9 Auxiliary Views - blogsRead a wide range of print and non-print texts to build an understanding of texts (NCTE) Mathematics Use visualization, spatial reasoning, and geometric modeling

9 Auxiliary Views

Chapter ObjectivesDetermine when an auxiliary view is required.Analyze the situ-ations in which a partial auxiliary view is required.Develop a primary auxiliary view.Project and draw an auxiliary section view using board-drafting techniques.Develop a second-ary auxiliary view using board-drafting techniques.

•

•

•

•

•

Section 9.1 Developing Auxiliary Views

Section 9.2 Drawing Secondary Auxiliary Views

Space Saver The Citation from the Pritzker Jury describes Gehry buildings as ‶juxtaposed collages of spaces.″ Explain how that description could be appropriate for his work.

304

Drafting Career

Frank Gehry has said that he is not a theorist but a vacuum cleaner. He listens. He looks. And then he re-presents with his tools. He thinks the blurring of the lines between art and architecture has got to happen. He fi nds the collaboration of the two much more interesting than each alone.

In presenting Gehry the Pritzker Architecture Prize

for Lifetime Achievement, the Pritzker jury noted “his sometimes controversial, but always arresting body of work, has been … described as iconoclastic [and] rambunctious.” However, the jury added, “One cannot think of anything he has done that does not make one smile.”

Academic Skills and AbilitiesMathPhysicsEnglishSocial studiesComputer useDrawing

Career PathwaysVisual orientation, creativity, computer literacy,

and the abilities to conceptualize and understand spatial relationships, communicate ideas visually to clients, and work independently and in a team are important for architects. They must have a bache-lor’s degree and complete a licensure examination.

••••••

Go to glencoe.com for this book’s OLC to learn more about Frank Gehry.

Frank Gehry, Architect

305Douglas Kirkland/Corbis

http://www.glencoe.com

9.1

Connect When the true size and shape of an inclined surface do not show on a drawing, you can make an auxiliary view or draw a revolution. How do auxiliary and revolution apply in this situation?

Content Vocabulary• auxiliary

view• auxiliary

plane

• primary auxiliary view

• partial auxiliary view

• edge view• reference plane

Academic VocabularyLearning these words while you read this section will also help you in your other subjects and tests.• elements

Graphic Organizer

On a chart like the one below, organize notes about auxiliary views and revolutions.

Go to glencoe.com for this book’s OLC for a downloadable version of this graphic organizer.

NCTE National Council of Teachers of English

NCTM National Council of Teachers of Mathematics

Academic Standards

English Language Arts

Read a wide range of print and non-print texts to build an understanding of texts (NCTE)

Mathematics

Use visualization, spatial reasoning, and geometric modeling to solve problems (NCTM)

Auxiliary Views Revolutions

Primary Secondary CAD

Developing Auxiliary Views

306 Chapter 9 Auxiliary Views


A

B

TOP VIEW

FRONT VIEW

FRONT VIEW

BOTTOM VIEWPARTIAL VIEWS

RIGHT-SIDE VIEW

RIGHT-SIDE VIEW

NORMAL VIEWS

AUXILIARY VIEWS

AUXILIARY VIEW IS PREFERRED

TRUE SIZE AND TRUE SHAPE

THREE NORMAL PLANES OFPROJECTION HINGED TOGETHER

PLANES UNFOLDED

H

H

VV PP

X

Y

X

YVERTICAL PLANE PROFILE PLANE

A B

C D

Primary Auxiliary ViewsWhy do technical drafters need to use auxiliary views?

When an object has an inclined surface, none of the normal views shows the inclined part in its true size and shape (see Figure 9-1A). However, a view on a plane parallel to the inclined surface does show its true size and shape (see Figure 9-1B). An auxiliary view is a projection on an auxil-iary plane that is parallel to an inclined sur-face (see Figure 9-2). It is a view that looks directly at the inclined surface in a direction perpendicular to it. Auxiliary views provide a clear image of the inclined surfaces on an object.

See Figure 9-3A for an anchor with a slanting surface. The three normal views are shown in Figure 9-3B. Not only are these views diffi cult to draw and understand, but also they show three circular features of the anchor as ellipses. In Figure 9-3C, the anchor is described completely in two views, one of which is an auxiliary view.

In Figure 9-4A, a simple inclined wedge block is shown in the normal views. In none of these views does the slanted surface (surface A) appear in its true shape. In the front view, the only thing that shows is its edge line MN. In the side view, surface A appears, but it is foreshortened. Surface A is also foreshortened in the top view. Line MN also appears in both views but appears shorter than its true length, which shows only in the front view. To show surface A in its true size and shape, you need to imagine an auxiliary plane parallel to it as in Figure 9-4B. Figure 9-4C shows the auxiliary view revolved to align with the plane of the paper. By following this method, you can show the true size and shape of any inclined surface.

Figure 9-1

Compare the information given in the normal views (A) with that given in the auxiliary views (B).

Figure 9-2

Basic relationship of the auxiliary plane to the normal planes

Section 9.1 Developing Auxiliary Views 307

TOP VIEW

FRONT VIEW

AUXILIARY VIEW

PERPENDICULAR

TO INCLINE

FRONT VIEW

RIGHT-SIDE VIEWNOT TRUE SIZE

THREE CIRCULAR FEATURESIN TRUE SIZE AND TRUE SHAPE

A

B

C

A

A

AUXILIARY PLANE

TOP PLANE

FRONT VIEW RIGHT-SIDE VIEW

X

BA

H

HW W D

M M

N

M

N

N

Y

X

TRUE SIZEAUXILIARY VIEW

D

C

X

PERPENDICULAR TOINCLINED SURFACE

A

A

A

A

A

A

I

Primary Auxiliary ViewsAuxiliary views are classifi ed according to

their origin and from which of the three nor-mal planes they are developed. A primaryauxiliary view is one that is developed directly from the normal views. There are three primary auxiliary views. Each is devel-oped by projecting the height, width, or depth obtained from a normal view as a pri-mary reference. See Figure 9-5 for the three primary auxiliary views.

When an auxiliary view is hinged on the front view, the view is a front auxiliary view. The primary reference of the front auxiliary view is depth. See Figure 9-5A for an exam-ple. An auxiliary view that is hinged on the top view is a top auxiliary view, as shown in Figure 9-5B. The primary reference of the top auxiliary view is the height of the object. Finally, a view hinged on the right-side view is a right-side auxiliary view. Its primary reference is the width of the object (see Figure 9-5C).

Partial Auxiliary ViewsIf you use break lines and centerlines prop-

erly, you can leave out complex curves and still describe the object completely (see Figure 9-6). An auxiliary view in which some elements have been left out is known as a partial auxiliary view. In Figure 9-6, a half view is suffi cient because the symmetrical (balanced) object is presented in a way that is easy to understand.

Figure 9-3

The pictorial view (A) and the three-view drawing (B) are diffi cult to draw. The auxiliary view (C) is easier to draw and describes the inclined surface completely.

Figure 9-4

Basic relationship of the auxiliary view to the three-view drawing


M

N

HINGED TOFRONT VIEW

HINGED TOTOP VIEW

M

NN

M

HINGED TO RIGHT SIDE

VVA

P

P

H

H

H

TOP AUXILIARYFRONT AUXILIARY RIGHT-SIDE AUXILIARY

PARTIAL

VIEW

V

A

A B C

D

H

W

FRONT VIEW

PARTIALAUXILIARY

VIEW

TOP VIEW

TOP VIEW

AUXILIARY SECTION

CUTTINGPLANE

A

A

Auxiliary SectionsSometimes it is useful to show a sectional

view of an object. When the cutting plane is not parallel to any of the normal views, the section is known as an auxiliary section. In Figure 9-7, the auxiliary section was located by

Figure 9-5

Three types of auxiliary views showing how the auxiliary plane is hinged

Figure 9-6

Partial auxiliary views provide a practical method for explaining details.

Figure 9-7

Drawing an auxiliary section is another way of explaining details clearly.

using the cutting plane line AA. See Chapter 8for more information about sections.

Describe What is the primary reference for the front auxiliary view?


LINE OFSIGHT

PARTIAL TOP VIEW

LEFT-SIDEVIEW

FRONTVIEW

X

Y

V1

2

VH 1

2

TOP VIEW

LEFT-SIDEVIEW

FRONTVIEW

1

2

1

2

DEPTHAUXILIARY

VIEW

A B C

Construction of a Primary Auxiliary ViewHow is the reference plane helpful in constructing primary and secondary auxiliary views?

To construct any primary auxiliary view, use the following steps, as illustrated in Figure 9-8. The method shown is for a front auxiliary view.

1. Examine and draw the normal views given for an inclined surface, as shown in Figure 9-8A.

2. Find the view that shows the edge viewgiven for an inclined surface. The inclined plane appears as a line in this view. The plane associated with this view is thereference plane—a plane that is paral-lel to an inclined surface and is used for creating auxiliary views—from which the auxiliary plane will be developed.

3. In this view, draw a light construction line at right angles to the inclined surface, as shown in magenta in Figure 9-8A. This is the line of sight.

4. Think of the auxiliary plane as being attached by hinges to the view from which it is developed (Figure 9-8B).

5. From all important points on the refer-ence view, draw projection lines at right angles to the inclined surface (parallel to the line of sight). In Figure 9-8, the important points are labeled 1 and 2.

6. Draw a reference line parallel to the edge view of the inclined surface and at a

convenient distance from it. The reference line is shown in magenta in Figure 9-8C.

7. Transfer the depth dimension to the ref-erence line.

8. Project the important points and con-nect them in sequence to form the auxil-iary view (see Figure 9-8C). If you labeled the points for reference, do not leave the labels on the fi nal drawing.

Drawing a View of a

Symmetrical ObjectFigure 9-9 shows how to make a primary

auxiliary view of a symmetrical object. In Figure 9-9A, the object is shown in a picto-rial view. Follow these steps:

1. Use a center plane as a reference plane, a plane that is parallel to an inclined sur-face and is used for creating auxiliary views (see Figure 9-9B). This is center-plane construction.

2. Find the edge view of the inclined plane. In Figure 9-9B, the edge view of this plane appears as a centerline, line XY, on the top view.

3. Label the points on the top view for reference.

4. Transfer these points to the edge view of the inclined surface on the front view, as shown in Figure 9-9B.

5. Parallel to this edge view and at a conve-nient distance from it, draw the line X′Y′(see Figure 9-9C).

6. In the top view, fi nd the distances from the numbered points to the centerline. These represent the depth measurement.

Figure 9-8

Steps to construct an auxiliary view.


2,3

1,4

6,5

4

2

3

6

5X Y

FRONT VIEW

1

CENTERPLANE

PARALLEL

Y

XI

I

CENTER PLANE

X

Y

4

2

3

6

5

1

2,3

1,4

6,5

4

2

3

6

5X Y

1

XI

2,3

1,4

6,5

42

3

6

51

D EBA

4

2

3

6

5X Y

1

2,3

1,4

6,5

I Y

XI

C

I YFRONT

I D2 D

I DI D

2 D

2 D

I DD2

I D2 D

I D2 D

TRUE SIZE AND SHAPE

FRONT VIEWLEFT-SIDE VIEW

VERTICALREFERENCEPLANE

VERTICALREFERENCEPLANE

A B

Y

X

D1

D1

D1

D2

D2

D2

D3

D3D3

TRUE SIZEAND SHAPE

Transfer them onto the corresponding construction lines you just drew, measur-ing them off on either side of line X′Y′(see Figure 9-9D). The result will be a set of points on the construction lines.

7. Connect and number the points on the construction lines (see Figure 9-9E) to fi nish the front auxiliary view of the inclined surface.

8. If desired, project the rest of the object from the center reference plane.

Explain What is the purpose of a reference plane?

Using a Vertical Reference PlaneFigure 9-10 shows how to draw a front aux-

iliary view of a nonsymmetrical object by using a vertical reference plane. Follow these steps:

1. Place the object on reference planes (see Figure 9-10A). These planes are located strictly for convenience in taking refer-ence measurements. The vertical plane can be in front or in back of the object. In this case, it is shown in back.

2. Construct the view as described for sym-metrical objects except lay off the depth measurements D1, D2, and D3 in front of the vertical plane. Figure 9-10B shows the entire object projected onto the front auxiliary plane.

Figure 9-9

Steps in drawing an auxiliary view using the center-plane reference method

Figure 9-10

Drawing a front auxiliary view using a vertical reference plane.


D2

D2

H2

H2

W

W

W

W

6,5 TOP VIEW

D2

H2

30°

HORIZONALREFERENCE PLANE XY

FRONT AUXILIARY1

1

1

1

11

1

12

2

2

22

2

2

33

3

3

4

5

5 4

32

63,4

REFERENCE PLANE

X

X YY

FRONT

SIDE

LEFT-SIDE VIEW

Y I

X I

X I

BA

Using a Horizontal Reference PlaneFigure 9-11 shows how to draw a top aux-

iliary reference plane. The object is a molding cut at a 30° angle. Follow these steps:

1. Imagine a reference plane XY under the molding (see Figure 9-11A).

2. Find points 1 through 6 in the top and left-side views. In the top view, fi nd the edge line of the slanted surface.

3. Draw reference line X′Y′ parallel to it and at a convenient distance away.

4. From every point in the top view, proj-ect a line out to the line X′Y′ and at right angles to it.

5. In the side view, fi nd height measure-ments for the various numbered points by measuring up from XY. Lay off these same measurements up from X′Y′ along the lines leading to the corresponding points in the top view. Locate more points on the curve as needed to draw it accurately (see the following section, “Drawing Curves on Auxiliary Views.”) The result is a top auxiliary view with its base on line X′Y′ (see Figure 9-11A). Figure 9-11Bshows the same process. However, in this illustration, a vertical reference plane is used.

Drawing Curves on Auxiliary ViewsTo draw an auxiliary view of a curved line,

locate a number of points along that line. Figure 9-12 shows how to make an auxiliary

view of the curved cut surface of a cylinder. The cylinder is shown in a horizontal posi-tion. It has been cut at an angle, so the true shape of the slanting cut surface is an ellipse.

This auxiliary view is a front auxiliary view with the depth as its primary reference. To draw it, follow these steps:

1. Locating the vertical centerline XY in the side view (see Figure 9-12A). This line represents the edge of a center reference plane.

2. Locate a number of points along the rim of the side view (see Figure 9-12B). The more points you locate, the more accu-rate your curve will be.

3. Project lines from these points over to the edge view of the cut surface in the front view.

4. Parallel to this edge view and at a conve-nient distance from it, draw the new cen-terline X′Y′.

5. From the points you have located on the edge view, project lines out to line X′Y′and perpendicular to it. Continue these lines beyond X′Y′.

6. Find the depth measurements in the side view by measuring off the distances D1, D2, and so on between the centerline XY and the points located along the rim. Take these distances and measure them off on either side of X′Y′.

7. Draw a smooth curve through the points marked to form the ellipse as shown.

Figure 9-11

Drawing (A) a top auxiliary view with a horizontal reference plane and (B) a front auxiliary view using a vertical reference plane.


YY

Y

X

X

X

BSIDE VIEWFRONT VIEW

A

12

3

4

5

1

2

3

4

5

5

4

3

21

YI

LOCATE X YCONVENIENTDISTANCE ANDPARALLEL TO X Y

I IX I

1D2D

1D2D

.76

.881.50

.76

.50

.62

.32.28

.50

135°

.38

PICK THESE TWO POINTSTO CREATE THE FIRSTCONSTRUCTION LINE

Summarize Explain how to draw a front auxiliary view of an asymmetrical object using a vertical reference plane.

Developing a Primary Auxiliary View in CADHow does the CAD technique apply principles discussed earlier for developing a primary auxiliary view?

Figures 9-13 through 9-18 show the pro-cedure for creating an auxiliary view using AutoCAD. Follow these steps:

1. Create the front and side views and a partial top view (see Figure 9-13). Do not dimension the views.

2. Create a construction line (XLINE com-mand) perpendicular to the line that rep-resents the inclined plane at the lower end of the inclined line in the front view. To do this, pick the two endpoints of the short end line (see Figure 9-14).

3. Copy the construction line to each important point in the front view. See Figure 9-15.

4. Copy the inclined line to another location on the construction lines (see Figure 9-16). Use the Nearest object snap to ensure that the endpoint of the inclined line is on the lowest construction line.

5. Offset the line you created in step 4 to the right by the depth dimension, .76

Figure 9-12

Drawing a curve (in this case, an ellipse) in an auxiliary view about the centerline of the cut surface of a cylinder

Figure 9-13

Steps to draw an auxiliary view using AutoCAD.

Figure 9-14

Figure 9-15


.76(Figure 9-16). This defi nes the depth of the object in the auxiliary view.

6. Trim the construction lines to form the other boundaries of the auxiliary view. Use the Layer Control above the drawing area or on the Dashboard to move the lines to their appropriate layers: Hidden, Centerline, and so on (see Figure 9-17).

7. Add the other centerline, the hole, and other details based on the dimensions given in Figure 9-13. The fi nished drawing should look like the one in Figure 9-18.

Section 9.1 AssessmentAfter You Read

Self-Check 1. Explain when an auxiliary view is

required. 2. Describe the situations in which a

partial auxiliary view is acceptable. 3. Outline the steps to develop a primary

auxiliary view using board-drafting techniques.

4. Describe how to create a primary auxiliary view using CAD.

Academic IntegrationEnglish Language Arts

5. The Industrial Revolution paved the way for modern business and industry. Using the Internet or library, research the Industrial Revolution and write three paragraphs that summarize the impact of the Revolution on people’s lives and how it changed agriculture, transportation, and manufacturing.

Drafting Practice 6. For Figures 9-19 and 9-20, only the

top view is given. Draw the top and front views and either complete the auxiliary view or just the inclined sur-face, as directed by the instructor. The total height of each front view is 3.75″.

Figure 9-19

Go to glencoe.com for this book’s OLC for help with this drafting practice.

.50

.50 1.002.00 SQ

1.00

.50

2.00

1.00.50

2.00

Figure 9-20

Figure 9-16

Figure 9-17

Figure 9-18



Preview Secondary auxiliary views can be used to show the true size and shape of a surface that lies along an oblique plane. Skim this section and write down the defi nitions of the content vocabulary terms secondary auxiliary view and oblique plane.

Content Vocabulary

• secondary auxiliary view • oblique plane

Academic VocabularyLearning these words while you read this section will also help you in your other subjects and tests.• inclined • projected

Graphic OrganizerUse a list like the one here to organize notes about drawing secondary auxiliary views using CAD techniques.

9.2 Drawing Secondary Auxiliary Views

Go to glencoe.com for this book’s OLC for a download-able version of this graphic organizer.

Academic Standards

English Language Arts

Use spoken, written, and visual language to accomplish their own purposes (e.g., for learning,

enjoyment, persuasion, and the exchange of information) (NCTE)

Mathematics

Problem Solving Build new mathematical knowledge through problem solving (NCTM)

Geometry Analyze characteristics and properties of two- and three-dimensional geometric

shapes and develop mathematical arguments about geometric relationships (NCTM)

NCTE National Council of Teachers of English

NCTM National Council of Teachers of Mathematics

Six Steps in Drawing Secondary Auxiliary Views

1.

2.

3.

4.

5.

6.

Section 9.2 Drawing Secondary Auxiliary Views 315


1D

1D

2D

2D

FIRST AUXILIARY VIEW

SECOND AUXILIARY VIEW

1

1

2

2,1

2

2

2

3

3

3

3

4

44

4 4

4

3

33

1

1 11 1

A

B

4

SECOND AUXILIARYTRUE SIZE AND TRUE SHAPE OF PLANES 0-1-2

FIRST AUXILIARYEDGE VIEW OF 0-1-2

OCTAHEDRON

0 0

0

0

0

0

0

4

4

4

1

1

11

1

2

2

22

2

3

3

3

1,3

2,1

3,4

2,4

X X

X

X

2

2

'

'

A

B

Secondary Auxiliary ViewsWhy must you understand the development of a primary auxiliary view before you can draw a secondary auxiliary view?

A view projected from a primary auxiliary view is called a secondary auxiliary view. It is used to fi nd the true size and shape of a surface that lies along an oblique plane. An oblique plane is one that is inclined to all three of the normal planes.

In Figure 9-21, surface 1-2-3-4 is inclined to the three normal planes. In Figure 9-21A, a fi rst auxiliary view has been drawn. It is on a plane perpendicular to the inclined surface. Note that, in this view, points 1, 2, 3, and 4 appear as a line or edge view of the plane. In Figure 9-21B, a secondary auxiliary view has been drawn from the fi rst auxiliary view and is on a plane paral-lel to surface 1-2-3-4. This secondary view shows the true shape of the surface.

Figure 9-22 shows an example of an octahedron (eight triangles making a regular solid) in three views. Triangle surface 0-1-2 is inclined to all three views. In Figure 9-22A,

a fi rst auxiliary view has been drawn. It is on a plane perpendicular to triangle surface 0-1-2. Note that line 1-2 in the top view appears as point 1-2 in this auxiliary view and that the triangle now appears as an edge line 0′-1-2. In Figure 9-22B, a secondary auxiliary view has been drawn. It is on a plane parallel to the edge view of triangle surface 0′-1-2 in the fi rst auxiliary view. This secondary auxiliary view shows the true shape of triangle 0-1-2.

Explain What is the purpose of a secondary auxiliary view?

Constructing a Secondary

Auxiliary ViewBefore you begin to draw a secondary aux-

iliary view, you must fi rst clearly understand the development of a primary auxiliary view.

Figure 9-21

A secondary auxiliary view assists in fi nding the true shape of surface 1-2-3-4.

Figure 9-22

A secondary auxiliary view is needed to develop the true shape of a triangular surface on this octahedron.


As mentioned earlier in the chapter, a second-ary auxiliary view is projected from a primary auxiliary view. Notice in Figure 9-23 that only partial front and top views are drawn initially. The auxiliary views will be used to complete these views.

To construct a secondary auxiliary view of the part shown in Figure 9-23A, follow these steps:

1. Draw partial front and top views (see Figure 9-23B). Be sure to allow suffi -cient space to complete these views later.

2. Project lines perpendicular to the inclined line in the top view and draw the primary auxiliary view (see Figure 9-23C).

3. Project lines perpendicular to the auxil-iary surface of the primary auxiliary view and draw the second auxiliary view (see

Angles of RotationBy default, AutoCAD rotates objects counterclockwise.

At what degree should the angle be entered if an object is to be rotated 45°?

Recall that angles in AutoCAD can be specifi ed up to 360°, as shown in the fi gure. Therefore, you can determine the correct angle to enter by subtracting 45 from 360 to get 315. If you enter a rotation value of 315°, AutoCAD will rotate the view correctly.

There is an easier way, however. To specify an angle of rotation in a clockwise direction, simply change the sign of the angle. Instead of entering 45°, enter –45°. The effect is the same as entering a positive angle of 315°.

180°315°

0°

270°

90°

45°

360– 45315

For math help, go to the Math appendix located at the back of this book.

Academic Standards

Mathematics

Geometry Analyze characteristics and properties

of two- and three-dimensional shapes and develop

mathematical arguments about geometric relationships

(NCTM)

Center-Plane Construction

One way to use the vertical con-struction line you created in step 5 is to use it as a centerline. Notice in the top view that the object is vertically and horizontally symmetrical. There-fore, you can use the center plane, represented by a centerline, as the basis for constructing the revolved view. Simply off set the centerline to the right and left at the appropriate distances to create the object lines. This method is known as center-plane construction.


SECONDARYAUXILIARY VIEW

PRIMARY AUXILIARY VIEW

SECONDARY AUXILIARY VIEW

THE PART

120°15°

75°

B DRAW PARTIAL TOP

AND FRONT VIEWS

PRIMARY AUXILIARY VIEW

C DRAW THE PRIMARY AUXILIARY VIEW

90°

SURFACE M

D DRAW THE SECONDARY

AUXILIARY VIEW

SURFACE N

A

F COMPLETE THE FRONT VIEW

ED

G ADD DIMENSIONS AND NOTES TO THE DRAWING

4.90

I.252.25

2.00

4.506.50

I.00

I.50

75°

HEXAGONI.50 ACRFLT

3.50

2.25

2XØ.531

.75

I20°

I5°

NOTE: MANY UNNECESSARYHIDDEN LINES ARE OMITTEDFOR CLARITY.

.62

TRUE SIZE AND SHAPE

E COMPLETE THE TOP VIEW

D

C

B

B

A

A

E

C

TRUE SIZE AND SHAPE

Figure 9-23

Steps in drawing a secondary auxiliary view


Revolving Solid ModelsIn practice, many companies create solid

models instead of orthographic drawings of parts or objects that contain oblique sur-faces. These models can be revolved using AutoCAD’s ROTATE or ROTATE3D command to show the true size and shape of an oblique surface. The advantage of using solid models is that they do not require you to draw extra views. You can revolve the model to show all of the necessary views, including normal views and auxiliary views that show the true size and shape of an oblique surface.

Section 9.2 AssessmentAfter You Read

Self-Check 1. Describe how to develop a second-

ary auxiliary view using board-drafting techniques.

Academic Integration 2. Finding Surface Area Rudy is designing a pool for a client.

The client would like to know the sur-face area of the pool if Rudy’s design would make a pool 12 feet in diameter, with a height of 4 feet.

Calculating Surface Area

To fi nd the surface area for a cylinder, fi nd the area of the base, and add the area of the face.

Drafting Practice 3. Draw the front, top, and complete aux-

iliary views, as shown in Figure 9-24. Then change the angle of incline to 45°. Is there any difference in the solution?

Go to glencoe.com for this book’s OLC for help with this drafting practice.

Figure 9-24

2.00

5.00

.75

1.00

R L2.00

R

L3.75

30°

RL = REFERENCE LINE

12 ft.

4 ft.

Figure 9-23D). Notice that the top edge of the secondary auxiliary view is parallel to surface N.

4. Complete the top view by projecting lines from the primary auxiliary view (see Figure 9-23E).

5. Complete the front view by projecting lines from the top view and distances, such as D and E, from the primary auxil-iary view (see Figure 9-23F).

6. Darken all lines and add dimensions and notes to complete the drawing (Figure 9-23G).



Chapter Summary

9

Section 9.1 An auxiliary view is required to solve problems involving inclined surfaces.A partial auxiliary view is acceptable when some curves can be left out but the object is still described completely.A primary auxiliary view is one that is developed directly from the normal views. Secondary auxiliary views are projected from primary auxiliary views.Drawing an auxiliary section is another way to explain an object’s details.Auxiliary views are developed by revolv-ing the plane of projection.The creation of an auxiliary view in CAD is similar to that used in board drafting but can be done in less time because the CAD software automates many of the more time-consuming tasks.

•

•

•

•

•

•

Section 9.2 A view projected from a primary view is a secondary auxiliary view. It is used to fi nd the true size and shape of a surface that lies along an oblique plane. An oblique plane is one that is inclined to all three of the normal planes. The steps used to construct a secondary auxiliary view are to draw partial and top views; project lines perpendicular to the inclined line in the top view and draw the primary auxiliary view. Then project lines perpendicular to the auxiliary surface of the primary auxiliary view and draw the second auxiliary view. Complete the top view by projecting lines from the top view and distances. Darken all lines and add dimensions and notes to complete the drawing.

•

•

•

Review and Assessment

Review Content and Academic Vocabulary 1. Use each of these content and academic vocabulary terms in a sentence or drawing.

Content Vocabulary auxiliary view (p. 307) auxiliary plane (p. 307) primary auxiliary view (p. 308) partial auxiliary view (p. 308)

••••

edge view (p. 310) reference plane (p. 310) secondary auxiliary view (p. 316) oblique plane (p. 316)

•••

•

Academic Vocabulary elements (p. 308) inclined (p. 316) projected (p. 317)

•••

Review Key Concepts 2. Explain how to determine when a full auxiliary view is required. 3. Analyze the situations when a partial auxiliary view is required. 4. List the steps to develop a primary auxiliary view using board-drafting techniques. 5. Develop a primary auxiliary view using CAD techniques. 6. Create a secondary auxiliary view using board-drafting techniques.


Short-Answer QuestionsDirections Answer the follow-ing questions in one to three sentences. 10. What is an axis of revolution? 11. How should you place an auxiliary

plane in relation to the inclined sur-face it describes?

Technology 7. Trend Analysis

Have you ever heard a classmate or friend use the word ‶trendy″ to describe a new hair-cut or a hot new singer? You may have also heard or used the word ‶trend″ or ‶trendy″ to describe an especially popular clothing style. In business and industry, trend analysis is a concept that product developers use when developing new products for the market-place. Using the Internet or library, research the term trend analysis and write a one-page summary that defi nes the term and gives spe-cifi c examples of how trend analysis has been used in the development of current and future products and technologies.

8. 21st Century Tools: CommunicationElectronic mail, or e-mail, is one of the

most important methods of communication in today’s workplace. Use the Internet to fi nd an e-mail provider, such as Gmail or Yahoo! Set up a personal e-mail account that you can use to send résumés and cover letters to pos-sible employers. Set up the address book to manage important professional contacts, and use the options features to create a profes-sional signature to attach to correspondence.

Mathematics 9. Calculating Age

Courtney wants to know the age of her brother’s wife. Her brother would only tell her that his wife is 1 __ 8 of their mother’s age younger than he is. If Courtney’s mother is 64 and her brother is 35, how old is her brother’s wife?

Algebra

Some problems can be made easier if you write an equation. An equation can be thought of as a sentence that explains how to solve a problem. The unknowns can be repre-sented as letters such as x or y.

Prep For

TEST-TAKING TIP

When you sit down to take a math test, jot down on your scrap paper important equations or formulas that you are trying to remember. This way, you will not worry about forgetting them during the test.

Win Competitive Events

12. Total Quality Management Organizations such as SkillsUSA offer a

variety of architectural, career, and draft-ing competitions. Completing activities such as the one below will help you pre-pare for these events.

Activity Work with a partner to defi ne Total Quality Management (TQM). What is the goal of TQM? How does TQM relate to customer satisfaction? How might it affect your mechanical drawing projects? At what stage of your project would you apply TQM? Create a fact sheet about TQM and its effect on the profession of drafting.

Go to glencoe.com for this book’s OLC for more information about competitive events.

Review and Assessment 321


1.00 SQ

2.00 SQ

A

.502.00

1.50

1.00

.50

.50

B

2.00

1.00

45°

C

45°

2.00

45°

2.00

D

2.00

2.00

30°

30°

2.001.50

2.00

1.50

60°

60°

E F

2.00 2.00

2.00

1.00

45°

G H

2.002.00

1.00

.50

1.00 .50

30°

.50 .501.75

R1.00

I J

R1.001.00

.50

1.00

.50

K

2.00

L

Problems9

Drafting ProblemsThe problems in this chapter can be performed using board drafting or CAD

techniques. The problems are presented in order of diffi culty, from least to most diffi cult.

1.

For each object in Figure 9-25, only the top view is given. Draw the top and front views and either complete the auxiliary view or just the inclined surface, as directed by the instruc-tor. Figure 9-26 has been developed as an example. The angle X in Figure 9-26 may be 45° or 60°, as assigned. The total height of the front view is 3.75” for Figure 9-25A through 9-25L.

Figure 9-25


X = 45°

2.25

2 SQ

D

D

2.25

3.75

.50

.75

.50

.50 1.00

1.00

3

3

6

6

7

7

8

8

22

1

1

4

4

5

52,3

1,8

7,6

5,4

X

50

24 SQ 50 Ø24R24

12

R18

48

36

12

R36

48

36

R36R36

A B C D E

1.50

.75

.50

1.50.50.50

2.00

A

SLOTTED GUIDE

TRACK WEDGE

B

2.00

1.25 1.25 .75 1.00 .75

Figure 9-26

Example for problem 1

2.

For each object in Figure 9-27, only the top view is given. Draw the top and front views and either complete the aux-iliary view or just the inclined surface, as directed by the instructor. The height of each object is 95 mm.

For problems 3 through 6, draw the views according to the instructions given for each problem.

3.

Draw the front, top, and side views and the front auxiliary projection of the object shown in Figure 9-28. Then change the angle of the inclined surface to 30° and redraw the problem.

4.

Draw the front, top, and side views and the front auxiliary projection of the object shown in Figure 9-29. Then change the angle of the inclined surface to 45° and redraw the problem.

Figure 9-27

Figure 9-28

Figure 9-29

METRIC

Problems 323

48

110

32

24

45°

48

R L

72

RL = REFERENCE LINE

45°

2.00

4.25

1.25

2.00

30°

60°1.00

2.26

4.25

2.25

1.50

1.38

.44

.75

30°

R1.502.00

3.25

2.25

2.00

45°

R12

48

12

12

48

82

58

45°

A B C D E

4.75

A

ANGLE

TOP VIEW

RIGHT SIDE

1.38

REFERENCE PLANER1.12

1.75

REVERSE MOLD GUIDE R

R

TRUE SIZETRUE SHAPE

Problems9

5. Draw the front, top, and complete auxiliary views, as shown in Figure 9-30. Then change the angle of incline to 30°. Is there any difference in the solution?

Figure 9-30

Figure 9-31

6. Draw the front, top, and auxiliary views of the object shown in Figure 9-31.


3.88 1.20

A

1.94

.8060°

30°

.25

.25

2.06

SLOTTED LOCK BLOCK

1.75

2X .50

R.88 2X .75

4.00

1.62

1.62

1.00

1.00

3.00

6.00

2.88

3.75

R.62

R.12

1.62 60°.62

1.501.00

.38 ANGLE PLATE

.50

60°

1.50

1.50

1.00

2.00.88

O

O

1.00

7. Develop the three views of the object shown in Figure 9-32. Draw angle A at 45° and develop the top auxiliary projection.

Figure 9-32

8. Determine the views necessary to complete the front auxiliary view of the object shown in Figure 9-33. Develop views with angle A = 60°. Alternate problems may be assigned with angle A at 45° or 75°.

Figure 9-33

Problems 325

28

45

45

32

1812

90

R3

76

12

22R3

12

70

30°

28 28 28

90

O16, 4 HOLES

O76O48

R10

ACROSSFLATS

OF OCTAGON

2.75TO BORDER

5.38TO BORDER

3.62TO BORDER

NOTE: FILLETS AND ROUNDS R.10

2.25

.25

.25

.50

.50 2.75

.50

.50

2.00

2.75

2.50

1.00

1.00

O

OO

3.00

3.50 2.00.50 .50

1.50R1.00

.75

3.0045°

.12.75.75

1.25

Problems9

9. A partial front view, a right-side view, and a partial auxiliary view of an angle cap are shown in Figure 9-34. Draw the views given and another auxiliary view where indicated on the layout. This will be a rear auxiliary view. Dimensioning is required.

Figure 9-35

Figure 9-34

10. Figure 9-35 shows a pictorial and layout of an inclined locator. The complete view in the middle is the right-side view. Draw the complete view and the partial views as necessary. Draw an auxiliary view of the inclined locator, as indicated in the layout.


SURFACES MARKED TO BE 2ROUNDS AND FILLETS R2MATL–G1

62

50

76

45

75

30

6

20

38

12

76

12

5026

12

25

25

12

13

38

50

12

6

30

63

O20 SLOT

O4X 12

19

R12

2X 12O

4040

2X 14 SLOTSOO 38

CENTEREDON SURFACE

30

Teamwork

1. Work as a team to design an automatic pet food dispenser. Provide all the information necessary to manufacture the dispenser.

2. Design a desk caddy to hold a hand-held calculator, paper clips, 77 mm diameter insert clock, and a 75 mm × 125 mm notepad. The clock should be set at an angle for easy reading.

3. Design a device to store and dispense up to 50 plastic grocery bags. The bags should be inserted at the top and removed from the bottom, one at a time. Design it to hang on a wall.

4. Design a cup rack to display up to 20 col-lectable cups. The rack can be either a wall unit or a counter-top unit.

Design ProblemsDesign problems have been prepared to challenge individual students or

teams of students. In these problems, you should apply skills learned mainly in this chapter but also in other chapters throughout the text. The problems are designed to be completed using board drafting, CAD, or a combination of the two. Be creative and have fun!

11. The engineers in your company have redesigned the connecting bar shown in Figure 9-36to be used on a new tractor hitch. Use the drawing setup shown and make all the design changes the engineer marked in color on the pictorial drawing. Draw front, top, and two auxiliary views. Include all shape and size information necessary for the manufacture of the part. Scale: 1:1.

Figure 9-36

Problems 327

Documents

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