Information
for the Descriptive Geometry subject
participant in the BSc course of the University of Miskolc,
Faculty of Mechanical Engineering and Informatics
for full-time mechanical engineering students
Lecturer: Dr. habil. Zsuzsanna Balajti Óváriné associate professor
I. The task and purpose of the subject:
The task of descriptive geometry is to represent the shapes of three-dimensional space in a reconstructable mapping, and to solve specific spatial geometry tasks in the plane of the constructing drawing.
Among the relationships that can be established between three and two dimensions, knowledge of the concepts and procedures of Monge's approach is irreplaceable during engineering activities. Knowing these guarantees you the freedom to choose visualisation options with computer programs.
II. The thematic of the subject
Monge's representation is the basis of true-to-scale engineering communication. Representation and reconstruction of the basic elements of the space. The mutual position, fit, parallelism and intersection of the basic geometric elements. Transformation of the plane of projection, target transformations and their applications. Image conditions of perpendicularity. Rotating a plane into a position parallel to the plane of projection. Dimensions between space elements. Representation of polyhedral, cutting with a straight line, cutting with a plane. Representation of circle and disc. Representing a sphere, a cylinder of revolution and a cone of revolution, intersecting it with a straight line and cutting it with a plane. Conic slices and their affine and central collineation relations. Editing sphere, cone and cylinder interactions. Helix, helicoid surfaces.
III. The way to finish the subject
The Descriptive Geometry subject is taught in the framework of 2 hours of lectures and 2 hours of practice in the autumn academic semester. The semester finishes with a signature and colloquium for mechanical engineering students.
III.1. Conditions for obtaining a signature
- Regular attendance at the lectures with due diligence, failure to attend six lectures (12 hours) or more will result in the final refusal of the signature.
- Regular participation in practical classes with due diligence, missing five practical classes (10 or more hours) will result in the final refusal of the end-of-semester signature.
- Complete 5 constructing drawing assignments separately at a minimum level and submit them by the deadline specified in the Timetable (the dean's permission is required for submission after the deadline).
- 2 written examines composed of constructing tasks, each with at least a sufficient grade, or completing them in correctional written examines. The prerequisite for written examines is the submission of the constructing drawing assignments issued by the deadline.
To acknowledge the semester and obtain a signature, the performance is evaluated by the practice leader.
III.1.1. Submission and assessment of the construction drawing tasks to be submitted during the semester
According to the "Constructing Drawing specification", the constructing drawing assignments must be independently constructed on an A4-sized technical drawing sheet framed by your own hand.
The submission deadlines are included in the "Schedule".
When submitting a constructing drawing, the content of the task must be justified!
In order to achieve a sufficient level, there must be no fundamental content errors in the solution of the task and the constructing drawing must also be aesthetically acceptable.
III.1.2. The qualification, date and evaluation of constructing exercises as completed during the semester
During the semester, the student must write two closed-door papers in 45 minutes each. The dates of the closed assignments are included in the "Schedule".
The mid-semester construction exercises can be written if the previously issued constructing drawing assignments have been submitted by the prescribed deadline.
50% of the achievable performance is required for a sufficient grade for construction exercises; the other grades are approximately linear.
The use of unauthorized tools and assistance during the assessment will automatically result in an insufficient grade.
III.1.3. The conditions of the trying again of the written examines and constructing drawings
Those students who did not complete the 1st and 2nd constructing exercises satisfactorily may write a one-time remedial constructing exercise during the study period if the I. and II. constructing drawings are submitted by them.
In order to obtain the signature, the results of the repairer's constructing exercise must also be at least sufficient individually.
Those students who did not obtain a signature during the study period must submit the missing constructing drawings by 12:00 on the working day preceding the "Signature Substitute Exam" and/or write a paper in private with at least sufficient results at the time announced by the department in the NEPTUN system.
III.2. Exam method and rating
At the end of the semester, there will be an exam on the entire material of the subject. The material of the exam is the material covered in the lectures and exercises.
Signature is a condition for applying for the exam. Registration for the exam is done through the NEPTUN system until 12:00 the day before the exam. The exam consists of a mandatory 90-minute written and optional oral part.
A sufficient grade requires 50% of the maximum score that can be obtained on the written exam, the other grades is approximately linear.
A student who does not obtain even 25% of the available score in the written part of the exam may not go to correct with the oral part.
The student receives a grade (E) for the mid-semester work, which is the average of the grades (R) for the constructing drawing assignments and the grades for the constructing exercises (Z1, Z2) as follows
The grade (E) received for the student's mid-semester work, and the grade (V) at the end of the writing exam form the grade for the exam as follows
Using unauthorised tools or help during the assessment will automatically result in an insufficient grade!
IV. Literature
Required:
- Óváriné Balajti, Zsuzsanna: Practice Worksheets for Mechanical Engineering Students, Miskolc, 2024.
- Petar Mladinic, Nikol Radovic: Descriptive Geometry, Perspective Monge’s procedure axonometry, Zagreb, 2019.
- Lajos Sándor: Sztereoszkópikus galéria
- V. O. Gordon; M. A. Sementsov-Ogievskii: A Course in Descriptive Geometry, 1980, Moscow
- Geiger János: Ábrázoló geometria, 2015.
- Bancsik Zs., Juhász I., Lajos S.: Ábrázoló geometria szemléletesen, elektronikus könyv, 2007.
Recommended:
- A. T. Chahly: Descriptive Geometry, 1968, Moscow
- Geiger János: Ábrázoló geometria feladat gyűjtemény 2012.
- Geiger János: Ábrázoló geometria, Csavarvonal, csavarfelületek
- Petrich Géza: Ábrázoló geometria,Tankönyvkiadó, Budapest, 1973.
- Popa-Müller Izolda: Ábrázoló geometria, Sapientia tankönyvek, Műszaki tudományok, Scientia Kiadó, Kolozsvár.
SCHEDULE
| Week | Date | Lecture | Practice and independent preparation | Task |
| 1. | IX. 8.- 12. | Truncated polyhedron representation. | Practice Worksheet | I.1. constructing drawing |
| 2. | IX. 15.-19. | Monge's representation, true-size engineering communication. Representation and reconstruction of the basic elements of space (point, line, plane). Special straight lines of the plane. Fitting of the basic elements. | Practice Worksheet | |
| 3. | IX. 22.-26. | Parallelism. Intersection. Creating a new plane of projection. | Practice Worksheet | I.2. constructing drawing |
| 4. | IX.29.-X.3. | Transforming straight lines and planes into a special position. Applications of transformation. Representation and creation of polyhedral. | Practice Worksheet | I.3. constructing drawing |
| 5. | X.6. – 10. | Applications of the transformation of the projection plane system: intersecting of the pyramid and prism with a straight line, a plane. Determining of the distance and angle of the elements of the space. | Practice Worksheet | Submitting of constructing drawings I. |
| 6. | X. 13. – 17. | Perpendicularity of space elements. Rotate a plane to the plane of projection. Application: angle of space elements (straight lines and planes). | Practice Worksheet | I. Mid-semester written exam |
| 7. | X. 20.–24. educational break | Representation of a disc. | Practice Worksheet | II.1. constructing drawing |
| 8. | X. 27.– 31. | Representation of a disc, sphere, its surface point, normal, tangent plane. | Practice Worksheet | II.2. constructing drawing |
| 9. | XI. 3.-7. | Representation of a rotating cylinder and cone, surface point, normal, tangent plane, and intersecting with a straight line. The intersection of a rotating cylinder with a plane. | Practice Worksheet | II.2. constructing drawing |
| 10. | XI. 10.– 14. | The intersection curves of a rotating cone with a plane. Curves of the plane section of a cone. | Practice Worksheet | II.3. constructing drawing |
| 11. | XI. 17.– 21. | The intersection curve of rotating cylinders and cones of rotation with an intersecting pair of axes (method of auxiliary spheres). | Practice Worksheet | Submitting of constructing drawings II. |
| 12. | XI. 24–28. | The intersection curve of rotating cylinders and cones of rotation with a non-intersecting pair of axes (method of a serious of auxiliary planes). | Practice Worksheet | Correct of constructing drawings |
| 13. | XII. 1.– 5. | Helix. Helicoid surfaces. | Practice Worksheet | II.Written exam |
| 14. | XII. 8.- 12. | Summary. Preparation for the exam. | Practice Worksheet | Correcting of mid-semester written exams |
For independent preparation, it is recommended that additional tasks be solved from the example library János Geiger: Descriptive Geometry Task Book, in Hungarian, University Publishing House 2012).
DRAWING TASKS
I. DRAWING TASK
I.1. Truncated polyhedron representation
Design and axonometrically sketch a truncated shape created from a cube, then mark its vertices in order with the letters A, B, C, ...!
According to the variation number, create three ordered views of the truncated shape so that the distances of point A of the shape from the planes of projections are given in the table!
| Variant number | 1 | 2 | 3 | 4 | 5 | 6 |
| K1 | 30mm | 30mm | 20mm | 20mm | 10mm | 10 mm |
| K2 | 10mm | 20mm | 10mm | 30mm | 20mm | 30 mm |
| K3 | 20mm | 10mm | 30mm | 10mm | 30mm | 20 mm |
I.2. Representation of the prism
Given a straight-line m and a point A that does not lie on it.
Using new projection planes, construct the projections of the straight prism based on the square (1) or regular triangle (2), whose line of height is the m and A is one of the vertices of the base polygon; furthermore, the dimension of the height mh is one and a half times the side length of the base polygon! Show the visibility too!
(Start constructing by creating a new projection plane connected to the first projection plane!)
II. DRAWING TASK
II.1. Representation of the disk
Given a straight-line t in the frontal straight-line position and a point P that does not lie on it. Represent the circular disc with axis t, of which P s a point on the circumference!
Construct it for the first projection ellipse of the circular disc
- the major axis AB and the minor axis of CD,
- tangents and hyperosculating circles at the axis’s endpoints,
- the tangent straight-line e at point P!
Sketch the first image ellipse, then indicate the visibility of the circular disc and its axis!
II.2. Intersections of a cone with a plane
Intersect a rotating cone lying on the projection plane K1 with a second projection plane V2 according to variation number!
| Variable number | 1 | 2 | 3 |
| Section | e | p | h |
Construct the
- the e ellipse section curve's first projection with the major axis AB and minor axis CD!
- the p parabola section curve's first projection with the axis point T, the axis straight line t and the directrix straight line d!
- the h hyperbola section curve's first projection with the real axis AB and imaginary axis CD, furthermore the asymptotes u and v!
Determine the first projection curve
- the focal point F, or focal points F1 and F2,
- a point P in general position, in it the tangent straight-line e!
Draw the first image of the section using the hyperosculating circle(s)! Represent the part of the cone between the base plane and the cutting plane according to visibility!
II.3. Intersection between the rotating cone and cylinder
Construct the intersection curve of a rotating cone with an axis in first projector line position and a rotating cylinder with an axis in second projector line position in such a way, that it has a self-intersection point!
Determine the
- self-intersecting point,
- points lying on the contours of the cylinder and the cone with the tangents,
- lowest points,
- a few points in general position with the tangent in one from it, of the intersection curve!
Represent the part of the conical body outside the cylindrical body with an indication of visibility!
Notes
According to the schedule, the drawings of the drawing assignments must be made in pencil on one A4 (210x297) size technical drawing sheet. Based on an individual decision, it is possible to draw with ink on pause. The standards of lines and letters (MSZ EN ISO 128-20) must be applied. To draw the lines, use line group with 0.13 or 0.18mm thin, 0.35mm thick and 0.70mm highlighted line thickness. A font size of h=3.5mm should be used for lettering the figures, and h=7.0mm for labelling the frame.
When drawing with a pencil, three different line thicknesses should be used in accordance with the above-mentioned line thicknesses. The order-lines between the views should also be promoted through the use of graphic elements, and the same content should be marked consistently by the same graphic elements.
Thin line thickness with 0.3mm H or HB pencil: construction lines, ordering-lines.
Center line thickness 0.5mm, with HB pencil: given elements and the invisible part of the final result with a dashed line.
Thick line thickness with a 0.7 mm B or 2B pencil: results and frame to be drawn with a solid line.
The title of the drawing task, the designer's name, student group number, signature, the academic year and date, the task number and the variation number should be indicated on the drawing sheet - based on the attached sample - in 7mm font size.
The practical instructor can provide more detailed information.