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G EO M ET RICD IM EN SIO N IN GA N DT O LERA N C IN G

C H A P T E R O B J E C T I V E S

Upon completion of this chapter students should be able to dothe following :s Describe w hat is m eant b y th e termgeneral

tolerancing.s Den e the conceptgeom etric dimensioning and

tolerancing.s Explain t he pu rpose of a m od ier.s D ist inguish b etw een the conceptsm axim um m ater ia l

condit ion (M M C)an d regardless of feature size (RFS).s Explain the conceptleast m aterial condition (LM C).s Describe wh at is m eant byprojected to leran ce zone.s M ake a sketch th at illustrates th e concept o f datum s.s D em onstrate how to establ ish d atum s.s App ly feature control sym bols w hen d im ensioning

ob jects.s Exp lain the concept ofTrue position.

All around sym bolAngularityBasic d im ensionBetw een sym bolBilateral toleranceCircularityCylindricityDatumDatum fea tureDatum feature sim ulatorDatum fea ture sym bolD a t u m p l an eD a t u m r eference fram eDatum sur faceDatum ta rge t sym bolFeature cont rol sym bol

FlatnessFree-state variationGeom etr ic d im ensioningand tolerancingGen eral tolerancingLeast m aterialcondi t ion (LM C)Lim it dim ensioning

M a x im u m m a te ria lc o n d it io n ( M M C )Modi ersParallelismPerpendicularityPositional tolerancingPro leProle of a lineProle o f a sur faceProjected tolerancezoneRegard less of featuresize (RFS)Rule # 1RunoutSize toleran ceStatistical tolerancingsymbolStraightnessTangent p laneTolerancingTrue positionUn ilateral toleranceVirtual cond it ion

C H A P T E R O U T L I N E

Su m m a ry o f g e o m e t ri c d i m e n si o n i n g a n d t o l er an c i n gt e r m s G e o m e t r ic d i m e n si o n i n g a n d t o l er a n c in g

d e n e d M o d i er s Fe at u r e c o n t r o l sy m b o l True po si t ion Ci rcu la r ity ( roun dn ess) Cyl indr ic i ty

A n g u l a r i t y Parallelism Perpendicu la r i ty Prole R u n o u t C o n c e n t r i c i t y S u m m a r y

Review qu est ion s Pr o b l e m s

K E Y T E R M S

4 6 8

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G e o m e t r i c D i m e n s i o n i n g a n d T o l e r a n c i n g

Sum m ary of GeometricDimensioning and T olerancingTerm sActual Local Size. The value of any individual distanceat any cross section of a featu re.Actual Mating Size. The dimensional value of theactual mating envelope.

Actual Size. Actual measured size of a feature.

Allowance. The d iff erence between the larger shaft sizelimit and the smallest hole size limit.Angularity. Tolerancing of a feature at a specied angleother than 90 degrees from a ref erenced datum .Basic Dimension. A theoretically perfect dimensionsimilar to a ref erence or nom inal dimension. It is used toidentify the exact location, size, shape, or orientation of af eature. Associated tolerances are applied by notes, featurecontrol frame, or other methods, excluding tolerancewithin t itle blocks.Bilateral To lerances. Tolerances that are applied to anominal dimension in the positive and n egative directions.

Bonus To lerance. The permitted allowable increase intolerance as the feature departs from the material conditionidentied within t he feature con trol frame.Circular Runout. A tolerance that identies an innitenumber of single circular elements measured at crosssections on a feature when the feature is rotated 360degrees for each cross section.Circularity. A tolerance th at cont rols the circular crosssection of round features that is independent of otherf eatures. The tolerance zone bou ndar y is formed by twoconcent ric perfect circles.

Clearance Fit. A condition between mating parts inwhich the internal part is always smaller than the externalparts it ts into.Coaxia lity. The condition of two or more featureshaving coincident axes.

Compound Datum Feature s. Two datum features used

to establish a datum or axis plane.Concentricity. A tolerance in which the axis of a featuremust be coaxial to a specied datum regardless of thedatums and th e features size. The lack of concentricity iseccentricity.Cylindricity. A tolerance that simu ltaneously controlsa surface of revolut ion for straightn ess, parallelism, andcircularity of a feature, and is independent of any other fea-tures on a part. The tolerance zone bou ndary is composedof two concen tric perfect cylinders.

Datum. Ref erence poin ts, lines, planes, cylinders, andaxes which are assumed to be exact. They are establishedf rom datum features.

Datum Axis. The axis of a ref erenced datum feature suchas a hole or shaft.

Datum Feature . A feature which is used to establish

a datum .Datum Feature of Size. A feature that h as size, such asa shaft, which is used to establish a datum .

Datum Identication Symbol. A special rectangular boxwhich contains the datum ref erence letter and a dash oneither side of the letter. It is used to identify datum features.

Datum: Feature Simulator. A surface of adequatelyprecise form (such as a surface plate, a gage surface, or amandrel) contacting the datum feature(s) and used toestablish the simulated datum(s).

Datum: Refere nce. Entering a datum ref erence letter ina compartment of the feature control frame followingthe to lerance value.

Datum: Reference Frame. Three mutually perpendi-cular planes that establish a coordinate system. It is createdby datum ref erences in a feature control frame or by a note.

Datum: Simulated. A point, axis, or plane established byprocessing or inspection equipment, such as the followingsimulator, surface plate, a gage surface, or a m andrel.

Datum Simulation. The use of a tool contacting adatum feature used to simulate a true geometric counter-part of the feature.

Datum Simulator. A tool used to contact a datum feature.

Datum Ta rget. Specied points, lines, or areas on af eature used to establish datum s.

Datum Ta rget Are a . A specied area on a part that iscontacted to establish a datum .

Datum Ta rget Line. A line on a surface that is con tactedto establish a datum .

Datum Ta rget Point. A specied point on a surface usedto establish a datum.

Datum Ta rget Symbol. A circle divided horizontallyinto halves containing a letter and number to identifydatum targets.

Envelope, Actual Mating. The term is dened accordingto th e type of features as follows:

(a) For an External Feature. A similar perfect featurecounterpart of smallest size that can be circum-scribed about the features so that it just contacts thesurface at the h ighest points. For example, a small-est cylind er of perfect form o r two parallel planes

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Runou t . The composite surface variation from thedesired form of a part of revolution d uring full rotation of the part on a d atum axis.Secondary Datum. The second datum ref erence in af eature control frame. Established after the primarydatu m, it has less design inuen ce and func tionally.

Size, Vi rtual Condition. The actual value of the virtualcondition boundary.Stra ightness. A tolerance that controls the allowablevariation of a su rface or an axis from a theo retically per-fect line.

Symmetry. A condition for which a feature (or features)is equally disposed or sh aped abou t the cen ter plane of adatum feature.Tangent Plane. A theoretically exact plane derivedf rom th e true geometric coun terpart of the specied fea-ture surface by con tacting the high points on the surf ace.

Tertiary Datum. The third datum ref erence in a featu recontrol frame. Established after the secondary datum, it hasthe least amou nt of design inu ence or functionality.To lerance. The acceptable dimensional variation orallowance of a part.

Total Runout. A tolerance that provides for a compos-ite control of all surface elements as the part is rotated 360degrees abou t a datum axis.Transition Fit. A condition in which the prescribedlimits of mating parts produce either a clearance or aninterf erence when the parts are assembled.

True Geometric Counterpart . The theoretically perf ectboundary (virtual condition or actual mating envelope) o rbest-t (tangent) plane of a specied datu m feature.True Position. The theoretically exact location of a feature.Unilateral To lerance. A tolerance which allows variationsin only one d irection.Virtua l Condition. A constant boun dary produced bythe com bined effects of the maximum material conditionsize and geometric tolerance. It represen ts the worst casecond ition of assembly at MMC.Zero Tolerance at MMC or LMC. A tolerancing m ethodwhere no tolerance is shown in th e feature control frame.The tolerance allowed is totally dependent on th e size of the feature departure from MMC or LMC.

GENERAL TOLERANCINGThe industrial revolution created a need for mass pro-duction; assembling interchangeable parts on an assemblyline to turn out great qu antities of a given nish ed prod-uct. Interchangability of parts was the key. If a particular

produ ct was composed of 100 parts, each individual partcould be produced in quantity, checked for accuracy,stored, and used as n ecessary.

Since it was h umanly and technologically impossible tohave every individual part produced exactly alike (it stillis), the concept of geometric and positional tolerancing wasintroduced. Tolerancing means setting acceptable limits of deviation . For example, if a mass produced part is to be 4"in length under ideal conditions, but is acceptable aslong as it is not less than 3.99" and n ot longer than 4.01",there is a tolerance of plus or min us .01",Figure 12-1 . Thistype of toleran ce is called asize tolerance.

There are three diff erent types of size tolerances: un i-lateral and bilateral, shown in Figure 12-2 , and limitdimensioning. When aunilatera l toleranceis applied to adimension, th e tolerance applies in one direction only (forexample, the object may be larger but not smaller, or it maybe smaller but not larger). When abilateral toleranceis

applied to a dimension, the tolerance applies in bothdirections, but not necessarily evenly distributed. Inlimit

FIGURE 12 -2 Two types of tolera nces

FIGURE 12 -1 Size tolerance

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dimensioning, the high limit is placed above the low value.Wh en placed in a single line, the low limit precedes thehigh limit and th e two are separated by a dash.

Tolerancing size dimensions offers a nu mber of advan-tages. It allows for acceptable error withou t compromisesin design, cuts down on unacceptable parts, decreasesmanu facturing time, and m akes the product less expensiveto produce. However, it soon became apparent that inspite of advantages gained from size tolerances, tolerancingonly the size of an object was not enough. Other charac-teristics of objects also needed to be toleranced, such as loca-tion o f features, orientation, form, ru nout, an d p role.

In order for parts to be acceptable, depending on theiruse, they need to be straight, round , cylindrical, at, angu-lar, and so forth . This concept is illustrated inFigure 12-3 .The object depicted is a shaft that is to be manu factured towithin plus or minus .01 of 1.00 inch in d iameter. The n-ished produ ct meets the size specications but, since it isnot straight, the part might be re jected.

The need to tolerance more than just the size of objects led to the d evelopm ent of a more precise systemof tolerancing called geometric dimensioning an dposi-tional tolerancing. This new practice improved on con-ventional tolerancing signicantly by allowing designersto tolerance size, form, orientation, prole, location,and runout, Figure 12-4 . In turn , these are the charac-

teristics that m ake it possible to achieve a high d egree of interchangability.

Geometric Dimensioning andTolerancing Den edGeometric dimensioning and tolerancingis a dimensioningpractice which allows designers to set tolerance limitsnot ju st for th e size of an object, but for all of the variouscritical characteristics of a part. In applying geometric

dimensioning and tolerancing to a part, the designermu st examine it in terms of its fun ction and its relation-ship to mating parts.

Figure 12-5 is an example of a drawing of an object thathas been geometrically dimensioned and toleranced. It istaken from the dimen sioning standards as dened by theAmerican National Standards Institute (ANSI), written bythe American Society of Mechanical Engineers (ASME) orASME Y14.5M1994. This manu al is a necessary ref erencefor drafters and designers involved in geometr ic dimen-sion ing and p ositional tolerancing.

The key to learning geometric dimensioning and p osi-tional tolerancing is to learn th e various building blockswhich make up the system, as well as how to properlyapply them. Figure 12-6 contains a chart of the buildingblocks of the geometric dimensioning and tolerancing sys-tem. In addition to the standard building blocks shown in

the gure, several modifying symbols are used whenapplying geometric tolerancing, as discussed in detail inupcoming paragraphs.

Another concept that must be understood in order toeffectively apply geometric tolerancing is the concept of datum s. For skilled, experienced designers, the geometricbuilding blocks, modiers, and datum s blend together asa single concept. However, for th e purpose of learn ing, theyare dealt with separately, and undertaken step-by-step asindividual concepts. They are presented now in the fol-lowing order: modiers, datum s, and geometric bu ildingblock s.

ANSIs dimen sionin g stand ards manual (Y14.5 series)chan ges from tim e to time as standards are upd ated. Forexample, the Y14.5 manual became Y14.5M in 1982 toaccommodate metric dimensioning. Revised again in1988, it became Y14.5M-R1988. In the latest edition,the standard takes on the n ame of the developing agency,the American Society of Mechan ical Engineers (ASME).ASME Y14.5M1994 is the latest edition in th e on goingrevision process of th e standard . This chapter helps stu-dents learn the basics of geometric dimensioning and posi-

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FIGURE 12-3 Tolera nce of form

FIGURE 12-4 Types of tolerances

FORINDIVIDUALFEATURES

FORINDIVIDUALOR RELATEDFEATURES

FORRELATEDFEATURES

FORM

PROFILE

ORIENTATIONLOCATIONRUNOUT

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tional tolerancing so they will be able to apply lateststandards set forth by ASME at any poin t in t ime and inaccordance with any edition of the man ual that is spec-ied. Students shou ld not use this chapter as a ref erencein p lace of th e ASME stand ard. Always refer to the latestedition of the standard for specics that go beyond thebasics covered h erein.

ModiersModiers are symbols that can be attached to the standardgeometric building blocks to alter their application orinterpretation. The proper u se of mod iers is fun damen-

tal to effective geometric tolerancing. Various m odiers areoften used: maximu m material cond ition, least materialcondition, projected tolerance zone, free-state variation, tan-gent plane, all around, between symbol, and statisticaltolerance, Figure 12-7A , Figure 12-7B , and Figure 12-7C .

MAXIMUM MATERIAL CONDITIONMaximum materia l condition ( MMC), is the cond ition of a characteristic when the most material exists. For exam-

FIGURE 12-5 Geometrically dimensioned and tolera nced drawing(From ASME Y14.5M1994 )

FIGURE 12 -6Building blocks

SYMBOL CHARACTERISTICGEOMETRICTOLERANCE

STRAIGHTNESS

FLATNESSFORM

CIRCULARITY

CYLINDRICITYPROFILE OF A LINE

PROFILEPROFILE OF A SURFACE

ANGULARITY

PERPENDICULARITY ORIENTATION

PARALLELISM

TRUE POSITION

CONCENTRICITY LOCATION

SYMMETRY

* CIRCULAR RUNOUTRUNOUT

* TOTALRUNOUT

* MAY BEFILLEDIN

FIGURE 12 -7A Modiers used when a pplying geometric tolera ncin

MAXIMUM MATERIALCONDITION

LEASTMATERIALCONDITION

PROJECTED TOLERANCE ZONE

FREE STATE VARIATION

TANGENTPLANE

ALLAROUND

BETWEEN SYMBOL

STATISTICALTOLERANCE

THE RFS SYMBOL CAN STILLBE USED BUTTHEPREFERRED PRACTICE IS TO OMITIT.

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ple, MMC of the external feature inFigure 12-8 is .77inch. This is the MMC because it represents the condi-tion where the most material exists on the part beingmanuf actured. The MMC of the internal feature in th e g-ure is .73 inch . This is the MMC because the m ost mate-rial exists when the hole is produced at the smallestallowable size.

In using this concept, the designer must remember thatthe MMC of an intern al feature is the smallest allowablesize. The MMC of an externa l feature is the largest allow-

able size within specied tolerance limits inclusive. A ruleof thumb to remember is that MMC means most material.

REGARDLESS OF FEAT URE SIZE

Regardless of feature size (RFS), tells machinists that atolerance of form or position or any characteristic must bemaintained regardless of th e actual produ ced size of theobject. Geometric tolerances are understood to applyregardless of feature size where the mod iersM or L are

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FIGURE 12-7B Form and proportion of geometric tolerancing symbols

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not used. It is permissible to show the RFS modier;however, it is redun dant and the pref erred p ractice is toomit it. The RFS concept is illustrated inFigure 12-9 . Inthe RFS example, the object is acceptable if produ ced insizes from 1.002 inch es to .998 inch inclusive. The formcontrol is axis straightness to a tolerance of .002 inchregardless of feature size. This means th at the .002-inchaxis straightn ess tolerance mu st be adh ered to, regardless

of the prod uced size of the part.Contrast this with the MMC example. In this case,

the produced sizes are still 1.002 inches to .998 inchHowever, because of the MMC modier, the .002 inch axisstraightness tolerance applies only at MMC or 1.002inches.

If the produ ced size is smaller, the stra ightness toler-ance can be increased proportionally. Of course, thismakes the MMC modier more popular with mach inistsfor several reasons: 1) it allows them greater room for error


FIGURE 12-7C Form a nd proportion of dimensioning symbols and letters

FIGURE 12 -8 MMC of an external and a n internal feature

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withou t actually increasing the tolerance, 2) it decreasesthe nu mber of parts rejected, 3) it cuts down on un ac-ceptable parts, 4) it decreases the n um ber of inspectionsrequired, and 5) it allows the u se of fun ctional gaging. Allof these advantages translate in to substantial nancial sav-ings while, at the same time, making it possible to produceinterchangeable parts at minimu m expense.

LEAST MATERIAL CONDITION

Least mater ial condition ( LMC), is the opp osite of MMC.It refers to the condition in which the least material exists.This concept is illustrated inFigure 12-10 .

In the top example, the external feature of the part isacceptable if produced in sizes ranging from .98 inch to

1.02 inch es inclu sive. The least material exists at .98 inch.Consequently, .98 inch is the LMC.

In the bottom example, the internal feature (hole) isacceptable if produced in sizes ranging from .98 inch t o1.02 inches inclusive. The least material exists at 1.02inches. Con sequently, 1.02 represents th e LMC.

PROJECTED TOLERANCE ZONEProjected tolerance zoneis a modier that allows a tolerancezone established by a locational tolerance to be extendeda specied distance beyond a given surface. This conceptis discussed furth er later in this chapter und er the headingTrue Position.

FREE-STAT E VARIAT IONFree-state var iationis the concept th at some parts cann otbe expected to be contained within a boundary of perf ectf orm. Some parts may vary in form beyond the MMC size

limits after forces applied du ring manufacture are removed.For example, a thin-walled part shape m ay vary in its freestate due to stresses being released in th e part. This vari-ation may require that th e part meet its tolerance require-men ts wh ile in its free state.

Parts that are subject to free-state variation do nothave to meet the Ru le #1 requiremen t of perfect form atMMC. These parts are standard stock such as bars, sheets,tubes, extrusions, structural shapes, or other items pro-duced to established industry or government standards.The appropriate standard would govern the limits of f orm variation allowed after man ufactu re.

The free-state symbol species the maxim um allow-able free-state variation. It is placed within a featurecontrol frame, following the tolerance and any modiers,Figure 12-1 1.

TANGENT PLANETh e tangent planeconcept u ses a modifying symbol withan orientation tolerance to modify the intended control of the su rface. Wh en an orientation tolerance is applied to asurface, the primary control is equivalent t o th e symbol-ogy used . An example is the pr imary cont rol of a parallelcallout is parallelism. However, wh en applied, th e speci-

ed symbol controls not on ly parallelism bu t other formvariations such as concavity, convexity, waviness, at-ness, and other imperfections as well.

If two such controlled surfaces are assembled, theabrupt variation in the surfaces can cause diff erent mat-ing effects and assembly conditions. There are severalways to control the effects of surface conditions whenapplying or ientation to lerances. The obvious m ethod isto rene th e surface control with a form tolerance suchas atness. This is permissible because the orientation tol-

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FIGURE 12 -9 Regardless of feature size (RFS)

FIGURE 12 -10 Least materia l condition (LMC)

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erance cont rols atness to the extent o f the specied tol-erance value.

Another method is to modify the orientation toler-ance to apply a tangent plane. When the modier isapplied, the orientation to lerance zone for a tangent planeis identical to any other orientation to lerance zones withone exception. The orientation tolerance no longer con-trols the form of the surface. The surface of the con-trolled feature m ust be w ithin th e specied limits of size,but is not required to fall within th e parallelism toleran cezone boundary. Only a plane tangent to the h igh points onthe surface must be within the tolerance zone bou nd ary.The symbo l is placed within t he feature control frame fol-lowing the stated tolerance,Figure 12-12.

ALL AROUND SYMBOLThe all around symbolis the symbolic means of indi-cating that the sp ecied tolerance applies all around thepart. The no rmal tolerance zon e of a geometric calloutextends the length of the feature in qu estion. If there isan abru pt ch ange in surface cond ition, such as an off-set, the tolerance zone would conclude at the beginningof the o ffset. Applying the all aroun d symbo l extendsthe tolerance zone all around the feature to includeabrup t surface variations,Fi gure 12-13. This conceptwill be discussed further later in th is chapter un der th eheading Prole.

BETWEEN SYMBOLThe between symbolis a symbolic means of ind icating th atthe stated to lerance applies to a specied segment of a sur-face between designated points. The normal tolerance

zone o f a geometric callout extends th e length of the fea-ture in question. Application of this symbol can be used tolimit the tolerance zone to a specied area. It can also beused to clarify the exten t of the prole tolerance wh en it isno t clearly visible due to surface variations.Figure 12-14illustrates the use of this symbol.

STAT ISTICAL TOLERANCING SYMBOLTh e statistical tolerancing symbolis a symbolic means of indicating that the stated toleran ce is based on statisticaprocess control (SPC). The symbol can be app lied in oneof two ways. When th e tolerance is a statistical size toler-ance, the symbol is placed next to t he size dimen sion asshown in Figure 12-15 . When th e tolerance is a statisticalgeometric tolerance, the symbol is placed in th e featurecontrol frame as shown inFigure 12-16.

FIGURE 12 -11 Feature control fra me with free-state symbol

FIGURE 12-12 Specifying a tangent plane

FIGURE 12-14 Between symbol

FIGURE 12-13 All around symbol

FIGURE 12-15 Statistical tolerance symbol

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DATUMSDatums are theoretically perfect points, lines, axes, surf aces,or planes used for ref erencing features of an ob ject. Theyare established by the physical datum features that are iden-tied on th e drawing. Identication of datum features isdone by using adatum feature symbol. This symbol consistsof a capital letter en closed in a squ are frame. A leader lineextends from th e frame to th e selected feature. A triangleis attached to the en d of the leader and is applied in t heappropriate way to indicate a datum feature. The symbolsshou ld on ly be applied to physical features. They shouldnot be attached to centerlines, axes, center planes, or

other theoretical entities.Figure 12-17 shows two ways inwhich datum feature symbols are placed on drawings. Thedatu m symbo l is attached to an extension line of the fea-ture outline, clearly separated from the dimension linewhen the datum feature is a surface or placed on the vis-ible outline of a feature su rf ace.

In Figures 12-18A , 12-18B, and 12-18C, the datum fea-ture symbol is placed on an extension of the dimension lineof a feature of size when the datum is an axis or centerplane. In Figures 12-18D , 12-18E, and 12-18F, the datum

is an axis. The symbol can be p laced on the ou tline of acylindrical sur face or an extension line of the feature ou t-line, separated from the size dimension. Figure 12-18Fshows one ar row of the dimension line being replaced bythe datum feature triangle when space is limited. If no fea-ture control frame is used, the symbol is placed on adimension leader line to the feature size dimen sion as seenby the example of Datum B in Figure 12-19 . In Figure12-20 the symbol is attached to the feature control framebelow (or above) when the feature(s) controlled is adatum center plane.

ESTA BLISHING DATUMSIn establishing datums, designers must consider thefun ction of the part, the manu facturing processes that will

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FIGURE 12 -16 Symbol indicating the specied tolera nce is a sta-tistical geometric tolerance

FIGURE 12 -17 Datum feature symbols on a feature surface and anextension line

FIGURE 12 -18 Placement of datum feature symbols on features of size

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be used in producing the part, how the part will be

inspected, and th e parts relationsh ip to oth er parts afterassembly. Designers and drafters m ust also un derstand thediff erence between a datum, datum feature, datum featuresimulator, datum surface, datum plane, and a datumf eature of size.

A datum is theoretical in nature and is located by thephysical datum features identied on the drawing. Adatum is considered to be the true geometric counterpartof the feature. It is the origin from which measurements aremade, or which provides geometrical ref erences to wh ich

other features are established. Adatum featureis the actualphysical feature on a part used to establish a datum,Figure 12-21 . It is identied on a drawing by use of adatum feature symbol,Figure 12-22 .

A datum feature simulatoris a surface, the form of

which is of such precise accuracy (such as a surface plate,a gage surface, or a mandrel), that it is used to simulate thedatum . The datum feature simu lator contacts the datumf eature(s) and simu lates the theoretical datum. Simu lationis necessary since measurements cann ot be made from thetheoretical true geometric counterpart. It is theref ore nec-essary to u se high-quality geometric features to simulatedatum s. Although the features are no t perfect, they are ofsuch a quality that they can be used for that purpose.Figures 12-23 an d 12-24 illustrate this concept withrespect to a surface and a feature of size.

A datum surf ace (f eature) is the inexact surface of the

object used to establish a datum plane. Adatum planeis atheoretically perfect plane from which measurements aremade. Since inaccuracies and variations in the surface con-dition of the datum surface make it impractical to takemeasurements from, then a theoretically perfect planemust be established from which measurements are made.To establish this datum plane, the high points of thedatu m sur face are brought in contact with, in th is case, asurface plate, which simulates the datum plane. Thisconcept is illustrated in Figure 12-21.


FIGURE 12-20 Placement of datum feature symbol in conjunctionwith a feature control fra me

FIGURE 12 -19 Datum ref erence on dimension leader line

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Notice the irregularities on the datum surface. Thehigh points on the datum surface actually establish thedatum plan e, which, in th is case, is the top of the manu -facturing equipment. All measurements ref erenced toDATUM A are measured from the theoretically perf ectdatum plane. High point contact is u sed for establishing

datums when the entire surface in question will be amachined surf ace.

A datum feature of size is established by associating thedatum feature symbol with the size dimension of theselected feature size. When identied, the theoreticaldatum is the axis, centerline, or center plane of the truegeometric coun terpart. it is simulated by th e processing

equipment (such as a chuck , vise, or centering device).The datu m feature simu lator establishes the datum axis,centerline, or center plane from which measurements canbe ref erenced. This concept is illustrated in Figures 12-23and 12-24.

DATUM TARGETSOn rougher, more irregular su rfaces, such as those asso-ciated with castings, specied points, lines, or area con-tacts are used for establishing datums. Datum targets

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FIGURE 12 -21 Datum feature, simulated datum , and theoretical datum plane

FIGURE 12-22 Dat um feature symbol

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designate specic points, lines, or areas of contact on a partthat are used in establishing a datum. They are usedwhen it is not always practical to identify an en tire surf aceas a datum feature.

A datum target symbolis used to identify datum targets.It consists of a circle divided in h alf with a horizontal line.The lower portion contains the datum identifying letter fol-

lowed by a datum target num ber. The nu mbers are sequen-tial, starting with one for each datum. The letter andnu mber establish a target label to identify planes or axesas datums. The upper half of the symbol is normallyempty except wh en using a diameter symbol followed bya value to identify the shape and size of the target area,Figure 12-25 . Figure 12-26 shows a part usin g datums tar-get areas to establish a datum p lane.

Dimensions used to locate targets may bebasic dimensionsor toleranced dimensions. A basic dimension is a theoret-ically perfect dimen sion, mu ch like a n ominal or design

FIGURE 12-23 Primary external datum diameter with datum featuresimulator

FIGURE 12 -24 Primary internal datum diameter with datum featuresimulator

FIGURE 12-25 Datum target symbol

FIGURE 12-26 Primary datum plane established by three datum target areas

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dimension. The dimension is identied by enclosing thevalue in a rectangular box as shown inFigure 12-27 .Tolerances p laced in general notes or within t he title block do not apply to basic dimensions. InFigure 12-28 , thedatum targets are located using basic dimensions. Points arelocated relative to on e another and d imensioned to sh owthe relationship between targets.

Wh en specic datum t arget points are used for estab-lishing datums, a minimum of three points, not in astraight line, are required for the p rimary datum, a m ini-mum of two for the secondary, and a min imum of one forthe tertiary, Figure 12-28. In Figure 12-28, pr imary datumplane A is the top of the object and it is established by pointsA1, A2, and A3. Secondary datum plane B is the front of the

object and tertiary datum plane C is the right side. Thedatum feature symbol is placed on a drawing in th e viewwhere the su rface in question appears as an edge.

Notice also that the secondary datum m ust be perpen-dicular to the rst, and the tertiary datum must be per-pendicular to both the primary and secondary datums.These three mutually perpend icular datum planes estab-lish what is called the d atum ref erence frame. Thedatumref erence fra meia a hypothetical, three-dimensional framethat establishes th e three axes of an X, Y, and Z coordinatesystem into which the object being produced ts andf rom which measurements can be made.Figure 12-29shows an object located within a datu m ref erence frame.For features that have sides (for example, rectangularand square objects), it takes three datums to establish adatum ref erence frame.

For cylindrical features, a complete ref erence frame isestablished with two datum ref erences. Figure 12-30

shows an object within a ref erence frame. Datum D is the

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FIGURE 12-27 Basic dimension symbol

FIGURE 12-2 8 Dimensioning datum ta rgets

FIGURE 12 -29 Datum ref erence fra me

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primary datum feature and is used to establish datum planeK. Notice that datum feature E is established by two th eo-retical planes intersecting at right angles on th e datum axis.The datum axis becomes the origin of measurements tolocate other features on the object. Datum feature E usesthe second an d th ird plane to locate the datu m axis. Theref erence frame is thus established u sing two datum s.

Figure 12-31 is an exam ple of a basic d imension. Abasic dimension is a theoretically perfect dimension,

much like a nominal or design d imension, that is used tolocate or specify the size of a feature. Basic dimen sions areenclosed in rectangular boxes, as shown in Figure 12-31.

Feature Control SymbolThe f eature control symbolis a rectangular box in wh ich alldata ref erring to the subject feature control are placed,including: the symbol, datum references, the featurecontrol tolerance, and modiers. These various feature con-trol elements are separated by vertical lines. (Figure 12-5contains a drawing sho wing how feature control symbolsare actually composed.)

The order of the data contained in a feature control frameis important. The rst element is the feature control sym-bol. Next is the zone descriptor, such as a diameter symbolwhere applicable. Then, there is the feature control toler-ance, modiers when u sed, and d atum ref erences listed inorder from left to right ,Figure 12-32 .

Figures 12-33 through 12-37 illustrate how feature con-trol symbols are developed for a variety of design situa-tions. Figure 12-33 is a feature control symbol whichspecies a .005 tolerance for symm etry and no datum ref-erence. Figure 12-34 species a tolerance of .005 for th etrue position of a feature relative to Datum A. Figures12-35 and 12-36 show the proper methods for con-structing feature control symbols with two and threedatum ref erences, respectively. Figure 12-37 illustrates afeatur control symbol with a mo dier and a controlleddatum added.

True PositionTrue position is the theoretically exact location of thecenterline of a product feature such as a hole. The toler-ance zone created by a position tolerance is an imaginarycylinder, the diameter of which is equal to the statedposition tolerance. The dimensions used to locate a fea-ture, that is to have a position tolerance, must be basicdimensions.

FIGURE 12 -30 Part with cylindrical datum feature

FIGURE 12-32 Order of elements in a feature control symbol

GEOMETRIC CHARACTERISTICSYMBOL

ZONE DESCRIPTOR

FEATURE TOLERANCE

MODIFIER

PRIMARY DATUMREFERENCE

SECONDARY DATUMREFERENCE

TERTIARY DATUMREFERENCE

.001 A B C

FIGURE 12 -31 Basic dimensions

3.625

BASIC DIMENSIONEXACT DIMENSION

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Figure 12-38 contains an exam ple of a part with twoholes drilled throu gh it. The h oles have a position toler-ance relative to three datu ms: A, B, and C. The holes arelocated by basic dimensions. The feature control frame

states that the positions of the centerlines of the holes

must fall within cylindrical tolerance zones having diam-eters of .030 in ch at MMC relative to DATUMS A, B, andC. The modier indicates that the .030 inch toleranceapplies only at MMC. As the holes are produced largerthan MMC, the diameter of the tolerance zones can beincreased correspondingly.

Figure 12-39 illustrates the concept of the cylindrical tol-erance zone from Figure 12-38. Th e feature control frameis repeated showing a .030 inch diameter tolerance zone.The broken -out section of the object from F igu re 12-38provides the interpretation. The cylindrical tolerancezone is shown in phan tom lines. The centerline of the hole

is acceptable as long as it falls anywh ere within th e hypo-thetical cylinder.

USING THE PROJECTED TOLERANCE ZONEMODIFIERASME recommends the use of the projected tolerance zoneconcept when the variation in perpendiculars of threaded

FIGURE 12-34 Feature control symbol with one datum ref erence

.005 A

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARY DATUM

REFERENCE

FIGURE 12-35 Feature control symbol with two dat um ref erences

FIGURE 12-36 Feature control symbol with three datum ref erences

FIGURE 12-37 Feature control symbol with a modier

FIGURE 12 -33 Feature control symbol with no da tum ref erence

.005

GEOMETRIC SYMBOL

FEATURE TOLERANCE

.002 A B

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARY DATUM

REFERENCE

SECONDARY DATUM

REFERENCE

.003 A B C

GEOMETRIC SYMBOL

FEATURE TOLERANCE

PRIMARY DATUM REFERENCE

SECONDARY DATUM

TERTIARY DATUM

.002 A

GEOMETRIC SYMBOL

FEATURE TOLERANCE

MODIFIER

PRIMARY DATUM

REFERENCE

B

THIS DATUM IS CONTROLLED BY THE ABOVE GEOMETRIC SYMBOL

FIGURE 12 -38 True position

FIGURE 12-39 Cylindrical tolerance zone

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or press-t holes could cause fasteners, such as screws,studs, or pins, to interf ere with m ating p arts.

The attitude of a threaded fastener is controlled by theinclination of the threaded hole into which it willassemble. There are instances where the inclinationcan be such th at the fastener interf eres with th e matingf eature. On e meth od of overcomin g this problem is touse a projected tolerance zone. When p rojected, the tol-erance zon es intend ed ou tcome is to decrease the incli-nation of the fastener p assing throu gh the m ating part.It is often thought that the tolerance zone extendsthrough th e feature being controlled to a poin t beyondthe part equ al to the projection, but this is not the case.Instead, the controlled feature has no internal toler-ance; the zone is totally outside of the feature being con-trolled. The height of the zone is equal to the valuespecied within th e feature con trol frame.Figure 12-40illustrates this concept.

The projected tolerance zone symbol is a capital Penclosed with a circle. It is placed within t he feature con-trol frame following the tolerance value or modier whereapplicable. The p rojection height is placed after the pro- ject ed to ler an ce zone sym bol, as illu strated in Figu re12-40. When a p rojected tolerance zone m odier is used,the su rface from wh ich th e tolerance is projected is iden-tied as a datum and the length of the projected to lerancezone is specied. In cases where it is not clear from wh ichsurface the projection extends, such as a through h ole, aheavy chain line is used with a dimension applied to it, asillustrated in Figure 12-41 . The resultant to lerance zone lies

totally outside the feature being con trolled.

FLAT NESSFlatness is a feature con trol of a surface which requires allelements of the surface to lie within two hypotheticalparallel planes. When atness is the feature control, adatum ref erence is neither required nor proper.

Flatness is applied by means of a leader poin ting to thesurface or by an extension line of th e surface. It cann otbe attached to the size dimen sion. The mod iersM or L

cannot b e used with atness because it is a surface con-trol only. The atness tolerance is not add itive and m ustbe less than the tolerance of size of the p art un less theappropriate note is added exempting it from Rule #1requirements.

Figure 12-42 shows how atness is called out in adrawing and the effect such a callout has on the pro-duced part. The surface ind icated must be at within a tol-erance zone of .010, as shown in Figure 12-42.

Flatness is specied when size tolerances alone arenot sufcient to control the form an d quality of the surf aceand wh en a surface must be at enough to p rovide a sta-

ble base or a smooth in terface with a mating part.Flatness is inspected for a full indicator movement

(FIM) using a dial ind icator. FIM is the n ewer term wh ichhas replaced the older total indicator movement orTIR. FIM means that the swing of the indicator needlef rom one extreme to the other cannot exceed the amou ntof the specied tolerance. The d ial indicator is set to runparallel to a surface table which is a theoretically perf ectsurface. The dial indicator is mounted on a stand orheight gauge. The machined surface is run under it,FIGURE 12 -40 Specied projected tolerance zone

FIGURE 12 -41 Projected tolerance zone using cha in line

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allowing the dial indicator to detect irregularities that fallout side of the tolerance zone.

STRAIGHTNESS

A straightness tolerance can be used to control surf aceelemen ts, an axis or a center plane. When used to controlsingle elements for a at su rface, it is applied in th e viewwhere the element to be con trolled is a straight line. Wh en

applied, it controls line elements in only one direction. Itdiffers from atness in that atness covers an ent ire surf acerather than just single elemen ts on a surface. A straightnesstolerance yields a tolerance zone of a specied width,within which all points on the line in question must lie.Straightness is generally applied to lon gitudinal elemen ts.

Another diff erence between straightness and atnessconcerns the application of the feature control frame.The method in which th e feature control frame is applieddetermines the intended control. If the feature controlframe is attached to an extension line of the surface or

attached to a leader pointing to the surface, the intendedcontrol is to the surface,Figure 12-43A . However, if the fea-ture control frame is attached to a dimension line or ad ja-cent to a dimension, the intended control is an axis orcenter plane,Figure 12-43B . Drast ically diff erent results arerealized based on the application method.STRAIGHTNESS OF A FLAT SURFACE

Figure 12-44 shows how a straightness tolerance is appliedon a drawing to the elements of a at surface. The straight-ness tolerance applies only to the top surface. The bottomsurface straightn ess error is controlled by th e limits of size.In th is case, the straightness tolerance is u sed as a rene-ment for the top su rface on ly. The feature contro l framestates tha t any longitudinal element for the ref erenced sur-face, in the direction indicated, must lie between twoparallel straight lines that are .002 inch apart.

STRAIGHTNESS OF A CYLINDRICAL SURFACE

Straightn ess applied to th e surface of a cylindr ical featureis shown in Figure 12-45 . It is similar to th at of a at sur-

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FIGURE 12-42 Flatness

FIGURE 12 -43 Dimensioning and tolerancing

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face, with one exception. Since the surface is round,opp osing surface lin e element s must also be con sideredwhen verifying straightness. The full straightness tolerancemay no t be available for th ese elements du e to cond itionssuch as wasting or barreling of the surface. Additionally, thestraightness tolerance is not additive to the size toler-ance and must be contained within the limits of size.This means th at if the part is made at MMC, no straight-ness tolerance is available because any variation in surf acestraightness would cause the part to exceed the MMCboundary of size. Figure 12-46 illustrates the relationshipbetween a straightness tolerance and a size tolerance of apart. Remember, each element of the surface must staywithin the specied straightness tolerance zon e and withinthe size tolerance envelope. Straightness is affected by run-ning the single-line elemen ts of a surface under a dial indi-cator for a full indicator movemen t (FIM).

Figures 12-47 through 12-52 further illustrate the

concept of straightness.Figure 12-47 shows a part witha size tolerance, but n o feature con trol tolerance. In th isexample, the form of the feature is controlled by thesize tolerance. The diff erence between maximum andminimu m limits denes the maximum form variation thatis allowed. ASME Y14.5M outlines the requirements of f orm control for individual features controlled on ly witha size dimension. This requirement is known as Rule#1. According to the standard, Rule #1 states: Where onlya tolerance size is specied, the limits of size of an in di-vidu al feature dene the extent to which variations in itsgeometric form , as well as size, are allowed. This mean s

that the size limits of a part determine the maximu m andminimum limits (boundaries) for that part. The MMClimit establishes a bou ndary limit of perfect form. If a partis at MMC, it mu st have perfect form. No variation in formis allowed. As the part varies in size toward LMC, the formof the part is allowed to vary equal to the variation in size

FIGURE 12-44 Straightness of a at surf ace

FIGURE 12-46 Straightness interpretedFIGURE 12-45 Straightness of surface elements

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f rom MMC. When the part is made at LMC, the form vari-ation is equal to the diff erence between the MMC andLMC sizes as illustrated in Figure 12-47 .

Figure 12-48 is the sam e part with a straightness tol-erance of .002 regardless of feature size tolerance. Theimplied regardless of feature size tolerance limits the

amou nt th e surface can be ou t of straightn ess to a maxi-mu m of .002 regardless of the produ ced size of the part.However, because the straightn ess control is on a cylin-drical surface, the .002 tolerance might not be available asthe part approaches MMC. The drawing at the top of thegure illustrates how the part would be drawn. The veillu strations below the part as drawn illustrate the actualshape of the object with each corresponding produced sizeand the available tolerance.STRAIGHTNESS OF AN AXIS OR CENTER PLANE

To locate the ax is of a part, the size of the part mu st beknown. To locate the cen ter p lane of two parallel features,

the distance between the featu res mu st be known . Theseare two examples of what is known as features of size.Logically, then , to con trol the axis of a part th e feature con-trol frame mu st be applied to the size dimen sion of thatpart, or to cont rol the center plane of a rectangular part itmust be applied to the size dimension, Figure 12-43B.When straightness is applied to contro l the axis of the fea-ture, the tolerance zone is cylind rical and extend s the fulllength of the cont rolled feature. Straightness applied to con-trol the center plane of a noncylindrical feature is shown

in Figure 12-49 . It is similar to that of straightness of acylindrical feature, except that the tolerance zone is awidth an d no d iameter symbol is used within the featurecontrol frame.

Straightness applied to the axis or center plane of a

f eature creates a boundary condition known asvir tualcondition. Virtual condition in ASME Y14.5 is dened as fol-lows: A constant boundary generated by the collectiveeffects of a size features specied MMC or LMC and thegeometric tolerance for that material condition. Thismeans that you are allowed to add the straightness toleranceto th e MMC size for a shaft and subtract th e straightn esstolerance from the MMC size for a hole. The resultantboundary represents the extreme form variation allowed forthe part. Although th is boundary is theoretical, it representsthe size boundary of mating features. Unlike straightn essof a feature con trol, a straightness control of an axis or cen-

FIGURE 12 -48 Straightness at RFS

FIGURE 12-49 Straightness

FIGURE 12 -47 Object with no feature control symbol (Rule #1applies)

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ter plane allows for th e availability of straightness toleranceeven when the part is made at MMC. Axis or center planecontrol of a feature becomes more desirable because of theincreased availability of tolerance and better control of mating features.

Figure 12-50 is the same part in the previous examp leswith a straightness tolerance of .002 at maximum materialcondition applied. The u se of the MMC modier is limitedto tolerances controlling the axis or center plane of features.It species the tolerance allowed wh en part is produced atMMC. The drawing at the top of the gure illustrates howthe part would be drawn. The ve illustrations belowthe part as drawn illustrate the actual shape of the objectwith each correspon ding produced size. A virtual condi-tion boundary of .506 is created. When the part is at.504, the .506 virtual condition boundary allows forstraigh tness of .002 at MMC. Since the .002 straightn esstolerance applies at maximum material condition, the

amoun t that th e part can be ou t of straightn ess increasescorrespond ingly as the produ ced size decreases. The tableat the bottom of Figure 12-50 summarizes the m anufac-tured sizes and the corresponding amoun ts that the partcan be ou t of straightn ess for each size.

Figure 12-51 is an example of the same part with a .002straightn ess tolerance at least material cond ition (LMC).It species the tolerance allowed when th e part is producedat LMC. This results in the op posite effect of what occurred

in Figure 12-49. Notice that the .002 straightness toleranceapplies at the least material condition. As the actual pro-duced size increases, the amount of out of straightnessallowed increases correspondingly.

Figure 12-52 illustrates the same part from a .002straightness tolerance and a regardless of feature sizetolerance. Notice in this example that the .002 straight-ness tolerance applies regardless of the actu al producedsize of th e part.

Circularity (Roundness)Circularity, sometimes ref erred to as roundness, is a featurecontrol for a surface of revolution (cylinder, sphere, cone,and so forth ). It species that all points o f a surface mustbe equidistant from th e centerline or axis of the object inquestion. Th e tolerance zone for circularity is formed by

two concentric and coplanar circles between which allpoin ts on th e surface of revolution m ust lie.

Figures 12-53 and 12-54 illustrate how circularity iscalled-out on a drawing and provides an interpretation ofwhat the circularity tolerance actually means. At anyselected cross section of the part, all points on the su rf acemust fall within the zone created by the two concentric cir-cles. At any point where circularity is measured , it must fallwithin the size tolerance. Notice that a circularity tolerancecanno t specify a datum ref erence.FIGURE 12-50 Straightness of an axis at MMC

FIGURE 12-51 Straightness of an axis at LMC

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Circularity establishes elemen tal single-line tolerancezones that may be located anywhere along a surface. Thetolerance zones are taken at any cross section of the feature.Theref ore, the object may be spherical, cylindr ical, tapered,or even hou rglass shaped so long as the cross-section forinspection is taken at 90 to the nominal axis of the

object. A circularity tolerance is inspected using a dial indi-cator and mak ing readings relative to the axis of the fea-ture. In measuring a circularity tolerance, the full indicatormovement (FIM) of the dial indicator shou ld not be an ylarger than the size tolerance, and th ere should be severalmeasurements m ade at diff erent points along the surf aceof the d iameter. All measurements taken mu st fall withinthe circularity tolerance.

Cylind ricityCylindricity is a feature con trol in which all elemen ts of

a surface of revolution form a cylinder. It gives theeffect of circularity extended the entire length of theobject, rather than just a specied cross section. The tol-erance zone is formed by two hypothetical concentriccylinders.

Figure 12-55 illustrates how cylind ricity is called-out ona drawing. Notice that a cylindricity tolerance does notrequire a datum ref erence.

Figure 12-55 also provides an illustration of what thecylindr icity tolerance actually means. Two h ypotheticalconcen tric cylinders form the tolerance zone. The outsidecylinder is established by the o uter limits of the object at

its produced size within specied size limits. The innercylinder is smaller (on radius) by a distance equal to thecylindr icity tolerance.

Cylindricity requires that all elemen ts on the surface fallwithin the size tolerance and th e tolerance established bythe feature control.

A cylindricity tolerance m ust be less th an th e size tol-erance and is not additive to the maximu m material con-dition of the feature. Cylindricity is inspected by passingthe tolerance object throu gh a gauge. The object shou ld

FIGURE 12 -53 Circular ity for a cylinder or cone

FIGURE 12-54 Circularity for a sphere

FIGURE 12 -52 Straightness of an a xis at RFS

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pass through a gauge that is equal to or greater than thediameter of the external envelope establishing the cylin-drical tolerance zone. It shou ld not pass through a gaugethat is slightly smaller than the in ternal envelope, whichestablishes th e cylind rical tolerance zone.

AngularityAngularity is a feature contro l in which a given su rf ace,axis, or center plane must form a specied angle otherthan 90 with a datu m. Con sequently, an an gularity tol-erance requires one or mo re datu m ref erences. The tol-

erance zone formed by an angularity callout consists of two hypothetical parallel planes wh ich form the speciedangle with th e datum . All points on the angular surface oralong the angular axis must lie between these parallelplanes.

ANGULARITY O F A SURFACEFigure 12-56 illustrates how an angularity tolerance on asurface is called out on a drawing. Notice that the speciedangle is basic. This is required when applying an angu lar-ity tolerance. Figure 12-56 also provides an interpreta-

tion of what th e angularity tolerance actually means. Thesurface must lie between two parallel planes of 0.4 apartwhich are inclined at 30 basic angle to datum plane A.

Angularity also controls the atness of the surface tothe same extent it controls the angular orientation.Wh en it is required that the atn ess of the feature be lessthan the orientation , a atness callout can b e used as arenement of the orientation callout. When using atnessas a renemen t, the tolerance is less than the orientationtolerance. The feature control frame is n orm ally placed

on an extension line below the orientation control,Figure 12-57 .

ANGULARITY O F AN AXIS OR CENTER PLANEAn angularity callout can a lso be used to con trol the axisor center plane of a feature. This is don e by placing the fea-ture control frame with the size dimension in an appro-priate manner as seen in Figure 12-58 . The tolerancezone for an axis control can be cylind rical in shape or twoparallel planes. Wh en the diameter symbol is used withinthe feature contro l frame, the tolerance zone is cylindricalWhen no diameter is used, the tolerance zone shape is twoparallel planes,Figure 12-59 .

FIGURE 12-55 Specifying cylindricity

FIGURE 12 -56 Specifying angular ity for a surf ace

FIGURE 12-57 Angular ity with atness renement

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Paralle lismParallelism is a feature con trol that species that all pointson a given surface, axis, line, or center plane must be equi-distant from a datum. Consequently, a parallelism tolerancerequires one or more datum ref erences. A parallelism tol-erance zone is form ed by two hypothetical parallel planesthat are parallel to a specied datum. They are spaced apartat a distance equal to t he p arallelism tolerance.

PARALLELISM O F A SURFACEFigure 12-60 illustrates how a parallelism is called out ona drawing and p rovides an interpretation of what the par-allelism tolerance actua lly means. Notice that all elemen tsof the toleranced surface must fall within the size limits.

Notice in Figure 12-60 th at the 0.12 parallelism toler-ance is called ou t relative to Datum A. You mu st specify adatum when calling out a parallelism tolerance. Parallelismshou ld be specied when features such as surfaces, axes,and planes are required to lie in a common orientation.

Parallelism is inspected by placing the part on an inspec-tion table and running a dial indicator a full indicatormovemen t across the surface of the part.

Parallelism also controls th e atness of the su rface tothe same exten t it cont rols parallel orientation. W hen itis required that th e atness of the feature be less than th eorientation, a atness callout can be used as a renement

of the orientation callout. When using atness as arenement, the tolerance is less than the orientationtolerance. Th e feature con trol frame is nor mally placedon an extension line below the orientation control,Figure 12-61 .

PARALLELISM O F AN AXIS OR CENTER PLANEParallelism can be used to con trol the orientation of an axisto a datu m plane, an axis to an axis, or the center p lane of non cylindrical parts. Wh en app lied to con trol the axis or

FIGURE 12-58 Angularity for an a xis (cylindrical tolerance zone)

FIGURE 12-59 Angularity for an axis (two parallel planes)(FromASM E Y14.5M 1994)

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center plane, the feature control frame must be placedwith the size dimension in th e appropriate fashion. W henused to control an axis to a datum plane, the tolerance zoneshape is two parallel planes separated by the amount of thestated tolerance. The to lerance control is only applicable rel-ative to th e specied datum surface,Figure 12-62 . Virtualcondition exists for the controlled feature, which allows foravailability of additional tolerance. TheM and L modierscan be used as a result of controlling a feature of size.

Wh en used to control an axis to a datum axis, the tol-erance zone shape is cylindrical and t he d iameter is equato the amount of the stated tolerance. The tolerance con-trol is three-dimensional, allowing the axis to oat relativeto orientation of the datum ,Figure 12-63 . Virtual conditionexists for the controlled feature, which allows for the avail-ability of additional tolerance. TheM and L modiers canbe used as a result of controlling a feature of size.

Wh en used to con trol a center plane to a datum planeor a center plane to a center plan e, the similarity is that ofan axis to a su rface or an axis to a datum axis. However, thetolerance zone shape is never cylindrical. The shape is two

parallel planes separated by the amoun t of the stated tol-erance. Virtual cond ition exists for th e controlled feature,which allows for availability of additional tolerance. TheMand L modiers can be used as a result of controlling a fea-ture of size.

Perpend icularityPerpendicularity is a feature con trol that species that a llelements of a surface, axis, center plane, or line form a 90angle with a d atum. C onsequen tly, a perpendicularity

FIGURE 12-60 Par allelism for a surface to datum pla ne

FIGURE 12-61 Par allelism with atness renement

FIGURE 12-62 Par allelism for a n axis to datum pla ne

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tolerance requires a datum ref erence. A perpend icularitytolerance is formed by two hypothetical parallel planes thatare at 90 to a specied datum. Th ey are spaced apart at adistance equal to the perpend icularity tolerance.

PERPENDICULARITY O F A SURFACEFigure 12-64 illustrates how a perpendicularity toler-ance is called out on a drawing and provides an inter-pretation of what the perpendicularity tolerance actuallymeans. The elements of the toleranced su rface must fall

within th e size limits and between two hypothetical par-allel planes that are a distance apart equal to the perpen-dicularity tolerance.

The perpen dicularity of a part such as the one shownin Figure 12-64 could be inspected by clamping the partto an inspection angle. The datum surface should restagainst the in spection angle. Then a dial indicator shouldbe passed over th e entire surface for a full indicator m ove-ment to determine if the perpendicularity tolerance hasbeen complied with.

Perpendicularity also con trols the atness of th e sur-face to the same extent it controls orientation. Wh en itis required that th e atness of the feature be less than th eorientation, a atness callout can be u sed as a renementof the orientation callout. When using atness as arenement, the tolerance is less than the orientationtolerance. The feature control frame is n ormally placedon an extension line below the orientation control,Figure 12-65 .

PERPENDICULARITY O F AN AXIS ORCENTER PLANEPerpendicularity can be used to control the orientation of anaxis to a datum plane, an axis to an axis, or the center plane

FIGURE 12-63 Par allelism for an a xis to datum axis

FIGURE 12 -64 Perpendicularity for a surface to a datum pla ne

FIGURE 12 -65 Perpendicular ity with atness renement

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of noncylindrical parts. When applied to cont rol the axis orcenter plane, the feature control frame must be placedwith the size dimension in th e appropriate fashion. W henused to con trol an axis to a datum p lane, the tolerance zone

shape is cylindrical, and its diameter equals the amou nt of the stated tolerance. The tolerance control is three-dimensional, allowing the axis to be at any orient ation rel-ative to the specied datu m su rface,Figure 12-66 . Virtualcondition exists for the controlled feature, which allows foravailability of additional tolerance. TheM and L modi-ers can be used as a result of con trolling a feature of size.

Wh en used to con trol an axis to a datum axis, the tol-erance zone shape is two parallel planes which are sepa-rated by a distance equal to the amount of the statedtolerance. The to lerance control is on ly applicable relativeto orientation of the datum,Figure 12-67 . Virtual condi-

tion exists for the controlled feature, which allows for avail-ability of additional tolerance. TheM and L modiers canbe used as a result of controlling a feature of size.

When used to control a center plane to a datum planeor a center plane to a center p lane, the similarity is that of an axis to a surface or an axis to a datum axis. However, thetolerance zone shape is never cylind rical. The shape is twoparallel planes separated by the amou nt of the stated tol-erance. Virtual condition exists for the controlled fea-ture, which allows for availability of additional to lerance.

Th e M and L modiers can be used as a result of con-trolling a feature of size.

Pro leProle is a feature control that species the amount ofallowable variance of a surface or line elements on a surf ace.There are three d iff erent variations of the prole tolerance:unilateral (inside), unilateral (outside), and bilateral (unequadistribution), Figure 12-68 . A prole tolerance is normallyused for controlling arcs, curves, and other unusual prolesnot covered by the other feature controls. It is a valuable feature control for use on objects that are so irregular that oth erf eature contro ls do n ot easily apply.

When applying a prole tolerance, the symbol usedindicates whether th e designer intends prole of a line orprole of a surface, Figures 12-69 and 12-70 (page 498).

Prole of a lineestablishes a toleran ce for a given single ele-ment of a surface.Prole of a surf ace applies to the entire sur-face. The d iff erence between prole of a line and prole of a surface is similar to the diff erence between circularityand cylindricity.

When using a prole tolerance, drafters and designersshould remember to use phantom lines to indicate whetherthe tolerance is applied unilaterally up or unilaterallydown. A bilateral prole tolerance requires no ph antomlines. An ALL AROUND symbol should also be placed on

FIGURE 12 -67 Perpendicularity for a n axis to a datu m axisFIGURE 12 -66 Perpendicular ity for an axis to a datum plane

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the leader line of the feature control frame to specifywhether th e tolerance app lies ALL AROUND or betweenspecic points on the object,Figure 12-71 .

Figure 12-72 provides an interpretation of what theBETWEEN A & B prole tolerance in Figure 12-71 actu-ally means. The roun ded top surface, and only the top sur-face, of the object must fall within the specied tolerance

zone. Figure 12-73 provides an interpretation of whatthe ALL AROUND p role tolerance in Figure 12-71 actu-ally means. The ent ire surface of the object, all around th eobject, must fall within the specied tolerance zone.

Prole toleran ces may be in spected using a dial indi-cator. However, because the tolerance zone must bemeasured at right angles to the b asic true prole and p er-

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FIGURE 12-68 Application of prole of a surf ace

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pendicular to the datum , the dial indicator must be set upto move and read in both directions. Other meth ods of inspecting prole tolerances are becoming m ore popular,however. Optical comparators are becoming widely usedfor inspecting prole tolerances. An op tical comparatormagnies the silhouette of the part and projects it on to ascreen where it is compared to a calibrated grid or tem-plate so that the prole and size tolerances may beinspected visually.

RunoutRunout is a feature control th at lim its the amou nt of devi-ation from perfect form allowed on surfaces or rotationthrough one full rotation of the object about its axis.Revolution of the object is aroun d a datu m axis. Conseq-uently, a runout tolerance does require a datum ref erence.

Runout is most frequently used on objects consistingof a series of concen tric cylinders an d oth er shapes of rev-olution that have circular cross sections; usually, the

types of objects manufactured on lathes,Figures 12-74and 12-75.

Notice in Figures 12-74 and 12-75 that th ere are twotypes of runout: circular runout and total runout. Thecircular runout tolerance applies at any single-line ele-ment th rough wh ich a section passes. The total runout tol-erance applies along an entire surface, as illustrated inFigure 12-75. Runout is most frequently used when theactual produced size of the feature is not as important as thef orm, and the quality of the feature mu st be related to someother feature. Circular runout is inspected using a dialindicator along a single xed position so that errors are readonly along a single line. Total runout requires that thedial indicator move in both directions along the entiresurface being toleranced.

Concen tricityIt is not uncommon in manufacturing to have a partmade up of several subparts all sharing the same cen-

FIGURE 12 -69 Prole of a line with size control

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terline or ax is. Such a part is illustrated inFigure 12-76 .In such a part it is critical that the centerline for each sub-sequent sub part be concentric with the centerlines of theother subparts. Wh en th is is the case, a concentricity tol-erance is applied. A concentricity tolerance locates the

axis of a feature relative to the axis of a datum. A con-centricity tolerance deals only with th e centerline rela-tionship. It does not affect the size, form, or surf acequality of the part. Con centricity deals on ly with axialrelationships. It is applied only on a regardless-of -f eature-size basis. Regardless of how large or sma ll the variouss ubpa rts of an overall part are, on ly their axes arerequired to b e concent ric. A concent ricity tolerance cre-ates a cylindrical tolerance zone in which all center-lines for each successive subpart of an overall part must

FIGURE 12 -70 Prole of a surf ace

FIGURE 12-71 Prole ALL AROUND

FIGURE 12 -73 Interpreta tion of ALL AROUN D

FIGURE 12-72 Interpretation of BETWEEN A & B

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fall. This concept is illustrated inFigure 12-77 . A con-centricity tolerance is inspected by a full indicator move-men t of a dial ind icator.

SYMMETRY

Parts that are symmetrically disposed about the center

plane of a datum feature are common in m anufacturingsettings. If it is necessary that a feature be located sym-metrically with regard to the center plane of a datum fea-ture, a symmetry tolerance may be applied,Figure 12-78 .The part in Figure 12-78 is symmetrical about a centerplane. To ensure that the part is located symm etrically withrespect to the center p lane, a .030 symm etry tolerance isapplied. This creates a .030 tolerance zone with in wh ichthe center plane in question mu st fall, as illustrated in thebottom portion of Figure 12-78.

TRUE POSITIONINGTrue position tolerancing is used to locate features ofparts that are to be assembled and mated. True po sition issymbolized by a circle overlaid by a large plus sign orcross. This symbol is followed by the tolerance, a modierwhen appropriate, and a ref erence datum , Figure 12-79 .Figures 12-80 and 12-81 illustrate th e diff erence betweenconvention al and tru e position dimen sion ing. The toler-

FIGURE 12-75 Specifying total runout relat ive to a da tum diam ete

FIGURE 12 -76 Part with concentric subpar ts

FIGURE 12-74 Specifying circular runout rela tive to a datum diameter

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ance dimensions shown in Figure 12-80 create a square tol-erance zon e. This means that th e zone within wh ich th ecenterline being located by the dim ensions mu st fall tak esthe shape of a square. As you can see in Figure 12 -81, thetolerancing zone is round when true position dimen-

sioning is used. The effect of this on manufacturing is thatthe round tolerancing zone with true position dimen-sioning increases th e size of the toleran ce zone by 57%,Figure 12-82 . This means that for the same tolerance themachin ist has 57% more room for error withou t produc-ing an ou t-of-tolerance part.

When using true position dimensioning, the toleranceis assumed to apply regardless of th e feature size un lessmodied otherwise.Figure 12-83 illustrates the effect of modifying a true position tolerance with a maximummaterial condition modier. In th is example, a hole is tobe drilled through a p late. The maximu m diameter is .254

and th e minimum diameter is .250. Theref ore, the max-imum material condition of the part occurs when thehole is drilled to a diameter of .250. Notice from thisexample that as th e ho le increases, the p osition al toler-ance increases. At maximum material condition (.250diameter) , the tolerance zone has a diameter of .042. Atleast material condition (.254 diameter), th e tolerancezone increases to .046 diameter. The tolerance zonediameter increases correspondingly as the hole sizeincreases.

REVIEW O F DATUMS

Fun damental to an und erstanding of geometric dimen-sioning and tolerancing is an understanding of datums.Since many engineering and drafting students nd the con-

cept of datums difcult to understand, this section willreview the concept in depth. It is important to un derstanddatums because they represent the starting poin t for ref-erencing dimensions to various features on p arts and formaking calculations relative to those dimensions. Datumsare usu ally ph ysical compon ents. However, they can alsobe invisible lines, planes, axes, or points that are located bycalcu lations or as th ey relate to other features. Featuressuch as diameters, width s, holes, and slots are frequentlyspecied as datum features.

Datu ms are classied as being a p rimary, secondary, ortertiary datum, Figure 12-84 . Three points are required to

establish a primary datum. Two points are requiredto establish a secondary datum . One point is required toestablish a tertiary datum, Figure 12-85 . Each point u sedto establish a datum is called off by a datum target symbol,Figure 12-86 . The letter designation in the datum targetsymbol is the datu m ident ier. For exam ple, the letter Ain Figure 12-87 is the datum d esignator for Datum A. Thenumber 2 in Figure 12-88 is the point designator forPoint 2. Theref ore, the complete designation of A2means Datum A-Point 2.

FIGURE 12 -77 Concentricity tolera ncing

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FIGURE 12-78 Symmetry tolerancing

FIGURE 12 -81 Tru e position dimensioning

FIGURE 12-82 Compar ison of tolerance z ones

FIGURE 12-83 True positioning at MMC

FIGURE 12-79 True position symbology

FIGURE 12-80 Conventional dimensioning

.042 A B C

MODIFIER ADDED

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Figure 12-89 illustrates how the points which establishdatums should be dimensioned on a drawing. In thisillustration, the three po ints which establish Datum A aredimensioned in the top view and labeled using the datumtarget symbol. The two points that establish Datum B

are dimensioned in the front view. The one point that estab-lishes Datum C is dimensioned in the right-side view.Figure 12-90 illustrates the concept of datum plane anddatum surface. The theoretically perfect plane is repre-sented by the top of the machine table. The less perf ectactual datum surface is the bottom surface of the part.Figure 12-91 shows how the diff erences between th e per-fect datum plane and the actual datum su rface are recon-ciled. The th ree points protruding from th e machine tablecorrespond with the three points wh ich establish Datum

A. Once th is diff erence has been reconciled, inspections of the part can be carried ou t.

FIGURE 12-84 Datums

FIGURE 12-85 Establishing datum s

FIGURE 12-86 Datum target symbol

FIGURE 12-87 Datum designation

FIGURE 12-88 Point designator

FIGURE 12 -89 Dimensioning datum points

FIGURE 12 -90 Datum plane versus datum surf ace

FIGURE 12 -91 Reconciling the datum surface to the datum p lane

EACH POINT IS CALLED OFFBY A DATUM TARGET SYMBOL

A2

THE 2INDICATES THE POINT

2

THE AINDICATES THE DATUM

A

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Sum m ary General tolerancing involves setting acceptable limits of

deviation for manufactured parts. Geometric dimen sioning and tolerancing involves set-

ting tolerance limits for all characteristics of a part.

Modiers are symbols that can be attached to th e stan-dard geometric bu ilding blocks to alter their applicationor interpretation.

MMC is when the most material exists in the part.RFS means that a tolerance of form o r position or an ycharacteristic must be maintained regardless of theactual produ ced size of the object.

Projected tolerance zone is a modier that allows atolerance zone established by a locational tolerance tobe extended a specied distance beyond a given surf ace.

Datums are theoretically perfect point s, lines, axes, sur-faces, or planes used for ref erencing features of an object.

True position is the theoretically exact location of thecenterline of a produ ct feature such as hole.

Review QuestionsAnswer the following questions either true or false.1. Tolerancing means setting acceptable limits of deviation.

2. The three types of size tolerances are unilateral, location,and runout.

3. The need to tolerance more than just the size of an

object led to the development of geometric dimen-sioning and tolerancing.

4. Geom etric dimensioning species the allowable varia-tion of a featu re from perfect form.

5. The term regardless of feature sizeis a modier whichtells machin ists th at a tolerance of form or p osition orany characteristic must be maintained, regardless of theactual produ ced size of the object.

6. Datum s are compon ents of a part such as a hole, slot,surface, or boss.

7. A datum is established on a cast surface by a ag or asymbol.

Answer the following questions by selecting the bestanswer.1. Which of the following is the identication for the

ASME standard on d imension ing?a. ASME Y14.5 M 1 994b. ASME Y24.5 M 1992c. ASME Y34.5 M 1990d. ASME Y44.5 M 1988

2. Which of the following has the incorrect symbol?a. Flatnessb. Circularityc. St raightness d. True position o

3. Which of the following has the incorr ect symbol?

a. Perpendicularity ==b. Straightness c. Parallelism / / d. Angu larity

4. Wh ich of the following isnot true regarding atness?a. It differs from straightness.b. The term atness is interchan geable with the term

straightness.c. When atness is the feature con trol, a datum ref er-

ence is neither required nor proper.d. Flatness is specied wh en size tolerances alone are

no t sufcien t to control the form and qu ality of thesurface.

5. The term least material condition means:a. The opp osite of MMC.b. A cond ition of a feature in wh ich it contains the

least amou nt of material.c. The theoretically exact location of a feature.d. Both a and b

6. Which of the following isnot true regarding feature con-trol symbols?a. The order o f data in a feature con trol frame is

important.b. The rst element is the feature control symbol.c. Various feature con trol element s are separated by //.d. Datum ref erences are listed in order from left to

right.

7. Which of the following feature controlsmust have adatum ref erence?a. Flatnessb. Straightnessc. C ylind ricityd. Parallelism

Chapter Twelve Pr ob lem sThe following problems are intended to give beginningdrafters practice in applying the pr inciples of geometricdimensioning and tolerancing.

The steps to follow in com pleting the prob lems are:STEP 1 Study the problem caref ully.STEP 2 Make a checklist of tasks you will need to

complete.

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STEP 3 Center the required view or views in th e work area.

STEP 4 Include all dimensions according to ASMEY14.5M 1994 .

STEP 5 Re-check all work. If its correct, nea tly ll outthe title block using light guidelines and free-

hand lettering.NO TE: These problems do not follow current dra fting standa rds.

You a re to use th e informa tion shown h ere to developproperly drawn, dimensioned, and toleranced drawings.

Problem 12-1

Ap ply to lerances so t hat t his par t is st raigh t tow i t h in . 0 0 4 at M M C .

Problem 12-2

Apply to le rances so tha t the top sur face oft h i s p a r t i s a t t o w i t h i n . 0 0 1 a n d t h e t w o

sides of th e slot are p arallel to each o ther w ithin .002 RFS.

Problem 12-4

App ly tolerances to lo cate the ho les using t ruep o si t i o n a n d b a si c d i m e n s io n s r el at i v e t od a t u m s A -B -C .

Problem 12-3

App ly to le rances so th a t the sm al le r d iam eterhas a cy l indr ic i ty to le rance of .005 and the

sm al le r d iam eter is con cent r ic to th e la rg er d iam eter tow i t h i n . 0 0 2 . T h e s h o u l d e r m u s t b e p e r p e n d i c u l a r t ot h e a x i s o f t h e p a r t t o w i t h i n . 0 0 2 .

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Problem 12-5

Ap ply ang ular ity, t rue po si t ion, and paral le l ismt o l e r a n c e s o f . 0 0 1 t o t h i s p a r t . S e l e c t t h e

approp riate datu m s. Th e parallelism to lerances sho uld b eapp l ied t o th e sides o f th e slo t .

Problem 12-6

App ly to le rances so th a t the ou tside d iam eter

o f t h e p a r t i s r o u n d t o w i t h i n . 0 0 4 a n d t h ee n d s a r e p a r a ll el t o w i t h i n . 0 0 1 a t m a x i m u m m a t e ri alc o n d i t i o n .

Problem 12-7

A p p l y a l i n e p r o l e t o l e r a n c e t o t h e t o p t h e p a r t b e t w e en p o i n t s X a n d Y o f .0

Ap ply t rue po s it ion to le rances to th e ho les o f .021para l le li sm to le rances o f .001 to t he tw o nished

Problem 12-8

Use the bo t tom of the part as Datum A and

righ t side of the p art as D atum B. App ly suaceprole to lerances o f .001 t o th e top of th e par t be twpo in ts X and Y.

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Problem 12-9

Selec t d a tum s and app ly to le rances in such aw ay as to ensure th at th e slot is sym m etr ical to

w i t h in . 0 0 2 w i t h t h e .5 0 d i am e t er h o l e, an d t h e b o t t o msur face is para l lel to th e top sur face to w i th in .0 04 .

Problem 12-10

A p p l y t o l e r a n c e s t o t h i s p a r t s o t h a t t h e

t a p e r ed e n d h a s a t o t a l ru n o u t o f . 0 0 2 .

Problem 12-11

App ly to le rances to t h i s par t so tha t d iam etersX a n d Z h a v e a t o t a l r u n o u t o f . 0 2 r e la t iv e t o

D atum A ( the large d iam eter o f th e par t ) and l ine runouto f . 0 0 4 t o t h e t w o t a p e r e d su r f a ce s.

Problem 12-12

Se l ec t d a t u m s a n d a p p l y a p o s it i o n a l t o l e r -

a n c e o f . 0 0 1 a t M M C t o t h e h o l e s, an d a p e r-p e n d i c u l a r i t y t o l e r a n c e o f . 0 0 3 t o t h e v e r t i c a l l e g o ft h e a n g l e.

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Problem 12-13

Problem 12-14

PRO BLEMS 12-13 TH RO UG H 12 -30

Fo r e a ch o f t h e r e m a in i n g g e o m e t r ic d i m e n si o n i n g a n dt o l e r an c i n g p r o b l e m s, ex a m i n e t h e p r o b l em c l o se lyw i t h a n e y e t o t h e p u r p o s e t h a t w i l l b e s e r v e d b y t h epart. Then select datu m s, tolerances, an d feature con trolsas app ropr ia te , and ap ply th em prop er ly to t he par t s. In

th i s w ay you w i l l beg in to d eve lop th e sk i ll s requir e d o f

a m e c h a n i ca l d e si g n e r. D o n o t o v e r d e sig n . Re m e mt h e c l o se r t h e t o l er an c e s, a n d t h e m o r e f e at u r e c o napp lied, the m o re expen sive th e part . Try to u se theleof thum b tha t says: Apply on ly as m any feature colsand tolerances as absolutely necessary to ensure that

par t w i l l p ro per ly serve i t s purp ose af te r assem bly

Problem 12-15

Problem 12-16

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Problem 12-17

Problem 12-18

Problem 12-19

Problem 12-20

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Problem 12-21

Problem 12-22

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Problem 12-25

Problem 12-23 Problem 12-24

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Problem 12-26

Problem 12-27 Problem 12-28

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PRO BLEM 12-31Problem 12-29

Problem 12-30

T h i s p r o b l e m d e a l s w i t h f e a t u r e c o n t r o l sy m b o l s. Ini t e m s 1 1 9 e x p l ai n w h a t e a ch sy m b o l m e an s . I n it e m s2 0 3 0 , d r a w t h e re q u i r e d sy m b o l s.

.005 A B C1)2)3)4)5)6)7)

8)9)

10)11)12)13)

20)21)22)23)24)25)26)27)28)29)30)

ANGULARITYTRUE POSITIONFLATNESSPROFILE OF A SURFACEPERPENDICULARITYCIRCULAR RUNOUTSTRAIGHTNESSTOTALRUNOUTPROFILE OF A LINECYLINDRICITYCIRCULARITY

SYMBOL MEANS SYMBOL MEANS

14)15)16)17)18)19)

MEANS

SYMBOL

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