ch01.ppt

7/17/2019 ch01.ppt

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Engineering Drawing

By : Bisrat GirmaBy : Bisrat Girma

Mechanical Engineering DepartmentMechanical Engineering Department21/Nov /200821/Nov /2008

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O!ective o" the chapter

E#plain the a$vantage o" graphicalE#plain the a$vantage o" graphical

lang%age "or technical comm%nicationlang%age "or technical comm%nication

&le to care an$ properly han$le $rawing&le to care an$ properly han$le $rawing

instr%mentsinstr%ments

E#plain the meaning o" lines' symolsE#plain the meaning o" lines' symols

Enale to $raw geometric o!ects toEnale to $raw geometric o!ects to

stan$ar$sstan$ar$s

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(ontents

)art one)art one

* +ntro$%ction+ntro$%ction

* (o%rse overview(o%rse overview* Drawing as a means o" comm%nicationDrawing as a means o" comm%nication

* Graphic lang%age or $ra"tingGraphic lang%age or $ra"ting

,ypes o" $rawing,ypes o" $rawing* (are an$ %se o" $rawing tools(are an$ %se o" $rawing tools

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(ontents -cont$.

)art one)art one

* ,ypes o" lines,ypes o" lines

* etteringettering

* (oor$inate system(oor$inate system

* Geometric constr%ctionGeometric constr%ction

Bisecting 'trisecting line an$ angleBisecting 'trisecting line an$ angle Divi$ing a line an$ an angle in to a n%mer o" partsDivi$ing a line an$ an angle in to a n%mer o" parts

Drawing $i""erent polygonsDrawing $i""erent polygons

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(ontents -cont$.

)art one)art one

* Geometric constr%ctionGeometric constr%ction Drawing special types o" c%rvesDrawing special types o" c%rves

(ircle' ellipse' paraola' hyperola an$ invol%tes(ircle' ellipse' paraola' hyperola an$ invol%tes

Drawing tangent linesDrawing tangent lines

Drawing tangent c%rves - internal an$ e#ternal.Drawing tangent c%rves - internal an$ e#ternal.

evisionevision

)ractical e#ercises)ractical e#ercises

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,raining ai$s

)ower)oint sli$es prepare$)ower)oint sli$es prepare$

e"erence oose"erence oos* Engineering $rawing an$ Graphic technologyEngineering $rawing an$ Graphic technology

y 3rench y 3rench

* Engineering $rawing y %4a$$er Engineering $rawing y %4a$$er

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,raining ai$s -cont$.

&ny availale $rawing oo &ny availale $rawing oo

5tan$ar$ training pacage -movie.5tan$ar$ training pacage -movie.

Drawing instr%mentsDrawing instr%ments

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+ntro$%ction+ntro$%ction

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Drawing as a means o"

comm%nications

+n$e"inite nee$s h%man nat%re+n$e"inite nee$s h%man nat%re

New pro$%ct New pro$%ct

* esearchesearch

* DevelopmentDevelopment

* DesignDesign

* )ro$%ction' constr%ction' an$ Operation)ro$%ction' constr%ction' an$ Operation

+t nee$s comm%nication+t nee$s comm%nication

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comm%nications

E#change o" i$eas nee$s means o"E#change o" i$eas nee$s means o"comm%nication6 &s the i$ea ecomescomm%nication6 &s the i$ea ecomes

technical the %s%al means o" comm%nicationtechnical the %s%al means o" comm%nication-tal or listen' rea$ or write. will e less-tal or listen' rea$ or write. will e lesse#act6 3or this reasone#act6 3or this reason vis%al lang%agevis%al lang%age isis$evelope$ to e technical an$ acc%rate$evelope$ to e technical an$ acc%rate

means comm%nication6 ,his vis%al lang%agemeans comm%nication6 ,his vis%al lang%agein roa$ term is calle$in roa$ term is calle$ graphic lang%agegraphic lang%age6 7e6 7ecall itcall it %niversal lang%age o" in$%stry%niversal lang%age o" in$%stry when itwhen itis %se$ "or pro$%ction p%rposeis %se$ "or pro$%ction p%rpose

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comm%nications

,he vloc is to e ma$e o" cast iron an$,he vloc is to e ma$e o" cast iron an$machine$ on all s%r"aces6 ,he overall si4es aremachine$ on all s%r"aces6 ,he overall si4es are

two an$ onehal" inches high' three inchestwo an$ onehal" inches high' three incheswi$e' an$ si# inches long6 & vshape$ c%twi$e' an$ si# inches long6 & vshape$ c%thaving an incl%$e$ angle o" 09 is to e ma$ehaving an incl%$e$ angle o" 09 is to e ma$ethro%gh the entire length o" the loc6 ,he c%tthro%gh the entire length o" the loc6 ,he c%tis to e ma$e with the loc resting on the threeis to e ma$e with the loc resting on the threeinch y si# inch s%r"ace6 ,he vc%t is to egininch y si# inch s%r"ace6 ,he vc%t is to eginone%arter inch "rom the o%tsi$e e$ges6 &t theone%arter inch "rom the o%tsi$e e$ges6 &t the

ottom o" the vc%t there is to e a relie" slot ottom o" the vc%t there is to e a relie" slotoneeighth inch wi$e y oneeighth inch $eep6oneeighth inch wi$e y oneeighth inch $eep6

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comm%nications

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comm%nications

;ow 7o%l$ <o% Descrie ,his=;ow 7o%l$ <o% Descrie ,his=

* +n teams o" two' $escrie %sing only wor$s+n teams o" two' $escrie %sing only wor$s

* ;ow e""ective is this approach=;ow e""ective is this approach=

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Graphic ang%age or Dra"ting

* +t is a "orm o" comm%nication that is+t is a "orm o" comm%nication that is technicaltechnical

an$ very e#act6an$ very e#act6

* +t is vis%al lang%age+t is vis%al lang%age* >tili4e>tili4e line an$ symolsline an$ symols agree$ all over theagree$ all over the

worl$6worl$6

Graphic comm%nicationGraphic comm%nication⇒⇒

written or $rawn written or $rawn

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,he most common names associate$ with,he most common names associate$ with

the graphic lang%ages are:the graphic lang%ages are:

* Dra"tingDra"ting : represent all graphic lang%ages6: represent all graphic lang%ages6

* ,echnical Drawing,echnical Drawing : &ny $rawing which: &ny $rawing which

e#pressese#presses technical i$eastechnical i$eas' incl%$ing setches'' incl%$ing setches'

instr%ment $rawings' charts' an$ ill%strations6instr%ment $rawings' charts' an$ ill%strations6Eg6 ,echnical 5etching? 3reehan$6Eg6 ,echnical 5etching? 3reehan$6

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,echnical 5etching,echnical 5etching: & technical $rawing %se$ to: & technical $rawing %se$ to

proportion shape o" i$eas so that other can proportion shape o" i$eas so that other can

%n$erstan$ the shape o" things6%n$erstan$ the shape o" things6 Mechanical DrawingMechanical Drawing : & technical $rawing ma$e: & technical $rawing ma$e

with $ra"ting instr%ments6with $ra"ting instr%ments6

Engineering DrawingEngineering Drawing : Drawing %se$ y: Drawing %se$ y

engineers an$ other memer o" the $esignengineers an$ other memer o" the $esign

engineering team to $escrie theengineering team to $escrie the pro$%ction o" pro$%ction o"

parts' shape' si4e an$ material6 parts' shape' si4e an$ material6

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Descriptive GeometryDescriptive Geometry : ,he grammar o": ,he grammar o"

graphic lang%age' the asic principle set %pgraphic lang%age' the asic principle set %p

to %se geometric $escriptions "or solvingto %se geometric $escriptions "or solvingtwo an$ three $imensional prolems6two an$ three $imensional prolems6

(omp%ter Graphics(omp%ter Graphics : >se o" comp%ter as: >se o" comp%ter as

$ra"ting instr%ment with printer or plotter6$ra"ting instr%ment with printer or plotter6

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,ypes o" ,echnical Drawings

,hree Basic ,ypes o",hree Basic ,ypes o"

,echnical Drawings,echnical Drawings

* 3reehan$ setches3reehan$ setches

* +nstr%ment $rawings+nstr%ment $rawings

* (omp%ter $rawings(omp%ter $rawings

an$ mo$elsan$ mo$els

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@is%ali4ation an$

+mplementation ,here are two principles in $rawing,here are two principles in $rawing

* @is%ali4ation@is%ali4ation

* ,he aility to see what an o!ect loos lie in the,he aility to see what an o!ect loos lie in themin$ o" eye6min$ o" eye6

* +mplementation+mplementation * Drawing o" an o!ect that has een vis%ali4e$Drawing o" an o!ect that has een vis%ali4e$

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)lane an$ soli$ Geometry

5t%$y o" $rawing can e categori4e$ as5t%$y o" $rawing can e categori4e$ as

* )lane geometry)lane geometry

epresentation o" an o!ect havingepresentation o" an o!ect having two $imensionstwo $imensions

* 5oli$ geometry5oli$ geometry epresentingepresenting three $imensionsthree $imensions o" o!ectso" o!ects

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(ont A6

)resent D o!ects with 2D me$ia)resent D o!ects with 2D me$ia

,wo Basic (ategories,wo Basic (ategories

2D2D DD

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Mechanical $rawing "or Engineer Mechanical $rawing "or EngineerMechanical $rawing "or Engineer

* &$vantage&$vantage

+t is technical+t is technical E#actE#act (learest way to comm%nicate(learest way to comm%nicate +t is a %niversal lang%age+t is a %niversal lang%age

* Disa$vantageDisa$vantage ,ime cons%ming to pro$%ce,ime cons%ming to pro$%ce +t nee$s sill+t nee$s sill

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(omm%nication Distance

* (omm%nication $istance is a "actor "or

selection o" graphic lang%age6Engineers + Designers

TECHNICIANS

Drafts man

Sketch

Mechanical

Drawing

Feed

Back Sketch

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,ypes o" Drawing

5etches5etches* $escrie the concept in general$escrie the concept in general

ayo%tayo%t* show the relationships o" parts an$ $e"ines eyshow the relationships o" parts an$ $e"ines ey

$imensions$imensions

DetailsDetails

&ssemly&ssemly )ictorial)ictorial

* "or technical man%als' sales literat%re' or +nternet"or technical man%als' sales literat%re' or +nternet

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,ypes o" Drawing

)ro$%ction Drawings)ro$%ction Drawings

* >se$ to:>se$ to:

transmit an$ comm%nicate in"ormation "or thetransmit an$ comm%nicate in"ormation "or the pro$%ction o" o!ects an$ assemlies -critical in pro$%ction o" o!ects an$ assemlies -critical in

conc%rrent engineering environmentC.conc%rrent engineering environmentC.

* (lassi"ie$ in two ma!or categories:(lassi"ie$ in two ma!or categories: $etail $rawings$etail $rawings

assemly $rawingsassemly $rawings

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,ypes o" $rawing

Detail $rawingDetail $rawing

* Drawings o" single partsDrawings o" single parts

* May e $rawn one part per sheetMay e $rawn one part per sheet

* May e several parts $etaile$ on a large shtMay e several parts $etaile$ on a large sht

* +ncl%$e in"o s%ch as+ncl%$e in"o s%ch as $imensions an$ notes$imensions an$ notes

relating to material' "inish' weight' or tolerancerelating to material' "inish' weight' or tolerance* incl%$es all o" the in"ormation nee$e$ toincl%$es all o" the in"ormation nee$e$ to

"aricate the part6"aricate the part6

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,ypes o" $rawing

&ssemly Drawings&ssemly Drawings

* 5how how parts "it together or are "%nctionally5how how parts "it together or are "%nctionally

relate$relate$* Dimensions typically re"er to relationshipsDimensions typically re"er to relationships

among the partsamong the parts

* O"ten a ill o" materials -listing o" all partsO"ten a ill o" materials -listing o" all partsnecessary to mae %p the total assemly. isnecessary to mae %p the total assemly. is

incl%$e$6incl%$e$6

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,ypes o" $rawing

&ssemly Drawings&ssemly Drawings

* &n assemly $rawing is&n assemly $rawing is

han$y "or a technicianhan$y "or a technicianservicing a machinery orservicing a machinery or

machinery component6machinery component6

* By st%$ying an assemlyBy st%$ying an assemly

$rawing an$ eeping it$rawing an$ eeping it

han$y as the part ishan$y as the part is

repaire$' yo% can e s%rerepaire$' yo% can e s%re

that all pails are installe$ inthat all pails are installe$ in

their proper place6their proper place6

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,ypes o" $rawing

E#plo$e$ pictorial $rawingsE#plo$e$ pictorial $rawings

* epresent several parts assemle$ accor$ing toepresent several parts assemle$ accor$ing to

the a#es o" their assemlythe a#es o" their assemly* )arts are not shown assemle$ %t are move$)arts are not shown assemle$ %t are move$

apart along the principal a#es o" the pro$%ctapart along the principal a#es o" the pro$%ct

* ,ypically not $imensione$,ypically not $imensione$* ;elp"%l "or assemly p%rpose$ on the;elp"%l "or assemly p%rpose$ on the

pro$%ction line pro$%ction line

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,ypes o" $rawing

E#plo$e$ pictorialE#plo$e$ pictorial

$rawings$rawings

* shows all o" theshows all o" thecomponents sprea$ o%t'components sprea$ o%t'

or e#plo$e$6 so yo% canor e#plo$e$6 so yo% can

see what each part loossee what each part loos

lie6lie6

* "re%ently %se$ in"re%ently %se$ in

ill%strate$ parts man%alsill%strate$ parts man%als

an$ service %lletins6an$ service %lletins6

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(are an$ %se o" $rawing instr%ment

+n engineering $rawing any o!ect is+n engineering $rawing any o!ect is

represente$ yrepresente$ y straight lines an$/or c%rvesstraight lines an$/or c%rves66

,hese lines sho%l$ e $rawn as acc%rate as,hese lines sho%l$ e $rawn as acc%rate as possile y the help o" possile y the help o" $rawing$rawing

instr%ments6instr%ments6

%ality o" a $rawing $epen$s to a large%ality o" a $rawing $epen$s to a largee#tent on thee#tent on the %ality ' a$!%stment' proper%ality ' a$!%stment' proper

%se an$ care o" $rawing instr%ments%se an$ care o" $rawing instr%ments66

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ist o" $rawing instr%mentsist o" $rawing instr%ments* Eraser Eraser

* Erasing shiel$Erasing shiel$* ,riangle -5ets%are. -F,riangle -5ets%are. -F00 an$ 0an$ 000 0 000..

* &rchitectHs or engineerHs scale&rchitectHs or engineerHs scale

* +rreg%lar c%rves -3rench c%rve.+rreg%lar c%rves -3rench c%rve.

* Drawing instr%ment set -(ompass' Divi$er' e#tensions.Drawing instr%ment set -(ompass' Divi$er' e#tensions.

* )rotractor )rotractor

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ist o" $rawing instr%mentsist o" $rawing instr%ments* Drawing oar$Drawing oar$

* ,s%are' or parallelr%ling straighte$ge' or $ra"ting,s%are' or parallelr%ling straighte$ge' or $ra"tingmachinemachine

* Drawing sheetsDrawing sheets

* Dra"ting tapeDra"ting tape

* Dra"ting pencilsDra"ting pencils

* )encil sharpener )encil sharpener

* ettering instr%mentettering instr%ment

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Drawing Broa$

Drawing tales come in many $i""erent si4eDrawing tales come in many $i""erent si4ean$ $esign6 +t co%l$ ean$ $esign6 +t co%l$ e "i#e$' movale' with"i#e$' movale' with$rawer' a$!%stale' etc6$rawer' a$!%stale' etc6

,hey are %se$ to attach $rawing sheet6,hey are %se$ to attach $rawing sheet6

Ieep yo%r $rawing taleIeep yo%r $rawing tale clean an$ $ryclean an$ $ry notnotto a""ect yo%r $rawing %ality6to a""ect yo%r $rawing %ality6

DonHt %se la$es to c%t $ra"tingDonHt %se la$es to c%t $ra"tingtapes on $rawing tale6tapes on $rawing tale6

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Drawing 5heet

* ma$e "rom $i""erentma$e "rom $i""erent

materials with $i""erentmaterials with $i""erent

%ality6%ality6

* )aper' tracing paper')aper' tracing paper'

vell%m' tracing cloth'vell%m' tracing cloth'

glass cloth or "ilmglass cloth or "ilm66

* Drawing sheets willDrawing sheets will

$etermine selection o"$etermine selection o" pencil gra$e pencil gra$e

>5 (>5,OM&<>5 (>5,OM&<

5E+E55E+E5+5O+5O

5,&ND& 5,&ND&

DD

5i45i4

ee

3irst3irst

serieseriess

5econ$5econ$

seriesseries

5i45i4

ee

,hir$ series,hir$ series

&& 8811//22 # 11# 11 # 12 # 12 &&

0081 # 11881 # 118

BB 11 # 1J11 # 1J 12 # 1812 # 18 &&11 F # 81F # 81

(( 1J # 221J # 22 18 # 218 # 2 &&22

20 # F20 # F

DD 22 # 22 # 2 # 2 # &&

2J # 202J # 20

EE # # # 8 # 8 &&

210 # 2J210 # 2J

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,s%are

* ,hey can e ma$e "rom,hey can e ma$e "rom$i""erent materials' mostly$i""erent materials' mostly"rom"rom woo$ or plastic6woo$ or plastic6

* )arts:)arts: la$e an$ hea$ la$e an$ hea$* two e$ges o" thetwo e$ges o" the la$e sho%l$ la$e sho%l$

e parallel6 e parallel6

* ,he hea$ is "i#e$,he hea$ is "i#e$ at 0at 000 to theto the la$e la$e

* ,he cleanness o" yo%r , K ,he cleanness o" yo%r , K s%are greatly a""ect yo%rs%are greatly a""ect yo%r$rawing %ality an$$rawing %ality an$cleanliness6cleanliness6

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,s%are >se$ "or >se$ "or

* Drawing hori4ontalDrawing hori4ontallineslines

* G%i$ing trianglesG%i$ing triangles

* )osition $rawing paper )osition $rawing paper

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Drawing )encils

* Most $rawing pencil lea$s are ma$e "rom

graphite6 ,hey are %s%ally ma$e in 1J $egrees

o" har$ness6

* B-so"test an$ lacest.B-so"test an$ lacest.

* FB-e#tremely so"t.FB-e#tremely so"t.

* B e#tra so"t.B e#tra so"t.

* B -very so"t.B -very so"t.

* 2B -so"t' pl%s.2B -so"t' pl%s.* B -so"t.B -so"t.

* ;B -me$i%m so"t.;B -me$i%m so"t.

* 3 -interme$iate' etween3 -interme$iate' etweenso"t an$ har$.so"t an$ har$.

* ; -me$i%m har$.; -me$i%m har$.

* 2; -har$.2; -har$.

* ; -har$' pl%s.; -har$' pl%s.

* ; -very har$.; -very har$.

* F; -e#tra har$.F; -e#tra har$.* ; -e#tra har$' pl%s.; -e#tra har$' pl%s.

* J; -e#tremely har$.J; -e#tremely har$.

* 8; -e#tremely har$' pl%s.8; -e#tremely har$' pl%s.

* ; -;ar$est.; -;ar$est.

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Drawing )encils

* 5election o" $rawing pencil5election o" $rawing pencil type and quality of drawing paper type and quality of drawing paper how thick and dark you want the linehow thick and dark you want the line to e6to e6

* )encil lines sho%l$ e)encil lines sho%l$ e clean an$ sharpclean an$ sharp6 ,hey m%st e6 ,hey m%st e$ar eno%gh$ar eno%gh "or the views to e seen when the stan$ar$"or the views to e seen when the stan$ar$lines are $rawn6lines are $rawn6

* +" yo% %se+" yo% %se too m%ch press%retoo m%ch press%re' yo% will groove the' yo% will groove the$rawing s%r"ace6 <o% can avoi$ this i" yo% %se$rawing s%r"ace6 <o% can avoi$ this i" yo% %se proper proper

gra$e o" lea$6gra$e o" lea$6* ,%rn the pencil etween yo%r th%m an$ "ore"inger as,%rn the pencil etween yo%r th%m an$ "ore"inger asyo% $raw a line6yo% $raw a line6

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Drawing instr%ment set

* +t may incl%$e+t may incl%$e compass with pen part an$ pencil part'compass with pen part an$ pencil part'$ivi$er' lengthening ar' ow pen' ow pencil an$$ivi$er' lengthening ar' ow pen' ow pencil an$r%ling pensr%ling pens

* Divi$ers:Divi$ers: %se$ to trans"er $istance%se$ to trans"er $istance* (ompass(ompass: %se$ to $raw circles or arcs -which are parts: %se$ to $raw circles or arcs -which are parts

o" a circle.o" a circle.

* Beam compassBeam compass: %se$ to $raw arcs or circles o" larger: %se$ to $raw arcs or circles o" larger

si4e6si4e6

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Drawing instr%ment set

3rench (%rves3rench (%rves

* >se$ to $raw irreg%lar c%rves>se$ to $raw irreg%lar c%rves

* +t is availale to align at least three points the+t is availale to align at least three points thec%rve to e $rawnc%rve to e $rawn

,riangles,riangles

* >se$ to $raw lines at stan$ar$ angles an$ y>se$ to $raw lines at stan$ar$ angles an$ yconnecting any two pointsconnecting any two points

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5cale o" Drawing

>5+NG )O)E 5(&E>5+NG )O)E 5(&E

<O> (&N E&D 3><O> (&N E&D 3>

5+LE ME&5>EMEN,55+LE ME&5>EMEN,53OM D&7+NG563OM D&7+NG56

Enlarged Enlarged Same size Same size Reduced Reduced

2000:12000:1

1000:11000:1 1:11:1 1:21:2

500:1500:1 1:F1:F

200:1200:1 1:101:10

100:1100:1 1:201:20

50:150:1 1:F01:F0

20:120:1 1:1001:100

10:110:1 1:2001:200

5:15:1 1:F001:F00

2:12:1 1:10001:1000

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,ypes o" lines

@isile o%tlines@isile o%tlines -o%n$ary-o%n$ary lines.lines.

&))+(&,+ON&))+(&,+ON

)hantom line' show alternate position)hantom line' show alternate positionong thin chain withong thin chain with

two $ash linestwo $ash lines

(%tting plane lines6(%tting plane lines6ong chain thic atong chain thic at

en$s an$ thinen$s an$ thin

elsewhere6elsewhere6

oc%s lines center lines'oc%s lines center lines'ong cong chaihainn tthhin linein line

+nvisile e$ges+nvisile e$ges5hort $ash5hort $ash

ong rea lines6ong rea lines6(ontin%o%s thin line(ontin%o%s thin line

with L+GL&G6with L+GL&G6

+rreg%lar o%n$ary lines' short rea lines'+rreg%lar o%n$ary lines' short rea lines'(ontin%o%s thin wavy(ontin%o%s thin wavy

line -$rawn "reeline -$rawn "ree han$.han$.

DimensionDimension lineslines'' lea$er lineslea$er lines'' e#tensione#tension

lineslines'' constr%ctionconstr%ction lines hatchinglines hatching

-5ection. lines6-5ection. lines6

(ontin%o%s thin line(ontin%o%s thin line

(ontin%o%s(ontin%o%s thic linethic line

+>5,&,+ON+>5,&,+ON,<)E O3 +NE5,<)E O3 +NE5

@isile o%tlines@isile o%tlines -o%n$ary-o%n$ary lines.lines.

&))+(&,+ON&))+(&,+ON

)hantom line' show alternate position)hantom line' show alternate positionong thin chain withong thin chain with

two $ash linestwo $ash lines

(%tting plane lines6(%tting plane lines6ong chain thic atong chain thic at

en$s an$ thinen$s an$ thin

elsewhere6elsewhere6

oc%s lines center lines'oc%s lines center lines'ong chain thin lineong chain thin line

+nvisile e$ges+nvisile e$ges5hort $ash5hort $ash

ong rea lines6ong rea lines6(ontin%o%s thin line(ontin%o%s thin line

with L+GL&G6with L+GL&G6

+rreg%lar o%n$ary lines' short rea lines'+rreg%lar o%n$ary lines' short rea lines'(ontin%o%s thin wavy(ontin%o%s thin wavy

line -$rawn "reeline -$rawn "ree han$.han$.

DimensionDimension lineslines'' lea$er lineslea$er lines'' e#tensione#tension

lineslines'' constr%ctionconstr%ction lines hatchinglines hatching

-5ection. lines6-5ection. lines6

(ontin%o%s(ontin%o%s thin linethin line

(ontin%o%s(ontin%o%s thic linethic line

+>5,&,+ON+>5,&,+ON,<)E O3 +NE5,<)E O3 +NE5

7/17/2019 ch01.ppt


,ypes o" lines

7/17/2019 ch01.ppt


Bor$ers an$ ,itle Blocs

Bor$ersBor$ers

* provi$es a sa"ety area to prevent the loss o" provi$es a sa"ety area to prevent the loss o"

important in"ormationimportant in"ormation* +mproves appearance "or presentation p%rposes+mproves appearance "or presentation p%rposes

,itle Blocs,itle Blocs

* some items stan$ar$:some items stan$ar$: $rawing n%mer' sheet$rawing n%mer' sheetn%mer' title' company name' logo' scale' $ate'n%mer' title' company name' logo' scale' $ate'

tolerances' $ra"ter' checer' s%pervisor tolerances' $ra"ter' checer' s%pervisor

7/17/2019 ch01.ppt


& "ew asic points "or a $rawing

5ho%l$ e complete an$ %namig%o%s5ho%l$ e complete an$ %namig%o%s

5ho%l$ e neat an$ easy to rea$5ho%l$ e neat an$ easy to rea$

>se only as many views as necessary to>se only as many views as necessary to

show all re%ire$ $etailshow all re%ire$ $etail

&pply tolerances realistically overly tight&pply tolerances realistically overly tight

tolerances can a$$ a great $eal o" a$$itionaltolerances can a$$ a great $eal o" a$$itional

cost with little or not a$$e$ val%e to the partcost with little or not a$$e$ val%e to the part

7/17/2019 ch01.ppt


Drawing paper arrangement

7/17/2019 ch01.ppt


ettering

ettering plays a ma!or role in overallettering plays a ma!or role in overall

appearance o" a $rawing6appearance o" a $rawing6

ettering sho%l$ e e#ec%te$ in one stroeettering sho%l$ e e#ec%te$ in one stroe

@ertical lettering@ertical lettering

;ori4ontal lettering;ori4ontal lettering

E#ercise on lettering a"ter rea$ingE#ercise on lettering a"ter rea$ing

assignmentassignment

7/17/2019 ch01.ppt


Basic Strokes

StraightStraight SlantedSlanted CurvedCurvedHorizontalHorizontal

1 1

!

Examples : Application of basic stroke

"I# letter "A# letter 1

!

$ %

&

"B# letter

S t d St k S

7/17/2019 ch01.ppt


Suggested Strokes Sequence

Straight line

letters

C'r(ed line

letters

C'r(ed line

letters )

N'merals

Uppercase letters ! "umerals

7/17/2019 ch01.ppt


The te*t s ,-d. height is a,-'t /! the height -f a ca0ital

letter

Suggested Strokes Sequence

#o$ercase letters

7/17/2019 ch01.ppt


Stroke Sequence

I L T F

E H

7/17/2019 ch01.ppt


V X W

Stroke Sequence

S k S

7/17/2019 ch01.ppt


N M K Z

Y A

Stroke Sequence

4

7/17/2019 ch01.ppt


O Q C G

Stroke Sequence

St k S

7/17/2019 ch01.ppt


D U P B

R J

Stroke Sequence

1 2

7/17/2019 ch01.ppt


5

Stroke Sequence

7

St k S

7/17/2019 ch01.ppt


6

!

"

Stroke Sequence

# $

St k S

7/17/2019 ch01.ppt


Stroke Sequence

% &

7/17/2019 ch01.ppt


Stroke Sequence

' ( ) *

+

St k S

7/17/2019 ch01.ppt


Stroke Sequence

, - .

/

0

St k S

7/17/2019 ch01.ppt


Stroke Sequence

3

8

St k S

7/17/2019 ch01.ppt


Stroke Sequence

9 : ; <

= >

7/17/2019 ch01.ppt


%ord Composition2,ser(e the f-ll-wing w-rd

3I4A52N6\

/\| )( )| (|

S0ace ,etween the letters de0ends -n the c-nt-'r -f

the letters at an ad7acent side

S0acing

C-nt-'r ||||

6eneral c-ncl'si-ns are8

6--d s0acing creates a00r-*imatel. e9'al background

area ,etween letters

7/17/2019 ch01.ppt


1 Straight : Straight

Straight : C'r(e

! Straight : Slant

$ C'r(e : C'r(e

Space &et$een #etters


7/17/2019 ch01.ppt


& Slant : Slant% C'r(e : Slant

; The letter "<# and "T#

≡ slant slant

≡

slant

straight


E l G d d P L tt i

7/17/2019 ch01.ppt


'(()

N-t 'nif-rm in st.le

N-t 'nif-rm in height

N-t 'nif-rml. (ertical -r inclined

N-t 'nif-rm in thickness -f str-ke

Area ,etween letters n-t 'nif-rm

Area ,etween w-rds n-t 'nif-rm

Example 8 Good and Poor Lettering

Sentence Composition

7/17/2019 ch01.ppt


<ea(e the s0ace ,etween w-rds e9'al t- the s0acere9'ires f-r writing a letter "2#

Example

Sentence Composition

ALL DIMEN#ION# ARE IN

MILLIMETER#

O O O

OUNLE##

OTHERWI#E #PECIFIED?O

7/17/2019 ch01.ppt


Geometric constr%ction

7/17/2019 ch01.ppt



&& point point'' lineline'' arcarc' an$' an$ circlecircle are the asicare the asicelements %se$ to create the most comple#elements %se$ to create the most comple#$rawings$rawings

Geometric elementsGeometric elements* & point& point

* & line& line

* & c%rve& c%rve

* &n angle&n angle

* )lanes)lanes

* (lose$ 2D elements(lose$ 2D elements

* 5%r"aces5%r"aces

* 5oli$s5oli$s

7/17/2019 ch01.ppt


& )oint

5peci"ies an e#act location in space5peci"ies an e#act location in space

,heoretical location that has neither wi$th',heoretical location that has neither wi$th'

height' nor $epth an$ $escries an e#actheight' nor $epth an$ $escries an e#actlocation in space6location in space6

& point is represente$ y intersection o"& point is represente$ y intersection o"

+ntersection o" 2lines+ntersection o" 2lines & short crossar on a line& short crossar on a line

Or y a small crossOr y a small cross

7/17/2019 ch01.ppt


& )oint

& point can e& point can e

$e"ine$ as a set o"$e"ine$ as a set o"

coor$inates -#'y. oncoor$inates -#'y. on

the (artesian plane6the (artesian plane6

7/17/2019 ch01.ppt


& ine

;as length an$ $irection %t no wi$th;as length an$ $irection %t no wi$th

&ll points are collinear &ll points are collinear

May e in"initeMay e in"inite

* &t least one point m%st e speci"ie$&t least one point m%st e speci"ie$

* Direction may e speci"ie$ with a secon$ point or with anDirection may e speci"ie$ with a secon$ point or with an

angleangle

May e "initeMay e "inite

* De"ine$ y two en$ pointsDe"ine$ y two en$ points

* De"ine$ y one en$ point' a length' an$ $irectionDe"ine$ y one en$ point' a length' an$ $irection

7/17/2019 ch01.ppt


& ine

& straight line: is the shortest $istance etween& straight line: is the shortest $istance etweentwo points an$ is commonly re"erre$ to simply astwo points an$ is commonly re"erre$ to simply asa linea line

+" the line is in$e"inite in e#tent' the length is a+" the line is in$e"inite in e#tent' the length is amatter o" convenience' an$ the en$ points arematter o" convenience' an$ the en$ points arenot "i#e$not "i#e$

+" the en$ points are signi"icant' they m%st e+" the en$ points are signi"icant' they m%st e

mare$ y means o" small mechanically $rawnmare$ y means o" small mechanically $rawncrossarscrossars

PP means parallel linesPP means parallel lines

7/17/2019 ch01.ppt


& line

ine May e straight' c%rve$' or aine May e straight' c%rve$' or a

comination %t straight line is the shortestcomination %t straight line is the shortest

$istance etween two points$istance etween two points

7/17/2019 ch01.ppt


& (%rve

,he loc%s o" points along a c%rve are not,he loc%s o" points along a c%rve are not

collinear collinear

,he $irection is constantly changing,he $irection is constantly changing 5ingle c%rve$ lines5ingle c%rve$ lines

* all points on the c%rve lie on a single planeall points on the c%rve lie on a single plane

& reg%lar c%rve& reg%lar c%rve* ,he $istance "rom a "i#e$ point to any point on,he $istance "rom a "i#e$ point to any point on

the c%rve is a constantthe c%rve is a constant

* E#amples: arc an$ circleE#amples: arc an$ circle

7/17/2019 ch01.ppt


& (%rve

& reg%lar c%rve& reg%lar c%rve

* ,he $istance "rom a,he $istance "rom a

"i#e$ point to any"i#e$ point to any point on the c%rve is point on the c%rve is

a constanta constant

* E#amples: arc an$E#amples: arc an$

circlecircle

7/17/2019 ch01.ppt


&n angle

&n angle is "orme$ y two intersecting lines&n angle is "orme$ y two intersecting lines

means an angle'means an angle'

,here are 0,here are 000 in a "%ll circlein a "%ll circle

2&ngles are (omplementary i" they total2&ngles are (omplementary i" they total

2&ngles are 5%pplementary i" they total2&ngles are 5%pplementary i" they total >se protractor to $raw an angle>se protractor to $raw an angle

∠

7/17/2019 ch01.ppt


&n angle

7/17/2019 ch01.ppt


)lanes

Planes are defined by: Planes are defined by:

T</88 &:0> :0 %-&:9 &: 3 >0/3&9<0%&:8

T( 3/3%%8% %&:8>

T( &:08/>80&:9 %&:8>

A &:0 3: 3 %&:8

7/17/2019 ch01.ppt


)lanes

BB

A A

,riangles,riangles* & triangle is a plane "ig%re o%n$e$

y three straight si$es6

* E%ilateral triangle -all si$es e%al' 0E%ilateral triangle -all si$es e%al' 0$eg6 angles.$eg6 angles.

* +sosceles triangle -two si$es e%al.+sosceles triangle -two si$es e%al.

* ight triangle -one angle is 0ight triangle -one angle is 0

$egrees.$egrees. &&22QBQB22R(R(22 -)ythagorean theorem.-)ythagorean theorem. 5in5inθθR&/(R&/( (os(osθ=θ=B/(B/(

CC

θθ

7/17/2019 ch01.ppt


)lane

,riangles,riangles* ,riangles: is a plane "ig%re o%n$e$ y three straight si$es6,riangles: is a plane "ig%re o%n$e$ y three straight si$es6

* ,he s%m o" the interior angles is always 180,he s%m o" the interior angles is always 18000

* &ny triangle inscrie$ in a semicircle is a right triangle i" the&ny triangle inscrie$ in a semicircle is a right triangle i" thehypoten%se coinci$es with the $iameter6hypoten%se coinci$es with the $iameter6

7/17/2019 ch01.ppt


)lanes

%a$rilateral an$ polygons%a$rilateral an$ polygons

#=3/8 A%% >&8> 8=3% .=/ /&9<0 3:9%8>?

R803:9%8 O>&08 >&8> 3/8 8=3%.=/ /&9<0 3:9%8>?

Q=3/&%308/3%

7/17/2019 ch01.ppt


)lanes


R<;=> A%% >&8> 8=3%O>&08 3:9%8> 3/8 8=3%?

R<;& O>&08 >&8> 3/88=3% O>&08 3:9%8> 3/8 8=3%?

Q=3/&%308/3%

7/17/2019 ch01.ppt


)lanes


T/38+& T( >&8> 3/3%%8%?

T/38+&=; N >&8> 3/3%%8%?

Q=3/&%308/3%

7/17/2019 ch01.ppt


)lanes


O0<8/P%-9:>

P8:039: H8)39: H8039:

O039: N:39: D839:

5 #IDE# 6 #IDE# 7 #IDE#

! #IDE# #IDE# 1" #IDE#

7/17/2019 ch01.ppt


)lanes

%a$rilateral: is a plane "ig%re o%n$e$ y %a$rilateral: is a plane "ig%re o%n$e$ y

straight si$es6straight si$es6

+" the opposite si$es are parallel' the %a$rilateral+" the opposite si$es are parallel' the %a$rilateralis also calle$ parallelogramis also calle$ parallelogram

)olygons: is any plane "ig%re o%n$e$ y straight)olygons: is any plane "ig%re o%n$e$ y straight

lines6lines6

eg%lar )olygon has e%al si$es an$ angle'eg%lar )olygon has e%al si$es an$ angle' eg%lar )olygon can e inscrie$ in oreg%lar )olygon can e inscrie$ in or

circ%mscrie$ aro%n$ a circlecirc%mscrie$ aro%n$ a circle

7/17/2019 ch01.ppt


)lanes


7/17/2019 ch01.ppt


)lanes

(ircles an$ &rcs(ircles an$ &rcs* Minor arcMinor arc

* Ma!or arcMa!or arc

* (entral angle(entral angle

* 5ector 5ector

* %a$rant%a$rant

* 5egment5egment* ,angent,angent

* (enter (enter

* (irc%m"erence(irc%m"erence

* a$i%sa$i%s

* (hor$(hor$

* Diameter Diameter

* 5ecant5ecant* &rc&rc

* 5emicircle5emicircle

l

7/17/2019 ch01.ppt


)lanes

(ircle: is a close$(ircle: is a close$

c%rve' all points o"c%rve' all points o"

which are the samewhich are the same

$istance "rom a point$istance "rom a point

calle$ the center calle$ the center

(irc%m"erence is(irc%m"erence is

re"erre$ to the circlere"erre$ to the circleor to the $istanceor to the $istance

aro%n$ the circaro%n$ the circ

l

7/17/2019 ch01.ppt


)lanes

(ircles an$ &rcs(ircles an$ &rcs

* a$i%s -.a$i%s -.

* Diameter -D.Diameter -D.

* &ngle -1 rev R 0&ngle -1 rev R 0oo 0H 0.0H 0.

* (irc%m"erence -2S611FS.(irc%m"erence -2S611FS.

* ,angent,angent

* (hor$(hor$ & line perpen$ic%lar to the mi$point o" a chor$ passes& line perpen$ic%lar to the mi$point o" a chor$ passes

thro%gh the center o" the circlethro%gh the center o" the circle

*(oncentric circles(oncentric circles

DD

44

θθ

)l

7/17/2019 ch01.ppt


)lanes

+nscrie$ polygonA: &:>/&8 %-9: 3: 8:>0/=08 - 808/;&:&:9 0<8

:=;8/ . >&8> 3: 0<8&>03:8 3/>> 0<8 /:8/>?

>&8 %-9:

C&/%8 &3;808/ &>03:8 3/>>/:8/>

E)3;%8There are 360° in a circle; for an eight-sided polygon

divide 360° by 8 (360

° ÷ 8=45

° ) to deterine the

C::80 /3&3% %&:8> (<8/8 0<8 8:>&:08/>80 0<8 &/=;.8/8:8

)l

7/17/2019 ch01.ppt


)lanes

(irc%mscrie$ )olygon

A &/=;>/&8 %-9: 3:8 :>0/=08 - 808/;&:&:9

0<8 :=;8/ . >&8> 3: 0<8&>03:8 3/>> 0<8 30>?

>&8 %-9:

C&/%8 &3;808/ &>03:8 3/>>0<8 30>

E)3;%8There are 360° in a circle; for an eight-sided polygon

divide 360° by 8 (360° ÷ 8=45 ° ) to deterine the

C::80 /3&3% %&:8> - /3(&:9 %&:8>89;8:0> 03:98:0 0 3/ >89;8:0>

)l

7/17/2019 ch01.ppt


)lanes

)arallelograms)arallelograms

* si$es si$es

* Opposite si$es are parallelOpposite si$es are parallel

* E#6 s%are' rectangle' an$ rhom%sE#6 s%are' rectangle' an$ rhom%s eg%lar polygonseg%lar polygons

* &ll si$es have e%al length&ll si$es have e%al length si$es: e%ilateral triangle si$es: e%ilateral triangle

si$es: s%are si$es: s%are F si$es: pentagonF si$es: pentagon

* (irc%mscrie$ or inscrie$(irc%mscrie$ or inscrie$

5 li$

7/17/2019 ch01.ppt


5oli$s

* ,hree $imensional,hree $imensional

* ,hey have a vol%me,hey have a vol%me

* eg%lar polyhe$raleg%lar polyhe$ral

;ave reg%lar polygons;ave reg%lar polygons"or "aces"or "aces

&ll "aces are the same&ll "aces are the same

)risms)risms

* ,wo e%al parallel,wo e%al parallel

"aces"aces

* 5i$es are5i$es are

parallelograms parallelograms

)yrami$s)yrami$s

* (ommon intersection(ommon intersection

point -verte#. point -verte#.

(ones(ones

(ylin$ers(ylin$ers

5pheres5pheres

G t i t ti li$

7/17/2019 ch01.ppt


Geometric constr%ctionsoli$s

)olyhe$ral: soli$s o%n$e$ y plane s%r"aces)olyhe$ral: soli$s o%n$e$ y plane s%r"aces

* ,hese s%r"aces are calle$ "ace,hese s%r"aces are calle$ "ace

* eg%lar )olyhe$ral: a soli$ with "aces e%al a reg%lar polygoneg%lar )olyhe$ral: a soli$ with "aces e%al a reg%lar polygon

G t i ( t i t

7/17/2019 ch01.ppt


Geometric (onstraints

7hen maing soli$ mo$els' constraints are7hen maing soli$ mo$els' constraints are

necessary to pro$%ce parts o" e#act shapesnecessary to pro$%ce parts o" e#act shapes

an$ si4es6 ,o mae a part parametric it isan$ si4es6 ,o mae a part parametric it isnecessary to %se as many geometricnecessary to %se as many geometric

constraints as possile6 ,he ne#t set o"constraints as possile6 ,he ne#t set o"

sli$es will show what that geometry is6sli$es will show what that geometry is6

G t i ( t i t

7/17/2019 ch01.ppt



Parallel L&:8> 0<30 3/8 8=3% &>03:8./;83< 0<8/ 30 83< &:0 3%:9 0<8&/

%8:90<? T<8>8 0( %&:8> 3/8 3/3%%8%? T<8 %&:8> 3/83%> /8/8>8:0&:9 0<8 >-;% ./ 3/3%%8%?

Perpendicular L&:8> 0<30 3/8 !" ./; :8 3:0<

T<8>8 0( %&:8> 3/8 8/8:&=%3/ 3:/8/8>8:0 0<8 >-;% ./ 8/8:&=%3/?

G t i ( t i t

7/17/2019 ch01.ppt



;ori4ontal & line is hori4ontal when it is;ori4ontal & line is hori4ontal when it is

parallel to the hori4on6 +n soli$ mo$eling' parallel to the hori4on6 +n soli$ mo$eling'

the line is also parallel in the hori4ontalthe line is also parallel in the hori4ontal pro!ection plane an$ will appear tr%e length6 pro!ection plane an$ will appear tr%e length6

@ertical & line is vertical when it is@ertical & line is vertical when it is

perpen$ic%lar to the hori4on6 ,his line will perpen$ic%lar to the hori4on6 ,his line will e parallel to the "ront an$ pro"ile pro!ection e parallel to the "ront an$ pro"ile pro!ection

planes6 planes6

G t i ( t i t

7/17/2019 ch01.ppt



,angent & line or arc that has one point in common with,angent & line or arc that has one point in common withan arc6 +" a line is tangent with a circle the line will ean arc6 +" a line is tangent with a circle the line will e

perpen$ic%lar with a line $rawn "rom the point o" tangency perpen$ic%lar with a line $rawn "rom the point o" tangencythro%gh the center point o" the arc6 +" two arcs are tangentthro%gh the center point o" the arc6 +" two arcs are tangent-3ig%re B.' a line $rawn etween the centers will intersect-3ig%re B.' a line $rawn etween the centers will intersectat the point o" tangency6at the point o" tangency6

G t i ( t i t

7/17/2019 ch01.ppt



Concentric C&/%8> / 3/> 0<30 ><3/8 0<8 >3;8 8&:0?

T<8>8 &/%8> 3: 0<8 3/> ><3/8 0<8 >38:08/ &:0?

Coincident P&:0> 0<30 ><3/8 0<8 >3;8 %30&:: 0<8 /&:308 %3:8? P&:0> ;3- 3%> 8 3/0>. 3/> / =/'8>?

G t i ( t i t

7/17/2019 ch01.ppt



Collinear L&:8> 0<30 &. /,808 30 83< 0<8/ (&%%8;8 0<8 >3;8 %&:8?

C%%&:83/ %&:8>

Coplanar T( / ;/8 ,80> 0<30 >&0 &: 0<8 >3;8%3:8?

Fixed Point A &:0 0<30 <3> 88: ./8 0 >03- &:

:8 %30&: &: >38?

Equal T( / ;/8 %&:8> 3/> / &/%8> 0<30 3/8 9&'0<8 >3;8 ;39:&0=8?


7/17/2019 ch01.ppt



Bisecting a line orBisecting a line orcirc%lar arccirc%lar arc

*3rom & B $raw3rom & B $rawe%al arcs withe%al arcs withra$i%s greater thanra$i%s greater thanhal" &Bhal" &B

* 6 Toin intersection D6 Toin intersection D E with a straight E with a straight

line to locate center line to locate center

G t i t ti

7/17/2019 ch01.ppt



Bisecting a line with a triangle ,5%areBisecting a line with a triangle ,5%are

* 3rom en$points & B' $raw constr%ction lines at3rom en$points & B' $raw constr%ction lines at0' F' or 0 $egrees with the given line60' F' or 0 $egrees with the given line6

* ,hen thro%gh their intersection' (' $raw a line,hen thro%gh their intersection' (' $raw a line perpen$ic%lar to the given line to locate the center perpen$ic%lar to the given line to locate the center((


7/17/2019 ch01.ppt



Bisecting an angle

&ngle B&( is to e isecte$:

* 5trie large arc * 3rom intersect points (

B' strie e%al arcs r with ra$i%s slightlylarger than hal" B(' tointersect at D

* Draw line &D' which isect the angle


7/17/2019 ch01.ppt



,rans"erring an angle

&ngle B&( is to e trans"erre$ to the new position &H BH:* >se any convenient ra$i%s ' an$ strie arcs "rom centers & an$ &H

* 5trie e%al arcs r' an$ $raw si$e &H(H


7/17/2019 ch01.ppt



Drawing a line thro%gh a point an$ parallel to aline


7/17/2019 ch01.ppt



Drawing a line parallel to a line an$ at a $istance


7/17/2019 ch01.ppt



Divi$ing a line into e%al parts


7/17/2019 ch01.ppt



Divi$ing a

line into

e%al parts

contin%e$


7/17/2019 ch01.ppt



Divi$ing a line into proportional parts


7/17/2019 ch01.ppt



Drawing a line thro%gh a point an$

perpen$ic%lar to a line* 7hen the point is not on the line

* 7hen the point is on the line

* 3ig%re c' $' an$ eAsel" rea$


7/17/2019 ch01.ppt



Drawing a triangle with si$es given* Draw one si$e' as (' in $esire$ position' an$ strie arc

with ra$i%s e%al to si$e &

* 5trie arc with ra$i%s e%al to si$e B* Draw si$e & an$ B "rom intersection o" arcs' as shown in

+++


7/17/2019 ch01.ppt



Drawing a right trianglewith hypoten%se an$one si$e given* Given si$es 5 an$ '

with &B as a $iametere%al to 5' $raw asemicircle

* 7ith & as a center an$ as a ra$i%s' $raw an arc

intersecting thesemicircle at (

* Draw &( an$ (B tocomplete the righttriangle


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Drawing an e%ilateral triangle


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Drawing a s%areDrawing a s%are


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Drawing a reg%lar pentagonDrawing a reg%lar pentagon


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Drawing a reg%lar he#agonDrawing a reg%lar he#agon


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Drawing a reg%larDrawing a reg%lar

he#agonhe#agon


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Drawing any reg%lar polygonDrawing any reg%lar polygon


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Drawing a circle tangent to a line at a given point* &t )' erect a perpen$ic%lar to the line

* 5et o"" the ra$i%s o" the re%ire$ circle on the perpen$ic%lar

* Draw a circle with ra$i%s ()


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Drawing a tangent to a circle thro%gh a point* Given point ) on the circle

* Move the ,s%are an$ triangle as a %nit %ntil one si$e o" thetriangle passes thro%gh the point ) an$ the center o" the circle

* ,hen sli$e the triangle %ntil the other si$e passes thro%gh point)' an$ $raw the re%ire$ tangent


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Drawing tangents to two circles* Move the triangle an$ ,s%are as a %nit %ntil one

si$e o" the triangle is tangent' y inspection' to thetwo circles6

* ,hen sli$e the triangle %ntil the other si$e passesthro%gh the center o" one circle' an$ lightly marthe point o" tangency6

* ,hen sli$e the triangle %ntil the sli$e passes thro%ghthe center o" the other circle' an$ mar the point o"tangency6

* 3inally' sli$e the triangle ac to the tangent position' an$ $raw the tangent lines etween the two points o" tangency6 Draw the secon$ tangent line ina similar manner


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Drawing tangents to two circles


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(onstr%cting arcs tangent to two lines


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(onstr%cting an arc tangent to a line an$ anotherarc


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(onstr%ctingan arc tangentto two givenarcs


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(onstr%cting an arc tangent to a given arc


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(onic 5ections: are c%rves pro$%ce$ y

planes intersecting a right circ%lar cone

types o" c%rves are pro$%ce$: circle'ellipse' paraola' hyperola


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Ellipse: 5inglec%rve$s%r"ace primitive Kcreate$ when a plan

passes thro%gh a rightcirc%lar cone at anangle to the a#is that isgreater than the angle

etween the a#is an$the si$es -a circle whenviewe$ at an angleappears as an ellipse.


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&n ellipse

* ,he long a#is is the ma!or a#is the short a#is is the

minor a#is

* Each ellipse has two 3O(+ points -E 3.

* ,he "oci points are "o%n$ y striing arcs with ra$i%s

e%al to hal" the ma!or a#is with center at the en$ o"

the minor a#is -point ( or D.

* &n ellipse is generate$ y a point moving so that thes%m o" its $istances "rom two points -the "oci. is

constant an$ e%al to the ma!or a#is


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(onstr%cting a 3oci

Ellipse


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Geo et c co st %ct o

(onstr%cting "oci ellipse(onstr%cting "oci ellipse


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(onstr%cting concentric circle ellipse(onstr%cting concentric circle ellipse


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(onstr%cting "o%r centere$ metho$ ellipse(onstr%cting "o%r centere$ metho$ ellipse


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)araola: (%rve

create$ when a

plane intersects aright circ%lar cone

parallel to the si$e

-elements. o" the

cone


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Engineering Applications

o* +ara&olas

+arallelogram

,ethod o*

)ra$ing

+ara&olas


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(onstr%cting a(onstr%cting a

paraola paraola


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(onstr%cting a paraola(onstr%cting a paraola


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;yperola: (%rve

o" the intersection

create$ when a

plane intersects a

right circ%lar cone

an$ maes a smaller

anglewith the a#is than

$o the elements


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;yperola;yperola


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(onstr%cting a hyperola(onstr%cting a hyperola


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(onstr%cting invol%tes o" a circle(onstr%cting invol%tes o" a circle


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(onstr%cting a spiral(onstr%cting a spiral

* & singlec%rve$ s%r"ace that egins at a point calle$ a pole an$& singlec%rve$ s%r"ace that egins at a point calle$ a pole an$

ecomes larger as it travels in a plane aro%n$ the origin ecomes larger as it travels in a plane aro%n$ the origin

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En$ o" part oneEn$ o" part one

ch01.ppt

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