Mel110 part3

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  • 1. ENGINEERING CURVESPoint dP i t undergoing two types of displacements i t tf di l tINVOLUTE: Locus of a free end of a string when it isgwound round a (circular) poleCYCLOID: Locus of a point on th periphery of aCYCLOID L f i tthe i h fcircle which rolls on a straight line path.SPIRAL: Locus of a point which revolves around afixed point and at the same time moves towards it.pHELIX: Locus of a point which moves around thesurface of a right circular cylinder / cone and at the f fi ht il li dd t thsame time advances in axial direction at a speedbearing a constant ratio to the speed of rotation.rotation

2. INVOLUTE OF A CIRCLE Problem: P3 P1Draw Involute ofa circle. Stringlength is equal totheP44 to p 4circumference of3 5circle. i l261 7 A 8P5P P8 1 2 3 456 7 8 P7P6D 3. Problem: Draw Involute of a circle. String length is MOREthan the circumference of circle.INVOLUTE OF A CIRCLE String length MORE than D Solution Steps:P2 In this case string length is more than D.But remember! Whatever may be the length of P3 P1 string, mark D distance horizontal i.e.along the string and divide it in 8 number ofd d v deu be o equal parts, and not any other distance. Rest all steps are same as previous INVOLUTE. Draw the curve completely. 4 to pP44 35261P578 p8P12 3 45 67 8P7165 mm P6(more than D) D 4. Problem: Draw Involute of a circle.String length is LESS than the circumference of circle.INVOLUTE OF A CIRCLE String length LESS than DSolution Steps:P2In this case string length is Lessthan D. But remember!Whatever may be the length ofP3 P1string, mark D distancehorizontal i.e.along the stringand divide it in 8 number of d d v deu be oequal parts, and not any otherdistance. Rest all steps are sameas previous INVOLUTE. Drawthe curve completely.4t p to P44 35 26 1P57 P 8P7 123456 7 8 P6 150 mm(Less than D)D 5. INVOLUTE OF A PENTAGON l5l Thread should be taut 5 6. Problem : A pole is of a shape ofINVOLUTE OFhalf hexagon (side 30 mm) and g ( ) COMPOSIT SHAPED POLEsemicircle (diameter 60 mm). Astring is to be wound havinglength equal to the pole perimeterg q p p Calculate perimeter lengthdraw path of free end P of stringP1when wound completely. P P21 to PP3 3 to P 3 42 51 6A 1 2 3 4 5 6 PP4 D/2 P6P5 7. PROBLEM : Rod AB 85 mm long rolls over a semicircular pole without slipping from itsinitially vertical position till it becomes up-side-down vertical. Draw locus of both ends A & B. BA4 4OBSERVE ILLUSTRATION CAREFULLY!B1when one end is approaching, A3other end will move away from y 3poll. R2A2 B22 131A14 AB3B4 8. DEFINITIONSSUPERIOR TROCHOID: If the point in the definition ofCYCLOID: cycloid is outside the circleLOCUS OF A POINT ON THEPERIPHERY OF A CIRCLE WHICHINFERIOR TROCHOID.:ROLLS ON A STRAIGHT LINE PATH. If it is inside the circle EPI-CYCLOID If the circle is rolling on another circle from outside HYPO-CYCLOID. If the circle is rolling from inside the other circle, 9. PROBLEM: Draw locus (one cycle) of a point (P) on the periphery of aCYCLOIDcircle (diameter=50 mm) which rolls on straight line path. p44p3 p53 5C p2 C1C2 C3 C4 C5 C6 C7 p6 C 82 6 p11p77P p8 DPoint C (zero radius) will not rotate and it will traverse on straight line. 10. PROBLEM: Draw locus of a point (P), 5 mm away from theperiphery of a Circle (diameter=50 mm) which rolls on straight SUPERIOR TROCHOIDline path.Using 2HUsing Hi 4p4p3 p5 3 5 p2C C1 CC3 C4 C5 C6 C7 C8 p626 2p7 1 p17 PD D p8 11. PROBLEM: Draw locus of a point , 5 mm inside the periphery of aINFERIORCi l which rolls on straight line path. T k circle diameter as 50Circle hi h lli h li h Take i l dit TROCHOIDmm p4 4p p5 35p23 CC1 C2 C3C4 C5C6 C7p6C8 26 p1p7 17 Pp8 D 12. CYCLOIDSUPERIOR TROCHOID INFERIOR TROCHOID 12 13. EPI CYCLOID :PROBLEM: Drawlocus of a point on the periphery of a circle(dia=50mm) which rolls on a curved path (radius 75 mm).Distance by smaller circle = Distance on larger circleSolution Steps:1. When smaller circle rolls on larger circle for one revolution it covers D distance on arc and it will be decided by included arc angle .2. Calculate by formula = (r/R) x 360.3. Construct a sector with angle and radius R.4.4 Divide this sector into 8 number of equal angular parts. parts 14. EPI CYCLOIDGenerating/Rolling Circle 4 5 C2 3 6EPI-CYCLOID7If the circle is rolling on2another circle from outside1 Pr = CP Directing Circle= r 3600R O 15. PROBLEM : Draw locus of a point on the periphery of a circle whichrolls from the inside of a curved path Take diameter of Rolling circlepath.HYPO CYCLOID50 mm and radius of directing circle (curved path) 75 mm.P7 P161 P2 P3 52 4P43P8 P5P6 P7r= 3600ROOC = R ( Radius of Directing Ci l ) R dif Di ti Circle)CP = r (Radius of Generating Circle) 16. CYCLOID SUPERIOR TROCHOIDINFERIORTROCHOID16 17. Problem: Draw a spiral of one convolution. Take distance PO 40 mm. SPIRALIMPORTANT APPROACH FOR CONSTRUCTION!FIND TOTAL ANGULAR AND TOTAL LINEAR DISPLACEMENTAND DIVIDE BOTH IN TO SAME NUMBER OF EQUAL PARTS.2 P23 1 P1 P34 P4 OP 7 6 5 4 32 1 P7P5P65 76 18. SPIRAL of two convolutionsProblem: Point P is 80 mm from point O. It starts movingtowards O and reaches it in two revolutions around. It Draw locusof point P (To draw a Spiral of TWO convolutions).2,10 P2 3,11P1 1,9P3 P10P9 P11P416 13108 P7 6 5 4 3 2 1 P 88,16 ,4,124 12P12 P15 P13 P14P7 P5 P6 5,13 7,15 6,14 19. Problem: A link 60 mm long, swings on a point O ob e :o g, sw gs opofrom its vertical position of the rest to the left through60 and returns to its initial position at uniformpvelocity. During that period a point P moves atuniform speed along the center line of the link from Op gat reaches the end of link. Draw the locus of P.O, P N M 20. PROBLEM: Draw a helix of oneHELIXconvolution, upon a cylinder. Given 80 mm(UPON A CYLINDER)P8pitch and 50 mm diameter of a cylinder. 8 P77P66 P55 Pitch: Axial advance during one4 P4 complete revolution .3 P32 P21P1PF6T 7 5P 4 1 32 21. PROBLEM: Draw a helix of one convolution,P8 HELIXupon a cone, diameter of base 70 mm, axis p , ,)(UPON A CONE)( P790 mm and 90 mm pitch. P6 P5 P4 P3 P2P1X P Y 675P6P5 P7 P4P 4 P8P1 P31 3P2 2 22. Interpenetration of Solids /I if S lidIntersection of Surfaces /Lines & Curves of IntersectionMore points common to both the solidsBasic required knowledge:~ Projections of Solid~ Section of Solid22 23. Projections of Solid .Problem: A cone 40 mm diameter and 50 mm axis isresting on one generator on Hp which makes 300inclination with Vp. Draw its projections. More number of generatorsBetter approximation.oa1h1 b1F g1f1 c X a hb c gf d e o e1 d1 1 o1 Y30 gg1g1 o1 hf1h1 h1 Tff1 a1 a oe e1 a1o1 e1 b1 1st. Anglebdd1 b1d123 c c1c1 24. Section of SolidFor TVSECTIONPLANE I Li Lines & CurvesSolidst C Interpenetration of S lid t tifxyof Intersection Intersection of Surfaces Apparent Shapeof section SECTION LINES (450 to XY)SECTIONAL T.V. 25. 25 26. 26 27. 27 28. How to make theseshapes 29. CURVES OF INTERSECTIONS are shown by WHITE ARROWS.Machine component havingIntersection of a Cylindrical ytwo intersecting cylindrical Industrial Dust collector. main and Branch Pipe.surfaces with the axis at acute angle to each other.Intersection of two cylinders.WHEN TWO OBJECTS ARE TO BEJOINED TOGATHER, MAXIMUM SURFACE CONTACT BETWEEN BOTH BECOMES A BASIC REQUIREMENT FORPump lid having shape of aSTRONGEST & LEAK-PROOF hLEAK PROOF hexagonal Prism and lP idFeeding Hopper. JOINT.Hemi-sphere intersectingeach other. 30. Minimum Surface Contact. ( Point Contact)(Maximum Surface Contact)Lines of Intersections.Li fI iCurves of Intersections. C fI iSquare Pipes. Circular Pipes. Square Pipes.Circular Pipes.MAXIMUM SURFACE CONTACT BETWEEN BOTH BECOMES A BASIC REQUIREMENT FOR STRONGEST & LEAK-PROOF JOINT. QTwo plane surfaces (e-g. faces of prisms and pyramids)intersect in a straight line.lineThe line of intersection between two curved surfaces (e-g.of cylinders and cones) or between a plane surface and acurved surface is a curve. More points common to both the solids 30 31. How to find Lines/Curves of IntersectionGenerator line MethodCutting Plane Method TT FF7531 75 32. Problem: Find intersection curve .Draw convenient number of lines on the surface of one of the solids.Transfer point of intersection to their corresponding p pp g positions in otherviews. When one solid completely penetrates another, therewill be two curves of intersection.32 33. Problem: A cylinder 50mm dia. & 70mm axis is completely penetrated by anotherof 40 mm dia. & 70 mm axis horizontally. Both axes intersect & bisect each other.Draw projections showing curves of intersections intersections. 12 4 34 132a a b h hb cg gc df df f d da eXY 41 3 33 2 34. Problem: CYLINDER (50mm dia.and 70mm axis ) STANDING & SQ.PRISM (25 mmsides and 70 mm axis) PENETRATING. Both axes Intersect & bisect each other. All faces ofprism are equally i li d t H Di ll inclined to Hp. Draw projections showing curves of i t j tih if intersections.ti 12 4 3 4 132 a db Projections of j Find lines ofof Solid 1. critical Solid2.Missing intersection cpoints at whichX Y curve changesdirection.direction 41 334 2 35. Problem. SQ.PRISM (30 mm base sides and 70mm axis ) STANDING & SQ.PRISM (25mm sides and 70 mm axis) PENETRATING. Both axes intersects & bisect each other. Allfaces of prisms are equally inclined to Vp Draw projections showing curves ofVp.intersections.1 24 34 13 2 aa a bb d b dd cccX Y 4 Preference of object line over dash lineline 1 3 2 35 36. Problem. SQ.PRISM (30 mm base sides and 70mm axis ) STANDING & SQ.PRISM (25mm sides and 70 mm axis) PENETRATING. Both axes Intersect & bisect each other. Twofaces of penetrating prism are 300 inclined to Hp. Draw p j pgpp projections showing curves ofgintersections in I angle projection system.1243413 2 a ffeb cc d dX300 Y4 13d"o2 Other possible arrangements ????b"36 37. Problem: A vertical cylinder 50mm dia. and 70mm axis is completely penetrated