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Unformatted text preview: 154 PART I Basic Drawing and Design BT
AT 4
CT
Dr T RL
F “U PROBLEM—TO DETERMINE
VISIBILITY OF LINES Fig. 734 Visibility of lines and surface by observation. 79 DISTANCES BETWEEN
LINES AND POINTS Distance from a Point to a Line When the front and side views are given, as in Fig. 735A,
and the shortest distance between line AB and point P is
required, the procedure is as follows: Step 1 Draw the Primary Auxiliary View 0 Draw reference line RL; at any convenient distance and
parallel to line r1535 shown in the side view. 0 Transfer distances designated as R, S, and U in the
front view to the primary auxiliary view. The resulting
line A18] in the auxiliary view is the true lenth of
line AB. Step 2 Draw the Secondary Auxiliary View I Next draw reference line RLJ at any convenient distance
and perpendicular to line AJBI. 0 Transfer distances designated as l/ and Win the side view
to the secondary auxiliary view, establishing points P3
and A382, the latter being the point view of line AB. 0 The shortest distance between point P and line AB is
shown in the secondary auxiliary view. Design Application Figure 'i36 illustrates the application
of the point—onpoint view of a line to determine the clear
ance between a hydraulic cylinder and a clip on the wheel
housing. The procedure is as follows: Step 1 Draw the Primary Auxiliary View 0 Draw reference line EL; at any convenient distance and
parallel to line A585 shown in the side view. BT
AT 4
CT
0T T
F 01:
Dr [Bl SOLUTION RLI ' Transfer distances R, S, and Tin the front view to the
primary auxiliary view, The resulting line 21.8; in the
primary auxiliary view is the true length of line AB. Step 2 Draw the Secondary Auxiliary View O Next draw the reference line ii’L;l at any convenient distance
and perpendiculzn to line A13. in the auxiliary view. 0 Transfer distances designated as Vand W in the side view
to the secondary auxiliary view, establishing points P3
and A383, the latter being the point view of line AB. 0 The minimum clearance between point P and line AB is
shown in the secondary auxiliary view. Shortest Distance between Two Oblique Lines When the front and top views are given, as in Fig. 737A on
page 156, and the shortest distance between the two lines AB
and CD is required, the procedure is as follows: Step 1 Draw the Primary Auxiliary View 0 Draw reference line RLZ at any convenient distance and
parallel to line AliBF shown in the front view. 0 Transfer distances R, S, U, and V in the top view to the
primary auxiliary view to establish lines A18. and CIDI.
The resultant line All}! is the true length of line AB. Step 2 Draw the Secondary Auxiliary View O Next draw the reference line at any convenient distance
and perpendicular to line AIB. shown in the primary
auxiliary view. 0 Transfer distances L. M, and N from the front view to the
secondary auxiliary view, establishing line C303 and the
point view of line A383. The shortest distance between
these two lines is shown in the secondary auxiliary view. RL [A] PROBLEM — TO DETERMINETHE
DISTANCE FROM A POINTTO A LINE PRIMARY
AUXILIARY RL2 VIEW STEP 1. DRAW THE PRIMARY AUXILIARY VIEW SHDHTEST DISTANCE SECONDARY SEELIARV «L POINT VIEW OF
I LINE A—B
A 232 PRIMARY
AUXILIARY
VIEW STEP 2. DRAWTHE SECONDARY AUXILIARY VIEW Fig. ?35 Distance from a1 point to a line. CHAPTER 7 Auxiliary Views and Revolutions
CLIP
F .
./ I
WHEEL HOUSING RLI {AI PROBLEMHTO FINDTHE DISTANCE
FROM A POINTTO A LINE PRIMARY
AUXILIARY
VIEW FIL2 STEP I. DRAWTHE PRIMARY AUXILIARYVIEW SECON DAIRY AUXILIARY VIEW MINIMUM CLEARANCE \ PRIMARY
AUXILIARY
VIEW STEP 2. DRAWTHE SECONDARY AUXILIARY VIEW Fig. 736 Design application of distance from a point
[0 a line‘ 155 156 PART 1 Basic Drawing and Design A
DT ><
c
T T
F
CF
AF
DF IAI PROBLEM—T0 FINDTHE DISTANCE
BETWEEN TWO LINES BT PRIMARY
AUXILIARY
VIEW c2 SHORTEST DISTANCE M SECONDARY
AUXILIARY
VIEW
STEP 2. DRAWTHE SECONDARY
AUXILIARY VIEW PRIMARY
AUXILIARY / VIEW STEP I. DRAWTHE PRIMARY
AUXILIARY VIEW Fig. 737 Shortest distance betwsen oblique lines. 710 EDGE AND TRUE VIEW OF PLANES The three primary planes of projection are horizontal, vertical
{or frontal), and profile. A plane that is not parallel to a primary plane is not
shown in its true shape. To show a plane in true view. it
must be revolved until it is parallel to a projection plane.
Figure 738A shows an oblique plane ABC in the top and
front views. The object is to find the true view of this plane.
When the top and front views are examined carefully. no
line is parallel to the reference line in either view. To ﬁnd
the edge and true views of these planes. the following steps
are used: c
AF F PROBLEM —TO FIND THETRUE
VIEW OFA PLANE PRIMARY 1;" A AUXILIARY
{S /...J_ VIEW .1 at2
EDGE VIEW or PLANE aec STEP . DRAW THE PRIMARY
AUXILIARY VIEW Fig. 7~38 Finding the true view of a plane. CHAPTER 7 Auxiliary Views and Revolutions 157 Step 1 Establish Point D on the Plane and Draw the
Primary Auxiliary View 0 Draw line C,D, on the top view. This establishes a line
parallel to reference line KLI. ' Project point 0, to the front view, locating point DF. The
line D;.C;. is shown in its true length. 0 Draw reference line KL: perpendicular to line DFCF in
the front view. 0 Project lines perpendicular to KL; from points AF. By.
C ,.. and 1),; to the primary auxiliary view area. II Transfer distances R. S. and U shown in the top view to
the primary auxiliary view area, establishing points all.
8.. and Cl. 0 Join these points with lines to establish the primary auxd
iliary view. The resulting line AIB. is the edge view of
the plane. Step 2 Draw the Secondary Auxiliary View 0 Draw reference line RL; at any convenient distance and
parallel to line (418.. II Draw reference line RL; at any convenient distance and
perpendicular to reference line RL; from points ,4]. B[.
C], and D] to the secondary auxiliary view area. 0 Transfer distances L. M. and N shown in the front view
to the secondary auxiliary view area. establishing points
A3, {33. C3. and DE. ' Join points £13.83, and C2 with lines. The true shape of
plane ABC is shown in this view. TRUE SHAPE OF PLANEABC seconoaav
AUXILIARY
STEP 2. DRAWTHE SECONDARY A
AUXILIARYVIEW / 2 WEW 158 PART 1 Basic Drawing and Design FIL AF
PROBLEM—TO SHOWTHE
LENGTH OF PIPE FROM ATO STEP 1' :Sgaﬁl'lell POINT C IN ITS TRUE SHAPE '32
secont A2 AUXILIA
VIEW STEP 2. DRAWTHE PRIMARY AUXILIARYVIEW STEP 3. DRAWTHE SECONDARY \ Fig. 739 Design application of true View ol‘ :1 plane AUXlLlARYVIEW for Fig. 738. Design Application Figure ?—39 shows the application of Step 1 Draw the Primary Auxiliary View
the procedure followed for Fig. 7—38. Points A, B, C. and D
correspond in both drawings, but line AC is omitted in
Fig. 7'69 since it serves no practical purpose in the design. 0 Draw reference line RL; parallel to line BFCF Show
the front View. I Project lines perpendicular to line [itCF from points
B,., C,., and D,. shown in the front View to the auxil Planes in Combination View Figure 7—40, demonstrates a solution in which a combination O Transfer distances E, F, G, and H shown in the topt
of planes is involved. Note that ATBTCT and AFBFCF form to the primary auxiliary View, establishing points Al.
one plane and BTCTDT and BFCFDF form another. Also, line C., and D1. BC is common to both planes. The objective in the problem 0 Join these points with lines to establish the print
is to find the true bends at the angles ABC and 3CD. The auxiliary View. The true length of line BC is short procedure is as follows. this View. CHAPTER 7 Auxiliary Views and Revolutions 159 CF
PROBLEM—To FIND THE TRUE LENGTHS
AND ANGLES OF PIPE ABCD PRIMARY AUXILIARY DI
VIEW STEP . DRAWTHE PRIMARY
AUXILIARY VIEW PRIMARYAUXILIARY 91' x /' /
VIEW , SECONDARY
/’ ,a’ AUXILIARWIEW I PHIMARVAUXILIAHY DI _..._———— L—'—'_'_'_""I
VIEW SECONDARY AUXILIARY VIEWI
STEP 2. DRAW THE SECONDARY AUXILIARY VIEW I TRUE
LENGTH TRUE ANGLE
‘Iuu—F' 3CD SECONDARY
Ba AUXILIARYVIEW3 A .
3 STEP 4. DHRWTHE SECONDARY AUXILIARY VIEW 3 SECONDARY
AUXILIARY ITdMJ ' [33 VIEW2 B I F‘FIIII"IIIIRII’IEIILIXILIAR‘I‘r DI
VIEW __ 2
SECONDARY “L4
AUXILIARY \IIEwI Ia—— 5
STEP 3. DRAWTHE SECONDARY AUXILIARY VIEW 2 Fig. 740 Use a!" pluncs‘ in L(II'I'IhiI'IaIiun. 160 PART 1 Basic Drawing and Design Step 2 Draw the Secondary Auxiliary View 1 0 Draw reference line RLy at any convenient distance and
perpendicular to line BIC. shown in the primary auxil
iary view. O Project lines parallel to line BICI from points AI, B], C],
and D. to the secondary auxiliary view 1 area. U Transfer distances J, K. and L, shown in the front view
of the secondary auxiliary view 1 area, establishing
points A3. BE, C3, and DE. 0 Join these points with lines to establish secondary aux
iliary view 1. This view shows line BC as a pointon
point view. The result is the edge view of both planes
ABC and BCD shown in this view. Step 3 Draw the Secondary Auxiliary View 2 0 Draw reference line RL4 at any convenient distance and
parallel to line {’1ng shown in the secondary auxiliary
view 1. 0 Project lines perpendicular to line AEB2 from points A3,
8;, C2, and D2 to the secondary view 2 area. 0 Transfer distances M, N, R, and 5 shown in the primary
auxiliary view to the secondary auxiliary view area,
establishing points A3, B3, C3, and D3. 0 Join these points with lines to establish secondary allx—
iliary view 2. ' Since any view adjacent to a point—on—point view of a
line must show the line in its trtre length, line BC is
shown in its true length in this view. Therefore, project—
ing perpendicularly from the edge view in secondary
auxiliary view 1 to the secondary auxiliary view 2 shows
not only the true length of lines BC and AB but also the
true angle of ABC. Step 4 Draw the Secondary Auxiliary View 3 0 Draw reference line RLS parallel to line C303 shown in
the secondary auxiliary view 1. 0 Project lines perpendicular to line C3D; from points Ag.
83, C3, and D3 to the secondary view 3 area. 0 Transfer distances M, N, R, and S shown in the primary
atrxiliary view to the secondary auxiliary 3 area, estab
lishing points Ag, 8;, C3, and D}. ' Join these points with lines to establish secondary aux
iliary view 3. 'I Since any view adjacent to a point—on—point view of a
line must show the line in its true length, line BC will
be shown in its true length in secondary auxiliary view
3. Therefore, projecting perpendicularly from the edge
views in secondary auxiliary view 1 to the secondary
auxiliary view 3 shows not only the true length of line
BC but also the true angle BCD. 711 ANGLES BETWEEN LINES
AND PLANES The Angle a Line Makes with a Plane The top and front views in Fig. 74l show a line UV passing
somewhere through plane ABC. The true angle between thr
line and the plane will be shown in the view that shows th:
edge view of the plane and the true length of the line. Thi
view is found as follows: Step 1 Draw a Line Parallel to Reference Plane Rh 0 Draw line AliDy in the top view parallel to reference linn
RLI.
0 Project point D; to the front view, locating point Dy. Step 2 Draw the Primary Auxiliary View * Draw reference line RLE at any convenient distance an
perpendicular to a Eine intersecting points A,_ and DFi
the front view. 0 Project lines perpendicular to reference line RL2 fnJi
points AF. By, C;., Up, and 14, shown in the front vier
to the primary auxiliary view area. I Transfer distances G, H, R, S, and T, shown in the to
view. to the primary auxiliary view area, establishiii
points Ul, V1, Al. BI, and Cl. 0 Join points UI to VI, and points A! to BI to Ci, to estal
lish the primary auxiliary view 1. 0 The point of intersection between the line and the edg
view of the plane is established. Project this point but
to the front view and then up to the top view to establis
the point of intersection of these two views. Step 3 Draw the Secondary Auxiliary View 1 0 Draw reference line Br:3 at any convenient distance at.
parallel to line ClB] shown in the primary auxiliary viei ' Project lines perpendicular to reference line BL} fret
points Al. BI, Cl. U], and VI, shown in the primary aur
iliary view, to the secondary auxiliary view 1 area. 0 Transfer distances D, E, L. M, and N from the front vie
to the secondary auxiliary view 1 area, establishir
points A3, 8;, C3, U3, and V3. C Join points A2, B2, and C2 to form the plane and jo
points U2 to V2 to form the line. 0 This view shows the true view of the plane and locatir
of the piercing point. Step 4 Draw the Secondary Auxiliary View 2 I Draw reference line RL4 at any convenient distance at
parallel to line ‘l/ZU2 shown in the secondary auxilia
view 2. 0 Project lines perpendicular from reference line Fl};1 frc
points A3, 3;. C1, V3, and U3 shown in the seconda
auxiliary view 1 to the secondary auxiliary view 2 are * Transfer distances W, X, and Y shown in the prima
auxiliary view to the secondary auxiliary view 2 are CHAPTER 7 Auxiliary Views and Revolutions 161 POINT OF
iNTE RSE CTION “T
3T
AT Dr
CT
v
RLI +—
F
V F
CF EDGE
VIEW OF
AF PLANE
Al POINT OF
POINT 0F / INTERSECTION
INTERSECTION
BF U F PROBLEM—TO FIND THE ANGLE STEP I. DRAWA LINE PARALLEL “1
A LINE MAKES WITH A PLANE TO REFERENCE PLANE RLI
PRIMARY AUXILIARY VIEW
STEP 2. DRAWTHE F’FIIIII‘IAR‘IIr
B UT AU XILIAFIY VIEW
T D V2 X_'—Iv3 F
A A
/\ 2 3
___
/ D M
“T h
i f M _H x RTHUEANGLE
' CF  POINT OF
AF CI INTERSECTION
I
‘ VI W 1 ‘ EDGEVIEW
or PLANE —w ' 
l E \._ \Bz B 3
U U3 SECONDARY
BF N 2/, _._ Y P AUXILIARYVIEW 2
a H N
H 3 / RL4 TRUE LENGTH
OF LINE L \ U SECONDARY
PRIMARY BI  RL AUXILIARY
HLZ AUXILIARYUIEW 3 VIEwI
STEP 3. DRAW SECONDARY STEP 4. DRAW SECONDARY
AUXILIARYVIEWI AUXILIARVVIEW 2
Fig. 741 The angle a line makes with a plane. establishing line U3V3 and the edge view of plane ABC. front views are given, the pointonpoint view of line AB and
This view shows the true length of line UV and the true the true angle between the planes are found as follows: angle between the line and edge view of the plane. Step 1 Draw the Primary Auxiliary View 0 Draw reference line RL; at any convenient distance and
. parallel to line AFB; shown in the front view.
Edge hues of Two Planes * Project lines perpendicular to reference line RL; from
Figure 742 on page 162, shows a line of intersection AB made points A,., BF, C F, and D1r shown in the front view to the
by two planes, triangles ABC and ABD. When the top and primary auxiliary view area. 162 Fig. PART I Basic Drawing and Design PROBLEM—TD FINDTHE EDGE
LINE OF TWO PLANES PRIMARY
AUXILIARY VIEW STEP I. DRAWTHE PRIMARY
AUXILIARYVIEW 742 Edge lines of two planes. Transfer distances R, S, and U. shown in the top view.
to the primary auxiliary view area. establishing points
Al. 8.. C], and 0.. Join these points to establish the primary auxiliary view.
The resulting line A113,, is the true length of line AB. PRIMARY
AUXILIARY ‘ 3
N
SECONDARY l
AUXILIARY
“'5‘” x 02 POINTVIEW
___. TRUE ANGLE OF UNEA B
C 2 BETWEEN PLANES
STEP 2. DRAWTHE SECONDARY
AUXILIARY VIEW Step 2 Draw the Secondary Auxiliary View Draw reference line EL3 at any convenient distance and
pErpendieular to line AIBI. Project lines parallel to line AIBI, from points A. C. and
.0 shown in the primary auxiliary view. to the secondary
auxiliary view area. Transfer distances L, M, and N. shown in the front view.
to the secondary auxiliary view, establishing points 21;.
8:, C3. and .03. Join these points with lines as shown. Point A383 is a point~onwpoint view of line AB. The true
angle between the two planes is seen in this view. ...
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 Spring '11
 LAOSIMKIM
 Distance, Euclidean geometry, Secondary Auxiliary View

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