Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

1. Engineering 22 AuxiliaryViews-2 Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Chp7 Goals • To Develop The Skill to Generate Views That Show Inclined And NonOrthographic (Oblique) Surfaces In TRUE Shape In Multiview Drawings • To Be Able to Integrate into Standard OrthoGraphic Drawings these AUXILIARY VIEWS to Clarify the Description of The Object • Find the TRUE SHAPE of Oblique Surfaces

3. Successive Auxiliary Views • Recall Uses for Auxiliary Views • True Length of a Line • Point-View of a Line • View a line from an End • Edge View of a Plane • View a Plane on Edge • True-Size/Area View of a Plane • ALL of the Above Found by the USE of SUCESSIVE Aux Views

4. Construction of Successive AuxVs • KEY to Successive Aux View Construction → Recognize That Fold Lines on EITHER EDGE of the Projection Plane Contain COMMON DISTANCES • In Fig at Left Note the Distance Xfer fromthe Hinge Lines Primary AuxV ALTERNATINGDistance-XFER Secondary AuxV

5. B Construct AuxV Step-by-Step • Consider Pt-1 with Secondary Aux Views Projected from All Three Principal Planes

6. Determine LoS for Aux View-A In Practice This is Done to Reveal Significant Information This Example is Only Illustrative Draw Fold Line (FL) H/A That is  to the LoS. CHOOSE Dist (D4) From Point 1H Extend from Pt 1H a  construction line into “A Space” B Step-by-Step: 1H → 1B 3 2

7. Using Acad DIST & OFFSET, Transfer Dim D1 from FrontV into Aux ProjPlane A along the  Construction Ln Determine the LoS for the 2nd Aux. View Draw Fold Line (FL) A/B That is  to the LoS. Place at any convenient distance From Point 1A 4 B 4 Step-by-Step: 1H → 1B cont 6

8. Extend from Pt 1H a  construction line into “B Space” Using DIST & OFFSET Transfer Dim D4 from TopV into Aux ProjPlane B Along the  Construction Ln This then Establishes the Location of the Desired Pt, 1B 8 B 8 Step-by-Step: 1H → 1B cont.2 7

9. Principal Lines • Characteristics • TRUE LENGTH in ONE of the Principal Views • PARALLEL to the Ref-Plane Line(a.k.a. Folding Line) in the OtherPrincipal Views • Frontal Line → TL in FRONTAL-Space • Horizonal Line → TL in Top-Space • Profile Line → TL in Profile-Space

10. Use of Principal Lines • Principal Lines are Always Parallel to one of the RP or FL lines; and TL in the ADJACENT View • This suggests that we Can find a TL Line by One of • Making a FL/RP Line Parallel to a Given Line • Drawing a Line that is Parallel to a Given FL/RP Line

11. Example – Oblique Distance • Given F&H Views at Right showing • 10 mm Tube, rk • 15 mm sphere at m • Determine the TRUE Clearance Between These Physical Objects

12. Example – Solution Plan • Since m is a BALL it appears in TRUE SIZE in ANY View • Thus Need to Construct the END VIEW of the Cylinder rk which will Appear as a Circle; i.e., want POINT-V for Line rk • Can then measure the Center-to-Center distance

13. Example – Solution (1) • Need TL view of rk • From TopV, Strike FL H/1 || to rHk • Extend in 1-Space  Construction Lines • In Prep for Distance Measurement Transfer, Set FL F/H 2 1 3

14. Example – Solution (2) • Measure Xfer Distances in F-Space • Transfer Distances to 1-space to Locate Pts on the Construction lines • Label Points • Draw AuxV1 showing • Sphere • TL Tube 7 True Length 6 5 4

15. Example – Solution (3) • Now need END VIEW of the CenterLINE of the Tube • LoS for AuxV2 || to CenterLINE • Draw FL 1/2  to CenterLine • Extend Construction Lines into 2-Plane • Measure Xfer Distances in H-Space True Length 8 9 10

16. Example – Solution (4) • Xfer Distances from H-Space to 2-Space • Label Points in 2-Spc • Draw CIRCLES for • Sphere • END VIEW of Tube True Length 11 13 12

17. Example – Solution (5) True Length • Measure the Clearance as 14.4 mm 14 Q.E.F.

18. True Size Plane Can Show • The Shortest Distance Between a Point & a Line • A line & NonCollinear Pt DEFINE a Plane • The Angle Between 2 Intersecting Lines • Intersecting Lines DEFINE a Plane • Allows Construction of the Angle BiSector

19. Normal View of a Plane • Normal View Description A NORMAL or TRUE-SIZE-and-SHAPE (TS) View of a Plane is Obtained in Any View for Which The LoS is  to the Plane • On the Dwg Surface this LoS Appears  to the EDGE View of a Plane • Construction of the TS View for an Oblique Plane Requires 2 Aux Views

20. Construct TS of Oblique Surface 1 • Determine True Size of Oblique Surface 1234 • Recognize that In the H-View Lines 12 & 34 are || the H/F FL • Thus Lines 12 & 34 are TRUE LENGTH (TL) in the Front View (Frontal Space, or F-Space)

21. Construct TS of Oblique Surface 3 2 • Determine LoS-P that is parallel to a TL Line Contained in the Plane: e.g.; 12 or 34 • Strike FL F/1 that is  to LoS-P

22. 4 4 Construct TS of Oblique Surface • Construct Primary Aux View at FL F/1 For Surface 1234 to Establish an EDGE VIEW of the Oblique plane • Construction lines  to FL F/1 • Xfer Depth Dimensions from TOP View FL H/F

23. 7 7 Construct TS of Oblique Surface 6 5 • Locate LoS-S that is  to the EV of Surface 1234 • Strike FL 1/2 that is  to LoS-S • Xfer Dims from F-Space to 2-Space to Locate Pts 1-4 in the 2-Plane

24. Construct TS of Oblique Surface 8 • Connect the Dots in the 2-Plane to Reveal the TRUE Nature (Size & Shape) of the Oblique Surface

25. Example → EX7-49 • Find Plane-ABC in TRUE SIZE

26. EX7-49 Pln True Shape & SIZE • Make DG Layers

27. Acad.dwt Limits = 180, 120 Set up Grid for Axis Layer Zero Offset X → 55 Y → 40 Make Prototype Point P Circle Point (size = 2) Plane in True SIZE - 2 • Dimension Style “12_5X” at Overall Scale of 12.5X

28. Leader for Axes dtext to label Axes Use copy@ to Locate pts per table ddedit to change Point Labels Pline to Make Triangular plan HalfWidth = 0.25 Plane in True SIZE - 3

29. Construct Plane ABC in Frontal Space Line with Ortho, cen Label Points with Copy@ ddedit Plane in True SIZE - 4 • Grid F-Space, Label Points, Connect Dots, to Construct Plane ABC Front-View

30. In F-Spc Draw an Arbitrary HORIZONTAL line AD Must be “Level” in F-Space Ln-AD will be TL in H-Space Project Ln-AD into Horizontal-Space Plane in True SIZE - 5

31. Construct RPA1 by “Sighting Down” the TL line AD Copy, Rotate 90° Project into 1-Spc Perpendicular Projectors from pts A, B, C Line w/ per Plane in True SIZE - 6

32. Go “One View Back” to find distances for A, B, C in 1 space Dist or Dim Offset RPA1 by these distances to Grid 1-Space Next → connect Dots in 1-space to Form Pln ABC Plane in True SIZE - 7 • Should Show Pln-ABC as EDGE VIEW

33. Construct RPA2 PARALLEL to the Pln ABC EdgeView Draw  Projectors into 2-Space Go “One View Back” (H-Spc) to get Offset Distances Offset RPA2 to grid 2-Space Plane in True SIZE - 8

34. “Flip Up” the Plane Edge-View by Connecting the Dots in 2-Space This Reveals the Plane in TRUE Shape Now Recall from Prob: SCALE: 2:1 Plane in True SIZE - 9

35. Measure Plane in 2-space using Dim-Aligned Use area command to calc included Area Plane in True SIZE - 10 Specify next corner point or press ENTER for total: Area = 641.5139, Perimeter = 116.7742

36. Scale DOWN by 50% (2-DwgUnits = 1 RealUnit) Use area command to calc included Area Plane in True SIZE - 11 Specify next corner point or press ENTER for total: Area = 160.3785, Perimeter = 58.3871

37. Plane True Size/Shape Summary • Make two ADJACENT Aux views • Draw ARBITRARILY positioned PRINCIPAL line (Frontal, Horizontal, Profile) in one view • Project principal line into the ADJACENT Principal (H or F or P) view to show the Principle Line in TRUE LENGTH

38. Plane True Size/Shape Summary • Draw AuxV RPA1-line Perpendicular to the TL PrinLine • This essentially "sights down" the TL Line which resides IN THE PLANE • Project into 1-space Using -Projectors and Dims from “One View Back” to Show • TL line in POINT VIEW • Since TL line in the plane is in Pt-V, then the Plane is in EDGE View

39. Plane True Size/Shape Summary • Strike RPA2 line PARALLEL to the EV • Project into 2-Space to "flip-Up" the Edge-Viewed Plane • Reveals the plane in TRUE SHAPE

40. All Done for Today AuxilliaryViews

41. Engr/Math/Physics 25 Appendix  Time For Live Demo Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

42. Given Oblique-Line Angle RK and NK Find the Magnitude of the angle RKN Construct in the Frontal and Horizontal Plane the Angle BISECTOR Example – Oblique Line Angle

43. Strike F/H FL Need TL Line in F-Plane → Draw in H-space Line rHm that is || to F/H FL Project Into F-Space Ln point mH Draw TL FRONTAL Line rFm Example – Oblique Line Angle (1) 2 1 3 4

44. Strike F/1 FL That is  to Frontal Line rFm Extend into 1-Space  Construction Lines Transfers Dims from H-Plane to 1-Plane to Locate Points in 1-Spc Connect Dots to Reveal in 1-Space the EDGE-VIEW of Plane RKN Ln rFm in POINT-View Example – Oblique Line Angle (2) 7 7 8 6 5

45. Strike 1/2 FL That is || to EV Extend into 2-Space  Construction Lines Xfer Dims: F-Spc → 2-Spc Connect Dots to Show TRUE SIZE Pln r2kn 11 11 Example – Oblique Line Angle (3) 9 10 12

46. Working Now in the TS Plane; Plane-2 Use the Digital Protractor to Measure TRUE angle at 49.5° Example – Oblique Line Angle (4) 13

47. Working Again in the TS Plane; BiSect Angle nk2r Using k2 as Vertex Strike Arc at a Convenient Radius At intersections of Arc-14 and Lines nk2 and rk2 Strike arcs with the SAME Radius to Locate BiSection Pt-p R15  R14 Draw Angle BiSector Line k2p Example – Oblique Line Angle (5) 16 15 14 15 16

48. Project back Across the AuxV FL-Chain 2→1→F→H the BiSection Point-P Connect in All View Pts k&p to Exposethe BiSector Line Example – Oblique Line Angle (6) 18 17 17 17 18

49. Clean Up by Removing Intermediate Lines and Points Example – Oblique Line Angle (7)