Lesson Eleven

1. Lesson Eleven Pictorial drawing (示意图，轴侧图) 1. Introduction: An orthographic drawing of two or more views describes an object accurately in form and size, but, since each of the views shows only two dimensions, such a drawing can convey information only to those who are familiar with graphic representation. Therefore, we need to use conventional picture drawings to convey specific information to persons who do not possess the trained imagination necessary to construct mentally an object from views. To make such drawings, one-plane pictorial drawing with the advantage of having the three dimensions to scale (按规定比例) have been devised.

2. 2. Definition: Pictorial drawing is a single-plane projection drawing and it may represent length, width and highness to scale simultaneity. 轴侧图是单面投影图，它可以按比例同时反映长、宽和高。 Note: Advantages and disadvantages between three views and pictorial drawing are as follows:

3. In pictorial drawing, to read is simple but to draw is difficult and do not representation true size. Three views may represent true size and to draw is simple but to read is difficult.

4. 3. Kinds of pictorial drawing Pictorial drawings are classified into axonometric projection and oblique projection。

5. 4. Axonometric projection (正轴测图) Theoretically, axonometric projection is a form of orthographic projection. The distinguishing difference is that only one plane is used instead of two or more, and the object is turned from its customary position so that three faces are displayed. The one plane is called axonometric projection plane (轴测投影面).

6. According to the turned angle, axonometric projection may be classified into isometric (等轴测), dimetric (二轴测) andtrimetric (三轴测). Isometric projection is the simplest of these, because three axes make equal angle with the plane of projection and the edges are therefore foreshortened equally. We only study isometric projection (正等测轴测图).

7. 4.1 Isometric Projection 1) Isometric axes and the angle between isometric axes. (轴测轴和轴间角) That spatial right coordinates O-XYZ project to axonometric projection plane to form isometric axes which are indicated by O –X Y Z . 1 1 1 1 空间直角坐标投影到轴测投影面形成轴测轴。

8. In isometric projection, the angle between isometric axes is 120°. Theangle between isometric axes is used to determine the position of isometric axes.

9. 2) Anamorphic coefficient (变形系数) Theratio of spatial length with isometric length is called anamorphic coefficient. In isometric projection, three anamorphic coefficients are equal to each other. 在正等测投影图中，三个轴向变形系数相等。 Actual anamorphic coefficient is that p=q=r=0.82. In order to draw simply, we often adapt approximate anamorphic coefficient. Approximate anamorphic coefficient is that p=q=r=1.

10. The isometric projection drawn by approximate anamorphic coefficient is bigger than by actual anamorpgic coefficient. But, since the proportions are the same, increased size does not affect the pictorial value of representation.

11. 3) Methods for drawing isometric drawing ① coordinates construction method (坐标法) ② cut construction method (切割法) ③ superposition (叠加法)

12. For example 1: Draw a pictorial drawing of the object indicated by three views.

13. Steps for drawing are as follows: 1) Determine coordinates origin and establish spatial right angle coordinates (coordinates origin O coincides with point C). 2) Draw isometric axes. 3) According to the coordinates construction method, draw isometric projections of each point 4) Connect two endpoints respectively. 5) Clean and deepen. Note that isometric axes and all auxiliary lines are erased in order to keep tidiness.

14. For example 2: Draw a pictorial projection of the object indicated by three views

15. Solution: 1) Determine coordinates origin and establish spatial right angle coordinates. Coordinates origin locates on the right-rear of base.

16. 2) Draw isometric axes. 3) First according to the cut construction method draw the rectangular prism.

17. Secondly middle rectangular prism is cut.

18. Thirdly right-front wedge (楔块) is cut.

19. 4) Clean and deepen.

20. 4.2 Circle and arc in isometric projection 4.2.1 In isometric projection, a circle appears as an ellipse.

21. In drawing ellipse, a four-center method (四心圆弧法)is generally used. Take a horizontal circle for example to illustrate the steps for drawing an ellipse in four-center method. The isometric projection of a horizontal circle is a horizontal ellipse.

22. 1) Determine coordinates origin and establish plane right angle coordinates O-XY. 2) Draw isometricaxes O -X Y . 1 1 1 3) Using a radius equal to the radius of the circle, swing arcs across the isometric center lines to obtain a, b, c, d. 4)Through each of these intersecting points erect lines parallel to isometric axes respectively to obtain a rhombus (菱形). a b d c

23. Draw long diagonal and short diagonal. 5) If connect line from lower endpoint of short diagonal to a and from the same endpoint to b; from upper endpoint of short diagonal to d and from the same endpoint to c, we may obtain four connecting center lines. 6) Draw large arcs. Using endpoint of short diagonal as center respectively and the length along the connecting center line as radius, draw two large arcs. a b c d

24. 7) Draw small arcs. Using the intersecting point of the two connecting center lines as center respectively and the length along the small radius as radius, draw two small arcs Two laree arcs and two small arcs form the ellipse. 8) Clean and deepen.

25. For example 3: Draw the pictorial projection of the given cylinder.

26. Solution: 1) Determine coordinates origin and establish plane right angle coordinates O-XY. 2) Draw isometric axes and isometric center lines. 3) Draw isometric projection of lower base with four-center method. Z X Y

27. 4) Draw upper base. The centers for the upper base are located by moving the centers for the lower base upward a distance equal to the height of the cylinder (the method is called moving center method.).

28. 5) Clean and deepen.

29. 4.2.2 In isometric projection, how to draw a arc. Give: From front view and top view, we know a motherboard (底板) is round by two arcs respectively. Draw the pictorial drawing of the given solid.

30. 1) Draw the rectangular prism

31. 2) Find out center of the arc of upper base. The radius of the arc is given. If first measure along edge and secondly draw perpendicular line of the edge respectively, we may obtain the center of the arc.

32. 3) Making use of moving center method to obtain the center of lower base.

33. 4) Draw the arcs and out common tangent. 5) Clean and deepen.

34. For example 4 : Draw the pictorial projection of the given cylinder.

35. 1) Determine coordinates origin and establish spatial right angle coordinates. Coordinates origin locates on the motherboard (底板)as shown picture.

36. 2) Draw isometric axes and motherboard and round.

37. 3) Draw vertical board possessed a half cylinder. 画半圆头立板。

38. 4) Draw tangent surfaceleft and right.

39. 5) Draw one hole located vertical board and two holes located motherboard.

40. 6) Clean and deepen.

41. 5. Oblique projection 5.1 introduction: In oblique projection, the view is produced by using parallel projectors that make some angle with the axonometric plane.

42. 5.2 axonometric axes and the angle between axonometric axes. (轴测轴和轴间角) O X and O Z are perpendicular to each other and O Y is at any desired angle (usually, 45°) with O X . 1 1 1 1 1 1 1 1

43. 5.3 Anamorphic coefficient (变形系数) Anamorphic coefficient is that p=r=1 and q=0.5 . Namely, the Y dimension is decreased a half. Y坐标减半。

44. For example 5 : Draw oblique projection of the solid indicated by Two views.

45. Supplement left view. Class is over.

47. For example 6 : Draw oblique projection of the solid indicated by Two views.

48. 1) Determine coordinates origin and establish spatial right angle coordinates. 2) Draw oblique projection axes.

49. 3) Draw half cylinder and vertical board.

50. 4) Cut two holes and slot.