1. Intersections & Developments (Text Chapter 31)
UAA ES A103
Week #11 Lecture
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2. Introduction
Intersections and developments are commonly found in many engineering disciplines.
Two surfaces that meet to form a line of intersection.
A development is the outside surface of a geometric form laid flat.
As an engineer you should be able to create the development of common shapes, such as cones, prisms, and pyramids.

3. Visibility
Visibility is the clear and correct representation of the relative positions or two geometric figures, in multiview drawings.

4. More Visibility
In each view, the visibility of the figures is indicated by drawing the figure that is front with object lines while drawing the second figure with both object lines and hidden lines.

5. Intersections
An intersection is a point or line where two geometric forms, such as lines or surfaces, meet or cross each other.

6. Intersecting lines Two lines that intersect share a common point.
If the lines do not have a common point that projects from view to view, the lines are nonintersecting.

7. Intersection of a Line and a Plane
The intersection of a line and a plane is referred to as the piercing point.
A line will intersect a plane if the line is not parallel to the plane.
Locations of piercing points can be found using either the EDGE VIEW or CUTTING PLANE methods.

8. Edge View Method
Create an auxiliary view showing the plane as an edge.
Project the intersecting point of the LINE to all views

9. Cutting Plane Method
Create a cutting plane that includes the line and is an edge view in one of the given views.
Trace the cutting plane intersection onto the other view.
The piercing point is where the cutting plane intersection with the plane intersects the line.

10. Intersection of Two Planes
The intersection of two planes is a straight line all of whose points are common to both planes.
The line of intersection between two planes is determined by locating the piercing points of lines from one plane with the other plane and drawing a line between the points.

11. Edge View Method

12. Cutting Plane Method

13. Intersection of a Plane and A Solid
To find the intersection between a plane and a solid,
determine the piercing points using either cutting planes or auxiliary views,
then draw the lines of intersection.

14. A Plane & A Prism

16. A Plane & A Cylinder

17. A Plane & A Cone

19. Intersection of Two Solids
Solids are represented by lines, planes and curved surfaces.
The basic principles of lines intersecting planes apply here.
Piercing points caused by lines one once surface intersecting another surface can be found in the various views and be connected with lines.

20. Two Prisms
Prisms are made up of planar surfaces so all intersections will be straight lines.
This means that you only need to find the ends of each intersection line.

21. A Prism & A Pyramid

22. Intersections in Axonometric, Oblique and Perspective Drawings
The author stops short of this discussion.
The same principles apply.
If one given view shows edge views of one of the intersecting planes then only two views are required. Otherwise an auxiliary view may be required.

23. Axonometric & Oblique Views
May need to draw the multi-view equivalents on the principle faces.
Use cutting planes to find piercing points then connect the piercing point.

25. Oblique Example

26. Developments
A development is the unfolded or unrolled, flat or plane figure of a 3-D object.
Called a pattern, the plane figure may show the true size of each area of the object. When the pattern is cut, it can be rolled or folded back into the original object.
A true development is one in which no stretching or distortion of the surface occurs, and every surface of the development is the same size and shape as the corresponding surface on the 3-D object.
Only polyhedrons and single-curved surfaces can produce true developments.

27. Approximate Development
An approximate development is one in which stretching or distortion occurs in the process of creating the development.
The resulting flat surfaces are not the same size and shape as the corresponding surfaces on the 3-D object.
Warped surfaces do not produce true developments, because pairs of consecutive straight-line elements do not form a plane.
Double-curved surfaces such as spheres do not produce true developments.

28. Types of Developments Parallel-line Radial-line Triangulation
Approximation

29. Examples

30. Some Observations All lines are true length All planes are true size
Each planar surface is either a principle view or an auxiliary view.

31. Inside Pattern Development

32. Development of a Right Rectangular Prism

33. Truncated Prism / Cylinder

34. Truncated Cylinder

35. All planar surfaces are TRUE SIZE
REMEMBER!
All lines are
TRUE LENGTH
All planar surfaces are TRUE SIZE

36. A Right Circular Cone

37. Truncated Right Circular Cone

38. Oblique Cone

39. Truncated Pyramid

40. Oblique Prism

41. Oblique Cylinder