1. ME 250: Design & Manufacturing I School of Mechanical Engineering
Engineering Drawing
ME 250: Design & Manufacturing I
School of Mechanical Engineering
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Course Outline
Descriptive Geometry
Spatial Visualization
Orthographic Projection
Auxiliary Views
Engineering Drawing
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Descriptive Geometry
What is Descriptive Geometry ?
Descriptive geometry is the use of orthographic projections in order to solve for advanced technical data involving the spatial relationships of points, lines, planes and solid shapes.
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Descriptive Geometry
Why do I need to understand it ?
With the advent of CAD software, computers are routinely being used to design and illustrate many projects which were formerly hand drawn. This (relatively) new technology eliminates the need for hand completed drawings but still requires the engineer (or artist) to be well versed in the theory and practice of multiview (or orthographic projection)
3-D Spatial visualization is a very powerful tool
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Descriptive Geometry
Engineers (and others) often use two-dimensional pictures to communicate three-dimensional shapes. The most common way to represent a three-dimensional object in a two-dimensional plane is by orthogonal projection.
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Descriptive Geometry
One can easily visualize the corresponding situation in 3D. However, it is also necessary to be able to go back and forth between 2D and 3D. That is, be able to:
represent a given three dimensional situation by a series of 2D views (i.e., orthographic views—principal and auxiliary)
visualize (and derive pertinent geometric information about) the three dimensional situation from a given set of orthographic views.
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7. Spatial Visualization
There are two types of projections to communicate engineering and technical illustration work
pictorial projections
multiview projections
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8. Pictorial projections
Pictorial projections consist of single view drawings that are suitable for representing preliminary ideas or sketches, but are not appropriate for communicating technical data. Examples of pictorial projections are the oblique, isometric or perspective projections (or views).
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Examples
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10. multiview projections
Multiview drawings present multiple different views of the same object. This method presents projections of the same object on three planes simultaneously, namely the top, front and side (or profile) planes, providing three views known as the principal views. All dimensions are drawn to scale and the three principal views can be used to form additional views known as auxiliary views.
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Examples
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12. Orthographic Projection
Orthographic projection is the method of projecting views of an object on three planes that are perpendicular to each other.
Imagine the object whose orthographic projections are needed to be enclosed by a box.
To obtain the orthographic projections on paper, visualize unfolding the top and the right sides of the box along the lines H/F and F/P respectively.
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13. Orthographic Projection
The method of obtaining orthographic projections of an object on paper
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14. Orthographic Projection
If the line of sight A is in the vertical direction and is perpendicular to the top side of the box, the projection of the object on the top side of the box, which is obtained by viewing the object along line of sight A is called the top view.
If the line of sight B is in the horizontal direction and is perpendicular to the front side of the box, the corresponding projection of the object onto the front side of the object is called the front view.
The projection of the object obtained on the right side of the box when the object is viewed from the right side looking along the line of sight B is called the side view (also known as the profile view).
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15. Orthographic Projection
As these sides of the box are unfolded, the top view of the object appears directly above the front view while the side or profile view appears to the right side of the front view.
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16. Orthographic Projection
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17. Orthographic Projection
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Auxiliary Views
An Auxiliary view is any view that lies in a projection plane other than the horizontal, frontal or profile (side) plane. It is necessary to obtain one or more auxiliary views of an object when that object is complex and has a variety of planes and lines that are not parallel to one of the three principal planes.
There are three types of auxiliary views, namely primary, secondary and successive auxiliary views.
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19. Primary auxiliary views
Primary auxiliary views are projected from one of the three principal views. A primary auxiliary view will be perpendicular to one of the three principal planes and inclined to the other two.
Horizontal Auxiliary View
Frontal Auxiliary View
Profile Auxiliary View
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20. Secondary auxiliary views
Secondary auxiliary views are auxiliary views taken off a primary auxiliary view.
Secondary auxiliary views are inclined to all three principal planes of projection.
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21. Successive auxiliary views
Successive auxiliary views are views projected from secondary auxiliary views.
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22. Horizontal Auxiliary View
The horizontal auxiliary view is projected from the horizontal view.
The auxiliary plane is perpendicular to the horizontal view plane but is inclined to the front view plane and the profile view plane.
The auxiliary view is obtained on paper by unfolding the auxiliary plane along its upper edge H/A until it is aligned with the horizontal plane, and then unfolding the horizontal plane and the auxiliary plane together along the edge H/F until they are aligned with the front plane.
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23. Horizontal Auxiliary View
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24. Frontal Auxiliary View
The frontal auxiliary view is projected from the front view.
The auxiliary plane is perpendicular (or orthogonal) to the front view plane but is inclined to the horizontal view plane and the profile view (or side) plane.
The auxiliary view is obtained on paper by unfolding the auxiliary plane along its front edge F/A until it is aligned with the front plane.
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25. Frontal Auxiliary View
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26. Profile Auxiliary View
The profile auxiliary view is projected from the profile view.
The auxiliary plane is perpendicular to the profile view plane but is inclined to the horizontal view plane and the front view plane.
The auxiliary view is obtained on paper by unfolding the auxiliary plane along its right edge A/P until it is aligned with the profile plane, and then unfolding the profile plane and the auxiliary plane together along the edge F/P until they are aligned with the front plane.
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27. Profile Auxiliary View
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28. Points, Lines and Planes
All geometric shapes can be thought of as being composed of points and lines. While practicing descriptive geometry, points are the most important elements that form the basic building blocks of all geometric constructions. For example, all graphical projections of lines, planes and solids can be formulated by identifying and locating a number of points that are associated with the object.
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29. Basic Concepts for Visualization
Views of points
Views of lines
The true length of a line
The point view of a line
The edge view of a plane
The normal view of a plane
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30. Orthographic Views of a Point
A point is a location in three dimensional space.
A point (labeled 1) is located by measuring its perpendicular distances from the three principal planes.
The projections of the point 1 on the three principal planes are labeled 1H , 1F and 1P identify the horizontal, front and profile (or side) projections respectively.
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31. Orthographic Views of a Point
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32. Auxiliary Views of a Point
Primary Auxiliary Views of a point – Auxiliary views taken from principal views are termed primary auxiliary views. The plane of a primary auxiliary view will be perpendicular to one principal plane and inclined to the other two principal planes.
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33. Primary Auxiliary Views of a point
The procedure of taking an auxiliary view and determining the location of a point in the auxiliary view
Given the orthographic views of a point, draw a line representing the auxiliary plane in the corresponding view at the desired inclination.
Draw a line perpendicular to the A/H to establish the line of sight in the auxiliary view.
To establish the location of the point 1A, measure the distance of the front projection 1F from the horizontal plane. Mark the point 1A at this distance from the auxiliary plane A/H along the line of sight.
The distance of 1A from A/H is the same as the distance of 1F from F/H .
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34. Primary Auxiliary Views of a point
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35. Primary Auxiliary Views of a point
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36. Secondary Auxiliary Views of a point
Secondary auxiliary views are views taken from primary auxiliary views. The plane of a secondary auxiliary view will be perpendicular to the primary auxiliary view plane and inclined to all three principal planes.
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37. Secondary Auxiliary Views of a point
Establish the line of sight for auxiliary view A and draw a fold line H/A perpendicular to the line of sight at a convenient distance from 1H.
From 1H, draw a projection line parallel to the line of sight and perpendicular to H/A.
Mark the point 1A on this projection line at a distance D1 from H/A. Note that D1 is the distance of 1F from H/F. 1A is the primary auxiliary view of the point.
To obtain the secondary auxiliary view 1, establish the line of sight and draw fold line A/B perpendicular to it.
From 1A, draw a projection line perpendicular to A/B and on it, mark the point 1at a distance D4. Note that D4 is the distance of the point 1H from fold line A/H.
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38. Secondary Auxiliary Views of a point
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39. Orthographic Views of a Line
A line is basically a sequence of two points.
Since only two points are needed to describe a line, obtaining the projections of the line on the three principal planes is straightforward and is achieved simply by taking the projections of the endpoints of the line on the three principal planes.
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40. Orthographic Views of a Line
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41. Auxiliary Views of a Line
In the case of a line, the auxiliary views of its end points are taken (according to the procedure described earlier for taking the auxiliary view of a point) and then connected in that view to form the auxiliary view of the line.
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42. Auxiliary Views of a Line
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True Length of a Line
The true length of a line of arbitrary orientation in threedimensional space can be obtained by viewing the line using a line of sight such that the plane which is perpendicular to the line of sight is also parallel to the line.
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True Length of a Line
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Point View of a Line
If a line is viewed in a plane that is perpendicular to the line, the resulting projection of the line on that plane is a point.
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Point View of a Line
A principal line is one that is parallel to at least one principal plane of projection. If a principal line is parallel to one principal plane and inclined with respect to the other two, then the projections of the line on these two planes will be parallel to the fold lines of these planes. For example, if a line is parallel to the horizontal plane and inclined to the front and profile planes, its front and profile projections will appear as horizontal lines. If a principal line is parallel to two principal planes, then the projection of the line on these planes will be parallel to the fold lines of these planes while its projection on the third plane will be a point because the third plane is perpendicular to the line.
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Point View of a Line
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Views of Planes
Planes
Horizontal, Frontal and Profile planes
Oblique and Inclined planes
Auxiliary Views of a Plane
Edge View of a Plane
Normal View of a Plane
True Size of a Plane
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Principal Planes
A principal plane is one that is parallel to a principal projection plane. There are three types of principal planes, namely horizontal, frontal and vertical.
For example, since the horizontal plane is parallel to the horizontal projection plane, its front view is a line parallel to the fold line H/F and its profile view is a line parallel to the fold line H/P.
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Principal Planes
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Principal Planes
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Principal Planes
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Vertical Planes
Vertical planes are planes perpendicular to the horizontal plane but can be inclined to the front and profile planes. The horizontal view of a vertical plane appears as a straight line.
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Vertical Planes
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55. Oblique and Inclined Planes
Oblique Planes – An oblique plane is one that is inclined to all three principal planes. An oblique plane will not appear as true size in any of the three principal views.
Inclined Planes – An inclined plane is one that is perpendicular to either the front or profile plane and is inclined to the other two.
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56. Oblique and Inclined Planes
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57. Auxiliary Views of Planes
Auxiliary views of planes are taken in the same manner as that discussed for lines earlier. In the case of a plane, the auxiliary views of the lines defining the plane when taken together constitute the auxiliary view of the plane.
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58. Auxiliary Views of Planes
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Edge View of a Plane
The edge view of a plane is the view that is obtained when the line of sight is parallel to the plane. The line of sight is parallel to a plane when it is parallel to a true length line that lies in the plane. Since the plane of projection of a view is always perpendicular to the line of sight of that view, it follows that a view drawn perpendicular to the plane (and as a consequence, perpendicular to a true length line that lies in that plane) shows that plane as an edge.
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Edge View of a Plane
To obtain the edge view of a plane that is oblique, it is necessary to obtain an auxiliary view of that plane using a line of sight that is parallel to the plane. To establish a line of sight that is parallel to this plane, it is necessary to obtain the true length view of a line that lies in this plane. The auxiliary view of the line in which the line appears as a point (the point view of the line) provides the edge view of the plane.
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Edge View of a Plane
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62. Normal View & True Size of a Plane
An arbitrarily oriented plane appears in its true size when it is viewed in a line of sight that is perpendicular to its edge view. Hence, the true size view of the plane is projected on a plane that is parallel to the edge view of the plane.
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63. Normal View & True Size of a Plane
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