course objective - fte.edu.iqfte.edu.iq/upload/upfile/ar/385ameer.pdf · descriptive geometry by:...

Descriptive Geometry By: Ameer Tofan

To develop the imagination and logical mathematical sense to solve different engineering problems specially in mechanical eng. Where the design & manufacturing of rockets & satellites depends on the principles of descriptive geometry. Annual System: 30 weeks Stage: Second Number of weekly hours: 1hr (Theoretical), 1hr (Practical Part) Number of units: 3

Week No. Subject Topics 1 Introduction 2 Theory of projection & projection of point 3 Examples on quadrants & dihedral angles

4-6 Projection of straight line 7-8 Representation of straight line in space 9 Examples on dihedral angles for straight line

10-13 The true length and inclinations of a straight line 14-15 Examples for the true length of straight line

16 Auxiliary plane 17-18 Type of auxiliary plane

19 Using Auxiliary plane to find the true length 20-24 Auxiliary plane application 25-26 Open cylinder and definition 27-28 Open cone and definition 29-30 Cut the cone using Auxiliary plane

Course Objective


Definition of Descriptive Geometry.

1. Over view 1.A –Target population: - For students of second class, Technical college-Baghdad, Engineering

Techniques of Materials, Welding, Dies and Tools, Automotive and Refrigeration and air conditioning.

- For students of first class, Technical college-Baghdad, Engineering Techniques of Surveying.

1.B – Rationale: Introduction, is very important subject to be studied in order to have a full knowledge for the Descriptive Geometry. 1.C – Central Idea:

Importance of Descriptive Geometry. 1.D - Performance Objectives: At the end of this lecture the student should be able to: Define the subject of Descriptive Geometry.

U2. Pre test 1. Is there any limitation for the space ? ( ) yes ( ) No 2. What do you see in the TV screen 2D or 3D picture. U3. The text We live in a three-dimensional world and we often want to represent this world in a drawing, a painting or a photography. Now, drawings, paintings and photos are two-dimensional. So are, indeed, the images formed in each of our eyes. Seen from two different points, those images are different. It is our brain that restores a three-dimensional view from the two images formed in our eyes. In technical drawing we must use another procedure. The aim of Descriptive Geometry is to describe the three-dimensional objects by two-dimensional drawings so as to allow to reconstitute their original forms.

Week Number: 1 Introduction


4. Quiz Q1: What is Descriptive Geometry describe. Q2: Why are we need to represent the 3D shape on 2D plane.

1. In technical drawing we must use:

5. Post test Choose the correct answer

a) Painting b) photos d) another procedure U6. References - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


Central projection.




1.B – Rationale: Theory of projection & projection of point, is very important subject to be studied in order to make the base of representation on the plane. 1.C – Central Idea:

Parallel projection. Orthographic projection. The two-sheet method of Monge.

1.D - Performance Objectives: At the end of this lecture the student should be able to: Project the point on planes.

U2. Pre test 1. Is the location of scene influence on projection view ? ( ) yes ( ) No 2. How many the direction of Orthographic projection.

Week Number: 2 & 3 Theory of projection & projection of point


3. The text


Examples: Project the points as the following: A(5,3) B(-2,6) C(-1,-1) D(0,-4)

4. Quiz Q1: Write the projection type. Q2: Project the point(2,1) at the principles plane.

5. Post test 1. The perpendicular trace of point on the plane called …………. . 6. References - (Descriptive Geometry), Dr. Yousef Nicola, National library-Baghdad 1976


Projection of straight line.




1.B – Rationale: Projection of straight line, is very important subject to be studied in order to Project the straight line plane surface. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: Draw the Projection of straight line on the principles planes.

U2. Pre test 1. Project the two points on the principles planes: P1(2,3) P2(4,1)

Week Number: 4 - 6 Projection of straight line


3. The text


Examples: Draw the elevation and plane of the straight line for the following: Page 20


4. Quiz Draw the elevation and plane of the straight line for the following: 1. A(1,2) B(4,3) right of A projector distance = 6 cm 2. A(6,3) B(5,4) right of A projector distance = 7 cm 3 A(-5,4) B(2,-1) right of A projector distance = 2 cm 5. Post test Write the procedure to project the straight line 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


Cases of the line in the space.




1.B – Rationale: Representation of straight line in space, is very important subject to be studied in order to understand the cases of the line in the space . 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: Imagine the line in the space.

U2. Pre test Draw the elevation and plane of the straight line below: 1. A(1,2) B(1,5) projector distance = 0 cm 2. A(6,2) B(3,2) projector distance = 0 cm 3. A(3,0) B(0,4) projector distance = 0 cm

Week Number: 7 - 8 Representation of straight line in space


3. The text


4. Quiz Draw the elevation and plane of the straight lines below and describe its case: 1. A(1,2) B(1,2) right of A projector distance = 5 cm 2. A(0,7) B(7,0) right of A projector distance = 6 cm

5. Post test Write the cases of the straight line in the space. 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976


Exercises on dihedral angles for straight line.




1.B – Rationale: Examples on dihedral angles for straight line, is very important examples to be studied in order to exercise for dihedral angles for straight line. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: Imagine and draw the line in the space.

U2. Pre test Draw the elevation and plane of the straight line below: 1. A(-1,2) B(-1,5) projector distance = 3 cm 2. A(-6,-2) B(-3,-2) projector distance = 4 cm

Week Number: 9 Examples on dihedral angles for straight line


3. The text


4. Quiz Draw the elevation and plane of the straight lines below and describe its position: 1. A(-5,2) B(-1,2) right of A projector distance = 5 cm 2. A(2,-7) B(6,-3) right of A projector distance = 6 cm

1. Passes through +V.P and +H.P

5. Post test Explain by drawing the projection of the straight line when:

2. Passes through +V.P and -H.P 3. Passes through -V.P and +H.P 4. Passes through -V.P and -H.P

6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


The true length and inclinations of a straight line.




1.B – Rationale: The true length and inclinations of a straight line, is very important subject to be studied in order to determine the true length and its inclinations. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: determine the true length and its inclinations.

U2. Pre test Determine the true length and inclinations of a straight line below: 1. A(2,2) B(2,5) projector distance = 0 cm 2. A(6,1) B(3,1) projector distance = 0 cm

Week Number: 10-13 The true length and inclinations of a straight line


3. The text ***********


1. draw (scale 1:1) the PLAN & ELEVATION of the line.

4. Quiz The straight line AB is placed such that A=(3 , 1) and B=(1, 5) right of A. The distance of projectors between A & B= 5 cm. The horizontal trace is H(-1,0).

2. determine the true length inclinations. 3. determine the inclinations.

5. Post test Define the symbols below: α , β , T.L 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


Examples for the true length of straight line.




1.B – Rationale: Examples for the true length of straight line, is very important examples to determine the true length and its inclinations. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: determine the true length and its inclinations.

U2. Pre test Determine the true length and inclinations of a straight line below: 1. A(2,1) B(3,4) right of A projector distance = 3 cm 2. A(4,2) B(3,1) right of A projector distance = 4 cm

Week Number: 14-15 Examples for the true length of straight line



3. The text ***********30 31 32 Example (1): The straight line AB is placed such that A=(2 , 4) and B=(5, 1) left of A. The distance of projectors between A & B= 6 cm.

2. determine the true length. 3. determine the inclinations.


Example (2): The straight line AB is placed such that A=(6 , 2) and B=(2, 2) left of A. The distance of projectors between A & B= 8 cm.

1. draw (scale 1:1) the PLAN & ELEVATION of the line. 2. determine the true length. 3. determine the inclinations.


4. Quiz The straight line AB is placed such that A=(1.5 , 5) and B=(Xb


, 2) right of A. The distance of projectors between A & B= 5 cm. The horizontal trace is H(-1,0).

2. determine the coordinates Xb 3. determine the inclinations.

.

4. determine the true length.

5. Post test Writ the procedures to determine the true length and its inclinations. 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


Auxiliary plane in the space with respect to the both V.P & H.P.




1.B – Rationale: Auxiliary plane, is very important subject to be studied in order to use the Auxiliary plane . 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: determine the Auxiliary plane in the space with respect to the both V.P & H.P.

U2. Pre test Are we need to project on the another plane with the V.P& H.P ?

Week Number: 16 - 18 Auxiliary plane


3. The text ***********


4. Quiz Write the positions of the Auxiliary plane in the space with respect to the principles planes of projections.

5. Post test Write the less importance positions of the Auxiliary plane in the space with respect to the principles planes of projections. 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976


Apply the Auxiliary plane to determine the true length.




1.B – Rationale: Using Auxiliary plane to find the true length, is very important subject to be studied in order to apply the Auxiliary plane to determine the true length. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: use the Auxiliary plane to determine the true length.

U2. Pre test Determine the auxiliary plane which is parallel the to the line A(2,2), B(3,4) right of A and projector distance = 5 cm.

Week Number: 19 Using Auxiliary plane to find the true length


3. The text ***********


4. Quiz Use the Auxiliary plane to determine the true length of the line A(2,1), B(4,2) right of A and projector distance = 5 cm.

5. Post test Writ the procedures to use the Auxiliary plane to determine the true length of the line . 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976


Apply the Auxiliary plane to project the plane shapes.




1.B – Rationale: Auxiliary plane application, is very important subject to be studied in order to apply the Auxiliary plane to project the plane shapes. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: use the Auxiliary plane to project the plane shapes.

U2. Pre test The equilateral lamina ABC is placed perpendicular to the V.P and having the following data: A(8,2) B(14,11) left of A C(2,11) left of A The distance of projector BC = 0 Required: 1. Draw scale 1:1 the elevation and plane of the lamina 2. Project a view on an auxiliary plane perpendicular to both the H.P and the V.P.

Week Number: 20-24 Auxiliary plane application


3. The text ***********


1. Draw scale 1:1 the elevation and plane of the lamina.

4. Quiz The equilateral lamina ABC is placed perpendicular to the V.P and having the following data: A(2,2) B(2,10) left of A C(2,11) left of A The distance of projector AB = 6 cm Required:

2. Project a view on an auxiliary plane perpendicular to both the H.P and the V.P. 3. Find the coordinates of point C.

5. Post test Writ the procedures to project the plane shapes on the Auxiliary plane. 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


Open the surface of cylinder.




1.B – Rationale: Open cylinder and definition, is very important subject to be studied in order to project the shapes on the cylindrical surface. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: project the shapes on the cylindrical surface.

U2. Pre test How can make a cylinder by surface of rectangle.

Week Number: 25-26 Open cylinder and definition


3. The text ***********102c 232


1. draw scale 1:1 the elevation and plane of the pyramid.

4. Quiz ***** 232 A right cylinder of height 9 cm and its base diameter 3 cm, The pyramid, is placed with its axis perpendicular to the H.P. Required:

2. on the elevation, draw the development of its surface.

5. Post test What do you see with the open a cylinder. 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


Open the surface of cone.




1.B – Rationale: Open cylinder and definition, is very important subject to be studied in order to project the shapes on the surface of cone. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: project the shapes on the surface of cone.

U2. Pre test What do you see by open the surface of the cone?

Week Number: 27-28 Open cone and definition


3. The text ***********222 135c


1. draw scale 1:1 the elevation and plane of the pyramid.

4. Quiz *****225 A right pentagonal pyramid of height 10 cm and its base is a square of side 4 cm, The pyramid is placed with its axis perpendicular to the H.P. Required:

2. on the elevation, draw the development of its surface.

5. Post test Why are we open the surface of cone. 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005


draw the section of the cone by the Auxiliary plane .




1.B – Rationale: Cut the cone using Auxiliary plane, is very important subject to be studied in order to draw the section of the cone. 1.C – Central Idea:

1.D - Performance Objectives: At the end of this lecture the student should be able to: draw the section of the cone by the Auxiliary plane.

U2. Pre test Draw the hyperbolic curve .

Week Number: 29-30 Cut the cone using Auxiliary plane


3. The text ***********130


4. Quiz A right pentagonal pyramid of height 16 cm and base-side 8 cm, is placed with its axis vertical. Its base ABCDE having A(2,2) and the side CD is parallel to the G.L, The pyramid is cut by a plane P-P parallel the H.P and 10 cm above the H.P. Required: 1. draw scale 1:1 the elevation. 2. sectional plane P-P.

5. Post test What will see by cut the cone with the inclined auxiliary plane with its base?

a) hyperbolic b)circle c) rectangle 6. References - (Descriptive Geometry), Dr. Yousef Nicola , National library-Baghdad 1976 - (An analytical introduction to Descriptive Geometry), Adrian B. Biran, Oxford, UK Samples - August 2005

course objective - fte.edu.iqfte.edu.iq/upload/upfile/ar/385ameer.pdf · descriptive geometry by:...

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