Auxiliary - 154 PART I Basic Drawing and Design BT AT 4 CT...

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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. 7-34 Visibility of lines and surface by observation. 7-9 DISTANCES BETWEEN LINES AND POINTS Distance from a Point to a Line When the front and side views are given, as in Fig. 7-35A, 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 'i-36 illustrates the application of the point—on-point 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. 7-37A 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 Ali-BF 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. 7-36 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. 7-37 Shortest distance betwsen oblique lines. 7-10 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 7-38A 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'lel-l POINT C IN ITS TRUE SHAPE '32 secont A2 AUXILIA VIEW STEP 2. DRAWTHE PRIMARY AUXILIARYVIEW STEP 3. DRAWTHE SECONDARY \ Fig. 7-39 Design application of true View ol‘ :1 plane AUXlLlARYVIEW for Fig. 7-38. 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 [it-CF 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 ‘I-uu—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 point-on- 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. 7-11 ANGLES BETWEEN LINES AND PLANES The Angle a Line Makes with a Plane The top and front views in Fig. 7-4l 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 Ali-Dy 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. 7-41 The angle a line makes with a plane. establishing line U3V3 and the edge view of plane ABC. front views are given, the point-on-point 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 7-42 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 7-42 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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This note was uploaded on 02/02/2012 for the course DRAW 101 taught by Professor Laosimkim during the Spring '11 term at University of Macau.

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Auxiliary - 154 PART I Basic Drawing and Design BT AT 4 CT...

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