1. Auxiliary Views
Chapter 7

2. Objectives Create an auxiliary view from orthographic views
Draw folding lines or reference-plane lines between any two adjacent views
Construct depth, height, or width auxiliary views
Plot curves in auxiliary views

3. Objectives (cont.) Construct partial auxiliary views
Create auxiliary section views
Produce views to show the true length of a line, point view of a line, edge view of a surface, and true size view of a surface

4. Objectives (cont.) Show the true size of the angle between two planes
Construct the development of prisms, pyramids, cylinders, and cones
Use triangulation to transfer surface shapes to a development
Create the development of transition pieces

5. Objectives (cont.) Graphically solve for the intersection of solids
Apply revolution to show true length edges and true size surfaces

6. Understanding Auxiliary Views
An auxiliary view is an orthographic view that is not a standard projection
Auxiliary views allow principal faces of features that are not parallel to the standard planes of projection to appear true shape and size

7. Primary Auxiliary Views
A primary auxiliary view is projected onto a plane that is perpendicular to one of the principal planes of projection and is inclined to the other two

8. Primary Auxiliary Views

9. Revolving a Drawing
Some times it is easier to visualize and draw and auxiliary view when revolved to the position of a regular view
It should be understood that an auxiliary view basically is like any other view

10. Revolving a Drawing

11. Classification of Auxiliary Views
Auxiliary views are named for the principal dimension shown in the auxiliary view such as:
Depth auxiliary
Height auxiliary
Width auxiliary

12. Successive Auxiliary Views
From primary auxiliary views, a secondary auxiliary view can be drawn
Third auxiliary views can be projected from secondary views
An infinite number of successive auxiliary views may be drawn

13. Successive Auxiliary Views

14. Reference Planes
Instead of using one of the planes of projection, reference planes parallel to the plane of projection and touching or cutting through the object are used in auxiliary views
Reference planes should be positioned so it is convenient to transfer distances

15. Reference Planes
Reference lines, like folding lines, are always at right angles to the projection lines between the views
A reference plane appears as a line in two alternate views, never in an adjacent view

16. Reference Planes
Measurements are always made at right angles to the reference lines or parallel to the projection lines
In the auxiliary view, all points are at the same distances from the reference line as the corresponding points are from the reference line in the alternate view, or the second previous view

17. Reference Planes

18. Circles and Ellipses in Auxiliary Views
Circular shapes appear as elliptical when viewed at an angle other than 90°

19. Hidden Lines in Auxiliary Views
Generally hidden lines should be omitted in auxiliary views unless they are needed to clearly communicate the drawing’s intent

20. Hidden Lines in Auxiliary Views

21. Partial Auxiliary Views
Partial auxiliary views are often sufficient to convey information and may be easier to read
Usually a break line is used to indicate the imaginary break in the views

22. Partial Auxiliary Views

23. Half Auxiliary Views
If an auxiliary view is symmetrical, and to save space or time, a half auxiliary view may be drawn

24. Auxiliary Sections
An auxiliary section is simply an auxiliary view in section
The cutting plane line indicates both the location of the cutting plane and the direction of sight for the auxiliary section

25. Auxiliary Sections

26. Uses of Auxiliary Views
Auxiliary views are used to show:
True length of a line
Point view of a line
Edge view of a plane
True size of a plane

27. Understanding Developments and Intersections
A development is a flat representation or pattern that when folded together creates a 3D object
An intersection is the result of two objects that intersect each other
Sheet metal construction is the most common application for developments and intersections

28. Ruled Surface
A ruled surface is one that may be generated by sweeping a straight line, called a generatrix, along a path which may be straight or curved
Any position of the generatrix is an element of the surface
A ruled surface may be a plane, single curved surface, or a warped surface

29. Ruled Surface

30. Plane
A plane is a ruled surface that is generated by a line, one point of which moves along a straight path while the generatrix remains parallel to its original position

31. Plane

32. Single-curved Surface
A single-curved surface is a developable ruled surface that can be unrolled to coincide with a plane
Any two adjacent positions of the generatrix lie in the same plane
Examples are the cylinder and the cone

33. Double-curved Surface
A double-curved surface is generated by a curved line and has no straight-line elements
A surface generated by revolving a curved line about a straight line in the plane of the curve is called a double-curved surface of revolution
Examples are the sphere, torus, ellipsoid, and hyperboloid

34. Warped Surface
A warped surface is a ruled surface that is not developable
No two adjacent positions of the generatrix lie in a flat plane
Warped surfaces cannot be unrolled or unfolded to lie flat

35. Warped Surfaces

36. Revolved and Extruded Solids
A revolved solid is created by revolving a plane figure about an axis
An extruded solid is formed by sweeping a shape along a linear path
Solids bounded by warped surfaces have no group name

37. Revolved Solids

38. Extruded Solids

39. Principles of Intersections
Typical examples of the need for accurate drawings showing the intersections of planes and solids include:
Openings in roof surfaces for flues and stacks
Openings in wall surfaces for pipes, chutes, etc.
The building of sheet-metal structures

40. Principles of Intersections
For solids bounded by plane surfaces, you need only find the points of intersection of the edges of the solid with the plane and join these points in consecutive order with straight lines

41. Principles of Intersections
For solids bounded by curved surfaces, it is necessary to find the points of intersection of several elements of the solid with the plane and to trace a smooth curve through these points
The intersection of a plane and a circular cone is called a conic section

42. Developments
The development of a surface is that surface laid out on a plane
Practical applications of developments occur in sheet-metal work, stone cutting, pattern making, packaging, and package design

43. Triangulation
Triangulation is simply a method of dividing a surface into a number of triangles and transferring them to the development
Since the development is symmetrical, only have the development needs laid out

44. Triangulation

45. Revolution
Revolution, like auxiliary-view projection, is a method of determining the true length and true size of inclined and oblique lines and planes

46. Revolution