Lecture 6 - Auxilliary Projections PDF

 LECTURE 6 [Summary on projection of Points, & Lines], & [Auxiliary Views] 1. Review of the Basic concepts for drawing projection of points  Basic concepts for drawing projection of points  Basic concepts for drawing projection of lines  Surface...

 LECTURE 6 [Summary on projection of Points, & Lines], & [Auxiliary Views] 1. Review of the Basic concepts for drawing projection of points  Basic concepts for drawing projection of points  Basic concepts for drawing projection of lines  Surfaces [normal, inclined or Oblique] 2. Auxiliary projections.  Purpose,  Types of auxiliary projections,  Methods of constructing auxiliary projections  Projection of points - SUMMARY The FV & TV of a point is always in the same vertical line, unless the POINT is in both the VP and HP The FV/pF of a point ‘p’ shows the position of the point with respect to HP and XY (reference) line If the point is above HP, pF is above the XY line. If the point is in the HP, pF is on the XY line. If the point is below the HP, pF is below the XY line. TV/pT of a point ‘p’ shows position of the point with respect to VP and XY (reference) line. If the point is in front of VP, pT is below the XY line. If the point is in the VP, pT is on the XY line. If the point is behind the VP, pT is above the XY line.  Projection of points - SUMMARY POINT a ABOVE HP POINT a ABOVE HP POINT a IN HP & IN FRONT OF VP & IN VP & IN FRONT OF VP For TV For TV For TV PICTORIAL PICTORIAL PRESENTATION a PRESENTATION aF aF a Y Y Y aF aT aT X aT X X a F or F or F or FV FV FV MULTI VIEW REPRESENTATIONS OF ALL ABOVE CASES. Fv above xy, Fv above xy, Fv on xy, Tv below xy. Tv on xy. Tv below xy. VP VP VP aF aF X Y X Y X aF Y aT aT aT HP HP HP  Projection of lines - SUMMARY  A line appears in True-Length if it is in a plane parallel to the projection plane  A line which is not parallel to the projection plane appears foreshortened  A line which is perpendicular to the projection plane appears as a point  A line parallel to a fold line will appear true length in the adjacent view  A true length line which is perpendicular to a fold line will appear as a POINT in the adjacent view  All views adjacent to a point view (PV) of a line will show the line in true length (TL)  A line which does not appear true length in any of the principal views is called an OBLIQUE line  Parallel lines do not have any common point between them  Parallel lines are seen as parallel in adjacent views  Parallel lines perpendicular to a FL, may (or may not) be parallel  To find out if lines are parallel, construct all 3 views Projection of lines - SUMMARY  Projection of lines - SUMMARY  Two intersecting lines are perpendicular if the TL projection is making 90° with the other projection bT 4T 1T TL 900 cT aT 3T 2T T T F 2F 4F F TL aF 3F cF 1F bT  2 lines; namely; , ,  3 lines; namely; , , , intersect in space. Since TL of intersect in space such that TL of , , is perpendicular & are perpendicular perpendicular to hence & , and & are  Projection of lines - SUMMARY  Two intersecting lines are perpendicular if the TL projection is making 90° with the other projection bT 4 1 900 cT aT 3 2 T 2 4 F aF 3 cF 1 bT  2 lines; namely; , ,  3 lines; namely; , , , intersect in space. Since TL of intersect in space such that TL of , , is perpendicular & are perpendicular perpendicular to hence & , and & are  Projection of lines - SUMMARY  Two intersecting lines are perpendicular if the TL projection is making 90° with the other line the figure show views of some lines in space. amongst others, p the views are not fully labelled. study the figure and answer the following 1.in what projection are the views giving your answer in numerals [Projection-in-Numerals] 2. what would be another way to designate HP [Alternative- r s Designation-for-HP] and VP [Alternative-Designation-for-VP] q HP 3. How many lines are there in space, giving your answer in numerals [Number-of-Lines-in-Space]? VP q r 4. Which of the views is TL, just one, [TL-line] 5. in alphabetic order, give the complete correct notations of the views located in HP (6 Marks) 6. also in alphabetic order, give the geometries of the views that s each of the original lines will project in PP (6 Marks) p pR-qR, qR-rR, qR-sR pR-qR will be a line, qR-rR will be point qR-sR will be a line  NORMAL SURFACES & LINES/EDGES 1. SURFACE A : is parallel to and a true size (TS) area in the FP. It is perpendicular to both the HP and PP, and thus appears as lines in those planes 2. Edge A: appears as true length (TL) lines in the FV and TV, & parallel to both FP & HP, but since the edge is perpendicular to the PP and it appears as a point view.  INCLINED SURFACES & LINES/EDGES 1. SURFACE A : is perpendicular to and an under-defined TL line in the FV, foreshortened in TV and RV, hence not true size (TS) or shape in any of the principal views/planes 2. Edge A: is a line in all three views; but because it is parallel to the FP, it is true length (TL) in the FV; but since it is at an angle to HP & PP, its TV & RV are foreshortened INCLINED SURFACES & LINES/EDGES…. Auxiliary Views Auxiliary Projections/Views Why Auxiliary View? Because  Inclined and  Dihedral angles (angles  Inclined or oblique Oblique planes & between -esp., inclined circular shapes Lines and oblique planes), DO NOT APPEAR TRUE IN ANY OF THE PRINCIPAL PLANES OF PROJECTION Auxiliary Views of TRUNCATED SOLIDS Triangle Ellipse ola rab Pa Hyperbola Ellipse Trapezium  Auxiliary Views: A TAXONOMY WHICH WHICH VIEW WHICH PLANE ARE ARE YOU DIMENSION YOU PROJECTING IS BEING PROJECTING PRIMAR FROM? FRONT ENHANCED? DEPTH FROM? Y AUXILI AUXILI AUXILI ARY ARY ARY SECON VIEW HEIGH TOP VIEW VIEW DARY T AUXILI AUXILI ARY AUXILI ARY VIEW ARY VIEW SIDE WIDTH VIEW TERTIA AUXILI AUXILI RY? ARY ARY VIEW VIEW  AUXILIARY VIEWS ACCORDING TO THE PLANE ON WHICH PROJECTION IS MADE AUXILIARY VIEWS ARE OF THREE GENERAL TYPES ACCORDING TO THE PLANE ONTO WHICH THE VIEW IS PROJECTED 1.PRIMARY AUXILIARY VIEWS: Primary auxiliary views are projected from one of the principal views onto a plane that is perpendicular to only one of the principal planes of projection and inclined to the other two. 2.SECONDARY AUXILIARY VIEWS: Secondary auxiliary views are projected from primary auxiliary views on to planes that are inclined to all three principal projection plane. 3.TERTIARY AUXILIARY VIEWS Are a single views projected from a secondary or another tertiary auxiliary view. INFORMATION IN MULTI VIEWS 1. FRONT VIEW: Height and Width (projected onto the Vertical Plane) 2. TOP VIEW: Width and Depth (projected onto the Horizontal Plane) 3. RIGHT SIDE VIEW: Depth and Height (projected onto the Profile Plane) DEPTH AUXILIARY VIEW HEIGHT AUXILIARY VIEW WIDTH AUXILIARY VIEW CONSTRUCTING AUXILIARY VIEWS THREE METHODS REFERE FOLD MITER NCE LINE LINE PLANE 1. REFERENCE PLANE METHOD 1. GIVEN  1. REFERENCE PLANE METHOD 2. CONSTRUCT A REFERENCE LINE Reference line  1. REFERENCE PLANE METHOD 4. TRANSFER THE DIMENSIONS 3. DRAW LIGHT PROJECTION LINES & ANOTHER REFERENCE LINE  2. FOLD LINE METHOD STEP 1: Draw fold line F-1 using a phantom line parallel to the edge view of the inclined surface STEP 2: Draw fold lines between the front and top, and front and right-side views – perpendicular to the projectors between the views and at distance X from the far edge of the views STEP 3: Project the length of the inclined surface from the front view to the auxiliary view perpendicular to the edge view  2. FOLD LINE METHOD STEP 4: Transfer the depth of the inclined surface from the top view to the auxiliary view (distance X from the fold line) STEP 5: From point C in the auxiliary view, draw a line perpendicular to the projectors. Depth dimension Y is transferred from the top view by measuring the perpendicular distance from the fold line to point A. This can then be transferred to the auxiliary view STEP 6: Darken the lines in the auxiliary view Note that only the inclined plane is shown in the auxiliary view. This is referred to as a partial auxiliary view. Also notice that Depth of shape is of the essence, hence the auxiliary view should of necessity be referred to as: DEPTH AUXILIARY VIEW 3. MITER LINE METHOD 3. MITER LINE METHOD 1. TRUE SHAPE OF OBLIQUE SURFACE USING THE FOLD LINE METHOD 30 2. TRUE SHAPE OF OBLIQUE SURFACE USING THE FOLD LINE METHOD 31 3. TRUE SIZE OF DIHEDRAL ANGLES FOLD LINE METHOD REIGNS SUPREME T.L. Line 1-2 T T Dim. D from front view Point view T T 1 & 2. 32 3. TRUE SIZE OF AN OBLIQUE LINE USING THE FOLD LINE METHOD 33 3. TRUE SIZE OF OBLIQUE CIRCULAR SHAPES USING THE FOLD LINE METHOD 34 TEST 1- QUESTION 1 35 TEST 1- QUESTION 8 36 TEST 1- QUESTION 8 37 TEST 1- QUESTION 11 38 TEST 1- QUESTION 11 39 TEST 1- QUESTION 11 40