ME 111: Engineering Drawing - iitg.ac.in

1 me 111 : Engineering Drawing Lecture 305-08-2011 SCALES AND Engineering CurvesIndian Institute of Technology GuwahatiGuwahati 781039 DefinitionAscale is defined as the ratio of the lineardimensions of the object as represented in adrawingtotheactual dimensionsof drawings drawn with the same size as the objects arecalled full sized Drawing . It is not convenient, always, to drawdrawings of ,Heavymachines,Bridges,Watches, ,Bridges,Watches,Electronicdevicesetc. Hence scales are used to prepare Drawing at Full size Reduced size Enlarged sizeReducing scales1:Y (Y>1)1:21:201:2001:20001:51:501:5001:500 01:101:1001:10001:10000 Enlarging scales50:120:110:1 BIS Recommended ScalesEnlarging scalesX:1 (X>1)50:15:120:12:110:1 Full size scales1:1 Intermediate scales canbe usedinexceptional caseswhererecommendedscalescannot beappliedforfunctional of Scale Engineers Scale:The relation between the dimension on the drawingand the actual dimension of the object is mentionednumerically(like10mm=15m).

2 Numerically(like10mm=15m). Graphical Scale:Scale is drawn on the Drawing itself. This takes careof the shrinkage of the engineer s scale whenthedrawing becomes of Graphical Scale Plain Scale Diagonal Scale Vernier Scale Comparative scaleRepresentative fraction ( )Whena1cmlonglineinadrawingrepresents1 Whena1cmlonglineinadrawingrepresents1met er length of the object, scale Aplain scale consists of a line divided into suitablenumber of equal units. The first unit is subdividedinto smaller parts. The zero should be placed at the end of the Fromthe zero mark, the units should be numberedto the right and the sub-divisions to the left. Theunits andthesubdivisions shouldbelabeledclearly. The should be mentioned below the scale. Construct a scale of 1:4, to showcentimeters and longenough to measure up to 5 decimeters. Length of the scale = max. length = 5 dm= cm. Draw a line cmlong and divide it in to 5 equal divisions, eachrepresenting 1 dm.

3 Mark 0 at the end of the first division and 1, 2, 3 and 4 at the endof each subsequent division to its right. Dividethefirstdivisioninto10equalsub-div isions,eachrepresenting 1 cm. Mark cmto the left of 0 as :Construct a scale of 1:4, to show centimeters andlong enough to measure up to 5 decimeters Drawthescaleasarectangleofsmallwidth(abo ut3mm) Drawthescaleasarectangleofsmallwidth(abo ut3mm)instead of only a line. Draw the division lines showing decimeters throughout the widthof the scale. Drawthickanddarkhorizontal linesinthemiddleof allalternate divisions and sub-divisions. Belowthe scale, print DECIMETERS onthe right handside,CENTIMERTERS on the left hand side, and in the Scale Through Diagonal scale, measurements can be up to second decimal ( ). Diagonal scales are used to measure distances in aunitanditsimmediatetwosubdivisions; ,unitanditsimmediatetwosubdivisions; ,cm&mm,oryard, foot &inch. Diagonal scale can measure more accurately than the plain At end B of line AB, draw a perpendicular.

4 Step-off ten equal divisions of any length alongthe perpendicular starting fromB and endingat C. Number the division points 9,8,7,..1. JoinAwithC. JoinAwithC. Throughthe points 1, 2, 3, etc., drawlinesparallel to AB and cutting AC at 1 , 2 , 3 , etc. Since the triangles are similar; 1 1 = AB,2 2 = , .. 9 9 = Gives divisions of agivenshort line ABinmultiples of 1/10 its length, , , , a Diagonal scale of RF= 3:200 ( 1:66 2/3) showingmeters, decimeters and centimeters. The scale should measure upto 6 meters. Show a distance of meters Length of the scale = (3/200) x 6 m = 9 cm Draw a line AB = 9 cm . Divide it in to 6 equal parts. Divide the first part A0 into 10 equal divisions. At Adrawaperpendicularandstep-off alongit 10equaldivisions, ending at Scale Complete the rectangle ABCD. Draw perpendiculars at meter-divisions 1, 2, 3, and 4. Draw horizontal lines through the division points on AD. Join Dwith the end of the first division along A0 ( 9).

5 Through the remaining points 8, 7, 6, ..draw lines // to D9. PQ= metersVernier Scales Similar to Diagonal scale, Vernier scale is used for measuring upto second decimal. A Vernier scale consists of (i) a primary scale and (ii) a vernier. The primary scale is a plainscale fully dividedinto minordivisions. Thegraduationsonthevernierarederivedfrom thoseontheLeast count (LC) is the minimum distance that can be Vernier Scale : MSD>VSD; LC = MSD-VSDB ackward Vernier scale: VSD>MSD; LC = VSD - MSD Thegraduationsonthevernierarederivedfrom thoseontheprimary Concept Length A0 represents 10 cmand is divided in to 10 equal partseach representing 1 cm. B0 = 11 ( 10+1) such equal parts =11 cm. Divide B0 into 10 equal divisions. Eachdivisionof B0 will beequal to 11/10 = cmor 11 mm. Differencebetween1partofA0andonepartofB0 = Differencebetween1partofA0andonepartofB0 = 1 :Draw a Vernier scale of = 1/25 to read up to 4 meters.

6 On it show lengths m and m LengthofScale=(1/25) (4 100)=16cm LengthofScale=(1/25) (4 100)=16cm Drawa 16 cmlong line and divide it into 4 equal parts. Each part is1 each of these parts in to 10 equal parts to showdecimeter (10 cm). Take 11 parts of dmlength and divide it in to 10 equal parts. Each ofthese parts will show a length of dmor 11 cm. To measure m, place one leg of the divider atAon 99 cmmarkand other leg atBon mark. ( + = ). To measure m, place the divider atCandD( + = ).Question:Draw a Vernier scale of = 1/25 to read up to 4 meters. On it show lengths m and m LengthofScale=(1/25) (4 100)=16cm LengthofScale=(1/25) (4 100)=16cm Drawa 16 cmlong line and divide it into 4 equal parts. Each part is1 each of these parts in to 10 equal parts to showdecimeter (10 cm). Take 11 parts of dmlength and divide it in to 10 equal parts. Each ofthese parts will show a length of dmor 11 cm. To measure m, place one leg of the divider atAon 99 cmmarkand other leg atBon mark.

7 ( + = ). To measure m, place the divider atCandD( + = ). Engineering Curves 1919 Indian Institute of Technology GuwahatiGuwahati 781039 Common Engineering CurvesElliptical shape Parabolic shape 20 Elliptical shape Hyperbola spiralConic curves (conics) Curves formedby the intersectionof a plane witharight circular Parabola, hyperbola and ellipseRight circular coneisaconethathasa21isaconethathasacirc ularbaseandtheaxisisinclinedat 900tothebaseand passes "smooth". More precisely, ,suchasaerodynamics,civilengg.,mechanica l engg, is defined as the locus of a point moving in a plane such thatthe ratio of its distance froma fixed point and a fixed straight line isalways point is called FocusFixed line is called Directrix23 When eccentricity<1 Ellipse=1 ParaboladirectricthefrompointtheofDistancefocusthefrompointtheofDistancetyEccentrici====24> 1 Hyperbolaeg. whene=1/2, the curve is anEllipse, whene=1, it is aparabola and when e=2, it is a ,25sectionplane,inclined to the axis, or Eccentricity MethodGiven :the distance of focus fromthe directrix andeccentricityExample: Drawan ellipse if the distance of focus fromthe directrix is 70mmand the eccentricity is 3 Drawthe directrix ABandaxis CC 2.

8 MarkFonCC suchthatCF = 70 , e = FV/ CV = 3 At V, erect a perpendicularVB = VF. Join CB. ThroughF, draw a line at 45 to meetCB produced at D. ThroughD,dropaperpendicularDV on CC . Mark Oat themidpointof V V .Focus-Directrix or Eccentricity Method ( Continued)5. With F as a centre and radius =1 1 ,cuttwoarcsontheperpendicularthrough1tol ocateP1andP1 . Similarly,with F as centre and radii = 2 2 , 3 3 , etc., cut arcs onthecorrespondingperpendicularstolocate P2andP2 , P3andP3 , etc. Also, cut similar arcsontheperpendicularthrough27ontheperp endicularthroughOto locate V1 and V1 .6. Drawasmoothclosedcurvepassing through V, P1, P/2, P/3,.., V1, .., V , .., V1 , ..P/3 ,P/2 , P1 .7. Mark F on CC such that V F = VF.