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ForewordForeword
Orthographic projection (sometimes referred to asOrthographic projection (sometimes referred to as multi-viewmulti-view projection), is a geometric projection), is a geometric procedure used in the engineering disciplines to project multiple graphic images of three- procedure used in the engineering disciplines to project multiple graphic images of three-dimensional objects, onto a single two-dimensional plane. he procedure is also calleddimensional objects, onto a single two-dimensional plane. he procedure is also calledengineering drawing engineering drawing oror drafting,drafting, and is the primar! means of communication used b!and is the primar! means of communication used b!designers and engineers in the design process. "ultiple #iews in an orthogonal orientationdesigners and engineers in the design process. "ultiple #iews in an orthogonal orientation(each rotated $%& from the other), is fundamental to the definition of feature and part(each rotated $%& from the other), is fundamental to the definition of feature and partcharacteristics'such as si e, location, orientation, and functional relationships.characteristics'such as si e, location, orientation, and functional relationships.
n its simplest form, orthographic projection pro#ides a range of si* orthographic-specificn its simplest form, orthographic projection pro#ides a range of si* orthographic-specific#iews of an object. n !our mind, imagine a ph!sical stationar! object that has been#iews of an object. n !our mind, imagine a ph!sical stationar! object that has beensuspended in the center of a glass cube. Each of the si* sides of the bo* represents asuspended in the center of a glass cube. Each of the si* sides of the bo* represents a viewing viewing oror projection projection plane. he orientation of the obser#er+s plane. he orientation of the obser#er+s line of sightline of sight mustmust alwaysalways be be
perpendicular or perpendicular or normal normal to the planes on the glass bo*, and the sides of the bo* must also beto the planes on the glass bo*, and the sides of the bo* must also be perpendicular to their adjacent sides. hat being the case, the object could perpendicular to their adjacent sides. hat being the case, the object could onlyonly be #iewed be #iewedfrom the front, top, right side, left side, bac , or bottom. ith the images indelibl! fi*ed onfrom the front, top, right side, left side, bac , or bottom. ith the images indelibl! fi*ed on
the planes, and the bo* unfolded, the projected images orthe planes, and the bo* unfolded, the projected images or viewsviews would alwa!s be orientedwould alwa!s be orientedorthographicall!, and aligned with each other, from #iew to #iew on the drawing.orthographicall!, and aligned with each other, from #iew to #iew on the drawing.
he process of orthographicall! projecting parts and or feature characteristics is nothe process of orthographicall! projecting parts and or feature characteristics is notnecessaril! complicated, but it is comple*. t is essential to the delineation of featurenecessaril! complicated, but it is comple*. t is essential to the delineation of featuregeometr! as an aide to the manufacturing process. his unit will gi#e !ou practice usinggeometr! as an aide to the manufacturing process. his unit will gi#e !ou practice usingthese principles, and will increase !our abilit! to understand and #isuali e the process.these principles, and will increase !our abilit! to understand and #isuali e the process.
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/ow to Proceed/ow to Proceed
n order to produce mechanical parts, detailed design information must be pro#ided to then order to produce mechanical parts, detailed design information must be pro#ided to thecraftsman'information that defines and describes rele#ant geometr! and relationships ofcraftsman'information that defines and describes rele#ant geometr! and relationships ofdescripti#e elements on the part. Graphic images or #iews, de#eloped from specificdescripti#e elements on the part. Graphic images or #iews, de#eloped from specific
orientations, are major elements in this communication process. 0 primar! objecti#e of thisorientations, are major elements in this communication process. 0 primar! objecti#e of thisunit is to ac1uaint !ou with the process of generating multiple (albeit, geometricall!unit is to ac1uaint !ou with the process of generating multiple (albeit, geometricall!related) #iews of mechanical components. he basic theor!, rationale, and productionrelated) #iews of mechanical components. he basic theor!, rationale, and productiontechni1ues are presented in a s!stematic order. t is anticipated that !ou will complete thistechni1ues are presented in a s!stematic order. t is anticipated that !ou will complete thisunit in one or possibl! two sessions (more time and practice ma! be re1uired if !ou are newunit in one or possibl! two sessions (more time and practice ma! be re1uired if !ou are newto the science of engineering graphics).to the science of engineering graphics).
2egin with a thoughtful pre#iew of the unit objecti#es, and carefull! consider the related2egin with a thoughtful pre#iew of the unit objecti#es, and carefull! consider the related#ocabular! words and terminolog!. 0s each topic is considered, eep in mind an o#erall#ocabular! words and terminolog!. 0s each topic is considered, eep in mind an o#erallobjecti#e of being able to read an engineering drawing, or to construct correctl! projectedobjecti#e of being able to read an engineering drawing, or to construct correctl! projected#iews that would be re1uired to describe part features, thus facilitating the manufacturing#iews that would be re1uired to describe part features, thus facilitating the manufacturing
process. process.
Follow each e*planation, and practice each techni1ue as outlined for sol#ing orthographicFollow each e*planation, and practice each techni1ue as outlined for sol#ing orthographic projection problems. 3e#iew concepts that seem unclear, and do each of the e*ercises that projection problems. 3e#iew concepts that seem unclear, and do each of the e*ercises thatare pro#ided'especiall! the self assessment e*ercises at the end of the presentation. 0sare pro#ided'especiall! the self assessment e*ercises at the end of the presentation. 0s!ou complete the e*ercises, carefull! compare !our own s etched solutions with the those!ou complete the e*ercises, carefull! compare !our own s etched solutions with the those
pro#ided, and re#iew the go#erning principles where necessar!. pro#ided, and re#iew the go#erning principles where necessar!.
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4nit Objecti#es4nit Objecti#es
hen !ou ha#e completed this unit, !ou will be able to5hen !ou ha#e completed this unit, !ou will be able to5
6 E*plain the principles upon which orthographic projection is based.E*plain the principles upon which orthographic projection is based.
6 3ecogni e and identif! hori ontal, frontal, and profile planes in engineering drawings, and e*plain3ecogni e and identif! hori ontal, frontal, and profile planes in engineering drawings, and e*plaintheir relationships to standard planes of projection.their relationships to standard planes of projection.
6 dentif! the si* principal #iews which ma! be generated, using the concept of the #iewing cube, anddentif! the si* principal #iews which ma! be generated, using the concept of the #iewing cube, ande*plain their specific orientation and relationships to each other.e*plain their specific orientation and relationships to each other.
6 dentif! normal, inclined, and obli1ue planes relati#e to the si* principal projection planes.dentif! normal, inclined, and obli1ue planes relati#e to the si* principal projection planes.6 3ead an engineering drawing, and e*plain the necessit! for creating multiple #iews.3ead an engineering drawing, and e*plain the necessit! for creating multiple #iews.
6 4se graphic tools such as reference planes and fold lines to sol#e orthographic projection problems.4se graphic tools such as reference planes and fold lines to sol#e orthographic projection problems.
6 0ppl! standard line and #iew con#entions on an engineering drawing.0ppl! standard line and #iew con#entions on an engineering drawing.
67ol#e orthographic problems using at least two techni1ues of locating and appl!ing data.7ol#e orthographic problems using at least two techni1ues of locating and appl!ing data.
6 E*plain and illustrate the differences between first- and third-angle projection.E*plain and illustrate the differences between first- and third-angle projection.
6 8emonstrate the appropriate applications for center lines and hidden lines in multi-#iew drawings.8emonstrate the appropriate applications for center lines and hidden lines in multi-#iew drawings.
Orientation of Object Features in Orthographic ProjectionOrientation of Object Features in Orthographic Projection8irections and Orientation in Orthographic Projection8irections and Orientation in Orthographic ProjectionOrthographic Projection Principles 3e#iewOrthographic Projection Principles 3e#iewOrthographic Projection heor! (First 0ngle Projection)Orthographic Projection heor! (First 0ngle Projection)"ulti-#iew Projection echni1ues"ulti-#iew Projection echni1ues
?ompass Projection echni1ue?ompass Projection echni1ueProjection Orientation -- 9iew 7electionProjection Orientation -- 9iew 7electionPictorial 9isuali ationPictorial 9isuali ation"easure and ransfer "ethod (;)"easure and ransfer "ethod (;)"easure and ransfer "ethod (<)"easure and ransfer "ethod (<)
"easure and ransfer "ethod (=)"easure and ransfer "ethod (=)"easure and ransfer "ethod (>)"easure and ransfer "ethod (>)Pictorial 9isuali ation (P!ramid'>a)Pictorial 9isuali ation (P!ramid'>a)"easure and ransfer "ethod (@)"easure and ransfer "ethod (@)0n 0lternati#e 7olution (@a)0n 0lternati#e 7olution (@a)
nclined 7urfaces in Orthographic Projectionnclined 7urfaces in Orthographic ProjectionObli1ue 7urfaces in Orthographic ProjectionObli1ue 7urfaces in Orthographic Projection0dditional E*amples (Practice Problems in Orthographic Projection)0dditional E*amples (Practice Problems in Orthographic Projection)?oncept "aster! E*amination (7elf E#aluation)?oncept "aster! E*amination (7elf E#aluation)
Orthographic Projection Table of Contents
able of ?ontentsable of ?ontentsopics5opics5
o assist !ou in !our stud! of the contents ofo assist !ou in !our stud! of the contents ofthis presentation, athis presentation, a Table of ContentsTable of Contents hashas
been prepared. he topics listed are lin ed been prepared. he topics listed are lin edto the specific content b! topic. hento the specific content b! topic. henselected with the mouse (in show mode), theselected with the mouse (in show mode), the
presentation materials will open at the presentation materials will open at there1uested location. he na#igation bar atre1uested location. he na#igation bar at
the bottom of the screen allows !ou to returnthe bottom of the screen allows !ou to returnto this slide at an! time. 7imilar tables ha#eto this slide at an! time. 7imilar tables ha#e been included in all of the presentations that been included in all of the presentations thatfollow.follow.
Station Point Station Point 'an! location in =-dimensional space that is infinitel! displaced from the 'an! location in =-dimensional space that is infinitel! displaced from the
object being #iewed.object being #iewed. Line of Sight Line of Sight (:O7)'the orientation of an obser#er relati#e to a specific object.(:O7)'the orientation of an obser#er relati#e to a specific object.
Projection Plane Projection Plane (also called a(also called a iewing Planeiewing Plane oror Picture Plane Picture Plane )'the plane onto which)'the plane onto whichthe image of an object is projected.the image of an object is projected.
isual !aysisual !ays 'an infinite number of parallel theoretical projectors which emanate from 'an infinite number of parallel theoretical projectors which emanate from
an object, to form the image of the object on the projection plane.an object, to form the image of the object on the projection plane. Pierce Points Pierce Points 'intersections created b! theoretical #isual ra!s as the! pass through or 'intersections created b! theoretical #isual ra!s as the! pass through or
collide with a projection plane.collide with a projection plane.
"raphic #mage"raphic #mage 'a s!mbolic representation of a =-dimensional part or assembl! of 'a s!mbolic representation of a =-dimensional part or assembl! of parts, or a schematic la!out or organi ation of entities, projected onto a <- parts, or a schematic la!out or organi ation of entities, projected onto a <-dimensional plane.dimensional plane.
$ormal iews $ormal iews '#iews of features or part characteristics that are oriented perpendicular '#iews of features or part characteristics that are oriented perpendicularto the obser#er+s line of sight.to the obser#er+s line of sight.
Contiguous iewsContiguous iews 'adjacent, orthographicall! projected #iews of an object. 'adjacent, orthographicall! projected #iews of an object.
%rthogonal iews%rthogonal iews 'projected, orthographicall! aligned #iews of an object. 'projected, orthographicall! aligned #iews of an object.
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iewing Cubeiewing Cube 'Glass 2o* conceptA si* projection planes configured as a cube. 'Glass 2o* conceptA si* projection planes configured as a cube.
&old Lines &old Lines 'the representation of intersections between the sides of the #iewing cube. 'the representation of intersections between the sides of the #iewing cube. !eference Planes !eference Planes 'a base line for ta ing and appl!ing measurements. 'a base line for ta ing and appl!ing measurements. Principal iews Principal iews also referred to asalso referred to as Primary iews Primary iews 't!picall! the front, top, and right 't!picall! the front, top, and right
side #iews.side #iews.Surface iewsSurface iews 'non-normal #iews of feature surfaces that displa! =-dimensional areas. 'non-normal #iews of feature surfaces that displa! =-dimensional areas.
'dge iews 'dge iews 'all points on a planar surface aligned parallel to the line of sight. 'all points on a planar surface aligned parallel to the line of sight. #nclined Surfaces #nclined Surfaces 'perpendicular to < of the B #iewing planesA parallel to none. 'perpendicular to < of the B #iewing planesA parallel to none.%bli(ue Surfaces%bli(ue Surfaces 'neither parallel nor perpendicular to an! of the B #iewing planes. 'neither parallel nor perpendicular to an! of the B #iewing planes.
Line )eights Line )eights 'there are three distinct line 'there are three distinct line weightsweights on engineering drawingsA thin lineson engineering drawingsA thin linesappro*imatel! .%%C - .%;% wide, medium lines, appro*imatel! .%;@ - .%<%appro*imatel! .%%C - .%;% wide, medium lines, appro*imatel! .%;@ - .%<%wide, and thic lines appro*imatel! .%=% - .%>% wide.wide, and thic lines appro*imatel! .%=% - .%>% wide.
Line Types Line Types 'there are man! 'there are man! line typesline types that are used on mechanical drawings, but therethat are used on mechanical drawings, but thereare onl! si* distinct line t!pes that will be used in our discussions regardingare onl! si* distinct line t!pes that will be used in our discussions regardingorthographic projection5 construction, object, center, hidden, phantom, andorthographic projection5 construction, object, center, hidden, phantom, ande*tension lines (also nown as projection, or witness lines).e*tension lines (also nown as projection, or witness lines).
he basic theor! of orthographic (third angle) projection, is that (;) objects arehe basic theor! of orthographic (third angle) projection, is that (;) objects are#iewed from a#iewed from a viewing stationviewing station located anlocated an infiniteinfinite distance from the object, (<) adistance from the object, (<) a
projection plane projection plane (often referred to as a #iewing plane, or picture plane) is(often referred to as a #iewing plane, or picture plane) isestablished at some locationestablished at some location betweenbetween the e!e of the obser#er and the object' the e!e of the obser#er and the object' perpendicular to the obser#er+s perpendicular to the obser#er+s line of sight line of sight , (=) an infinite number of, (=) an infinite number of parallel parallel projectors projectors , or, or visual raysvisual rays , e*tend from the object to the projection plane, and (>) at, e*tend from the object to the projection plane, and (>) atthose points where the projectors pierce the projection plane, thethose points where the projectors pierce the projection plane, the two-dimensionaltwo-dimensionalimageimage of the object is created on the plane. he image, thus created, is what isof the object is created on the plane. he image, thus created, is what isseen b! the obser#er. t should be remembered, thatseen b! the obser#er. t should be remembered, that the primary purpose servedthe primary purpose servedby this multi-view projection process, is to generate the graphic images that areby this multi-view projection process, is to generate the graphic images that arere(uired to understand and communicate the description or definitions of there(uired to understand and communicate the description or definitions of the
physical properties and characteristics of feature or part geometry* physical properties and characteristics of feature or part geometry*
Note: ?omple* geometr! will li el! ha#e surfaces that would not be #isible?omple* geometr! will li el! ha#e surfaces that would not be #isiblewhen #iewed from an! specific location. 7uch surfaces are included in thewhen #iewed from an! specific location. 7uch surfaces are included in thedrawing using hidden lines'consisting of short dashes, drawn appro*imatel! ; Ddrawing using hidden lines'consisting of short dashes, drawn appro*imatel! ; Dinch in length, separated b! a space or gap that is appro*imatel! ; ;B inch. 0inch in length, separated b! a space or gap that is appro*imatel! ; ;B inch. 0common industrial practice is to eliminate hidden lines in #iews, unless greatercommon industrial practice is to eliminate hidden lines in #iews, unless greaterclarit! ma! be gained b! their inclusion. n this course, howe#er, !ou are re1uiredclarit! ma! be gained b! their inclusion. n this course, howe#er, !ou are re1uiredto include hidden lines in all #iews.to include hidden lines in all #iews.
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Orthographic Projection heor!Orthographic Projection heor!Obser#ation of an object begins with the direction from which the object is to beObser#ation of an object begins with the direction from which the object is to be#iewed'the#iewed'the line of sight*line of sight*
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he #iewing station for the obser#er is alwa!s an infinite distance from the object.he #iewing station for the obser#er is alwa!s an infinite distance from the object.
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he plane of projection is located between the #iewing station and the objecthe plane of projection is located between the #iewing station and the object(third angle projection).(third angle projection).
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2ecause the obser#ation location is at infinit!,2ecause the obser#ation location is at infinit!, parallel parallel #isual ra!s e*tend from the#isual ra!s e*tend from theobject to the plane of projection, and produce the image on the projection plane.object to the plane of projection, and produce the image on the projection plane.
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9iewing an Object From an nfinite9iewing an Object From an nfinite8istance8istance
0ssuming a position at infinit!, and0ssuming a position at infinit!, andloo ing towards the object, we would seeloo ing towards the object, we would seethe image of the object on the projectionthe image of the object on the projection
plane (notice the line contrast between plane (notice the line contrast betweenobject, center and hidden lines).object, center and hidden lines).
Projection PlaneProjection Plane
+ per/anent i/age of theobject is for/ed on theprojection plane by visual
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9isuali ing orthographic #iews using pictorial #iews9isuali ing orthographic #iews using pictorial #iews
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hree-dimensional (pictorial) #iews of objects are fre1uentl! easier to understand than multi-#iewhree-dimensional (pictorial) #iews of objects are fre1uentl! easier to understand than multi-#ieworthographic projections of the same object. 7 etching the object in a manner shown can often help studentsorthographic projections of the same object. 7 etching the object in a manner shown can often help students#isuali e the details of the part. 7tudents who are new to these concepts are encouraged to use s etches.#isuali e the details of the part. 7tudents who are new to these concepts are encouraged to use s etches.
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he glass bo* concept theori es that an object is suspended inside a si*-sided glass cubehe glass bo* concept theori es that an object is suspended inside a si*-sided glass cube(notice the use of hidden lines on the glass bo*, depicting lines that would not be #isible(notice the use of hidden lines on the glass bo*, depicting lines that would not be #isiblefrom the gi#en perspecti#e).from the gi#en perspecti#e).
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0s the object is #iewed from a specific orientation (perpendicular to one of the sides of the cube) #isual0s the object is #iewed from a specific orientation (perpendicular to one of the sides of the cube) #isualra!s project from the object to the projection plane. hese projectors arera!s project from the object to the projection plane. hese projectors are alwaysalways parallel to each other. parallel to each other.
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he object+s image is formed on the projection plane b! the pierce points of the #isual ra!s.he object+s image is formed on the projection plane b! the pierce points of the #isual ra!s.
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he process is repeated to construct the right side #iew on the profile planehe process is repeated to construct the right side #iew on the profile plane
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7imilarl!, the top #iew is projected7imilarl!, the top #iew is projectedto the hori ontal planeto the hori ontal plane
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For man! three-dimensional objects, two to three orthographic #iews are sufficientFor man! three-dimensional objects, two to three orthographic #iews are sufficientto describe their geometr!.to describe their geometr!.
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he bo* can be unfolded to show thehe bo* can be unfolded to show themultiple #iews in a single *-! planemultiple #iews in a single *-! plane
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FRON
O!
R"#$ %"&'
2ecause the obser#ation point is located at2ecause the obser#ation point is located atinfinit!, the integrit! of feature si e andinfinit!, the integrit! of feature si e andlocation are maintained, and the #iews arelocation are maintained, and the #iews areoriented orthogonall! in relationship to eachoriented orthogonall! in relationship to eachother.other.
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FRON
O!
R"#$ %"&'
otice that the projectors or e*tension lines, are otice that the projectors or e*tension lines, are perpendicular to the folding lines of the glass bo*. perpendicular to the folding lines of the glass bo*.(Fold lines and e*tension lines are drawn #er!(Fold lines and e*tension lines are drawn #er!lightl!, when used, and arelightl!, when used, and are not not part of the finished part of the finished
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8imensional 8ata ?an then be8imensional 8ata ?an then beadded to the drawingadded to the drawing t is important to note that all lines on engineeringt is important to note that all lines on engineering
drawings are the same densit!'the same opacit!drawings are the same densit!'the same opacit!or dar ness. he difference in line #alues is theiror dar ness. he difference in line #alues is theirwidth, or thic ness. here are = distinct linewidth, or thic ness. here are = distinct lineweights to be aware of5weights to be aware of5 object linesobject lines are thicare thic(appro*imatel! .%=%-.%>% thic ),(appro*imatel! .%=%-.%>% thic ), hidden lineshidden lines arearea medium thic ness (.%;@-.%<%), anda medium thic ness (.%;@-.%<%), and e+tension,e+tension,dimension, and center linesdimension, and center lines are thin (.%%C-.%;%).are thin (.%%C-.%;%).
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/eight H hidth H w
8epth H dn each of the si* principal orthographic #iews,n each of the si* principal orthographic #iews,two specific dimensional characteristics aretwo specific dimensional characteristics are
pro#ided pro#ided
Object Feature Orientation in Orthographic ProjectionObject Feature Orientation in Orthographic Projection
8irectional Orientation in Orthographic Projection8irectional Orientation in Orthographic Projection
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R"#$ %"&'
d
h
FRON
O!
d
w
w
h
8irectional Orientation in Orthographic Projection8irectional Orientation in Orthographic Projection
wo or three #iews of a =-dimensionalwo or three #iews of a =-dimensionalobject are often sufficient for a completeobject are often sufficient for a completedefinition of part geometr!. idth anddefinition of part geometr!. idth anddepth are displa!ed in the top #iewA heightdepth are displa!ed in the top #iewA heightand width in the front #iew, height andand width in the front #iew, height anddepth in the side #iew.depth in the side #iew.
/eight H hidth H w
8epth H d
8irectional Orientation in Orthographic Projection8irectional Orientation in Orthographic Projection
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R"#$ %"&'FRON
O!
g p jg p j/eight H h
idth H w8epth H d
wo of the three si e characteristics arewo of the three si e characteristics aredispla!ed in each #iew. 2ecause contiguousdispla!ed in each #iew. 2ecause contiguous#iews are alwa!s projected $%#iews are alwa!s projected $% & to each& to eachother, all three dimension characteristics canother, all three dimension characteristics can
be displa!ed in a single be displa!ed in a single two-dimensional two-dimensional plane. plane.
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6 he #iewing station is an infinite distance from the object.he #iewing station is an infinite distance from the object.6 he line of sight is alwa!s perpendicular to projection plane.he line of sight is alwa!s perpendicular to projection plane.6 he projection plane is alwa!she projection plane is alwa!s betweenbetween the object and #iewing stationthe object and #iewing station **6 9isual ra!s are alwa!s perpendicular to the projection plane.9isual ra!s are alwa!s perpendicular to the projection plane.6 Projectors (#isual ra!s for a specific #iew) must alwa!s be parallel to each other, andProjectors (#isual ra!s for a specific #iew) must alwa!s be parallel to each other, and
perpendicular to projectors from adjacent #iews. perpendicular to projectors from adjacent #iews.
he basic difference between third- and first-angle projection is that inhe basic difference between third- and first-angle projection is that in first-angle first-angle projection projection , the, the object object is placedis placed between the observer and the projection planebetween the observer and the projection plane ..
he image of the front #iew is formed as the projectors intersect the projection plane. t ishe image of the front #iew is formed as the projectors intersect the projection plane. t isimportant to note that the front #iew actuall! ends upimportant to note that the front #iew actuall! ends up behind behind the bac surface of the object.the bac surface of the object.:et me tr! to illustrate the concept using three planes of the glass bo* theor!.:et me tr! to illustrate the concept using three planes of the glass bo* theor!.
projection. ( he projection. ( hetraditional hori ontaltraditional hori ontal
(top), frontal, and(top), frontal, and profile (right side) profile (right side) panels of the glass panels of the glass bo* ha#e been bo* ha#e beenremo#ed for clarit!.)remo#ed for clarit!.)Jou are loo ingJou are loo ing
down on thedown on theremaining threeremaining threesides of the bo*'asides of the bo*'a
bird+s e!e #iew. bird+s e!e #iew.
Object oriented in first-angleObject oriented in first-angle projection framewor projection framewor
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H :ine of 7ightH :ine of 7ight
0n object has been0n object has beensuspended in the glasssuspended in the glass
bo*. op, front, and bo*. op, front, andright side #iews will beright side #iews will begenerated using first-generated using first-angle projection.angle projection.
Object oriented in first-angleObject oriented in first-angle projection framewor projection framewor
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Front 9iewFront 9iew
First 0ngle ProjectionFirst 0ngle Projection he !ellow arrow indicates the linehe !ellow arrow indicates the lineof sight. he image of the frontof sight. he image of the front#iew is projected to the projection#iew is projected to the projection
plane behind the object. plane behind the object.
he top (hori ontal) #iew is projected from abo#e the object but is created on the planehe top (hori ontal) #iew is projected from abo#e the object but is created on the plane
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Front 9iewFront 9iew
/ori ontal/ori ontalor op 9iewor op 9iew
below. below.
0s with the pre#ious two projections, the right side #iew is projected to the opposite side of the0s with the pre#ious two projections, the right side #iew is projected to the opposite side of the
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he reference frame can behe reference frame can beunfolded to show the multipleunfolded to show the multiple#iews in a single -J plane#iews in a single -J plane
Profile or Profile or 3ight 7ide3ight 7ide9iew9iew
Front 9iewFront 9iew
/ori ontal/ori ontalor op 9iewor op 9iew
First-angle projection re1uires thatFirst-angle projection re1uires thatthe bo* unfoldthe bo* unfold awayaway from thefrom theobser#er rather than towards theobser#er rather than towards theobser#er.obser#er.
he 4nited 7tates and ?anada are the onl! two major countries that use third-he 4nited 7tates and ?anada are the onl! two major countries that use third-
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Right Side 0ie2ront0ie
Top0ie
jangle projection. 0ll other industrial nations throughout the world use first-angleangle projection. 0ll other industrial nations throughout the world use first-angle
projection. t is important that !ou understand the differences because man! 4.7. projection. t is important that !ou understand the differences because man! 4.7.companies are now internationall! established. he! will e*pect !ou to be able tocompanies are now internationall! established. he! will e*pect !ou to be able toread and interpret either method used in engineering documentation.read and interpret either method used in engineering documentation.
his is an e*ample of how to use a miter (>@&) line to assist in constructing anhis is an e*ample of how to use a miter (>@&) line to assist in constructing anorthographic solution for the top or hori ontal #iew. he front and right sideorthographic solution for the top or hori ontal #iew. he front and right side#iews are gi#en.#iews are gi#en.
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E*planations regarding solution techni1ues ma! #ar! between instructors, but theE*planations regarding solution techni1ues ma! #ar! between instructors, but theresults are the same. 9erif! the projection b! placing e*tension lines between theresults are the same. 9erif! the projection b! placing e*tension lines between theend points of the line'#iew to #iew, and label the points (care should be ta en toend points of the line'#iew to #iew, and label the points (care should be ta en tolabel the separate #iews consistentl!).label the separate #iews consistentl!).
Establish a fold line somewhere between the #iews (ma e certain that the fold lineEstablish a fold line somewhere between the #iews (ma e certain that the fold line
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stab s a o d e so ew e e betwee t e ews ( a e ce ta t at t e o d e(is perpendicular to the projection lines between the two #iews). 0lthough the foldis perpendicular to the projection lines between the two #iews). 0lthough the foldline does not necessaril! ha#e to beline does not necessaril! ha#e to be betweenbetween the two #iews, the problem isthe two #iews, the problem issimplified b! placing it there. :ater on, we will discuss placement alternati#es.simplified b! placing it there. :ater on, we will discuss placement alternati#es.
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0t the point where the two fold lines intersect, insert a >@& miter line. he miter0t the point where the two fold lines intersect, insert a >@& miter line. he miterline ser#es to rotate points $%&.line ser#es to rotate points $%&.
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Project the points that define the line (;,<), in the right side #iew, in a directionProject the points that define the line (;,<), in the right side #iew, in a directionthat isthat is perpendicular perpendicular to the fold line that is between the #iew and the >@& miterto the fold line that is between the #iew and the >@& miterline. 3emember, when de#eloping a new #iew, projectors between the #iews mustline. 3emember, when de#eloping a new #iew, projectors between the #iews mustalwaysalways be perpendicular to the fold lines that separate the two #iews. be perpendicular to the fold lines that separate the two #iews.
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he point formed b! the intersection on the >@& miter line is then projected acrosshe point formed b! the intersection on the >@& miter line is then projected acrossthe #ertical fold line into the hori ontal #iew.the #ertical fold line into the hori ontal #iew.
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Project points ; and < from the front #iew into the hori ontal (top) #iew. oticeProject points ; and < from the front #iew into the hori ontal (top) #iew. oticethat an intersection is formed b! this projection line and the hori ontal linethat an intersection is formed b! this projection line and the hori ontal line
projected from the point on the >@& miter line. projected from the point on the >@& miter line.
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here the two projectors intersect, is the point (end) #iew of line ;,<. 0ll of thehere the two projectors intersect, is the point (end) #iew of line ;,<. 0ll of the points are now accounted for in all three #iews. :abel the points. points are now accounted for in all three #iews. :abel the points.
From a #iewing position abo#e the fold line, with the line of sight perpendicular to theFrom a #iewing position abo#e the fold line, with the line of sight perpendicular to the
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From a #iewing position abo#e the fold line, with the line of sight perpendicular to theFrom a #iewing position abo#e the fold line, with the line of sight perpendicular to the projection plane (represented b! the fold line), point ; would be closer to !our e!e. projection plane (represented b! the fold line), point ; would be closer to !our e!e.
hus, point ; is in front of point < in the labeling of the hori ontal or top #iew.hus, point ; is in front of point < in the labeling of the hori ontal or top #iew.
he front and side #iews of line ;,< are gi#en. ?onstruct the hori ontal or tophe front and side #iews of line ;,< are gi#en. ?onstruct the hori ontal or top
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he front and side #iews of line ;, are gi#en. ?onstruct the hori ontal or tope o t a d s de ews o e ;, a e g e . ?o st uct t e o o ta o top#iew of the line. 2egin b! #erif!ing the projection. his is done b! placing#iew of the line. 2egin b! #erif!ing the projection. his is done b! placinge*tension (projection) lines between the #iews connecting the points.e*tension (projection) lines between the #iews connecting the points.
Position a fold line at some con#enient location between the #iews 3emember inPosition a fold line at some con#enient location between the #iews 3emember in
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Position a fold line at some con#enient location between the #iews. 3emember, inPosition a fold line at some con#enient location between the #iews. 3emember, ineveryevery case where fold lines are constructed between adjacent orthographic #iews,case where fold lines are constructed between adjacent orthographic #iews,the! must be perpendicular to the projectors.the! must be perpendicular to the projectors.
0t some location along the #ertical fold line construct a hori ontal fold line0t some location along the #ertical fold line construct a hori ontal fold line
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0t some location along the #ertical fold line, construct a hori ontal fold line.0t some location along the #ertical fold line, construct a hori ontal fold line.
? t t it (>@&) li th h th i t ti f th t f ld li? t t it (>@&) li th gh th i t ti f th t f ld li
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?onstruct a miter (>@&) line through the intersection of the two fold lines.?onstruct a miter (>@&) line through the intersection of the two fold lines.
Project points ; and < from the right side #iew up to intersect with the miter lineProject points ; and < from the right side #iew up to intersect with the miter line
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Project points ; and < from the right side #iew, up to intersect with the miter line.Project points ; and < from the right side #iew, up to intersect with the miter line.
0t the points where the intersections are formed on the miter line project lines0t the points where the intersections are formed on the miter line project lines
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0t the points where the intersections are formed on the miter line, project lines0t the points where the intersections are formed on the miter line, project linesinto the hori ontal (top) #iew.into the hori ontal (top) #iew.
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From the front #iew, project points ; and < into the hori ontal #iew to completeFrom the front #iew, project points ; and < into the hori ontal #iew to completethe projection of the line.the projection of the line.
here the projectors intersect in the hori ontal #iew, !ou ha#e located points ;here the projectors intersect in the hori ontal #iew, !ou ha#e located points ;
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p j , p ;p j , p ;and <. :abel and join the points together to complete the projection.and <. :abel and join the points together to complete the projection.
?lean up the drawing b! eliminating the construction lines.?lean up the drawing b! eliminating the construction lines.
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he resulting #iews represent the correct solution for the top, front, and right sidehe resulting #iews represent the correct solution for the top, front, and right side
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"iter :ine echni1ue'E*ample umber =iter :ine echni1ue E*ample umber =his drawing represents the top and front #iews of a line. ?onstruct the right sidehis drawing represents the top and front #iews of a line. ?onstruct the right side
#iew'using the miter line techni1ue. :abel the end points on the line.#iew'using the miter line techni1ue. :abel the end points on the line.
9erif! the projection of the two #iews b! e*tending9erif! the projection of the two #iews b! e*tending parallelparallel lines which connectlines which connect
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9erif! the projection of the two #iews b! e tending9erif! the projection of the two #iews b! e tending parallel parallel lines which connectlines which connectthe points of the line.the points of the line.
? f ld li b d di l h #i f h li? t t f ld li b t d di l t th #i f th li
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e t, construct a second fold line perpendicular to the hori ontal one, thus e t, construct a second fold line perpendicular to the hori ontal one, thusestablishing the location for the right side #iew.establishing the location for the right side #iew.
Establish the miter line through the point of intersection of the two fold lines.Establish the miter line through the point of intersection of the two fold lines.
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Project points ; and < in the top #iew hori ontall! across the fold line until the!Project points ; and < in the top #iew hori ontall! across the fold line until the!
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j p ; pj p ; pintersect with the miter line.intersect with the miter line.
From the intersections on the miter line, construct projectors #erticall! across theFrom the intersections on the miter line, construct projectors #erticall! across the
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hori ontal fold line into the right side #iew.hori ontal fold line into the right side #iew.
Project points ; and < from the front #iew, across the #ertical fold line, into theProject points ; and < from the front #iew, across the #ertical fold line, into the
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j p ; , ,j pright side #iew.right side #iew.
here the projectors from the top and front #iews intersect, !ou ha#e locatedhere the projectors from the top and front #iews intersect, !ou ha#e located points ; and < in =-8 space. Point ; lines up with and projects to point ;, and points ; and < in =-8 space. Point ; lines up with and projects to point ;, and
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point < li ewise, lines up with and projects to point < in all other #iews. otice point < li ewise, lines up with and projects to point < in all other #iews. oticethat the! project in a completed rectangle. n the strictest order of si*-#iew, glassthat the! project in a completed rectangle. n the strictest order of si*-#iew, glass
bo* projection theor!, this will bo* projection theor!, this will alwaysalways be the case. oin and label be the case. oin and label
the points.the points.
?lean up the drawing b! remo#ing the projection lines between the #iews.?lean up the drawing b! remo#ing the projection lines between the #iews.
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he drawing is now complete, showing the front, top, and right side #iews of thehe drawing is now complete, showing the front, top, and right side #iews of the
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n this problem, front and top #iews of a s ewed planar triangle in =-8 space is gi#en.n this problem, front and top #iews of a s ewed planar triangle in =-8 space is gi#en.0n orthographic projection of the right side #iew is re1uired. 9erif! the projection.0n orthographic projection of the right side #iew is re1uired. 9erif! the projection.
7et up the right side #iew b! constructing a projection plane.7et up the right side #iew b! constructing a projection plane.
Front and right side #iews are gi#en. 4se a reference plane off of the bac of theFront and right side #iews are gi#en. 4se a reference plane off of the bac of the
object to determine the location of the miter line, and project the top #iew of thisobject to determine the location of the miter line, and project the top #iew of thissolid object.solid object.
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Establish a hori ontal line at a reasonable location along these projectors.Establish a hori ontal line at a reasonable location along these projectors.
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here the two projectors (representing the bac surface) intersect, construct a >@& line.here the two projectors (representing the bac surface) intersect, construct a >@& line.
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Project the front surface from the right side #iew until it intersects with the miterProject the front surface from the right side #iew until it intersects with the miterline, then project the point of intersection to the hori ontal #iew to complete theline, then project the point of intersection to the hori ontal #iew to complete theboundar! outline of the top #iewboundar! outline of the top #iew
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boundar! outline of the top #iew. boundar! outline of the top #iew.
he boundar! in the top #iew can be established with object lines, and thehe boundar! in the top #iew can be established with object lines, and thedrawing cleaned up.drawing cleaned up.
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From the profile (right side) #iew, project the #ertical surface to the miter line, andFrom the profile (right side) #iew, project the #ertical surface to the miter line, andthen to the top #iew.then to the top #iew.
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his problem depicts the #erified front and side #iews of the part. Follow thehis problem depicts the #erified front and side #iews of the part. Follow thesame projection techni1ue as in the last problem, but use the front surface tosame projection techni1ue as in the last problem, but use the front surface toestablish the >@& miter line.establish the >@& miter line.
0 point is established at the intersection of the projection from the front surface in0 point is established at the intersection of the projection from the front surface in both the top and right side #iews. Project the bac surface in the right side #iew both the top and right side #iews. Project the bac surface in the right side #iewto intersect with the hori ontal projection of the front surface from the top #iewto intersect with the hori ontal projection of the front surface from the top #iew
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to intersect with the hori ontal projection of the front surface from the top #iew.to intersect with the hori ontal projection of the front surface from the top #iew.
?enter !our compass on the intersection of the front surface projectors, with a?enter !our compass on the intersection of the front surface projectors, with asetting e1ual to the distance from that point to the intersection formed b! thesetting e1ual to the distance from that point to the intersection formed b! the
projection of the bac surface from the right side #iew. ?onstruct the arc to projection of the bac surface from the right side #iew. ?onstruct the arc to
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intersect with the #ertical projection of the front surface in the right side #iew.intersect with the #ertical projection of the front surface in the right side #iew.
Project the bac and #ertical surface into the top #iew.Project the bac and #ertical surface into the top #iew.
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ith the boundaries of the top #iew established, we can clean up the #iew. 0lso,ith the boundaries of the top #iew established, we can clean up the #iew. 0lso, project the features in the right side #iew, set !our compass to the proper radius, project the features in the right side #iew, set !our compass to the proper radius,and complete the top #iew.and complete the top #iew.
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9 E 7E:E? O0 8
7O:4 O 2J P3O E? O
7electing as the front #iew the orientation that re#eals the most detail about the part,7electing as the front #iew the orientation that re#eals the most detail about the part,minimi es the re1uirements for additional detail projection methods. n this e*ample, forminimi es the re1uirements for additional detail projection methods. n this e*ample, forinstance, the same part can be projected without the use of a miter line.instance, the same part can be projected without the use of a miter line.
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P ? O3 0: 9 740: L0 O
7 etching is a 1uic and eas! method of sol#ing man! orthographic projection7 etching is a 1uic and eas! method of sol#ing man! orthographic projection problems. n man! cases, !ou can start with a rectangular prism and remo#e those problems. n man! cases, !ou can start with a rectangular prism and remo#e those
i f h bl h d l! 2 i b! l i h i #ii f h bl h d l! 2 i b! l i h i #i
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portions of the bloc that do not appl!. 2egin b! placing the appropriate #iews on portions of the bloc that do not appl!. 2egin b! placing the appropriate #iews onthe surface of the bloc .the surface of the bloc .
Ordinaril!, the frontal plane of a technical illustration is on the left side of theOrdinaril!, the frontal plane of a technical illustration is on the left side of the bloc , and the profile #iew (right side) is to the right of the frontal plane. bloc , and the profile #iew (right side) is to the right of the frontal plane.
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7 etch in the surfaces that are against the boundaries of the bloc in both the top7 etch in the surfaces that are against the boundaries of the bloc in both the topand the right side #iews. 0nd complete the s etch b! joining the lines that wouldand the right side #iews. 0nd complete the s etch b! joining the lines that would
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form the intersections of the planes on the part.form the intersections of the planes on the part.
f necessar!, at this point, !ou can remo#e the lines from the s etch that wouldf necessar!, at this point, !ou can remo#e the lines from the s etch that wouldha#e been remo#ed if the model was made from cla! or soap.ha#e been remo#ed if the model was made from cla! or soap.
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Jour =-dimensional s etch is now complete, and shows all of the lines necessar!Jour =-dimensional s etch is now complete, and shows all of the lines necessar!to define the part.to define the part.
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easu e a d a s ewo orthogonal #iews of a line are gi#en. e will construct the hori ontal or topwo orthogonal #iews of a line are gi#en. e will construct the hori ontal or top
#iew of the line, without using the >@& miter line.#iew of the line, without using the >@& miter line.
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dentif! the end points of each #iew of the line b! labeling them. 9erif! thedentif! the end points of each #iew of the line b! labeling them. 9erif! the projection of the two #iews b! e*tending parallel projectors between the two projection of the two #iews b! e*tending parallel projectors between the two#iews.#iews.
e*t, add a fold line at some location between the #iews. 3emember, the fold line e*t, add a fold line at some location between the #iews. 3emember, the fold linerepresents the projection plane onto which the image has been projected, when therepresents the projection plane onto which the image has been projected, when the
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obser#er is an infinite distance from the lines. 3emember also, that the fold lineobser#er is an infinite distance from the lines. 3emember also, that the fold linemust alwa!s be perpendicular to the projectors.must alwa!s be perpendicular to the projectors.
0dd a second fold line that is perpendicular to the #ertical fold line, and will0dd a second fold line that is perpendicular to the #ertical fold line, and willseparate the top #iew from the front #iew.separate the top #iew from the front #iew.
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sepa ate t e top ew o t e o t ew.p p
Project points ; and < in the front #iew across the fold line, into the hori ontalProject points ; and < in the front #iew across the fold line, into the hori ontal plane. plane.
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"easure the distances"easure the distances from the vertical fold line from the vertical fold line to the points in the right sideto the points in the right side#iew, and transfer them into the hori ontal #iew b! measuring from the hori ontal#iew, and transfer them into the hori ontal #iew b! measuring from the hori ontal
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fold line to ascertain the position of points ; and < in the top #iew.fold line to ascertain the position of points ; and < in the top #iew.
0 rule worth remembering is that0 rule worth remembering is that any measurement any measurement , from a reference plane or fold, from a reference plane or foldline separating the front and right side #iews, to an! point in the right side #iew,line separating the front and right side #iews, to an! point in the right side #iew,
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a
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will alwa!s be duplicated in the top or hori ontal #iew when ta en from itswill alwa!s be duplicated in the top or hori ontal #iew when ta en from itshori ontal fold line or reference plane. ow, simpl! joint the points together withhori ontal fold line or reference plane. ow, simpl! joint the points together witha line.a line.
he drawing is now complete with a correct solution, and can now be cleaned up.he drawing is now complete with a correct solution, and can now be cleaned up.
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Note: Fold lines and reference planes are not present in the final drawing. he!Fold lines and reference planes are not present in the final drawing. he!are included here so that !ou can see the logic of their relationships to theare included here so that !ou can see the logic of their relationships to thedifferent #iewsdifferent #iews
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"easure and ransfer echni1ue"easure and ransfer echni1ue
Reminder:
0 newl! projected #iew is constructed b! measuring data points in one #iew from0 newl! projected #iew is constructed b! measuring data points in one #iew from
its reference plane, and appl!ing them in the new #iew'relati#e to its referenceits reference plane, and appl!ing them in the new #iew'relati#e to its reference plane. his process plane. his process alwaysalways follows the same procedureA b! pi#oting around (orfollows the same procedureA b! pi#oting around (ors ipping) one intermediate #iew.s ipping) one intermediate #iew.
o demonstrate this principle, we will sol#e a similar single-line problem. hiso demonstrate this principle, we will sol#e a similar single-line problem. histime, howe#er, we will construct thetime, howe#er, we will construct the right-sideright-side #iew b! ta ing data from the#iew b! ta ing data from the toptop
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Front and top #iews of the line are gi#en. Jou are re1uired to complete the drawing b!Front and top #iews of the line are gi#en. Jou are re1uired to complete the drawing b!adding the right side #iew of the line. he same basic principles we ha#e practiced beforeadding the right side #iew of the line. he same basic principles we ha#e practiced beforeare followed again to reinforce the concepts. First, e*tend the projectors between theare followed again to reinforce the concepts. First, e*tend the projectors between the#iews to #erif! that the projection is accurate (projectors are alwa!s parallel to each other,#iews to #erif! that the projection is accurate (projectors are alwa!s parallel to each other,
perpendicular to the fold line, and will line up with the points in each of the two #iews). perpendicular to the fold line, and will line up with the points in each of the two #iews).:abel the points.:abel the points.
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0 second fold line or reference plane needs to be constructed'perpendicular to0 second fold line or reference plane needs to be constructed'perpendicular tothe first one. 0t some point along the hori ontal fold line, insert a #ertical foldthe first one. 0t some point along the hori ontal fold line, insert a #ertical foldline. his step determines the direction for the projection of the right side #iew.line. his step determines the direction for the projection of the right side #iew.
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Project the points ; and < from the front #iew across the #ertical fold line into theProject the points ; and < from the front #iew across the #ertical fold line into thearea where !ou will be constructing the right side #iew. 3emember, projectorsarea where !ou will be constructing the right side #iew. 3emember, projectorsmustmust alwaysalways be perpendicular to the fold line (this rule be perpendicular to the fold line (this rule never never changes).changes).
"easure the distances to points ; and"easure the distances to points ; and< from the hori ontal fold line< from the hori ontal fold line(between the front and top #iews)(between the front and top #iews).
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(between the front and top #iews).(between the front and top #iews).hen, transfer those measurementshen, transfer those measurements
into the new right side #iew b!into the new right side #iew b!
measuring from the #ertical fold line.measuring from the #ertical fold line.M"! personal approach to this t!pe ofM"! personal approach to this t!pe of
problem is to refer to the intermediate problem is to refer to the intermediate#iew as the#iew as the view in the middle*view in the middle* N JouN Jouwill notice that the orientation, as wellwill notice that the orientation, as wellas the measurements, are replicated inas the measurements, are replicated inthe two #iews that surround the pi#otthe two #iews that surround the pi#ot#iew. his is a standing principle that#iew. his is a standing principle thatwillwill not not change.change.
ith the data points established in the right side #iew, join them together as in theith the data points established in the right side #iew, join them together as in theother #iews, label them appropriatel!, and remo#e the construction lines.other #iews, label them appropriatel!, and remo#e the construction lines.
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Once again, we ha#e let the fold reference lines remain for #isuali ation purposes.Once again, we ha#e let the fold reference lines remain for #isuali ation purposes.3emember, howe#er, the! are3emember, howe#er, the! are not not included in the final drawing.included in the final drawing.
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"easure and ransfer'E*ample umber ="easure and ransfer'E*ample umber =
7ol#ing problems in#ol#ing single lines can help us understand the concepts, but7ol#ing problems in#ol#ing single lines can help us understand the concepts, butthe process becomes more interesting as the problems become more comple*.the process becomes more interesting as the problems become more comple*.
he ne*t set of problems re1uires the de#elopment of orthographic solutions thathe ne*t set of problems re1uires the de#elopment of orthographic solutions thatha#e more lines in#ol#ed. n fact, the! are solid, =-dimensional objects withha#e more lines in#ol#ed. n fact, the! are solid, =-dimensional objects withspecific form and mass. (3emember, if it seems confusing at first, !ou can reducespecific form and mass. (3emember, if it seems confusing at first, !ou can reducemost problems to amost problems to a one-line-at-a-timeone-line-at-a-time solution procedure if necessar!.)solution procedure if necessar!.)
he #iews in this problem represent ahe #iews in this problem represent asingle solid object he front and topsingle solid object he front and top
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single solid object. he front and topsingle solid object. he front and top#iews are complete as shown. he right#iews are complete as shown. he rightside #iew of the object is re1uired.side #iew of the object is re1uired.2ecause this is the first solid object we2ecause this is the first solid object weha#e had to sol#e, we will e*amine inha#e had to sol#e, we will e*amine insome detail, the procedure followed to findsome detail, the procedure followed to finda correct solution.a correct solution.
f gi# thi bl t l#f was gi#en this problem to sol#e
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f was gi#en this problem to sol#e, f was gi#en this problem to sol#e, would first want to now that all of thewould first want to now that all of the
points and lines in the two #iews are points and lines in the two #iews arealigned properl!'in other words, wouldaligned properl!'in other words, would#erif! the projection. 8o !ou understand#erif! the projection. 8o !ou understandhow to do that First, will e*tend parallelhow to do that First, will e*tend parallel
projectors between the two #iews, projectors between the two #iews,connecting the nown correspondingconnecting the nown corresponding
points. will then place a fold line points. will then place a fold line between the #iews'properl! oriented in between the #iews'properl! oriented inreference to the projectors. 8o !oureference to the projectors. 8o !ouremember the relationships betweenremember the relationships between
projectors and fold lines will also projectors and fold lines will alsoconsistentl! number the points in bothconsistentl! number the points in both
#iews that thin will be significant in#iews that thin will be significant insol#ing the problem.sol#ing the problem.
he relationship of fold lines to projectors ne#erhe relationship of fold lines to projectors ne#erchanges. he! mustchanges. he! must alwaysalways be perpendicular to be perpendicular toeach other. hile some rules of geometriceach other. hile some rules of geometricconstruction will be modified to e*pand the rangeconstruction will be modified to e*pand the range
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3emember, fold lines are3emember, fold lines are alwa!salwa!sPerpendicular to projectorsPerpendicular to projectors
p gp gof possible #iew orientations, this ruleof possible #iew orientations, this rule never never failsfailsin orthographic projection'and all of itsin orthographic projection'and all of itsau*iliar! e*tensions. ow, with this stepau*iliar! e*tensions. ow, with this stepcompleted, add a #ertical fold line tocompleted, add a #ertical fold line toaccommodate the addition of the right side #iew.accommodate the addition of the right side #iew.
3eflecting bac on the glass bo* concept,3eflecting bac on the glass bo* concept,!ou will remember that when we restrict!ou will remember that when we restrictour projection planes to the B planes on aour projection planes to the B planes on acube (the standard #iews) the fold linescube (the standard #iews) the fold lines
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cube (the standard #iews), the fold linescube (the standard #iews), the fold linesmust be normal or perpendicular to eachmust be normal or perpendicular to eachother. Project the nown boundar! linesother. Project the nown boundar! linesand data points from the front #iew intoand data points from the front #iew intothe area where the right side #iew will bethe area where the right side #iew will beconstructed.constructed.
"easure from the hori ontal fold line to the"easure from the hori ontal fold line to the front frontand bac and bac surfaces as displa!ed in thesurfaces as displa!ed in the toptop #iew,#iew,and transfer those data points to theand transfer those data points to the right sideright side
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pp gg#iew'relati#e to its fold line.#iew'relati#e to its fold line.
"easure from the fold line to the frontal"easure from the fold line to the frontal plane in the top #iew, and transfer the plane in the top #iew, and transfer themeasurement along one of the projectorsmeasurement along one of the projectorsinto the right side #iew (relati#e to theinto the right side #iew (relati#e to the
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*
into the right side #iew (relati#e to theinto the right side #iew (relati#e to the#ertical fold line). his will establish the#ertical fold line). his will establish the
front surface in the side #iew.front surface in the side #iew.
3epeat the procedure but measure to the bac surface in the top #iew. hen transfer the3epeat the procedure but measure to the bac surface in the top #iew. hen transfer thelinear distance into the right side #iew (relati#e to the #ertical fold line), to establish thelinear distance into the right side #iew (relati#e to the #ertical fold line), to establish thelocation of thelocation of the bac bac surface of the object in the right side #iew.surface of the object in the right side #iew.
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e*t, determine the location of the line in the center of the top #iew b! measuring e*t, determine the location of the line in the center of the top #iew b! measuringcarefull! from the hori ontal fold line, and transfer that linear distance into the right sidecarefull! from the hori ontal fold line, and transfer that linear distance into the right side#iew, appl!ing it relati#e to the #ertical fold line. 0lso, project the intermediate line from#iew, appl!ing it relati#e to the #ertical fold line. 0lso, project the intermediate line fromthe front #iew to the right side #iew.the front #iew to the right side #iew.
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*
:abel all of the significant points in all three #iews, starting with the hori ontal or:abel all of the significant points in all three #iews, starting with the hori ontal ortop #iew.top #iew.
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hen labeling points, alwa!s place the one that is closest to the projection plane first in the order. Points ; andhen labeling points, alwa!s place the one that is closest to the projection plane first in the order. Points ; andC represent a line which is #iewed from the end. 2ecause point ; is closest to the projection plane in the topC represent a line which is #iewed from the end. 2ecause point ; is closest to the projection plane in the top#iew, it is identified in front of point C. he same rule applies to points @ and B, and > and D in the top #iew.#iew, it is identified in front of point C. he same rule applies to points @ and B, and > and D in the top #iew.:ocate the points in the front and right side #iews.:ocate the points in the front and right side #iews.
n the front #iew, points > and D are connected, as are points @ and B. n both the top andn the front #iew, points > and D are connected, as are points @ and B. n both the top andthe front #iews, points B and C are connected as are points D and $. ?onnect them in thethe front #iews, points B and C are connected as are points D and $. ?onnect them in theright side #iew.right side #iew.
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!
!
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13 ( " '3 ) 1 )3 ('3 "
(
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""3 !
13 #
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!3 !
&3 #
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?onnecting the points in the right side #iew, the same as the! are connected in the?onnecting the points in the right side #iew, the same as the! are connected in the parent #iews, completes the problem solution. here are no missing lines in an! parent #iews, completes the problem solution. here are no missing lines in an!of the = #iews. 0 pictorial #iew of the object will help !ou to #isuali e the object.of the = #iews. 0 pictorial #iew of the object will help !ou to #isuali e the object.
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!
!
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13 ( " '3 ) 1 )3 ('3 "
(
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13 #
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!3 !
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his slide depicts the three orthographic #iews of the objectAhis slide depicts the three orthographic #iews of the objectAfront, top, and right side, plus a pictorial #iew showing all threefront, top, and right side, plus a pictorial #iew showing all three projection planes in one a*onometric #iew. projection planes in one a*onometric #iew.
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his problem represents another solid object. he front and right side #iews arehis problem represents another solid object. he front and right side #iews arecomplete as shown'no lines are missing in either #iew. Jou are to project thecomplete as shown'no lines are missing in either #iew. Jou are to project thetop #iew from the information pro#ided in the two gi#en #iews. 2egin b!top #iew from the information pro#ided in the two gi#en #iews. 2egin b!e*tending the projectors between the two gi#en #iews, to #erif! the projection.e*tending the projectors between the two gi#en #iews, to #erif! the projection.
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n this e*ample, we will use a reference plane instead of a fold line. 3emembern this e*ample, we will use a reference plane instead of a fold line. 3ememberthat t!picall!, a reference plane either contacts the object, or passes through it.that t!picall!, a reference plane either contacts the object, or passes through it.:et+s establish the reference plane through the center of the object in the right side:et+s establish the reference plane through the center of the object in the right side#iew.#iew.
?onstruct a second reference plane, perpendicular to the first, that will pass?onstruct a second reference plane, perpendicular to the first, that will passthrough the center of the object in the top or hori ontal #iew.through the center of the object in the top or hori ontal #iew.
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he orthographic principle of measure and transfer does not change when ahe orthographic principle of measure and transfer does not change when areference plane is used in place of a fold line. /owe#er, there is one change thatreference plane is used in place of a fold line. /owe#er, there is one change thatma! be re1uired. 3emember that a geometric rule demands that all pointsma! be re1uired. 3emember that a geometric rule demands that all points(relati#e to their reference plane or fold line) in the #iew being constructed, must(relati#e to their reference plane or fold line) in the #iew being constructed, must
be e*actl! the same in their orientation relati#e to the reference plane or fold line be e*actl! the same in their orientation relati#e to the reference plane or fold linein the #iew from which the! are ta en. n other words, the relationship of pointsin the #iew from which the! are ta en. n other words, the relationship of pointsto their reference plane in a top #iew, must be e*actl! the same as the relationshipto their reference plane in a top #iew, must be e*actl! the same as the relationshipof points to their reference plane in the #iew from which the information is ta en.of points to their reference plane in the #iew from which the information is ta en.
n this case the front #iew is the middle #iew about which the information isn this case the front #iew is the middle #iew about which the information ismeasured and applied. f measurements are ta enmeasured and applied. f measurements are ta en toward toward the #iew in the middlethe #iew in the middleto obtain the data points, !ou must also appl! the data b! measuringto obtain the data points, !ou must also appl! the data b! measuring towardtoward thethe#iew in the middle to appl! the measurement. 7imilarl!, if !ou measure awa!#iew in the middle to appl! the measurement. 7imilarl!, if !ou measure awa!from the #iew in the middle to ac1uire the data points, !ou must also measurefrom the #iew in the middle to ac1uire the data points, !ou must also measure
awa! from the #iew in the middle to appl! the data. he concept of the #iew inawa! from the #iew in the middle to appl! the data. he concept of the #iew inthe middle is significant, and will be used fre1uentl! throughout this unit and thethe middle is significant, and will be used fre1uentl! throughout this unit and thene*t. One final note concerning the #iew in the middleAne*t. One final note concerning the #iew in the middleA the view in the middle isthe view in the middle is alwaysalways the view from which a new view is being projected the view from which a new view is being projected ..
he distance d; is applied b! measuring from the reference plane towards the front #iew (the #iew inhe distance d; is applied b! measuring from the reference plane towards the front #iew (the #iew inthe middle), while distance d< is applied from the reference plane, but in a direction opposite'awa!the middle), while distance d< is applied from the reference plane, but in a direction opposite'awa!from the front #iew. /ea#! up the outline of si e boundaries in the top #iew, clean up the drawing andfrom the front #iew. /ea#! up the outline of si e boundaries in the top #iew, clean up the drawing andlabel all of the points.label all of the points.
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d(
d1
d(
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E*amine the drawing #iews to ensure that all of the points are connectedE*amine the drawing #iews to ensure that all of the points are connectedconsistentl! in all three #iews. For e*ample, points > and @ in the right side #iewconsistentl! in all three #iews. For e*ample, points > and @ in the right side #iew(and front #iew) are connected with a line. ?onstruct a line in the top #iew that(and front #iew) are connected with a line. ?onstruct a line in the top #iew thatconnects points > and @. :i ewise follow through with all of the other points, toconnects points > and @. :i ewise follow through with all of the other points, toshow connecting lines where intersections of planes occur in the top #iewshow connecting lines where intersections of planes occur in the top #iew
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1 (
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show connecting lines where intersections of planes occur in the top #iew.show connecting lines where intersections of planes occur in the top #iew.
he correct projection of the top #iew in this problem is now complete. 0ll pointshe correct projection of the top #iew in this problem is now complete. 0ll pointsand lines are shown in all #iews, and ha#e been #erified using a reference plane.and lines are shown in all #iews, and ha#e been #erified using a reference plane.
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1 (
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0 pictorial #iew of this problem, which is a >-0 pictorial #iew of this problem, which is a >-sided p!ramid, can assist in #isuali ing thesided p!ramid, can assist in #isuali ing thecharacteristics of the model.characteristics of the model.
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Problem umber > 0nimationProblem umber > 0nimationf !ou are inf !ou are in Show odeShow ode , !ou can acti#ate an orthographic projection animation of, !ou can acti#ate an orthographic projection animation of
the pre#ious problem b! a single clic within the blac area on the screen. f !outhe pre#ious problem b! a single clic within the blac area on the screen. f !oui Sh d ! i# h i i i h d bl li i hi
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are not inare not in Show odeShow ode , !ou can acti#ate the animation with a double clic within, !ou can acti#ate the animation with a double clic withinthe blac area on the screen. Jou ma! run the animation as man! times as !outhe blac area on the screen. Jou ma! run the animation as man! times as !oudesire. he animation can be stopped b! a single clic of the mouse'an!wheredesire. he animation can be stopped b! a single clic of the mouse'an!whereon the screen. f the animation is stopped b! clic ing the mouse when the cursoron the screen. f the animation is stopped b! clic ing the mouse when the cursoris inside the blac area, howe#er, a second clic will be re1uired outside theis inside the blac area, howe#er, a second clic will be re1uired outside thedar ened area to resume the presentation.dar ened area to resume the presentation.
clic on image to animate - clic outside for ne*t slide
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7 etching a solution, b! remo#ing pieces from a rectangular prism, can clarif!7 etching a solution, b! remo#ing pieces from a rectangular prism, can clarif!uncertainties about specific orthographic #iews of an object. n the case of the >-uncertainties about specific orthographic #iews of an object. n the case of the >-sided p!ramid, for instance, locate the center of the bloc on the top surface, andsided p!ramid, for instance, locate the center of the bloc on the top surface, andremo#e the front portion which e*tends down to the baseline in the frontal plane.remo#e the front portion which e*tends down to the baseline in the frontal plane.
3emo#e the bac portion in the same wa!, creating a triangular prism.3emo#e the bac portion in the same wa!, creating a triangular prism.
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e*t, locate the center point along the ridge at the top, and remo#e the portion e*t, locate the center point along the ridge at the top, and remo#e the portione*tending from that point to the baseline on the right side.e*tending from that point to the baseline on the right side.
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Finall!, remo#e the left portion of the object in the same wa! !ou remo#ed theFinall!, remo#e the left portion of the object in the same wa! !ou remo#ed theright sideA from the mid-point on the top ridge line to the base of the left side ofright sideA from the mid-point on the top ridge line to the base of the left side ofthe object.the object.
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he finished s etch or model, depicted in a =-dimensional illustration, lea#es littlehe finished s etch or model, depicted in a =-dimensional illustration, lea#es littledoubt about the characteristics of the object.doubt about the characteristics of the object.
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t should be clear to !ou now that when #iewed from the front and right side, thet should be clear to !ou now that when #iewed from the front and right side, theresulting #iews appear as triangles.resulting #iews appear as triangles.
n this e*ample, we will once again use a reference plane. hen this e*ample, we will once again use a reference plane. hetwo #iews that are shown in the illustration are complete (notwo #iews that are shown in the illustration are complete (nolines are missing in either #iew). he right side #iew islines are missing in either #iew). he right side #iew isre1uired. he projection has been #erified, and the hori ontalre1uired. he projection has been #erified, and the hori ontalreference plane correctl! positioned. ?onstruct the referencereference plane correctl! positioned. ?onstruct the reference
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plane to project the right side #iew. plane to project the right side #iew.
Project all rele#ant points from the front #iew into the right side #iew. 3emember theProject all rele#ant points from the front #iew into the right side #iew. 3emember thestrict orientation between projectors and reference planes.strict orientation between projectors and reference planes.
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3eference planes are effecti#e in man! wa!s. One3eference planes are effecti#e in man! wa!s. Onead#antage the! pro#ide is that measurements needad#antage the! pro#ide is that measurements neednot be ta en and transferred for locating points thatnot be ta en and transferred for locating points thatlie on the reference plane. he front surface in thelie on the reference plane. he front surface in thetop #iew is on the reference plane herefore thetop #iew is on the reference plane herefore the
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top #iew is on the reference plane. herefore, thetop #iew is on the reference plane. herefore, thefront surface in the right side #iewfront surface in the right side #iew must must also be on itsalso be on itsreference plane.reference plane.
"easure the distance from the hori ontal reference plane to the bac surface in the"easure the distance from the hori ontal reference plane to the bac surface in thetop #iew, and transfer that distance to the right side #iew'relati#e to the #erticaltop #iew, and transfer that distance to the right side #iew'relati#e to the #erticalreference plane.reference plane.
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a
n similar fashion, transfer all of the data points from the top #iew into the rightn similar fashion, transfer all of the data points from the top #iew into the rightside #iew, and using the projections from the front #iew, complete the boundaries ofside #iew, and using the projections from the front #iew, complete the boundaries ofthe right side #iew.the right side #iew.
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e*t, label all of the significant points and intersections in the top #iew and identif! the e*t, label all of the significant points and intersections in the top #iew and identif! thecorresponding points in the front and right side #iews.corresponding points in the front and right side #iews.
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?arefull! e*amine the front and top #iews to determine?arefull! e*amine the front and top #iews to determinewhich points are joined b! connecting lines. ?ompletewhich points are joined b! connecting lines. ?ompletethe right side #iew b! connecting the same points thatthe right side #iew b! connecting the same points thatare connected in the front and top #iews.are connected in the front and top #iews.
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otice the interconnecti#it! of points =, >, and @ in the top otice the interconnecti#it! of points =, >, and @ in the topand front #iews. ?ompleting the right side #iew re1uiresand front #iews. ?ompleting the right side #iew re1uiresthat these points be joined b! connecting lines'the samethat these points be joined b! connecting lines'the sameas in the parent #iews. his is the most ob#ious solution.as in the parent #iews. his is the most ob#ious solution.0n alternati#e solution to this problem also e*ists,0n alternati#e solution to this problem also e*ists,
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phowe#er, which we will consider presentl!.howe#er, which we will consider presentl!.
Once again, a pictorial #iew adds clarit! to theOnce again, a pictorial #iew adds clarit! to theorthographic solution to this problem.orthographic solution to this problem.
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Problem umber @ 0nimationProblem umber @ 0nimation
f !ou are inf !ou are in Show odeShow ode , !ou can acti#ate an orthographic projection animation of the, !ou can acti#ate an orthographic projection animation of the pre#ious problem b! a single clic within the blac area on the screen. f !ou are not in pre#ious problem b! a single clic within the blac area on the screen. f !ou are not inShow odeShow ode !ou can acti#ate the animation with a double clic within the blac area on!ou can acti#ate the animation with a double clic within the blac area on
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Show odeShow ode , !ou can acti#ate the animation with a double clic within the blac area on, !ou can acti#ate the animation with a double clic within the blac area onthe screen. Jou ma! run the animation as man! times as !ou desire. he animation can bethe screen. Jou ma! run the animation as man! times as !ou desire. he animation can bestopped b! a single clic of the mouse'an!where on the screen. f the animation isstopped b! a single clic of the mouse'an!where on the screen. f the animation isstopped b! clic ing the mouse when the cursor is inside the blac area, howe#er, a secondstopped b! clic ing the mouse when the cursor is inside the blac area, howe#er, a secondclic will be re1uired outside the dar ened area to resume the presentation.clic will be re1uired outside the dar ened area to resume the presentation.
clic on image to animate - clic outside for ne*t slide
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0 0: E3 0 E 7O:4 O
O /E 70"E P3O2:E"
E*ample Problem @aE*ample Problem @a
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One might determine that another point or intersection (point B)One might determine that another point or intersection (point B)could e*ist in the top #iew, below point number =. ?onsideringcould e*ist in the top #iew, below point number =. ?onsideringthat possibilit!, point B has been located in the front #iew, behindthat possibilit!, point B has been located in the front #iew, behind
point @, and on the bac surface in the right side #iew as shown. point @, and on the bac surface in the right side #iew as shown.
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9erif! that all of the points joined together with lines in the top and9erif! that all of the points joined together with lines in the top andfront #iews are also connected in the right side #iew. otice thatfront #iews are also connected in the right side #iew. otice that
points > and B are also connected in the top and front #iews. ?onnect points > and B are also connected in the top and front #iews. ?onnect points > and B in the right side #iew for an alternate solution. points > and B in the right side #iew for an alternate solution.
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he alternate solution is #alid, and has application in ahe alternate solution is #alid, and has application in astud! of orthographic projection principles. /owe#er,stud! of orthographic projection principles. /owe#er,
part function would determine the design before an! part function would determine the design before an!drawing was created. his e*ercise is gi#en simpl! todrawing was created. his e*ercise is gi#en simpl! todemonstrate the geometric possibilities that e*ist'baseddemonstrate the geometric possibilities that e*ist'based
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he pictorial (in addition to the orthographic #iews)he pictorial (in addition to the orthographic #iews)assists us in percei#ing an alternate right side #iewassists us in percei#ing an alternate right side #iewsolution. his is an e*ample of a need for = #iews tosolution. his is an e*ample of a need for = #iews to
define and control part geometr!.define and control part geometr!.
f !ou are inf !ou are in Show odeShow ode , !ou can acti#ate an orthographic projection animation of the, !ou can acti#ate an orthographic projection animation of thealternati#e solution b! a single clic within the blac area on the screen. f !ou are not inalternati#e solution b! a single clic within the blac area on the screen. f !ou are not inShow odeShow ode , !ou can acti#ate the animation with a double clic within the blac area on the, !ou can acti#ate the animation with a double clic within the blac area on the
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,,screen. Jou ma! run the animation as man! times as !ou desire. he animation can bescreen. Jou ma! run the animation as man! times as !ou desire. he animation can bestopped b! a single clic of the mouse'an!where on the screen. f the animation isstopped b! a single clic of the mouse'an!where on the screen. f the animation isstopped b! clic ing the mouse when the cursor is inside the blac area, howe#er, a secondstopped b! clic ing the mouse when the cursor is inside the blac area, howe#er, a secondclic will be re1uired outside the dar ened area to resume the presentation.clic will be re1uired outside the dar ened area to resume the presentation.
clic on image to animate - clic outside for ne*t slide
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he top and right side #iews are complete as shown (no missing lines).he top and right side #iews are complete as shown (no missing lines).?omplete the front #iew.?omplete the front #iew. ote ote 5 7urfaces 0, 2, and ? are5 7urfaces 0, 2, and ? are inclinedinclined surfacessurfaces
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From earlier discussions on the subject of inclined surfaces in orthographicFrom earlier discussions on the subject of inclined surfaces in orthographic projection, !ou will recall that an inclined surface is one that is not parallel to an! projection, !ou will recall that an inclined surface is one that is not parallel to an!of the si* principle planes on the #iewing cube, but itof the si* principle planes on the #iewing cube, but it isis perpendicular to two of perpendicular to two ofthem. ( hene#er a surface is oriented in =-dimensional space so that it isthem. ( hene#er a surface is oriented in =-dimensional space so that it is
perpendicular to one of the si* projection planes in the #iewing cube (glass bo* perpendicular to one of the si* projection planes in the #iewing cube (glass bo*concept), it logicall! follows that it would also be perpendicular to the oppositeconcept), it logicall! follows that it would also be perpendicular to the opposite
plane.) herefore, it would be perpendicular to two of the si* planes which ma e plane.) herefore, it would be perpendicular to two of the si* planes which ma eup the cube. 0 principle !ou must remember is that an inclined surface willup the cube. 0 principle !ou must remember is that an inclined surface willalwaysalways appear as anappear as an edge viewedge view in those #iews where it is perpendicular to itsin those #iews where it is perpendicular to its
projection plane. n this ne*t problem, we are re1uired to construct a right side projection plane. n this ne*t problem, we are re1uired to construct a right side#iew of an object that has three inclined, planar surfaces. he top and right side#iew of an object that has three inclined, planar surfaces. he top and right side#iews are complete as shown. he fact that surfaces 0, 2, and ? are inclined in#iews are complete as shown. he fact that surfaces 0, 2, and ? are inclined inthis problem, limits the possibilit! of a correct answer to one. 3emember, anthis problem, limits the possibilit! of a correct answer to one. 3emember, an
inclined surface, in orthographic projection, will displa! as an edge #iew of theinclined surface, in orthographic projection, will displa! as an edge #iew of thesurface in one out of e#er! three contiguous orthographic #iews.surface in one out of e#er! three contiguous orthographic #iews.
Gi#en this problem to sol#e, would project the points identified in the top #iew,Gi#en this problem to sol#e, would project the points identified in the top #iew,into the front #iew, and e*tend the top surface in the front #iew to compl! with theinto the front #iew, and e*tend the top surface in the front #iew to compl! with the
projection form the top #iew. projection form the top #iew.
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Project the lines defining and delimiting the right side #iew into the front #iew.Project the lines defining and delimiting the right side #iew into the front #iew.
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:abel the points on the highest surface in the top #iew and transfer the data to the front and right side #iews. he height:abel the points on the highest surface in the top #iew and transfer the data to the front and right side #iews. he heightof the object is gi#en in both the front and right side #iews. otice that the left side of the front #iew displa!s the fullof the object is gi#en in both the front and right side #iews. otice that the left side of the front #iew displa!s the fullheight of the object'as determined b! the right side #iew. For the time, label onl! the left portion of the top #iew.height of the object'as determined b! the right side #iew. For the time, label onl! the left portion of the top #iew.
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here no hidden lines are gi#en in the top #iew, which b! definition is ahere no hidden lines are gi#en in the top #iew, which b! definition is a completecomplete #iew, we are assured that the bottom of the object will fall directl! underneath the#iew, we are assured that the bottom of the object will fall directl! underneath theoutline of the top surface (object linesoutline of the top surface (object lines alwaysalways ta e precedence o#erta e precedence o#er all other linesall other lines on the drawing). 7o, e*tend the bottom surface to the same si e e*tents as the topon the drawing). 7o, e*tend the bottom surface to the same si e e*tents as the topsurface.surface.
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0 basic principle regarding inclined planes is that the! will0 basic principle regarding inclined planes is that the! will alwaysalways displa! as edge #iews indispla! as edge #iews inone out of three contiguous orthographic #iews. otice that points > and = are separated inone out of three contiguous orthographic #iews. otice that points > and = are separated inthe front #iew, along the top surface. hat fact alone denies the possibilit! of an edge #iew ofthe front #iew, along the top surface. hat fact alone denies the possibilit! of an edge #iew ofsurface 0 in the front #iew. herefore, let+s presume that the edge #iew of surface 0 is in thesurface 0 in the front #iew. herefore, let+s presume that the edge #iew of surface 0 is in thetop #iew, and assign labels beneath points = and > in addition to other points defining the toptop #iew, and assign labels beneath points = and > in addition to other points defining the top#iew#iew.
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Points @, B, C, and D are all on the same hori ontal plane. he! are also depictedPoints @, B, C, and D are all on the same hori ontal plane. he! are also depictedconnected. ?onstruct a line from point @ through point D in the front #iew. 0lso,connected. ?onstruct a line from point @ through point D in the front #iew. 0lso,
based upon the conclusion that the bottom is e*actl! the same as the top, connect based upon the conclusion that the bottom is e*actl! the same as the top, connectall of the points on the line directl! below points @ through D in the front #iew.all of the points on the line directl! below points @ through D in the front #iew.
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:ines =, B and >, @ are shown to be connected in the top #iew and right side #iews.:ines =, B and >, @ are shown to be connected in the top #iew and right side #iews.?onnect them in the front #iew to displa! surface 0. 0lso, because no hidden lines are?onnect them in the front #iew to displa! surface 0. 0lso, because no hidden lines are
present in the complete top #iew, we ha#e presumed that the bottom surface has the same present in the complete top #iew, we ha#e presumed that the bottom surface has the samecharacteristics as the top. herefore, connect the lines that would impl! intersections oncharacteristics as the top. herefore, connect the lines that would impl! intersections onsurface ?, and show this surface.surface ?, and show this surface.
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?omplete the projection drawing of the orthographic #iews b! adding the object?omplete the projection drawing of the orthographic #iews b! adding the objectlines in the front #iew, depicting the intersections shown in the top #iew, andlines in the front #iew, depicting the intersections shown in the top #iew, andoutlining the e*tents of surface 2.outlining the e*tents of surface 2.
0 pictorial s etch, in addition to the orthographic #iews can assist us in our0 pictorial s etch, in addition to the orthographic #iews can assist us in ourinterpretation of the solution of this problem.interpretation of the solution of this problem.
O th g hi P j ti T bl f C t t M t T bl f C t tR t t th P i Slid Slid (%' Q itGl
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Problem umber B 0nimationProblem umber B 0nimationf !ou are inf !ou are in Show odeShow ode , !ou can acti#ate an orthographic projection animation of this, !ou can acti#ate an orthographic projection animation of this
problem b! a single clic within the blac area on the screen. f !ou are not in problem b! a single clic within the blac area on the screen. f !ou are not in ShowShow ode ode , !ou can acti#ate the animation with a double clic within the blac area on the, !ou can acti#ate the animation with a double clic within the blac area on thescreen. Jou ma! run the animation as man! times as !ou desire. he animation can bescreen. Jou ma! run the animation as man! times as !ou desire. he animation can be
O th g hi P j ti T bl f C t t M t T bl f C t tR t t th P i Slid Slid (%" Q itGl
stopped b! a single clic of the mouse'an!where on the screen. f the animation isstopped b! a single clic of the mouse'an!where on the screen. f the animation isstopped b! clic ing the mouse when the cursor is inside the blac area, howe#er, astopped b! clic ing the mouse when the cursor is inside the blac area, howe#er, asecond clic will be re1uired outside the dar ened area to resume the presentation.second clic will be re1uired outside the dar ened area to resume the presentation.
O th hi P j ti T bl f C t t M t T bl f C t tR t t th P i Slid Slid (% Q itGl
3eaching bac to an earlier part of this unit, !ou will recall that as we discussed inclined3eaching bac to an earlier part of this unit, !ou will recall that as we discussed inclinedand obli1ue surfaces, the principle was emphasi ed that obli1ue planar surfaces are neitherand obli1ue surfaces, the principle was emphasi ed that obli1ue planar surfaces are neither
parallel nor perpendicular to an! of the si* normal (principal) projection planes in the parallel nor perpendicular to an! of the si* normal (principal) projection planes in the#iewing cube. his is significant because the true shape and si e of geometric#iewing cube. his is significant because the true shape and si e of geometriccharacteristics and features on parts are shown onl! in normal #iews. Obli1ue lines arecharacteristics and features on parts are shown onl! in normal #iews. Obli1ue lines areforeshortened. he! do not displa! true lengths, and therefore, the true si es and shapes offoreshortened. he! do not displa! true lengths, and therefore, the true si es and shapes offeatures are not displa!ed in obli1ue #iews.features are not displa!ed in obli1ue #iews.
o complete the right side #iew, using both a miter line and the measure and transfero complete the right side #iew, using both a miter line and the measure and transfermethod, !ou will ha#e to create a reference plane somewhere on or through the object.method, !ou will ha#e to create a reference plane somewhere on or through the object.For simplification, construct a reference plane that is associated with the frontal line onFor simplification, construct a reference plane that is associated with the frontal line onthe surface in both #iews.the surface in both #iews.
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9erif! the projection b! e*tending the points from the top #iew into the front9erif! the projection b! e*tending the points from the top #iew into the front#iew. 3emember, projectors (e*tension lines) between #iews must be#iew. 3emember, projectors (e*tension lines) between #iews must be
perpendicular to the reference plane or fold line set between the #iews. perpendicular to the reference plane or fold line set between the #iews.
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o demonstrate the consistenc! betweeno demonstrate the consistenc! betweentechni1ues of projection, add a >@techni1ues of projection, add a >@ & line at the& line at theintersection of the reference planes, and projectintersection of the reference planes, and projectthe points from the top #iew through the >@the points from the top #iew through the >@degree line, and down into the right side #iew.degree line, and down into the right side #iew.
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:abeling points can be #er! helpful. :abel the points in the top #iew and transfer:abeling points can be #er! helpful. :abel the points in the top #iew and transferthem to the front #iew.them to the front #iew.
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9erif! the consistenc! of the two s!stems of projection b! measuring the points9erif! the consistenc! of the two s!stems of projection b! measuring the pointsfrom the reference plane in the top #iew, and transferring the locations into thefrom the reference plane in the top #iew, and transferring the locations into theright side #iew from its reference plane.right side #iew from its reference plane.
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/a#ing #erified the point locations in the right side #iew, connect the points in the/a#ing #erified the point locations in the right side #iew, connect the points in thesame wa! the! are connected in the front and top (parent) #iews.same wa! the! are connected in the front and top (parent) #iews.
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he right side #iew is complete'and correct. 2oth measure and transfer, and usehe right side #iew is complete'and correct. 2oth measure and transfer, and useof the miter line, wor well to produce #iews that would be projected in a line ofof the miter line, wor well to produce #iews that would be projected in a line ofsight that is perpendicular to the projection plane on the #iewing cube (glass bo*).sight that is perpendicular to the projection plane on the #iewing cube (glass bo*).
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o pro#ide a better understanding how the surface could be #iable and actuall!o pro#ide a better understanding how the surface could be #iable and actuall!e*ist on a part, a bloc has been added to the surface to illustrate the relationshipe*ist on a part, a bloc has been added to the surface to illustrate the relationshipof the surface to the part.of the surface to the part.
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he #isual images in this animation are produced slightl! different than the others. 0nhe #isual images in this animation are produced slightl! different than the others. 0nactual orthographic image is burned onto the screen, showing the actual orthographicactual orthographic image is burned onto the screen, showing the actual orthographic
projection from the #arious positions, as the part rotates through the procedure. 3un it projection from the #arious positions, as the part rotates through the procedure. 3un ith ti th t ! f t bl ith th i i l i # l# dgh ti th t ! f t bl ith th i i l i # l# d
Problem umber C 0nimationProblem umber C 0nimation
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Obli1ue 7urfacesObli1ue 7urfaces 0n obli1ue surface is0n obli1ue surface isone that is neitherone that is neither parallel nor parallel nor perpendicular to an! of perpendicular to an! ofthe B principal planes onthe B principal planes onthe #iewing cube. 0llthe #iewing cube. 0ll
2ecause the obli1ue surface is not parallel to the projection plane, some of the lines on the2ecause the obli1ue surface is not parallel to the projection plane, some of the lines on theimage will be foreshortened, thus the true si e and shape #iew of the obli1ue surface willimage will be foreshortened, thus the true si e and shape #iew of the obli1ue surface willnot displa! on the projection plane.not displa! on the projection plane.
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0 similar problem is encountered in the right side #iew of the object. 0 majorit!0 similar problem is encountered in the right side #iew of the object. 0 majorit!of the surface will be displa!ed in true si e and shape. 2ut the obli1ue #iew willof the surface will be displa!ed in true si e and shape. 2ut the obli1ue #iew will
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0s ma! be seen, all but the obli1ue surface is shown in its true si e and shape.0s ma! be seen, all but the obli1ue surface is shown in its true si e and shape.Once again, the obli1ue surface is foreshortened.Once again, the obli1ue surface is foreshortened.
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he image on the projection plane is correct'projection wise, but the true si ehe image on the projection plane is correct'projection wise, but the true si e
and shape of the obli1ue surface is not displa!ed on the projection plane.and shape of the obli1ue surface is not displa!ed on the projection plane.
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t should be clear to !ou b! now, that there must be methods of constructing au*iliar!t should be clear to !ou b! now, that there must be methods of constructing au*iliar!
#iews to displa! true si es and shapes of surfaces that are inclined or obli1ue to #iewing#iews to displa! true si es and shapes of surfaces that are inclined or obli1ue to #iewingcube projection planes. hose t!pes of de#eloped #iews will be discussed in unit <.cube projection planes. hose t!pes of de#eloped #iews will be discussed in unit <.
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O3 /OG30P/ ? P3O E? OPractice Problems
here are missing lines in all three #iews in thishere are missing lines in all three #iews in this problem. 7tud! the #iews carefull!. here is problem. 7tud! the #iews carefull!. here isenough information pro#ided to complete allenough information pro#ided to complete allthree #iews. 4se an! projection techni1ue thatthree #iews. 4se an! projection techni1ue that!ou are most familiar with. a e some time!ou are most familiar with. a e some timeright now. 4singright now. 4sing Problem ;Problem ; in !our boo ,in !our boo ,
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right now. 4singright now. 4sing Problem ;Problem ; in !our boo ,in !our boo , project all of the missing lines. hen !ou ha#e project all of the missing lines. hen !ou ha#efinished, chec !our answer against the solutionfinished, chec !our answer against the solutionslides that follow.slides that follow.
"ost of the missing lines can be added b! projecting feature characteristics from"ost of the missing lines can be added b! projecting feature characteristics fromone #iew to the other. Project the o#erall si es between each #iew. hen projectone #iew to the other. Project the o#erall si es between each #iew. hen projectthe internal characteristics as the! appl!.the internal characteristics as the! appl!.
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e*t, hea#!-up the lines that would be #isible from !our #iewing station, and add e*t, hea#!-up the lines that would be #isible from !our #iewing station, and addan! hidden line characteristics that would not be #isible from the gi#enan! hidden line characteristics that would not be #isible from the gi#en perspecti#e. 2e sure to construct a center line depicting the a*is of the hole. perspecti#e. 2e sure to construct a center line depicting the a*is of the hole.
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4se either the front or bac surface in the top #iew and locate the hole a*is, and4se either the front or bac surface in the top #iew and locate the hole a*is, andtransfer that date point to the right side #iew.transfer that date point to the right side #iew.
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a
a
he problem is now complete. here are no missing lines in an! of the threehe problem is now complete. here are no missing lines in an! of the three#iews. ?lean up the drawing b! remo#ing the construction lines.#iews. ?lean up the drawing b! remo#ing the construction lines.
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a
a
hile !ou probabl! followed a slightl! different procedure, !our answer and minehile !ou probabl! followed a slightl! different procedure, !our answer and mineshould agree. Jours should loo just li e this one. 0 significant number ofshould agree. Jours should loo just li e this one. 0 significant number of
practice problems follow. he! ha#e been designed to reinforce the principles of practice problems follow. he! ha#e been designed to reinforce the principles oforthographic projection. 8o each problem on !our own before loo ing at the e!.orthographic projection. 8o each problem on !our own before loo ing at the e!.
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his problem also has missing lines in all three #iews. 7ee how far !ou can get withouthis problem also has missing lines in all three #iews. 7ee how far !ou can get withoutloo ing at the procedure e! that follows. 7top now. 4singloo ing at the procedure e! that follows. 7top now. 4sing Problem <Problem < in !our boo , addin !our boo , addall of the lines that are missing in each of the three orthographic #iews. hen chec !ourall of the lines that are missing in each of the three orthographic #iews. hen chec !ourwor against the ne*t se1uence of slides.wor against the ne*t se1uence of slides.
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2egin b! projecting all of the nown information2egin b! projecting all of the nown information between the #iews. 3emember that points that between the #iews. 3emember that points thatrepresent end #iews of lines will project to linesrepresent end #iews of lines will project to linesagain in the ne*t #iew. Ieep the projectorsagain in the ne*t #iew. Ieep the projectors
parallel and if !ou use labeling, be consistent from parallel and if !ou use labeling, be consistent from#iew to #iew.#iew to #iew.
?omplete the right side #iew b! projecting all of?omplete the right side #iew b! projecting all ofthe rele#ant lines and points. ?lean up thethe rele#ant lines and points. ?lean up thedrawing.drawing.
/opefull!, !our s etch turned out the same as this/opefull!, !our s etch turned out the same as thisdrawing. f it did not, !ou ma! want to tr! itdrawing. f it did not, !ou ma! want to tr! itagain. 8id !ou remember to insert a center line toagain. 8id !ou remember to insert a center line torepresent the a*is of the hole 8id !ou use a foldrepresent the a*is of the hole 8id !ou use a foldline or reference plane to get the distances !ouline or reference plane to get the distances !ouneededneeded
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hene#er !ou feel that !ou are read!, ad#ance tohene#er !ou feel that !ou are read!, ad#ance tothe ne*t problem.the ne*t problem.
0s has been the case with all of the pre#ious0s has been the case with all of the pre#ious problems, there are missing lines in all three problems, there are missing lines in all threeof the orthographic projections of this object.of the orthographic projections of this object.4sing4sing Problem =Problem = in !our boo , add all linesin !our boo , add all linesthat are missing'in each #iew. Once again,that are missing'in each #iew. Once again,do as much as !ou can without chec ing !ourdo as much as !ou can without chec ing !our
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wor against the e!. hen !ou ha#ewor against the e!. hen !ou ha#ecompleted !our s etch, c!cle through thecompleted !our s etch, c!cle through thesolution series, beginning with the ne*t slide.solution series, beginning with the ne*t slide.%uggestion: hen sol#ing this problem, usehen sol#ing this problem, usethe >@& miter line techni1ue.the >@& miter line techni1ue.
Project either the front or bac surface on the object, in both the top and right sideProject either the front or bac surface on the object, in both the top and right side#iews, to the point of intersection. 0t that point of intersection, construct a >@&#iews, to the point of intersection. 0t that point of intersection, construct a >@&miter line.miter line.
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Project the significant and ob#ious points and lines between these two #iews.Project the significant and ob#ious points and lines between these two #iews.0lso, project the basic feature characteristics between the front and top #iews.0lso, project the basic feature characteristics between the front and top #iews.
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One of the most ob#ious characteristics is the #ertical feature at the bac of theOne of the most ob#ious characteristics is the #ertical feature at the bac of theobject. Project it #erticall! from the right side #iew until an intersection is formedobject. Project it #erticall! from the right side #iew until an intersection is formedwith the miter line, then hori ontall! through the object. ?on#ert the projectionwith the miter line, then hori ontall! through the object. ?on#ert the projectionline into an object line through the e*tents of the part (right to left sides).line into an object line through the e*tents of the part (right to left sides).
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he surfaces created b! the remo#al of the corner'in the upper right side of thehe surfaces created b! the remo#al of the corner'in the upper right side of thefront #iew, can be projected to both the top and right side #iews. ?onstruct objectfront #iew, can be projected to both the top and right side #iews. ?onstruct objectlines where the actual edge #iews of the surfaces would be on the object.lines where the actual edge #iews of the surfaces would be on the object.
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?ontinue projecting the feature characteristics between the #iews, and where?ontinue projecting the feature characteristics between the #iews, and whereapplicable, clean up the drawing b! con#erting the e*tension (projection) linesapplicable, clean up the drawing b! con#erting the e*tension (projection) linesinto the appropriate line st!le and weight.into the appropriate line st!le and weight.
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4sing the miter line again, add the details with reference to the hole in the front4sing the miter line again, add the details with reference to the hole in the frontand right side #iews.and right side #iews.
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he drawing is now complete. here is enough graphic information gi#en thathe drawing is now complete. here is enough graphic information gi#en thatdimensions could be assigned, and the part produced.dimensions could be assigned, and the part produced.
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his problem also has missing lines in all three #iews. Follow the same procedure andhis problem also has missing lines in all three #iews. Follow the same procedure andcomplete all three #iews. 3efer tocomplete all three #iews. 3efer to Problem >Problem > in !our boo . 0fter completing !our solutionin !our boo . 0fter completing !our solutions etch, chec !our wor against the series of slides that follow this one.s etch, chec !our wor against the series of slides that follow this one.
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0s the part is e*amined, !ou will disco#er0s the part is e*amined, !ou will disco#erthat there is a #ertical portion at the bac ofthat there is a #ertical portion at the bac ofthe object, as shown in the right side orthe object, as shown in the right side or
profile profile #iew. 4sing the bac surface as a#iew. 4sing the bac surface as areference plane measure the thic ness andreference plane measure the thic ness andtransfer the measurement to the top #iew.transfer the measurement to the top #iew.
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0lso the flat hori ontal plane in the front0lso the flat hori ontal plane in the front#iew can be projected into the right side#iew can be projected into the right side#iew.#iew.
he 9-notch in the #ertical up-right at thehe 9-notch in the #ertical up-right at the bac can be projected to the top and right bac can be projected to the top and rightside #iews. he a*es for the two holes canside #iews. he a*es for the two holes canalso be projected from the front #iew intoalso be projected from the front #iew intothe top and right side #iews.the top and right side #iews.
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heir locations projected, hea#!-up theheir locations projected, hea#!-up theobject lines for clarit!. e*t complete theobject lines for clarit!. e*t complete thedetail of the holes in the top and right sidedetail of the holes in the top and right side#iews.#iews.
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otice that the hidden lines representing the otice that the hidden lines representing thehole surfaces is suppressed b! the object line inhole surfaces is suppressed b! the object line inthe top #iew. Onl! one step remains5 measurethe top #iew. Onl! one step remains5 measurefrom the bac surface to the bac side of thefrom the bac surface to the bac side of thelarge notch best shown in the top #iew, andlarge notch best shown in the top #iew, andtransfer the distance into the right side #iewtransfer the distance into the right side #iew
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(also measured from the bac surface). hen,(also measured from the bac surface). hen,complete the problem b! projecting the rightcomplete the problem b! projecting the rightand left surfaces of the notch into the front #iew.and left surfaces of the notch into the front #iew.
?hec the drawing carefull! to see if an! lines are missing in an! #iew. f it is?hec the drawing carefull! to see if an! lines are missing in an! #iew. f it iscomplete remo#e !our construction lines.complete remo#e !our construction lines.
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/ow did !ou do 8id !ou remember the rule about center lines depicting a*es of/ow did !ou do 8id !ou remember the rule about center lines depicting a*es ofholesholes
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4se4se Problem @Problem @ in !our boo , and s etch in all of the missing lines. Emplo! whate#erin !our boo , and s etch in all of the missing lines. Emplo! whate#ertechni1ue suits !ou, but follow the rules go#erning center and hidden lines. ?omplete thistechni1ue suits !ou, but follow the rules go#erning center and hidden lines. ?omplete this
problem before chec ing the e! in the slides that follow. problem before chec ing the e! in the slides that follow.
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will use the >@& miter line as an e*clusi#e method to sol#e this problem. 2egin will use the >@& miter line as an e*clusi#e method to sol#e this problem. 2egin b! projecting either the front or bac surface'in both the front and profile #iews, b! projecting either the front or bac surface'in both the front and profile #iews,to establish the intersection point through which the miter line must pass ( electedto establish the intersection point through which the miter line must pass ( electedto use the front surface.to use the front surface.
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ith the miter line set, project the most ob#ious points and features into the right side andith the miter line set, project the most ob#ious points and features into the right side and
front #iews. hile doing this tas , con#ert the projection lines into their proper line t!pesfront #iews. hile doing this tas , con#ert the projection lines into their proper line t!pesand establish them in the appropriate #iews. e can start with the #ertical element at theand establish them in the appropriate #iews. e can start with the #ertical element at the
bac of the object, and the hori ontal shelf in the profile #iew. bac of the object, and the hori ontal shelf in the profile #iew.
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e*t project the contours in the top #iew into the front and side #iews. Jou ma! e*t project the contours in the top #iew into the front and side #iews. Jou ma!
also project the center a*es for the two holes into the top and profile #iews. henalso project the center a*es for the two holes into the top and profile #iews. henfinish the drawing b! projecting the hole diameter details into the top and profilefinish the drawing b! projecting the hole diameter details into the top and profile#iews.#iews.
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Jour answer should be just li e this one. f it is not, go bac through theJour answer should be just li e this one. f it is not, go bac through the
de#elopment series and determine where the differences are. 8on+t rush throughde#elopment series and determine where the differences are. 8on+t rush throughthese problemsA the! are designed to help !ou understand the projection processthese problemsA the! are designed to help !ou understand the projection processand gi#e !ou important practice.and gi#e !ou important practice.
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Practicing orthographic projection problems li ePracticing orthographic projection problems li ethese builds confidence and self assurance. herethese builds confidence and self assurance. hereare se#eral more problems to come'some moreare se#eral more problems to come'some morecomple* than others. ?ollecti#el!, the! arecomple* than others. ?ollecti#el!, the! aredesigned to broaden !our awareness of principlesdesigned to broaden !our awareness of principlesthat guide solution philosophies. he more ofthat guide solution philosophies. he more of
them !ou do the more confident (and competent)them !ou do the more confident (and competent)
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them !ou do, the more confident (and competent)them !ou do, the more confident (and competent)!ou will become.!ou will become.
his problem needs additional lines in all threehis problem needs additional lines in all three#iews. or with it until !ou are sure of !our#iews. or with it until !ou are sure of !ouranswers. 4seanswers. 4se Problem BProblem B in !our boo . henin !our boo . hen!ou ha#e finished, chec !ourself against the slide!ou ha#e finished, chec !ourself against the slideseries that guides the solution.series that guides the solution.
his problem, li e all of our earlier problems inhis problem, li e all of our earlier problems in
orthographic projection, re1uires additional linesorthographic projection, re1uires additional linesin each #iew to be complete. 7tud! it carefull!.in each #iew to be complete. 7tud! it carefull!.2egin b! projecting the ob#ious points and lines2egin b! projecting the ob#ious points and lines
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"easure from the front or from the bac of the"easure from the front or from the bac of theobject in the top #iew to determine the depth ofobject in the top #iew to determine the depth ofthe protrusion on the right side. 0lso, measurethe protrusion on the right side. 0lso, measurefor location of the intermediate step, andfor location of the intermediate step, andtransfer these two locating measurements to thetransfer these two locating measurements to the
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d1 d(
"easure from the front or from the bac of the object in the top #iew to determine the depth"easure from the front or from the bac of the object in the top #iew to determine the depthof the protrusion on the right side. 0lso, measure for location of the intermediate step, andof the protrusion on the right side. 0lso, measure for location of the intermediate step, andtransfer these two locating measurements to the profile (right side) #iew. /ea#! up the linestransfer these two locating measurements to the profile (right side) #iew. /ea#! up the linesdepicting edge #iews.depicting edge #iews.
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d(
d1
d(
d1
?omplete the drawing b! measuring from the reference plane on the bac of the?omplete the drawing b! measuring from the reference plane on the bac of the part, to the center a*is of the hole'in the right side #iew. ransfer the part, to the center a*is of the hole'in the right side #iew. ransfer themeasurement to the top #iew and add the hole at its proper location.measurement to the top #iew and add the hole at its proper location.
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d1
he problem is complete now, which means that there are no missing lines in an!he problem is complete now, which means that there are no missing lines in an!of the three #iews. Jou ha#e probabl! noticed that in each instance, bothof the three #iews. Jou ha#e probabl! noticed that in each instance, both
projection and measurements are used to complete the drawings. projection and measurements are used to complete the drawings.
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n sol#ing this problem, want !ou to anal! e the drawing carefull!. 4sen sol#ing this problem, want !ou to anal! e the drawing carefull!. 4se Problem CProblem C inin!our boo , and add the lines that are missing in each #iew. 4se an! techni1ue that !ou are!our boo , and add the lines that are missing in each #iew. 4se an! techni1ue that !ou arecomfortable with, but docomfortable with, but do not not loo at the solution (ne*t slide), until !ou ha#e done all !ouloo at the solution (ne*t slide), until !ou ha#e done all !oucan do to complete the drawing. hen !ou ha#e finished, ad#ance to the ne*t slide. herecan do to complete the drawing. hen !ou ha#e finished, ad#ance to the ne*t slide. herewill not be a series of slides to guide !ou through a process of sol#ing the problem'onl!will not be a series of slides to guide !ou through a process of sol#ing the problem'onl!the solution itself. 2e sure !ou understand the solution, and that !ou are comfortable with atthe solution itself. 2e sure !ou understand the solution, and that !ou are comfortable with atleast one method of achie#ing the same results.least one method of achie#ing the same results.
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/ow closel! does !our solution resemble the e! as there an! part of this problem that/ow closel! does !our solution resemble the e! as there an! part of this problem that presented special concerns 0re !ou prepared to mo#e on 7tud! and re#iew this problem presented special concerns 0re !ou prepared to mo#e on 7tud! and re#iew this problemuntil !ou completel! understand the process used to sol#e it.until !ou completel! understand the process used to sol#e it.
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4sing the illustration on4sing the illustration on Problem DProblem D in !our boo , construct the three standard front, top, and right sidein !our boo , construct the three standard front, top, and right sideorthographic #iews of the object. 8etermine a scale that suits !ou, and s etch the #iews of the object,orthographic #iews of the object. 8etermine a scale that suits !ou, and s etch the #iews of the object,showing the proper orientation and relationships between the #iews. hen !ou ha#e completed !ourshowing the proper orientation and relationships between the #iews. hen !ou ha#e completed !ours etch, ad#ance to the ne*t screen and compare !our drawing to the answer e!.s etch, ad#ance to the ne*t screen and compare !our drawing to the answer e!.
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Front
Jour s etch should loo li e the la!out on theJour s etch should loo li e the la!out on thescreen. /ow did !ou do Pictorial #iews arescreen. /ow did !ou do Pictorial #iews aret!picall! easier to read than orthographict!picall! easier to read than orthographicdrawings. /owe#er, pictorial (a*onometric)drawings. /owe#er, pictorial (a*onometric)drawings are foreshortened on one, two, or alldrawings are foreshortened on one, two, or all
three a*es, in order to minimi e the distortionthree a*es, in order to minimi e the distortionthat would occur if full si e dimensions werethat would occur if full si e dimensions were
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,,that would occur if full-si e dimensions werethat would occur if full-si e dimensions wereused. he ne*t slide shows the two depictions,used. he ne*t slide shows the two depictions,side b! side.side b! side.
/ere !ou see the differences and comparisons on the same slide. "an! students, new to the/ere !ou see the differences and comparisons on the same slide. "an! students, new to thescience of graphics, e*perience difficulties reading orthographic drawings.science of graphics, e*perience difficulties reading orthographic drawings.
8uring the 7econd orld ar, man! women and !oung people wor ed in the arms plants8uring the 7econd orld ar, man! women and !oung people wor ed in the arms plantsacross 0merica. t was disco#ered that orthographic drawings of parts or assemblies wereacross 0merica. t was disco#ered that orthographic drawings of parts or assemblies weredifficult for untrained people to understand. n conse1uence of that finding, pictorial #iewsdifficult for untrained people to understand. n conse1uence of that finding, pictorial #iewswere added to assist in the interpretation of comple* drawings.were added to assist in the interpretation of comple* drawings.
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his e*ercise is similar to the last one. 0 pictorial drawing of an object is gi#en, and !ou arehis e*ercise is similar to the last one. 0 pictorial drawing of an object is gi#en, and !ou areto s etch the three principle orthographic projections'top, front, and right side #iews. 4seto s etch the three principle orthographic projections'top, front, and right side #iews. 4seProblem $Problem $ in !our boo . 8o not continue on to the ne*t slide until !ou ha#e completed !ourin !our boo . 8o not continue on to the ne*t slide until !ou ha#e completed !ours etch. hen chec !our wor against the answer e! which follows.s etch. hen chec !our wor against the answer e! which follows.
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his is the arrangement and orientation of #iews that !ou should ha#e drawn inhis is the arrangement and orientation of #iews that !ou should ha#e drawn in!our s etch. f !ou do not ha#e this solution, ad#ance to the ne*t screen to see the!our s etch. f !ou do not ha#e this solution, ad#ance to the ne*t screen to see the pictorial and orthographic projections together on the same slide. "a e sure !ou pictorial and orthographic projections together on the same slide. "a e sure !ouunderstand this de#elopment before !ou progress to the ne*t e*ercise.understand this de#elopment before !ou progress to the ne*t e*ercise.
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?arefull! compare !our s etch to this solution.?arefull! compare !our s etch to this solution.he additional pictorial drawing ma! help !ouhe additional pictorial drawing ma! help !ou
to understand the placement of all lines on theto understand the placement of all lines on theobject. hen !ou are read!, ad#ance to the ne*tobject. hen !ou are read!, ad#ance to the ne*te*ercise.e*ercise.
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otice that the right side otice that the right sideand the frontal plane restand the frontal plane reston the same hori ontalon the same hori ontal
bottom plane of the part. bottom plane of the part.he front is nothe front is not
ele#ated. "an! ma eele#ated. "an! ma ethe mista e of tr!ing tothe mista e of tr!ing to
justif! a different justif! a differentsolution based upon thesolution based upon theangular cut on theangular cut on thefront right corner.front right corner.
his ishis is Problem ;%Problem ;% found in !our boo . ?omplete the projection b! adding all lines that ma! be missing in one,found in !our boo . ?omplete the projection b! adding all lines that ma! be missing in one,two, or all three #iews. 4se whate#er method seems easiest to !ou, but ma e certain that all object, hidden, andtwo, or all three #iews. 4se whate#er method seems easiest to !ou, but ma e certain that all object, hidden, andcenter lines are accounted for in each of the three #iews.center lines are accounted for in each of the three #iews.
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7elf-E#aluation7elf-E#aluationOrthographic ProjectionOrthographic Projectionhere ma! be missing lines in an!, or all of the three #iews. he solution will not e*tend be!ond thehere ma! be missing lines in an!, or all of the three #iews. he solution will not e*tend be!ond the
boundaries of the object lines shown in an! #iew. 4sing boundaries of the object lines shown in an! #iew. 4sing Problem ;;Problem ;; in !our boo , complete the drawingin !our boo , complete the drawing b! adding the lines that are missing. b! adding the lines that are missing.
here are some things about this e*ercise that will be slightl! different from the pre#ious onesAhere are some things about this e*ercise that will be slightl! different from the pre#ious onesAthe object is c!lindrical as shown in the right side #iew, andthe object is c!lindrical as shown in the right side #iew, and thethe front view front view is complete asis complete as
shown shown . he projection principles remain constant, so !ou should ha#e no problem with the. he projection principles remain constant, so !ou should ha#e no problem with thesolution. 4singsolution. 4sing Problem ;<Problem ;< in !our boo , s etch the completed solution.in !our boo , s etch the completed solution.
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7elf-E#aluation7elf-E#aluation
Orthographic ProjectionOrthographic Projectionhis problem presents the same challenges that pre#ious problems ha#eA find in an! or all of thehis problem presents the same challenges that pre#ious problems ha#eA find in an! or all of theorthographic projections of the object, an! missing lines that need to be included to properl!orthographic projections of the object, an! missing lines that need to be included to properl!
displa! the completed #iews. 4sedispla! the completed #iews. 4se Problem ;=Problem ;= in !our boo , and s etch its solution.in !our boo , and s etch its solution.
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Orthographic ProjectionOrthographic Projection E*ercise umber OneE*ercise umber One
his is the last problem in the orthographic series of practice e*ercises. here ma! be missing lines in one, two, orhis is the last problem in the orthographic series of practice e*ercises. here ma! be missing lines in one, two, orall three #iews. 4seall three #iews. 4se Problem ;>Problem ;> in !our boo , and add all lines that are missing in each of the #iews. 4se thein !our boo , and add all lines that are missing in each of the #iews. 4se the
projection techni1ue that !ou are most comfortable with'or !ou ma! tr! combining techni1ues as we ha#e done on projection techni1ue that !ou are most comfortable with'or !ou ma! tr! combining techni1ues as we ha#e done onsome other problems.some other problems. $int: he small hole in the front #iew is a threaded (tapped) hole. he small hole in the front #iew is a threaded (tapped) hole.
Orthographic Projection Table of Contents Master Table of ContentsReturn to the Previous Slide Slide ( ( QuitGlossary
End of 4nit OneEnd of 4nit One
hen !ou are comfortable with the information co#ered in this presentation, !ouhen !ou are comfortable with the information co#ered in this presentation, !ou
hen !ou are comfortable with the information co#ered in this presentation, !oup ,will be read! to complete the ?ontent "aster! E#aluation for orthographicwill be read! to complete the ?ontent "aster! E#aluation for orthographic
projection. f !ou feel uncertain about !our nowledge related to some of the projection. f !ou feel uncertain about !our nowledge related to some of the basic principles or materials included in this presentation, it ma! be wise to basic principles or materials included in this presentation, it ma! be wise toconsider a careful re#iew. a e the time that is necessar! to thoughtfull! e#aluateconsider a careful re#iew. a e the time that is necessar! to thoughtfull! e#aluate
the illustrations and accompan!ing te*t to assure !ourself that !ou are read!.the illustrations and accompan!ing te*t to assure !ourself that !ou are read!.hen !ou feel prepared, call for the e#aluation. here are @; objecti#e 1uestionshen !ou feel prepared, call for the e#aluation. here are @; objecti#e 1uestionsin the e#aluation on orthographic projection principles and con#entional practices.in the e#aluation on orthographic projection principles and con#entional practices.
