1. Auxiliary views Descriptive geometry Section of solids Flóra Hajdu
B406

2. Content Auxiliary views Descriptive geometry
Section and intersection of solids
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3. Auxiliary views
Many machine parts have surfaces that are not perpendicular or at right angles to the planes of projection (sloping or inclined surfaces)
In regular ortographic views such surfaces appear to be distorted and their true shape is not shown
When an inclined surface has important characteristics that should be shown clearly and without distorsion an auxiliary view is used
Then the drawing completely and clearly explains the shape of the object
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4. Auxiliary views
In many cases the auxiliary view will explain one of the regular views
One of the regular orthographic views will have a line representing the edge of the inclined surface
The auxiliary view is projected from this edge line at right angles and is drawn parallel to the edge line
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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5. Auxiliary views
Only the true-shape feature on the views need to be drawn
The auxiliary view shows only the true shape and detail of the inclined surface or features a partial auxiliary view is all that necessary
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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6. Construction of auxiliary views
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Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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7. Construction of auxiliary views
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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8. Multi-auxiliary view drawings
Some objects have more than 1 surface not perpendicular to the plane of projection
An auxiliary view may be required for each surface
Depends upon the the amount and type of detail lying on these surfaces
Some objects require a secondary auxiliary view to show the true shape of the surface or feature
The surface or feature is usually oblique (inclined) to the principal planes of projection
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Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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9. Multi-auxiliary view drawings
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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10. Secondary auxiliary view
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
Secondary auxiliary view
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11. Revolved views
when the true size and shape of inclined surface do not in a drawing
Auxiliary view
Keep using the regular reference planes while imagining that the object has been revolved
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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12. Descriptive geometry
Major problem: find the true view of lines and planes
Solve engineering problems with geometric elements
Structures have 3D forms made up a combination of geometric elements
The graphic solution of 3D forms require an understanding of the space relations that points, lineas and planes share in forming any given shape
Problems that require mathematical solution can be solved graphically
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13. Points in space Normally identified by 2 or more projections scan
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14. Lines in space
Lines are grouped into 3 classes depending on how they are positioned in relation to the reference lines
Normal lines: perpendicular to the reference plane
Inclined lines: appear inclined in one plane
Oblique lines: appear inclined in all 3 views
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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15. True length of an oblique line
Place an auxiliary reference line RL3 to any parallel oblique lines
Transfer distances M and N shown in the regular views to the auxiliary view locating points A1 and B1
Join points A1 and B1 with a line
A1B1 is the true length of AB
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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16. Point on a line The line AFBF contains a point C
Poject construction lines perpendiculat to reference lines RL1 and RL2
The construction lines are projected to line ATBT and line ASBS
If C is to be located on the true lenght of line AB another reference line is required and the distances M and N are used to locate the true lenght of line A1B1 in the auxiliary view
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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17. Planes in space
Planes are considered to be without thickness and can be extended without limit
May be represented or detemined by intersecting lines, 2 parallel lines, a line and point, 3 points or a triangle
3 basic planes are identified by their relationship to 3 principal reference planes
Normal plane: surface appears in its true shape in the front view and as a line in the 2 other views
Inclined plane: the shape of the triangular plane appears distorted in 2 views and as a line in the other view
Oblique plane: shape appears distorted in all 3 views
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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18. Locating a line in a plane
Given triangular plane ABC and line RS
RS Line RTST crosses over lines ATBT and and ATCT at points DT and ET
Project points DT and ET down to the front view locating points DF and EF
Extend a line through points DF and EF
The length of the line can be found by projecting poits RT and ST to the front view locatong the end points RF and SF
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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19. Locating a point in a plane
Given triangular plane ABC and point R
Draw a line from AT passing through point RT to s point MT on line BTCT
Project point MT to front view locatong point MF
Join points AF and MF with a line
Project points RT to top view locating point RF
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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20. Locating the piercing point of a line and a plane
Given line UV passing through plane ABC
Locate points DT and ET
Project points DT and ET locating points DF and EF
Connect points DF and EF with a line
The instersection of lines DFEF is the piercing point
Project OF to the other view locating point OT
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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21. Locating the piercing point of a line and a plane
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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22. Establishing visibility of lines in space
Given 2 nonintersecting lines in space
Label the crossing of lines ATBT and CTDT as 1 and 2
Project the cossing point to the other view establishing point 1 on line AFBF and point 2 on CFDF
Point 1 on line AFBF is closer to the reference line, which means that line ATBT is visible
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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23. Visibility of lines and surfaces
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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24. Visibility of lines and surfaces
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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25. Distance from a point to line
Given front and side views. The shortest distance between line AB and point P is required
Draw the primary auxiliary view
Draw reference line RL2 at any convenient distance and parallel to line ASBS
Transfer distances designated as R, S and U in the front view to the primary auxiliary view. The resulting line A1B1 is the true lenght of line AB
Draw the secondary auxiliary view
Draw reference line RL3 at any convenient distance and perpendiculat to line A1B1
Transfer distances designatet as V and W in the side view to the secondary auxiliary view, establishing points P2 and A2B2
The shortest distance between point P and line AB is shown in the secondary auxiliary view
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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26. Shortest distance between 2 oblique lines
Given front and side views. The shortest distance between line AB and point P is required
Draw the primary auxiliary view
Draw reference line RL2 at any convenient distance and parallel to line AFBF
Transfer distances designated as R, S and U in the other view to the primary auxiliary view to establish lines A1B1 (true length of line AB) and C1D1
Draw the secondary auxiliary view
Draw a reference line at any convenient distance and perpendiculat to line A1B1
Transfer distances L, M and N from the front view to the secondary auxiliary view, establishing line C2D2 and the point view of line A2B2
The shortest distance between these 2 lines is shown in the secondary auxiliary view
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Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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27. The angle a line makes with a plane
Draw a line parallel to the perpendicular reference plane RL1
Draw the primary auxiliary view
Draw the secondary auxiliary view 1
Draw the secondary auxiliary view 2
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
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28. Edge lines of 2 planes
Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design
Given 2 planes ABC and ABD (intersection at line AB)
Draw the primary auxiliary view
Draw reference line RL2 at any convenient distance and parallel to line AFBF
Project lines perpendicular to reference line RL2 from points AF, BF, CF and DF shown in the front view to the primary auxiliary view
Transfer distances R, S and U shown in the top view to the primary auxuliary view area, establishing points A1, B1, C1 and D1
Join these points to establish the primary auxiliary view
Draw the secondary auxiliary view
Draw reference line Rl3 at any convenient distance and perpendicular to line A1B1
Project lines parallel to line A1B1 from points A, C and D shown the primary auxiliary view to the secondary auxiliary view
Transfer distances L, M, and N shown in the front view to the secondary auxiliary view, establishing points A2, B2, C2 and D2
Join these points with lines
Point A2B2 is a point-on-view of line AB, the true angle between the 2 planes is seen in this view
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29. Section of solids Pyramid cut by a plane Cylinder cut by a plane
Cone cut by a plane
Sphere cut by a plane
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30. Pyramid cut by a plane
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31. Cylinder cut by a plane
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32. Cone cut by a plane
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33. Sphere cut by a plane
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34. Intersection of solids
Prism and pyramid
Cone and cylinder
Cylinders with different diameter and position
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35. Intersection of prism and pyramid
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36. Intersection of cone and cylinder
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37. Intersection of cone and cylinder
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38. Intersection of Cylinders with different diameter and position
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39. Summary Auxiliary views Descriptive geometry
Points, lineas and planes in space
Section and intersection of solids
Next week: Basic dimensioning

40. Thank You for Your attention!