Isometric drawings (perspectives)

1. Working document Linguistic review 29-09-07 Isometricdrawings(perspectives)

2. A cube shown with this type of projection pivots 45º to show two faces on the projection plane instead of a single face. Isometric projections It is then tilted frontward or backward, allowing three faces to be observed.

3. A cube shown with this type of projection pivots 45º to show two faces on the projection plane instead of a single face. It is then tilted frontward or backward, allowing three faces to be observed. Isometric projections

4. Three views of a cube in multi-view orthogonal projection. Top view Right side view Front view Isometric projections

5. We pivot the cube 45º to show two of its faces. 45º Top view Right side view Front view Isometric projections

6. The cube turns around point O until the AB diagonal becomes horizontal. A The cube is lifted and pivots around point O. B O Isometric projections

7. True dimensions This front view shows the isometric projection of the cube in its new position. Because the cube is tilted, most of the dimensions of its isometric projection are about 80% of their true dimensions. Isometric projections

8. This front view shows the isometric projection of the cube in its new position. Because the cube is tilted, most of the dimensions of its isometric projection are about 80% of their true dimensions. True dimensions Isometric projections

9. 120º 2 1 3 Characteristics of isometric projections Axes 1, 2 and 3 form 120º angles between one another. The projection is isometric (equal measures) because the height of axis 1, the length of axis 2 and the width of axis 3 are all proportionally reduced. All lines parallel to axes 1, 2 and 3 are isometric lines. Isometric projections The sides of the cube and all planes parallel to them are isometric planes. The lines not parallel to axes 1, 2 and 3 are non-isometric lines. The isometric lines are angled at 30º.

10. Characteristics of isometric projections Axes 1, 2 and 3 form 120º angles between one another. The projection is isometric (equal measures) because the height of axis 1, the length of axis 2 and the width of axis 3 are all proportionally reduced. All lines parallel to axes 1, 2 and 3 are isometric lines. 120º 2 1 3 The sides of the cube and all planes parallel to them are isometric planes. The lines not parallel to axes 1, 2 and 3 are non-isometric lines. The isometric lines are angled at 30º. Isometric projections

11. Isometric drawing 50 20 20 28 35 10 14 8 We will illustrate the main stages of isometric drawing of the object shown above in multi-view. We will use a method called box construction.

12. Isometric drawing 50 20 20 28 35 10 14 8 To create the box, use construction lines to outline an isometric box as large as the overall object to be drawn. We will illustrate the main stages of isometric drawing of the object shown above in multi-view. We will use a method called box construction. The vertical axis is equal to the real height. The two other axes, drawn at 30° to horizontal, correspond to the actual width and length of the object.

13. Isometric drawing 50 To create the box, use construction lines to outline an isometric box as large as the overall object to be drawn. We will illustrate the main stages of isometric drawing of the object shown above in multi-view. We will use a method called box construction. The vertical axis is equal to the real height. The two other axes, drawn at 30° to horizontal, correspond to the actual width and length of the object. 20 20 28 35 10 14 8

14. Isometric drawing Measurements are reported on the isometric axes, or on lines parallel to these axes. The box is an isometric drawing as large as the overall object to be shown. Its lines are drawn very faintly. The object is drawn by removing volumes from the box. A 30º- 60º set square is used to trace the isometric lines.

15. Isometric drawing Measurements are reported on the isometric axes, or on lines parallel to these axes. The box is an isometric drawing as large as the overall object to be shown. Its lines are drawn very faintly. The object is drawn by removing volumes from the box. A 30º- 60º set square is used to trace the isometric lines.

16. Isometric drawing STAGE 1 STAGE 2 STAGE 3 STAGES OF DRAWING IN ISOMETRIC PERSPECTIVE Measure on the axesand trace the details in construction lines. Carry out the final layout. Sketch the box.

17. Isometric drawing STAGES OF DRAWING IN ISOMETRIC PERSPECTIVE STAGE1 STAGE2 STAGE3 Measure on the axes and trace the details in construction lines. Carry out the final layout. Sketch the box.

18. A B D C C D A B Isometric drawing How to draw non-isometric lines and surfaces Non-isometric (oblique) lines and surfaces are not true to size in isometric perspective. Dimensions of inclined lines and surfaces are determined by using their coordinates which must be located on isometric lines.

19. How to draw non-isometric lines and surfaces Non-isometric (oblique) lines and surfaces are not true to size in isometric perspective. A B D C C D A B Dimensions of inclined lines and surfaces are determined by using their coordinates which must be located on isometric lines. Isometric drawing

20. Isometric drawing Grids and isometric drawing A grid which includes all three isometric axes may be used to draw isometric perspectives.

21. Grids and isometric drawing A grid which includes all three isometric axes may be used to draw isometric perspectives. Isometric drawing

22. Isometric drawing Showing circles and arcs of circles in isometrics Circles and arcs of circles on isometric planes are shown in isometric projection using ellipses within an isometric square. The sides of the square are equal to the diameter of the circle and each side of the circle touches the square. To draw a circle in isometric perspective on the computer, use a modified circle inserted into an isometric square. To draw it as a sketch or with a compass, draw four arcs of the circle in an isometric square.

23. Isometric drawing How to draw an ellipse composed of four arcs using a compass 1- Trace an isometric square. 2-Find the center of the square using diagonals, then trace the axis lines.

24. 1- Trace an isometric square. 2- Find the center of the square using diagonals, then trace the axis lines. Isometric drawing How to draw an ellipse composed of four arcs using a compass 3- Finally, trace the median lines.

25. 1- Trace an isometric square. 2- Find the center of the square using diagonals, then trace the axis lines. Isometric drawing How to draw an ellipse composed of four arcs using a compass 3-Finally, trace the median lines. The meeting point of the medians shows the center of the four arcs of the circle.

26. «Construction box» Isometric drawing How to draw an object containing rounded parts ORTHOGRAPHIC MULTI-VIEW PROJECTION ISOMETRIC PROJECTION

27. Bibliography GIESECKE, Frederick E., MITCHELL, Alva, SPENCER, Henry Cecil, HILL, Ivan Leroy, GYGDON, John Thomas et NGUYEN, Dinh N. « Dessin technique », Montréal, Éditions du Renouveau Pédagogique inc., 1982, 769 p JENSEN, C.H. « Dessin industriel », Montréal, McGraw-Hill, 1972, 752 p. STIRLING, Norman. « Éléments de dessin industriel », Montréal, HRW, 1979, 372 p.