Fundamentals of Descriptive Geometry

1. Fundamentals of Descriptive Geometry AT 301 Dr. Trent

2. Introduction • Most of the concepts of this chapter have already been touched on in prior lectures and exercises. • The intent of this lecture to provide another view of the principles and concepts from an analytical standpoint.

3. Descriptive Geometry • Descriptive geometry is the graphic representation of plane, solid, and analytical geometry used to describe real or imagined technical devices and objects. • It is the science of graphic representation in engineering design. • Students of technical or engineering graphics need to study plane, solid, analytical, and descriptive geometry because it forms the foundation or grammar of technical drawings.

4. Uses of Descriptive Geometry • Descriptive geometry principles are used to describe any problem that has spatial aspects to it. • For example the application of descriptive geometry is used in: • The design of chemical plants. For the plant to function safely, pipes must be placed to intersect correctly, and to clear each other by a specified distance, and they must correctly intersect the walls of the buildings. • The design of buildings • The design of road systems • The design of mechanical systems

5. Methods of Descriptive Geometry • There are three basic methods • Direct View • Fold Line • Revolution • The differences is in how information is transferred to adjacent views.

6. Direct View Method • Reference plane is used to transfer depth info between related views. • Length information comes by projection lines from the adjacent view.

7. Fold-Line Method • A variation on the Direct View method. • The reference line is moved between the views to represent the folds in a glass box.

8. Revolution Method • The projectors from the adjacent view are not parallel to the viewing direction (as related to the object) • Need to rotate the length information about an axis before projecting it to the new adjacent view.

9. Reference Planes • The reference plane is perpendicular to the line of sight project lines. It appears as a line in related views. • Gives a reference for measuring depth information for related views.

10. Basic Elements • The basic elements used in descriptive geometry include: • Points • Lines • Planes • Coordinate systems are mathematical tools useful in describing spatial information • Cartesian coordinate systems are the most commonly used.

11. Cartesian Coordinate System • Points are located relative to the origin of the coordinate system.

12. Points • A point has no width, height, or depth. • A point represents a specific position in space as well as the end view of a line or the intersection of two lines. • The graphical representation of a point is a small symmetrical cross.

13. Lines • Lines represents the locus of points that are directly between two points. • A line is a geometric primitive that has no thickness, only length and direction. • A line can graphically represent the intersection of two surfaces, the edge view of a surface, or the limiting element of a surface. • Lines are either vertical, horizontal, or inclined. A vertical line is defined as a line that is perpendicular to the plane of the earth (horizontal plane).

14. Multi View Representations of Lines

15. True Length Lines • A true length line is the actual straight-line distance between two points. • In orthographic projection, a true-length line must be parallel to a projection plane in an adjacent view.

16. True Length Lines • True length lines are ALWAYS parallel to the reference plane in ALL adjacent views. • To find the true length of a line, draw a view of the line where the reference plane is parallel to an adjacent view of the line.

17. Principles of Descriptive Geometry Rule #1 If a line is positioned parallel to a projection plane and the line of sight is perpendicular to that projection plane, then the line will appear as true length