. Competing points of skew lines ……………………………………………………..
2.7. Right-angle projection ………………………………………………………………..
Control test ………………………………………………………………………………...
LECTURE 3. PLANE PROJECTIONS …………………………………………………………
3.1. Methods of a plane determination …………………………………………………..
3.2. Plane traces …………………………………………………………………………...
3.3. Points and lines are contained in plane ………………………………………………
3.4. Position of a plane to the coordinate planes ………………………………………….
3.5. The principle lines of a plane …………………………………………………………
3.6. Intersecting planes ……………………………………………………………………
3.7. The line and plane …………………………………………………………………….
3.8. The line is parallel to plane …………………………………………………………..
3.9. The line and plane are perpendicular ………………………………………………..
3.10. The planes are parallel ………………………………………………………………
3.11. The planes are perpendicular ……………………………………………………….
Control test …………………………………………………………………………….......
LECTURE 4. DRAWINGS TRANSFORMATION …………………………………………….
4.1. The main problems of drawings transformation ……………………………………
4.2. Change of the projection plane ……………………………………………………….
4.3. Methods of rotation …………………………………………………………………..
4.3.1. Rabbatement …………………………………………………………………...
4.3.2. Rotation around plane traces (or coinciding method) ………………………
Control test ………………………………………………………………………………...
LECTURE 5. PLANE SURFACES (POLYHEDRONS) ……………………………………….
5.1. Prism and prismoid …………………………………………………………………...
5.2. Pyramid ……………………………………………………………………………….
5.3. Intersecting polyhedron and plane …………………………………………………..
5.4. Intersecting polyhedron and line ……………………………………………………..
5.5. Intersecting of two polyhedrons …………………………………………………….
Control test ………………………………………………………………………………...
LECTURE 6. DEVELOPMENT OF POLYHEDRONS ……………………………………….
6.1. Development by right section determination ………………………………………..
6.2. Method of flattening ………………………………………………………………….
6.3. Development by triangulation ………………………………………………………..
Control test ………………………………………………………………………………...
TASKS FOR SELF-STUDY …………………………………………………………………….
GLOSSARY ……………………………………………………………………………………..
LIST OF RECOMMENDED TEXTBOOKS …………………………………………………
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