Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 1

Introduction to Cax (Part 1)

The Lab Exercise will give an introduction into the possibilities of computer aideddevelopment in general. It consists of two parts.

The first part is an introduction to the computer aided Design (CAD), in particular thecreation of technical drawings with the CAD-system MegaCAD.

Syllabus:

Lecturer:

Prof. Dr.-Ing. Peter Köhler

(Room: MA 225, Phone: (0203) 379 2790, email: peter.koehler@uni-due.de)

Dipl.-Ing. Norman Lupa

(Room: MA 227, Phone: (0203) 379 3431, email: norman.lupa@uni-due.de)

http://www.uni-due.de/cae/einfuehrung_cax.shtml

Web:

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 2

Timetable

Systems, Techniques,…Introduction to MegaCAD

Basics in technical drawing

Nov., 22th

Product structure, Bill of Material

Basics in technical drawing

Nov., 15th

Technical drawing standards

Basics in technical drawing

Nov., 8th

• sheets of blanc paper (A4)

• pencil• compasses• ruler• set square

Projections, line styles, dimensioning, ...

ST 025

8.15 – 9.30

Basics in technical drawing

Oct., 25th

TestMaterial to bring alongLecture ContentLocation

and timeTopicDate

Part 1, theoretical part

To successfully pass through the theoretical part you will have to pass a test!

The test will take place during the last lecture on Nov. 16th.!

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 3

Timetable

Working on basic examples

Practise on

MegaCADDec., 06th

• sheets of blanc paper (A4)

• pencil

Working on basic examplesWill be

announced in the group lists on our we site!

Practise on

MegaCADNov., 29th

Material to bring alongLecture ContentLocation and

timeTopicDate

Part 1, practical part

In the lecture on Nov., 15th the group lists for the practical part will be announced! You can have a look at this group lists on the internet! So visit our website frequently.

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 4

Visuelle Illusionen (Visual illusions)

Maurits Cornelis Escher, Wasserfall, Lithografie 1961.

Oscar Reutersvärd, Opus 1 no 293aa, 1934

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 5

Projektionsverfahren(projection methods)

Zentralprojektion(perspective)

Parallelprojektion(parallel projection)

Schiefe Parallelprojektion(oblique parallel projection)

Rechtwinklige Parallelprojektion(orthographic parallel projection)

Axonometrische Projektion(axonometric)

(isometric, dimetric, ...)

Tafelprojektion(multi-view projection)

Geometrische Grundlagen (Geometrical bases)

Darstellende Geometrie (representing geometry)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 6

Projektionsverfahren(projection methods)

Zentralprojektion(perspective)

Parallelprojektion(parallel projection)

projection plane

center of projection

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 7

ORIGINAL

VIEW

Zentralprojektion (perspective)

Projectors coverage at center of projection

projection planeprojection plane

The projection is larger than the original. The projection is smaller than the original.

center of projection

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 8

Fluchtpunkt auf einem Foto

(Vanishing point in a photo)

Zentralprojektion (perspective)

Parallel lines (which are not parallel to the projection plane) on the object converge at a single point in the projection (the vanishing point).

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 9

Zentralprojektion (perspective)

In mechanicalengineering,

perspective projectionsare used only rarely.

Parallel lines (which are not parallel to the projection plane) on the object converge at a single point in the projection (the vanishing point).

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 10

Projektionsverfahren(methods of projection)

Zentralprojektion(perspective)

Parallelprojektion(parallel projection)

projection plane

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 11

ORIGINAL

Rechtwinklige Parallelprojektion(orthographic projection)

VIEW

projection plane

Schiefe Parallelprojektion (oblique parallel projection)

VIEW

B) The projection linesare not perpendicular to the projection plane.

A) Projectors are orthogonal to projection surface

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 12

Parallelprojektion (Parallel projection)

Rechtwinklige Parallelprojektion (orthographic parallel projection)

Schiefe Parallelprojektion (oblique parallel projection)

Projektionauf eine gewölbte

Fläche (Projection on a curved surface)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 13

Axonometrische Projektionen(Axonometric Projections)

General obliqueprojection

Cavalier-, cabinet-, military projections, ...

Isometric, Dimetric, Trimetric

Objekt schief zur Bildebene (Object oblique

to projection plane)

Objekt parallel zur Bildebene (Projection plane is parallel to principal face)

Projektionsverfahren(methods of projection)

Zentralprojektion (perspective)

Parallelprojektion (parallel projection)

Rechtwinklige Parallelprojektion (orthographic parallel projection)

Schiefe Parallelprojektion (oblique Projection)

Objekt parallel zur Bildebene (Projection plane is parallel to principal face)

Objekt schief zur Bildebene (Object oblique

to projection plane)

Ein- oder Mehrtafel-projektionen

(multiview Projections)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 14

Räumliche Darstellungen (Spatial representations in the image of a space coordinate system)

x y

z

Axonometrische Projektion (Axonometric Projections)

(The z-axis is vertical. This is an arbitrary definition.)

parallel lines

parallel lines

parallel lines

z.B. einer Pyramide

(for example a pyramid)

Aufgabe 1: Skizzieren Sie eine Pyramide mit a=b=h in einer axonometrischen Projektion!

(Task1: Sketch a pyramid with a=b=h in an axonometric projection!)

ab

h

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 15

xa

ya

za

x

zezyeyxex

za

ya

xa

⋅=⋅=⋅=

Axonometrische Projektion der Einheitsstrecken(Axonometric Projections of the unit distances)

ez

ey

ex

z

y

1

1

1

They are scaled

Usually special projection directions and scalings are used

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 16

a

c

b

a : b : c = 1 : 1 : 1

30° 30°

za

xa

ya

32eee zyx ===

Senkrechte Axonometrie (Orthographic axonometry)Isometrische Projektion (Isometric projection)

Theoretical:

Practical:

All scaling factors have the same value

Vergrößerung(The object is represented

larger than the original one)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 17

(Exampel: isometric projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 18

c

b

42°

7°

a

32

ex =

322ee zy ⋅== a : b : c = 0.5 : 1 : 1

Vergrößerung

(Enlargement)

Senkrechte Axonometrie (Orthographic axonometry)Dimetrische Projektion (Dimetric projection)

Two scaling factors have the same valueTheoretical:

Practical:

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 19

(Example: dimetric projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 20

45°

za

xa

yac

b

a

a : b : c = 0.5 : 1 : 1

Schiefe Axonometrie (Oblique axonometry)Kavalierprojektion (cavalier projection)

In the exerciseswe will use this

projection

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 21

Beispiele: Kavalierprojektion

(cavalier projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 22

c

ba

45° 45°

xaya

za

Schiefe Axonometrie (Oblique axonometry)Militärprojektion (military projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 23

4050

20

1570

20

20010

0

6030Skizziertechniken

(methods of freehand sketching)

(Step by step)

Axonometrische Projektion (Axonometric Projections)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 24

Schrittweiser Skizzenaufbau(Step by step)

Aufgabe 2: Zeichnen Sie einen Pyramidenstumpf mit a=b=h1=40mm und h1=h/2

in einer Kavalierprojektion!

(Task 2: Draw a pyramid stump with a=b= h1=40mm and h1=h/2 in a cavalier-projection!)h1

h

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 25

Axonometrische Projektionen(Axonometric Projections)

General obliqueprojection

Cavalier-, cabinet-, military projections, ...

Isometric, Dimetric, Trimetric

Objekt schief zur Bildebene (Object oblique

to projection plane)

Objekt parallel zur Bildebene (Projection plane is parallel to principal face)

Projektionsverfahren(methods of projection)

Zentralprojektion (perspective)

Parallelprojektion (parallel projection)

Rechtwinklige Parallelprojektion (orthographic parallel projection)

Schiefe Parallelprojektion (oblique Projection)

Objekt parallel zur Bildebene (Projection plane is parallel to principal face)

Objekt schief zur Bildebene (Object oblique

to projection plane)

Ein- oder Mehrtafel-projektionen

(multiview Projections)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 26

S''

A'',D''

B'',C''

S'A'

D' C'

B'

1E

2E

S

B

CD

A

Zweitafelprojektion (Two-view projection)

S'A'

D' C'

B'

E2

E1

S''

A'',D'' B'',C''

E1 , E2 - projection planes

Vorderansicht (front)

Draufsicht (top)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 27

Darstellende Geometrierepresenting geometry

Tafelprojektion(orthographic projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 28

20

25

50

25

2525

25

60

10

50

∅20

Aufgabe 3: Zeichnen Sie die Vorderansicht und die Draufsicht des Bauteils!

(Task 3: Draw the front and the top view of the part!)

Vorderansicht (f

ront view)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 29

Draufsicht (top)

Vorderansicht

(front view)

Ebene Vorderansicht (front)

Ebene Draufsicht (top)

Ebene Seitenansicht (left-side)

Seiten-

Ansicht

(left-side view)

Dreitafelprojektion (Three-view projection)

Nach der Projektionsmethode E bzw. 1(as a first Angle Projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 30

Aufgeklappte Raumecke (unfolded space corner)

yx

y

z

Vorderansicht (front)

0

Seitenansicht (left-side)

Draufsicht (top)

Dreitafelprojektion (Three-view projection)

Aufgabe 4: Ergänzen Sie die Seitenansicht für Aufgabe 3!

(Task 4: Complement theside view for task 3!)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 31

Wo liegt die Bohrung in der Draufsicht?

Where ist the hole in the top view?

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 32

Symbol for third angle projection

Symbol for first angle projection

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 33

Dreitafelprojektion (Three-view projection)

Nach der Projektionsmethode A bzw. 3(as a 3rd Angle Projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 34

Projektionsmethode A bzw. 3(3rd Angle Projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 35

FRONT

TOP

RIGHT SIDE

Projektionsmethode A bzw. 3(3rd Angle Projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 36

Dreitafelprojektion (Three-view projection)

Projektionsmethode E bzw. 1(First Angle Projection)

We will use the First Angle Projection!

front

top

left-side

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 37

front

front

top

left-side

Beispiel: Dreitafelprojektion

(Three-view projection)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 38

55

35

25

20

3015

55 30

352520

15

Dreitafelprojektion (Three-view projection)

Aufgabe 5: Zeichnen die 3 Ansichten des Bauteils!

(Task 5: Draw 3 views of the part (Top, front and left-side)!)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 39

A

C

DA

BC

D

S S

AB

C

D

Aufgabe 6: Zeichnen die 3 Ansichten einer schräg geschnittenen Pyramide!

(Task 6: Draw the 3 views of a diagonally cut pyramid!)

Aufgabe 7: Zeichnen die 3 Ansichten eines schräg geschnittenen Zylinders!

(Task 7: Draw the 3 views of a diagonally cut cylinder!)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 40

Schnittebene

(cut plane)

Aufgabe 8: Zeichnen die 3 Ansichten einer schräg geschnittenen Pyramide!

(Task 8: Draw the 3 views of a diagonally cut pyramid!)

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 41

Aufgabe 9: Konstruktion der Seitenansicht und Komplettierung der Draufsicht!

(Task 9: Draw the side view and completion of the top view!

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 42

Aufgabe 9: Konstruktion der Seitenansicht und Komplettierung der Draufsicht!

(Task 9: Draw the side view and completion of the top view!

Introduction to CAxProf. Dr.-Ing. Dipl.-Math. P. Köhler V1 - Sheet 43

Durchdringung von Kegel und Ebene

Aufgabe 10: Konstruktion der Seitenansicht eines geschnittenen Kegels!

(Task 10: Draw the side view of a cut cone!

(Penetration of cone and plane)