logging in or signing up engineering drawing curve part1 akashdjkid Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: Embed: Flash iPad Copy Does not support media & animations WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 6182 Category: Education License: All Rights Reserved Like it (7) Dislike it (0) Added: December 11, 2010 This Presentation is Public Favorites: 8 Presentation Description Hi, This is a first part of the Engineering Drawing and MADED by : AKASH SOOD Comments Posting comment... By: sasipk129 (5 month(s) ago) good.thx Saving..... Post Reply Close Saving..... Edit Comment Close By: amitabhyadav2 (7 month(s) ago) nice pptS send it to amitabhyadav96@gmail.com Saving..... Post Reply Close Saving..... 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See all Premium member Presentation Transcript Slide 1: ENGINEERING CURVES Part- I {Conic Sections} ELLIPSE 1.Concentric Circle Method 2.Rectangle Method 3.Oblong Method 4.Arcs of Circle Method 5.Rhombus Metho 6.Basic Locus Method (Directrix – focus) HYPERBOLA 1.Rectangular Hyperbola (coordinates given) 2 Rectangular Hyperbola (P-V diagram - Equation given) 3.Basic Locus Method (Directrix – focus) PARABOLA 1.Rectangle Method 2 Method of Tangents ( Triangle Method) 3.Basic Locus Method (Directrix – focus) DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 2: CONIC SECTIONS ELLIPSE, PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE THESE CURVES APPEAR ON THE SURFACE OF A CONE WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES. Section Plane Through all the Generators Ellipse Section Plane Parallel to end generator. Parabola Section Plane Inclined at an angle Greater than that of end generator. Hyperbola α α α α β β β β< α β= α β> α e<1 e=1 e>1 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 3: What is eccentricity ? eccentricity = Directrix Axis P F A B C D N Distance from focus Distance from directrix = PF PN V = VF VC Conic section Vertex Focus DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 4: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 5: COMMON DEFINATION OF ELLIPSE, PARABOLA & HYPERBOLA: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 6: A B C D F1 F2 P AB: Major Axis CD: Minor Axis PF1+PF2=Constant=AB= Major Axis SECOND DEFINATION OF AN ELLIPSE:- It is a locus of a point moving in a plane such that the SUM of it’s distances from TWO fixed points always remains constant. {And this sum equals to the length of major axis.} These TWO fixed points are FOCUS 1 & FOCUS 2 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 7: Problem: Draw an ellipse by general method, given distance of focus from directrix 50 mm and eccentricity 2/3. Also draw normal and tangent on the curve at a point 50 mm from the focus. A B 1. Draw a vertical line AB of any length as directrix and mark a point C on it. C 2. Draw a horizontal line CD of any length from point C as axis D 3. Mark a point F on line CD at 50 mm from C F 4. Divide CF in 5 equal divisions V 5. Mark V on 2nd division from F 6. Draw a perpendicular on V and mark a point E on it at a distance equal to VF E 7. Join CE end extend it 8. Mark points 1,2,3…on CF beyond V at uniform distance, and draw perpendiculars on each of them so as to intersect extended CE at 1’,2’,3’... 1 2 3 4 5 6 7 8 9 10 11 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ 11’ 90º TANGENT NORMAL 90º DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 8: Problem: Draw a parabola by general method, given distance of focus from directrix 50 mm. Also draw normal and tangent on the curve at a point 50 mm from the focus. A B 1. Draw a vertical line AB of any length as directrix and mark a point C on it. C 2. Draw a horizontal line CD of any length from point C as axis D 3. Mark a point F on line CD at 50 mm from C V 5. Mark V on mid point of CF 6. Draw a perpendicular on V and mark a point E on it at a distance equal to VF E 7. Join CE end extend it 8. Mark points 1,2,3…on CF beyond V at uniform distance, and draw perpendiculars on each of them so as to intersect extended CE at 1’,2’,3’... 1 2 3 4 5 6 7 8 9 F 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 90º 90º TANGENT NORMAL DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 9: Problem 1:- Draw ellipse by concentric circle method. Take major axis 150 mm and minor axis 100 mm long. Also draw normal and tangent on the curve at a point 25mm above the major axis ELLIPSE BY CONCENTRIC CIRCLE METHOD O Tangent Normal DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 10: 1’ 2’ 3’ 4’ Problem 2 Draw ellipse by Rectangle method.Take major axis 100 mm and minor axis 70 mm long. Also draw a normal and a tangent on the curve at a point 25 mm above the major axis. ELLIPSE BY RECTANGLE METHOD O Normal Tangent DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 11: F1 1 2 3 4 A B C D ELLIPSE BY ARCS OF CIRCLE METHOD O F2 P1 P1 P1 P1 P2 P2 P2 P2 P3 P3 P3 P3 P4 P4 P4 P4 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 12: Q TANGENT NORMAL TO DRAW TANGENT & NORMAL TO THE CURVE FROM A GIVEN POINT ( Q ) JOIN POINT Q TO F1 & F2 BISECT ANGLE F1Q F2 THE ANGLE BISECTOR IS NORMAL A PERPENDICULAR LINE DRAWN TO IT IS TANGENT TO THE CURVE. ELLIPSE TANGENT & NORMAL Problem 13: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 13: 1 2 3 4 ELLIPSE BY OBLONG METHOD DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 14: 1 2 3 4 5 6 1’ 2’ 3’ 4’ 5’ 6’ PARABOLA RECTANGLE METHOD Scale 1cm = 10m. DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 15: 7.5m A B Draw a parabola by tangent method given base 7.5m and axis 4.5m 4.5m E O Take scale 1cm = 0.5m 4.5m F 1 2 3 4 5 6 7 8 9 10 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 16: P O 3’ 4’ 5’ 2 1 3 4 5 2’ 1’ HYPERBOLA THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1) Extend horizontal line from P to right side. 2) Extend vertical line from P upward. 3) On horizontal line from P, mark some points taking any distance and name them after P-1, 2,3,4 etc. 4) Join 1-2-3-4 points to pole O. Let them cut part [P-B] also at 1,2,3,4 points. 5) From horizontal 1,2,3,4 draw vertical lines downwards and 6) From vertical 1,2,3,4 points [from P-B] draw horizontal lines. 7) Line from 1 horizontal and line from 1 vertical will meet at P1.Similarly mark P2, P3, P4 points. 8) Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P6, P7, P8 etc. and join them by smooth curve. Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 17: Problem 14: Two points A and B are 50 mm apart. A point P moves in a plane in such a way that the difference of its distance from A and B is always constant and equal to 20 mm. Draw the locus of point P. Draw a line and mark two points A & B on it at a distance of 50 mm. A B o Mark O as mid point of AB. Mark two points V1 and V2 at 10 mm on either side of O. V1 V2 Mark points 1, 2,3 on the right of Bat any distances. 1 2 3 As per the definition Hyperbola is locus of point P moving in a plane such that the difference of it’s distances from two fixed points (F1 & F2) remains constant and equals to the length of transverse axis V1 V2. Take V11 as radius and A as centre and draw an arc on the right side of A. Take V21 as radius and B as centre and draw an arc on the left side of B so as to intersect the previous arc. Repeat the same steps on the other side to draw the second hyperbola. Repeat the step with V12, V22 as radii and V13, V23 as radii respectively. Arc of circle Method DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 18: ELLIPSE TANGENT & NORMAL T T N N Q 900 Problem 14: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 19: Q T N N T 900 PARABOLA TANGENT & NORMAL Problem 15: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 20: HYPERBOLA TANGENT & NORMAL Q N N T T 900 Problem 16 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
engineering drawing curve part1 akashdjkid Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: Embed: Flash iPad Copy Does not support media & animations WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 6182 Category: Education License: All Rights Reserved Like it (7) Dislike it (0) Added: December 11, 2010 This Presentation is Public Favorites: 8 Presentation Description Hi, This is a first part of the Engineering Drawing and MADED by : AKASH SOOD Comments Posting comment... By: sasipk129 (5 month(s) ago) good.thx Saving..... Post Reply Close Saving..... Edit Comment Close By: amitabhyadav2 (7 month(s) ago) nice pptS send it to amitabhyadav96@gmail.com Saving..... Post Reply Close Saving..... Edit Comment Close By: amar01 (11 month(s) ago) plz send this to amarthkr66@gmail.com Saving..... Post Reply Close Saving..... Edit Comment Close By: dnyanadamone (13 month(s) ago) mail to to dishaventures@hotmail.com....nice one Saving..... Post Reply Close Saving..... Edit Comment Close By: nsk1127 (14 month(s) ago) please send drawing curves part1 and part2 to this email(nsk911127@hotmail.com) if u can send me those, it'll be very helpful to me Saving..... Post Reply Close Saving..... Edit Comment Close loading.... See all Premium member Presentation Transcript Slide 1: ENGINEERING CURVES Part- I {Conic Sections} ELLIPSE 1.Concentric Circle Method 2.Rectangle Method 3.Oblong Method 4.Arcs of Circle Method 5.Rhombus Metho 6.Basic Locus Method (Directrix – focus) HYPERBOLA 1.Rectangular Hyperbola (coordinates given) 2 Rectangular Hyperbola (P-V diagram - Equation given) 3.Basic Locus Method (Directrix – focus) PARABOLA 1.Rectangle Method 2 Method of Tangents ( Triangle Method) 3.Basic Locus Method (Directrix – focus) DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 2: CONIC SECTIONS ELLIPSE, PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE THESE CURVES APPEAR ON THE SURFACE OF A CONE WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES. Section Plane Through all the Generators Ellipse Section Plane Parallel to end generator. Parabola Section Plane Inclined at an angle Greater than that of end generator. Hyperbola α α α α β β β β< α β= α β> α e<1 e=1 e>1 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 3: What is eccentricity ? eccentricity = Directrix Axis P F A B C D N Distance from focus Distance from directrix = PF PN V = VF VC Conic section Vertex Focus DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 4: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 5: COMMON DEFINATION OF ELLIPSE, PARABOLA & HYPERBOLA: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 6: A B C D F1 F2 P AB: Major Axis CD: Minor Axis PF1+PF2=Constant=AB= Major Axis SECOND DEFINATION OF AN ELLIPSE:- It is a locus of a point moving in a plane such that the SUM of it’s distances from TWO fixed points always remains constant. {And this sum equals to the length of major axis.} These TWO fixed points are FOCUS 1 & FOCUS 2 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 7: Problem: Draw an ellipse by general method, given distance of focus from directrix 50 mm and eccentricity 2/3. Also draw normal and tangent on the curve at a point 50 mm from the focus. A B 1. Draw a vertical line AB of any length as directrix and mark a point C on it. C 2. Draw a horizontal line CD of any length from point C as axis D 3. Mark a point F on line CD at 50 mm from C F 4. Divide CF in 5 equal divisions V 5. Mark V on 2nd division from F 6. Draw a perpendicular on V and mark a point E on it at a distance equal to VF E 7. Join CE end extend it 8. Mark points 1,2,3…on CF beyond V at uniform distance, and draw perpendiculars on each of them so as to intersect extended CE at 1’,2’,3’... 1 2 3 4 5 6 7 8 9 10 11 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ 11’ 90º TANGENT NORMAL 90º DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 8: Problem: Draw a parabola by general method, given distance of focus from directrix 50 mm. Also draw normal and tangent on the curve at a point 50 mm from the focus. A B 1. Draw a vertical line AB of any length as directrix and mark a point C on it. C 2. Draw a horizontal line CD of any length from point C as axis D 3. Mark a point F on line CD at 50 mm from C V 5. Mark V on mid point of CF 6. Draw a perpendicular on V and mark a point E on it at a distance equal to VF E 7. Join CE end extend it 8. Mark points 1,2,3…on CF beyond V at uniform distance, and draw perpendiculars on each of them so as to intersect extended CE at 1’,2’,3’... 1 2 3 4 5 6 7 8 9 F 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 90º 90º TANGENT NORMAL DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 9: Problem 1:- Draw ellipse by concentric circle method. Take major axis 150 mm and minor axis 100 mm long. Also draw normal and tangent on the curve at a point 25mm above the major axis ELLIPSE BY CONCENTRIC CIRCLE METHOD O Tangent Normal DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 10: 1’ 2’ 3’ 4’ Problem 2 Draw ellipse by Rectangle method.Take major axis 100 mm and minor axis 70 mm long. Also draw a normal and a tangent on the curve at a point 25 mm above the major axis. ELLIPSE BY RECTANGLE METHOD O Normal Tangent DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 11: F1 1 2 3 4 A B C D ELLIPSE BY ARCS OF CIRCLE METHOD O F2 P1 P1 P1 P1 P2 P2 P2 P2 P3 P3 P3 P3 P4 P4 P4 P4 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 12: Q TANGENT NORMAL TO DRAW TANGENT & NORMAL TO THE CURVE FROM A GIVEN POINT ( Q ) JOIN POINT Q TO F1 & F2 BISECT ANGLE F1Q F2 THE ANGLE BISECTOR IS NORMAL A PERPENDICULAR LINE DRAWN TO IT IS TANGENT TO THE CURVE. ELLIPSE TANGENT & NORMAL Problem 13: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 13: 1 2 3 4 ELLIPSE BY OBLONG METHOD DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 14: 1 2 3 4 5 6 1’ 2’ 3’ 4’ 5’ 6’ PARABOLA RECTANGLE METHOD Scale 1cm = 10m. DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 15: 7.5m A B Draw a parabola by tangent method given base 7.5m and axis 4.5m 4.5m E O Take scale 1cm = 0.5m 4.5m F 1 2 3 4 5 6 7 8 9 10 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 16: P O 3’ 4’ 5’ 2 1 3 4 5 2’ 1’ HYPERBOLA THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1) Extend horizontal line from P to right side. 2) Extend vertical line from P upward. 3) On horizontal line from P, mark some points taking any distance and name them after P-1, 2,3,4 etc. 4) Join 1-2-3-4 points to pole O. Let them cut part [P-B] also at 1,2,3,4 points. 5) From horizontal 1,2,3,4 draw vertical lines downwards and 6) From vertical 1,2,3,4 points [from P-B] draw horizontal lines. 7) Line from 1 horizontal and line from 1 vertical will meet at P1.Similarly mark P2, P3, P4 points. 8) Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P6, P7, P8 etc. and join them by smooth curve. Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it. DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 17: Problem 14: Two points A and B are 50 mm apart. A point P moves in a plane in such a way that the difference of its distance from A and B is always constant and equal to 20 mm. Draw the locus of point P. Draw a line and mark two points A & B on it at a distance of 50 mm. A B o Mark O as mid point of AB. Mark two points V1 and V2 at 10 mm on either side of O. V1 V2 Mark points 1, 2,3 on the right of Bat any distances. 1 2 3 As per the definition Hyperbola is locus of point P moving in a plane such that the difference of it’s distances from two fixed points (F1 & F2) remains constant and equals to the length of transverse axis V1 V2. Take V11 as radius and A as centre and draw an arc on the right side of A. Take V21 as radius and B as centre and draw an arc on the left side of B so as to intersect the previous arc. Repeat the same steps on the other side to draw the second hyperbola. Repeat the step with V12, V22 as radii and V13, V23 as radii respectively. Arc of circle Method DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 18: ELLIPSE TANGENT & NORMAL T T N N Q 900 Problem 14: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 19: Q T N N T 900 PARABOLA TANGENT & NORMAL Problem 15: DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.) Slide 20: HYPERBOLA TANGENT & NORMAL Q N N T T 900 Problem 16 DESIGNED BY : AKASH SOOD M.I.T.M. (GWL.)