Lecture 5 Descriptive Geometry PDF

Orientation of drawing sheet & margins: A3 10mm 25mm 10mm 12mm 10mm  Laying out a drawing in the Drawing Space Centralize the multi-views of the system given on the LHS, supp...

Orientation of drawing sheet & margins: A3 10mm 25mm 10mm 12mm 10mm  Laying out a drawing in the Drawing Space Centralize the multi-views of the system given on the LHS, supposing the drawing 75 area on an A3 size paper are 300mm WIDTH x 247mm HEIGHT, whereby the title block is 30 mm high & the notes column is 85 mm wide 70 130 75 NOTES Sheet size c(min) d(min) 247 DRAWING SPACE A4 10 25 A3 10 25 B.O.M A2 10 25 300 85 A1 20 25 A0 20 25 TITLE BLOCK   Laying out a drawing in the Drawing Space 75 70 130 75 NOTES DRAWING 247 SPACE B.O.M 300 TITLE BLOCK   Drawing scales  Some objects are drawn to the size they appear physically. These drawings are referred to as FULL SCALE. e.g. the outline of an aluminium beverage can on an A4 size paper.  Dimensions of large objects must be reduced to fit into standard drawing paper sizes. This leads to what is called a REDUCING SCALE. e.g. Botswana can fit into the A4 paper of your notebook.  Similarly dimensions of tiny object must be increased to make them easier to drawn and also make them stand out in standard drawing paper, leading to ENLARGING SCALE. e.g., components of a wristwatch, atomic bonds in an engineering material can be drawn big enough to take up a quarter of the   Different ways of expressing Scales GRAPHICAL/ NUMERICAL LINEAR SCALES SCALES ENGINEER’S REPRESENTATIV (VERBAL) SCALE E FACTOR 10 CM = FRAC RATIO 100 KM TION 1 : 1; 1 : X; X : 1; WHE RE: X>1   Types of scales  NUMERICAL SCALES express Representat the relationship ive ratio between map Fractio and ground n Scale distances using numbers Enginee r’s Scale   Drawing scale or Representative factor Representative factor/R.F. is a ratio between the linear dimensions of a drawing and the actual object. 1 : 2 10 20 Drawing Actual  Drawing scale or Representative factor   Drawing scale or Representative factor Representative factor/R.F. is a ratio between the linear dimensions of a drawing and the actual object. 1 : 2 10 20 Drawing Actual   Scales according to the R.F. Scales are found written in title blocks consisting of the word “SCALE” followed by RATIO, as follows SCALE 1:1 for FULL scales SCALE X:1 (X > 1) for ENLARGEMENT scales typical standard scales in this category are: 2:1, 5:1, 10:1, 20:1, 50:1, 100:1 SCALE 1:X (X > 1) for REDUCTION scales typical standard scales are: 1:2, 1:5, 1:10, 1:20, 1:50, 1:100  Drawing scale or Representative factor   Drawing Graphical Scales Plain Scales Diagonal scales Comparative scales Vernier scales Scales of chords   Graphical Scales: Plain Scales PLAIN SCALES: are graphical scales constructed as thin rectangles as per the example below: Example: Construct a scale of 1:4 to show centimetres (cm) and long enough to measure up to 5 decimetres (dm). Whereby: 1 dm = 10 cm: a). Given data: RF = 1 : 4 b). Measurable Maximum Length, MML = 5 dm = 50cm (expressed in lowest units to be measured) Solution: 1. Write the RF as a fraction, RF = ¼ 2. Calculate the Length of the Scale, LOS = RF x MML = ¼ x 50cm = 12.5cm 3. Draw a thin rectangle (3mm height) of 12.5cm length and divide it into 5 equal parts (where each division is 1 dm) and at each division draw a vertical line to divide the thin rectangle into a series of rectangles. 12.5 cm   Graphical Scales: Plain Scales 4. Mid-height (1.5mm) of the first rectangle, draw a slightly thicker line, and repeat the same in the 3rd, 5th, etc., up to the end. 5. Mark the end of the 1st rectangle zero (0), and 1, 2, 3, and 4 at the end of each subsequent rectangles to its right 6. Write the label CENTIMETRES under the 1st rectangle, DECIMETERS under the last rectangle, and RF=1/4 in the middle of the original thin rectangle constructed in step 3 above 7. Divide the 1st rectangle into 10 equal divisions, and at each division draw vertical lines to the thick midline drawn in step 4 above to cut that lower thinner rectangle into a series of small rectangles 8. Mark the beginning of the 1st small rectangle 10. 9. Starting from the Left, midway in the 2nd small rectangle, draw a slightly thick line, and repeat the same in the 4th, 6th, etc., up to the end. 10. Your plain scale is complete and good to go with your drawing/map For more information on Plain Scales, read Chapter 4 (pages 46 to 49 ONLY 10 0 1 2 3 4 CENTIMETRES RF=1/4 DECIMETERS  Basic line types  Basic line types  Visible line/Outline  Hidden lines  Phantom lines  Text on Drawings Text on engineering drawing is used : To communicate nongraphic information. As a substitute for graphic information, in those instance where text can communicate the needed information more clearly and quickly. Thus, it must be written with Legibility - shape - space between letters and words Uniformity - size - line thickness Example Placement of the text on drawing Dimension & Notes Notes Title Block Basic Strokes Straight Slanted Horizontal Curved Examples : Application of basic stroke 4 5 “B” 1 “I” letter 1 “A” letter 1 2 letter 3 6 3 2  Upper-case letters & Numerals Straight line letters Curved line letters Curved line letters & Numerals  Lower-case letters The text’ s body height is about 2/3 the height of a capital letter. Stroke Sequence T F I L E H Stroke Sequence V X W Stroke Sequence N M K Z Y A 4 Stroke Sequence O Q C G Stroke Sequence D U P B R J 1 2 Stroke Sequence 5 7  Stroke SSequence 0 3 6 8 9  Stroke Sequence l i  Stroke Sequence v w x k z  Stroke Sequence j y f t r  Stroke Sequence c o a b d p q e  Stroke Sequence g n m h u s  Word Composition Look at the same word having different spacing between letters. A) Non-uniform spacing JIRAPONG B) Uniform spacing JIR APONG Which one is easier to  Word Composition Spacin JIR APONG g Contou ||| \ \ | )( )| |( r | General conclusions a/re: Space between the letters depends on the contour of the letters at an adjacent side. Good spacing creates approximately equal  Space between Letters 1. Straight - Straight 3. Straight - Slant 2. Straight - 4. Curve - Curve Curve  Space between Letters 5. Curve - Slant 6. Slant - Slant 7. The letter “L” and “T” ≡ slan slan t t slan ≡ straig t ht Example : Good and Poor Lettering GOOD Not uniform in style. Not uniform in height. Not uniformly vertical or inclined. Not uniform in thickness of stroke. Area between letters not  Sentence Composition Leave the space between words equal to the space requires for writing a letter “O”. Example ALL O D I M E N S I O N S O A R E O I N MILLIMETERS O U NLE SS OTHERWISE O SPECIFIED. Lecture 5: Descriptive Geometry Discussion Points Why study Fold Lines Descriptive Geometry? Projection of points Notations in DG Principal Views  interested in Descriptive Geometry  because we want to solve problems to do with the following: Projections of POINTS, LINES and PLANES True length of LINES True distances between LINES or between LINES and POINTS, between POINTS and PLANES Intersections between LINES and PLANES, True angles between surfaces, True shape of   Notations POINTS in space PLANES in space use lowercase use lowercase letters. letters. a, b, c, d abcd a a d LINES in space use b c two lowercase letters to identify end points a of line. Line a-b b c a b   Notations: Lines and Planes terminology LINES end at PLANES are indicated points LIMITED (stops at unless specified as the indicated EXTENDED (i.e. boundaries) or continues without UNLIMITED end) (limitless a b boundaries) a d b c   Notations: Principal Views vs Principal Planes VIEWING PLANES or PRINCIPAL PLANES also PRINCIPAL VIEWS use use uppercase letters: uppercase letters: 1. Vertical Plane [VP] F: Frontal View/plane 2. Horizontal Plane [HP] T: Top View/plane 3. Profile Plane [PP] R: Right Side a. Left Profile Plane View/plane [LPP] b. Right Profile Plane L: Left side View/plane [RPP] A: Auxiliary View/Plane  FOR T.V.. FO S.V R R F.V FO.  What about this in SolidWorks?  Lines FOLD LINES: indicates a 90- degrees intersection between two viewing planes Represented by thin black line, similar to phantom line, labeled with uppercase letters T F MITER LINE: the miter line is not used in Descriptive Geometry projections   Notations: POINTS AND LINES IN SPACE aF: Front View of aT-bT: Top View of a point [a] line [a-b ]  Notations: POINTS AND LINES IN SPACE aT-bT-cT: Top view of a plane [a-b-c]  Notations: Summary VIEW POINT a LINE a-b TOP VIEW aT aT-bT FRONT VIEW aF aF-bF RIGHT VIEW aR aR-bR  Notations from other sources VIEW POINT A LINE AB TOP VIEW a ab FRONT VIEW a’ a’ b’ SIDE VIEW a” a” b” Notations NOT preferred in this course!!   Projection of Points in space Given the F.V and T.V of point [a], find its R.P.V   Finding R.P.V Drop a perpendicular projector from T.V (aT) to F.V (aF) Drop another perpendicular projector from F.V (aF) across F/R. R.P.V (aR) lies somewhere along the projector Measure the distance X from F/T to T.V (aT) and transfer it along the projector from F.V (aF) across F/R to locate R.P.V (aR) exactly.  VP 2 nd Quad. 1ST Quad. Y Observer X Y HP X 3rd Quad. 4th Quad. OBSERVING THE QUADRANT PATTERN ALONG THE X-Y LINE (RED ARROW) GIVES THE PATTERN ON THE RIGHT RABATM 2ND QUADRANT VP 1ST QUADRANT ENT: the VP a’ [aF] a A [a] process aF of aT aligning HP OBSERVER planes HP OBSERVER For the point, a, a [aT] shown in the four quadrant 3RD QUADRANT 4TH QUADRANT s, its FV aT & TV are brought into the HP HP OBSERVER OBSERVER same plane by rotating aT aF TV on a aF a the HP 900, VP VP clockwis e to align TAXONOMY OF POINTS PROJECTION NINE PERMUTATIONS: TERMS 1. In FIRST QUADRANT (Above H.P. , In front of V.P.) 2. In SECOND QUADRANT (Above H.P. , Behind V.P.) 3. In THIRD QUADRANT (Below H.P. , Behind V.P.) 4. In FOURTH QUADRANT (Below H.P. , In front of V.P.) 5. In PLANE (On V.P. , Above H.P.) 6. In PLANE (On H.P. , Behind V.P.) 7. In PLANE (On V.P. , Below H.P.)  VP II QUADRANT I QUADRANT ABOVE HP ABOVE HP INFRONT OF VP BEHIND VP OBSERVER DIRECTION HP HP BELOW HP BELOW HP BEHIND VP INFRONT OF VP III QUADRANT VP I V QUADRANT  VP II QUADRANT I QUADRANT ABOVE HP ABOVE HP BEHIND VP INFRONT OF VP BEHIND RPP INFRONT OF RPP BEHIND LPP INFRONT OF LPP OBSERVER DIRECTION HP HP BELOW HP BELOW HP INFRONT OF VP BEHIND VP INFRONT OF RPP BEHIND RPP INFRONT OF LPP BEHIND LPP III QUADRANT VP I V QUADRANT IN FIRST QUADRANT a1- point P. V. Y a1F - FV.a F 1. a1 F a1T - TV. a1 Y X Y P..a T X.a T 1 1 H. (2 (3D X D) ) In 3D In 2D Above H.P. Front View Above Reference Line IN SECOND QUADRANT a2- point a2F - FV Y a2T - TV.a2.a X T 2.a T 2 a2..a T 2 Y X Y T X In 3D In 2D Above H.P. Front View Above Reference Line IN THIRD QUADRANT Y a3 - point a3F- FV. a3 T Y a3T - TV In 3D In 2D. a3 X Below H.P. Front View Below Reference Line.a F3 Behind V.P. Top View Above Reference Line IN FIRST QUADRANT (SEE.a T 3 X PREVIOUS SLIDE) In 3D In 2D X Y Above H.P. Front View Above Reference Line In front of V.P. Top View Below Reference Line.a F 3  Y IN FOURTH QUADRANT a4 - point X a4F - FV.a T4.. a4T - TV a4 F a4 In 3D In 2D Below H.P. Front View Below Reference Line X Y In front of V.P. Top View Below Reference Line IN THIRD QUADRANT (PREVIOUS.a F SLIDE) In 3D In 2D.a T 4 4 Above H.P. Front View Above Reference Line On V.P., Above H.P. aa F- point 5. a5 a5 F - FV5 Y a5T - TV. X a5 T In 3D In 2D Above H.P. Front View Above On V.P. Reference Line Top View On Reference. a5 a5F Line X.a T5 Y On V.P., Below H.P. aa F- point 6 - FV Y.a T 6 a6T - TV 6 X In 3D In 2D. a6 a6 F Below H.P. Front View Below Reference Line On V.P. Top View On Reference Line X. a6 T Y. a6 a6 F ON H.P., IN FRONT OF V.P. a - point7 a7F - FV Y a7T - TV. a7 T X. a7 a7 F In 3D In 2D. On H.P. Front View On Reference Line a7 T In Front of V.P. Top View Below Reference Line X Y. a7 a7 F ON H.P., BEHIND V.P. aa F- point - FV 8 8 a8T - TV. a8 a8 T Y. a8 F In 3D In 2D X On H.P. Front View On Reference Behind V.P. Line Top View Above Reference. a8 a8 T Line X.a F 8 Y ON H.P., ON V.P. aa F- point 9 - FV 9 a9T - TV Y a9 T. a9 a9 F X In 3D In 2D On H.P. Front View On Reference Line. On V.P. Top View On Reference a9 T a F Line X 9 Y a9  How to project lines in space   Finding T.V. (aT-bT) Drop a perpendicular projectors from R.V. (aR-bR) to F.V. (aF-bF) Drop other perpendicular projectors from F.V. (aF-bF) across F/T. T.V. (aT-bT) lie along the projectors Measure the distance Y and X corresponding to R.V. (aR- bR) from F/R and transfer them along the projector from (aF-bF) across F/T to locate T.V. (aT-bT) exactly.  Finding the True Length of a Line  True Length of a Line  True Length of a Line ICE BREAKER 1: class activity REFLECTING ON THE FOREGOING minute SLIDE: HOW ARE LINES DIFFERENT FROM POINTS? Their ends are POINTS They have to have a size dimension: referred to as LENGTH – HOW IS THE ABOVE DIFFERENT FROM 3-D ENGINEERING SYSTEMS? 3-D systems have the three basic size dimensions: HEIGHT, WIDTH and DEPTH And unlike points, lines have ANGLE DIMENSIONS – WITH RESPECT TO the planes and the reference line ( ϴ, Φ, α, and β) END PROJECTOR DISTANCE: NOTATIONS OF VIEWS & OTHER PARAMETERS FOR A LINE AB NOTATIONS TRUE LENGTH (TL) ab = 100mm FRONT VIEW LENTGH (FVL) aFbF= 70mm TOP VIEW LENGTH (TVL) a b = 50mm INCLINATION OF TL WITH H.P. ϴ = 50º INCLINATION OF TL WITH H.P. Φ = 40º INCLINATION OF FVL WITH XY α = 30º INCLINATION OF TVL WITH XY β = 20º  TAXONOMY OF LINES PROJECTION TERMS ANCHORED ON THE FOLLOWING: THREE NEW ADJECTIVES: 1. PARALLEL TO 2. PERPENDICULAR TO 3. INCLINED TO PLUS THE FIVE PREVIOUS ADJECTIVES FOR A POINT: 4. IN FRONT 5. BEHIND 6. BELOW 7. ABOVE 8. ON PERMUTATIONS EXIST BASED OR ANCHORED ON A: 1. Line PARALLEL to two planes and PERPENDICULAR to the third plane. 2. Line INCLINED to one plane and PARALLEL to another 3. Line INCLINED to both planes. Position 1: Parallel to two planes & perpendicular to the other In 3D In 2D Parallel to H.P. Front View – Parallel line to reference line Parallel to V.P. Top View – Parallel Line to reference line Perpendicular to P.P. Y Side View – Point on the side of front view P P.P. V. V.P.. bF aR-bR. RP aR-b aF Fv bF.P. b aF Y X Y a aT bT TV bT X. P. H aT H.P. z x Position 1: Parallel to one plane and inclined to the other In 3D In 2D Inclined to H.P.  by Front View – Line inclined to reference line Parallel to V.P. Top View – Parallel Line to reference line V.P. True bF. V.P bF Length. b F.V. V aF F.   Y aF X Y  a aT bT bT T.V. X V. T. aT H.P. Position 1: Inclined to both the planes In 3D In 2D Inclined to H.P.  by Front View – Line inclined to reference line  Parallel to V.P. Top View – Line inclined by to reference line V. P. V.P. bF bF FV b aF  Y  X Y aF a  aT  P X aT bT H. TV. H.P. bT ICE BREAKER minute 2 ACTIVITY 1: A line pj, 50 mm long is perpendicular to H.P. and is below H.P. Point p is on H.P. and 30 mm behind V.P. Draw projections of line pj. pT-jT 30 pT-jT p 30 X pF Y pF 50 j 50 50 30 jF jF Problem 2 A line mj, 35 mm long, is perpendicular to the profile plane. The end m is 20 mm below H.P., 30 mm behind V.P. Draw projections on H.P. and V.P. mT jT 35 mT jT m 20 30 35 j mF X Y 30 jF 20 jF 35 mF Problem 3 A line kp, 70 mm long, is parallel to H.P. & inclined to V.P. by 60O. Point p is 20 mm above H.P. and 30 mm in front of V.P. Point k is behind V.P. Draw to projection of line kp. kT pF kF 20 X Y 60 70 pT Problem 4 A Line AB, 90 mm long, is inclined to H.P. by 30° and inclined to V.P. by 45º. The line is in first quadrant with Point A 15 mm above H.P. and 25 mm in front of V.P. Draw the projection of line AB. Data Given : Locus of bF bF b 1F (1) T.L.=90 mm 90 (2) θ =30° F.V. L. = T. (3) φ =45° aF. θ α b 2F (4)Point A 15 above H.P. 25 mm in Front 25 15 X Y of V.P.. aT φβ b1 Answers :- (1) F.V.= 64 T.V. mm= 78 (2) T.V b 2T Locus of bT (3)  =mm 45° (4)  = bT