GDT Workbook Questions

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PREFACE

This workbook is for the purpose of testing the user's knowledge of geometric dimensioningand tolerancing as part of an educational or training progrrm. The workbook may also beused as an independent reference, thus providing a learning mechanism for review of thesubject matter o to extend existing knowledge.The author ssumes the user has some familiarity with basic engineering drawing practices.This workbook builds upon such knowledge and extends the learning experience intodetailed study of geometric dimensioning and tolerancing as based upon the nationalstandard A{SI/ASME Y14.5M-1994. This workbook, and its associated answebook, aredesigned as companion materials for the author's full text'Geo-Metrics III."The workbook contains avariety of materialwhich can be used in a number of waysappropriate to both the academic classroom and the in-industry training progam. Containedwithin the workbook is a series of questions and exercises, and some problem examples. Theproblern example pages are found at the rear of the workbook as indicated in theappropriate questions as the user proceeds.The answer to the questions and problems are contained in a separate answer bookwhichmay be distibuted to the particant alongwith this workbook or retained by the instructorat his discretion.


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Fundamentals................. ....................... 1FortR, Orientation, hofile, andRunout Tolerances .,......... 10Location Tolerances. ....,...25Figures ..........65


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QTIESTIONS


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- FOR NOTES OR CALCULATIONS -


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FurdcnrentqlsGENERAI AI'FSTTOI{S

1. Geometric Dimensioning and Tolerancing provides numerous advantages' List foru of them'(1)(2)(3)(4)

3 . The fist magninrde of conuol on any pan is its lerances. Where;;;,;;;'*niJq** to control part configuration or specific relationships of fea'tres,ulle,r.L'wDvr-------5-r,or_rtolerancgsargused2, In dermining geometric dimensioning and tolerancing requirements and applicatioq^,:ryokey words toemUerfor guiOance le F r.rvrgJ and ll c4'.r ce^/s ,? '

4. For delineating tlrese requirements on a drawing, the method ttal provides best uniformiryand efciency - is ecmmended by the National Standard AI'{SI Y14'5' is:(Check one.)symbolicallYby no

GEOIYEIRIC CHARCIERXSflC SYI{BOIS5. Here are ttre fonren variedes of geometric chaacistics. Place the correct symbol desigoionbeside each one-

CicularrunoutTotal rutoutProfiIe of a srrfaceProfrle of a linePositionConcentricitYSymmetry


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6.COIDITIONS - MODIFIERS

In using certain geomeuic rclerance characristics, as applied to size featues, the "marerialcondition" under which the tolerance applies must be considered. The thee "marerial conditions"(also loown as modifiers where applicable) are h ^ - ,R.rs .ad L r\C-.7. The symbols rsed to indicate two of these marial conditions or modiftes are:

The third material condition, is impted by Rule lt2 on all size feueswhere the other marial condition (modifien) symbols re not specified-IYKIMITM I\TAIERIAI COI{DITION

8. In the case of a hole, the MA)ilMUM IvIAIERIAL CONDHON MMC) is its (which:minimum or maximum) 'w c^,r -r u,n size? In the case of a pin, ttre MMC size is its(minimum or maximum) r-' + --= ,-n u^ ' sizg?.zoo 1:838

2x .2o5 ::333

The LMC size of the holes above is o.zoEIVhat would a disunce meued between two opposite poina of .206 size becallet +


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10. When MMC is used as a design basis for functional inrrelationship of featrues of sizeof inrchangeability, the form, orientadon or position tolerance (increes/decreases)with the feaure acftal mating size deparnue from MMC'11. Where the MMC conditioncemed features is to remainis not desirable to the design requirement and size of the con-independent of any affect on the form, orientation or position

-isaPPlied-tolerance, the condition

12.

13.

BASIC OR EKACT DIMEI{SIONA basic (or exact) dimension specied on adrawing ^ T Ll t:kLT r


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r1,?r,. tsl, 7,1Lt7.18.

19.

datum fearue.Dums on parrs are idendfied by letn of the alphabet (do not use I, 0, or Q) and placed ina squarc frame wittrg leade and triangle direcd to the feanre. This is known as a- 1p->,,,


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FENfl RE CONTROT FRtYfE23. List the fou elements of geometric control ttrat may be used in making up a compleFeatrre Control Frame.

(1)(2)(3)(4)

24. Draw a feanue conuol frame which indicas 'rpendicularity" of a hole wittn .005' atximum material condition, relative to daum plne "B.''

CoMBINED TEATTTRE CONIROT TRAME I.TD Dfl'M TEIII'RE STMBOTDuplica the feature control frame drwn for the preceding question and add a danmfearue symbol ("C") to make a combined symbol'Which of ttrese nrmbered smen is correct?In the combined symbol shown in answer to question 25:

l. Danrm *C. is a part of the datum reference fo the perpendicularity requiremenr2. Danrm..C- is complely separate from the perpendicutarity requirement and onlyidentifies the featrre for othe relationships.Dn'MREFERENCEFRAME.oRDERoFPRECEDENCE

In these feature control frames thee datum references are used- According to establishednles, which ae the primary, secondary, afid tertiary datusts?

( .oto 6D A B G.oro D F DIM

25.26.

27.

a)b)

28. In the preceding symbols is the atphabetic order signicant? l\l 0 -Danm order otcedence is established by placing the danrm reference leuen readingL E - @ (1T G t inttrefeatruecontrolframe'


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tq Illustra how datum idenrification letters are shown in the feanre control frame when no danm(or equal danrm) precedence is desired- (Use the runout characteristicsymUf, datum r.i.r.n . lerers A and B, .002 tolerance, and place them in a feaure conuolframe below.)

FORM, ORIENTArION, PROFII.E, RI'NOUT AI{D IOCAION TOI.ERANCE30. Form tolerances relae to the following characristics; (Show their symbols below.)3L. Orienation tolerances relas to the following characristics: (Show their symbols below.)32. pole tolerances rela to the following characristics: (Show their symbols below-)33. Runout tolerances rela to the foltowing chaacristics: (Show their symbols below-)34. Locarion tolerances relare to the following characrisircs: (Show their symbols below.)

ST.IDARD RII.ES {D PRINCIPLES35. For this illustration, which statement below most correctly describes the geometic (form)conuoi on the part?

----.0O2(l) The toleranced dimensions for the size of a featrue conuols the form as well as size.No element of rhe acgal featue shall exnd beyond the specified higb or low limis ofsize or the boundary of perfect form at MMC. Fearre sizes shall not exceed 500 diamer and 1.510 lengt-

36. What is the basis for the corect answer in question 35?L Lf^^f5 F s?8,


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3?. Where size control gives inadequa control of part geometry,tolerances are sPecified-

offeanues.40. Wh common

3g. Refeaing to the illustrion in question 35, draw a representation of the "boundary ofperfectform MMC" of the Parro' Soo

l+--- \ 5l !i39. The inrpretation prescribiirg a boundary of perfect forrr at MMC applies onlyr^ .'-tt Lf1..i ,,.'/t,.- fganrgsandnot9g ^'-;L, tl LL\- !i''''"-'"J'',w+ ( [' (- "'' :14'r(' 'r i!'qpe of geomeric relionship of feanues not controlled by ttre condidonsof Rule 1?

4I. Does the interpnetation of Rule I apply to commercial stock, such as bars, sheets, andnrbing?42. Rule 1 may be removed from the application by ano such asplaced on the drawing.

Rule#

44. Rule 2 applies in conjunction with the fearue control fame and can be applied only to feares of

45. Which of these would be a feanue of "size'?'(1) A hole(2) A flat srrface


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46. The Pirch Diameter Rute: Each toleranceqpecified for a screw thead applies to theof orientation orposition ad dum reference

47. On the symbols shown below, add ttre notadon o indica that re geometric tolerance anddailm feure basis is an exception to the Sew Thead Rule and applies at the majordianer. 0l.oos@lB

48. Show on these symbolsspecified- how a gear or spline geomeric relionship to ttre pirch diameter would betrJ

.ooz @lc49. A virnal condition exists where a featue, or a datum feature, of size is controlled by a

separae olerance of form, orientation, or location tolerance. It is ttre collecve effect of the staed6o wt', K c TL(,&fr;^


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51. Place a check mark beside the most significant reasons for stating the marial conditions(modien) under Rule 2.(1) It is required-(2) Stas the condition under which the design requirement applies.(3) Is universally understood through ISO inmational standards and practices.52. Wh is the resultant condition of ttre .3001:38nof" under question 50 if the hole is producedto the acnal mating envelope size of .302?

TOIER,,,AI{CE ZONE SHAPE53. a-) Whee the feane ds is to be controlled and the desired tolerance zone shape is cylin-drical, the sYmbol is sPecified'

b.) True or False? Where rhe feanre is non+ylindrical and its center plane or axis is to becontrolled within a total wide tolerance zone, no shape of olerance zone is designad ,


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FORM, ORIENTATION, PROFII AI{D RI'NOITT TOLERI{CINGYou have now progressed ttrough the steps necessary to learn the fundamenmls, rules, adnomenclane of geometric dimensioning and tolerancing. It is time to test your ability to applythese principles in actual application.The nex series of questions and examples e designed to exercise yor:r knowledge of properFORM, ORIENTAIION, PROFILE AND RUNOIJT TOLERANCE contols, nomenclanre, andinrpretation.

54. Geometric tolerances should be specified for all feanues criticat to function and interchange-ability and whee:(1) Established practices cnnot be relied upon to provide therequired accurrcy.Documents establishing suitable2)

(3)(4)

are either not specified or are

do not provide the necessary control.are not to be depended upon.

55. Referring to Figrue 1 (found at rear of book), speafy the accuracy of the lower surface(lower extremity of 1.610 dimension) to allow a total (ma,rimum) tolerance for bow andother surface inaccuracies of .002.

Suppo the lower part surface of Figure 1 was produced as shown here. Using the form toler-ance control selecd in question 55, srch in the tolerance zone applicable.

57. The upper surface (upper exuemiry of the 1.610 dimension) is required in the pan functiot"o be in a parallel orientation of .002 total (maximum) tolerance to the lower surface. Addthis requirement to Figure 1. Use letter "A" for the datum.

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5g. Show below (srch) how the tolerance zone and rhe danm are established on the producedpart (Figrue l) for ttre requiremenr of question 57. Assume ttre produced Pan surfaces asirregutu, as in question 56.

Sg. Assuming rhe .002 flamess lerance, ttre .002 parallelism tolerance, and the 1-6101'005size rcleance, what is the boundary of perfect form at MMC size (remember Rule 1)?In Figrue 1 (lower figrue), suppose the vertical 1.610 surface is required to be in a squarcoriention ro ttre lower surfac wfthin .003. Add this requirement to Figue 1.Show below (skerc how rhe tolerance zone is established for the requirement of quesdon60.

60.

61.

lt


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62. Suppose that in Figure 1 (upper view), the vertical 1.500 srrface is required to be in a squarcoriention to the lowe surface (of the 1.500 dimension) within.003. Add this requirementto Figrue 1. Use letter "B" for the datum.63. In questions 60 and 62the 1.610 by 1.500 end face surface was conEolled in its perpet-Ocutarity (squareness) in vo directions from separa dums. Why are two sePara qpecifi-cations required? (Choose most significantteasons from below statements.)

(1) Perpendiculariry of a srrface should be specified in the view most ctearly showing isreladonship with iu specific datum.(2) Perpendicularity controls form as well a-s oriention.

64. Assume thar in Figure l the.376 hole has been located witt position dimensions and toler-ance (do nor yer concern yoruself wittr ttre method), but the orientation of the .376holemusr be maintained to a finer degree than the position tolerance. Specify on Figrre 1 thatthis orientation control with reqpect to datum *4" is .003 total' RFS.

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65. Show below (skerch) how the tolerance zone is established for ttre requirement of quemion&.

66. Referring to tbe perpendiculariry tolerance used in question 65 on Figrne 1, what is the totaltolerance permissible wittr hole size produced at3767 At-378267. The answers to question 66 ae deived because: (Selea the mo conect answer.)

(1) The tolerance is implied or stad as RFS rnder Rule 2- AIl tolerarces smred ae totals.

68. Suppose the perpendiculariry tolerance of .003 on the 376!'ffilot. of Figure I (refer-ence also question 64) was required by the pan rnction to be on an MMC basis. How wouldthe feare control frase be shown?

If the hole is produced ar.376 (MMC), what is the marimum permissible perpendicularirytolerance?If the hole is produced at.378, wh is the maximum perpendicularityolerance?

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69. From questions 64 tbrough 68 we see th whenever a fearue of size such as a hole is in-volved, \ile mrst consider whether the conditions .-

orare desired as a designrequirement

70. From the response to question 68, we see that use of the MMC principle, when appropriareto the desig requirement, (gains/loses)finction and inrchangeabitity. production tolerance yet assurs

71. In Figure 1, the surface identified as datum'B" (in quesion 62) is to be square inorientation within .002 to danm "4," ttle base srrface. In the lower space on the Figrue IsheeL skerch an end view and ssw this requiremenr72. In Figure 1, tbe 25" and 30o angles e critical o e extent of a.010 maximrm oleranceas they rela to tbeirrespective danms'4" and'8." Show these requiremens on Figrre 1.

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73. Referring to the 30" angle requirement of Figrue 1 (see question 12)'the acal Pa comefat the veflex end must within the dimension and tolerance.74. Show below (skeh) how the tolerance zone is established for the requirement of question72 onthe 30o angle. Also, show how the anguiar tolerance zone relias to the '500 t '005dimension.

75. Reviewing the Figure 1 questions and applications, it can be nod that of the forr types ofgeometric form and orientation characristics used' theerequire a datum reference.76. Dusr references ae used wherever a specificof one fearrre to another is required- Flutn ss, for exarnple as seen in the Figure I applica-tion, does not re4vre a datum because the 'telationship" of the specified surface is essen-tially to a perfect counterPart of itself, t-"

and

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^*\t) 77. Referring to Figure 2a(atblonginrdinal elements of theand the "boundary of perfectform at M t.ffiwhich will represent a critical size control for bearing mounting of the pa at each end-78. Specified as shown in Figrue 2a, sraightness of the pan is conrolled tqmaximum. What is the bis for this answer?79. Assume on Figrue 2b ttr ttre pan is to mount into bearings, and also that the straighmess ofthe longinrdinal elements of the cylindrical surface is critical to the design requirements andmusr wirhin .0003 total as a refinement of ttre size control (see questions 77 and 78).Specfy this requirement on Figure 2b).80. Wh is the ma,rimum permissible snaighmess tolerance of Figue 2b?81. Assume on Figure 2c ha the part is to mount into bearings on the ends but staightness oftlre longitudinal axis of the cylindrical surface is less critical, to a maximum of .0L5 rclaLRFS, and that the "boundary of perfect form MMC" (Rule 1) does rct apply. Spectfythis requirement on Figure 2c.

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82.83.

The collective effect ofthe size and form error on Figure 2c (question 81) results in apossible size ofSince the .0L5 straightness olerance of question 81 was specied on an RFS basis, what isttre suaightness tolerance permissibte if the pan size is at .6t0?Il at599?

84. Assume the pin shown in Figure 2d is to semble with the hole shown in Figure 2e. Whereinterchangeabity of parts of this tpe is required, the conditionoften desirable. With less critical assembly as the criterion, we will assume P{t2d can beperrrined a straighmess tolerance of .0L5 MMC exceeding the boundary of perfect form MMC. Show this requirement on Figue 2d.

rwh is the virrual condition of part 2dandthus the minimum (also virual condition)perrrissible boundary of cleaance of the hole of part 2e?What is the straightness tolerance permissible with ttre pin (pan 2d) size .6A0? 11.597?-

85.

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86. In Figrge ?, andthe responses to quesons 84 and 85, it is seen that the deviation fromMMC size resulted in (added/less) tolerance equal to the deparurefrom MMC.8i. Sraighmess tolerance is applicable only to cylindrical parts. Tnre False88. A straighmess rolerance is normally specified in the drawing view in which the toleranceapplies. True- False89. Name one rype of surface, other than cylindrical, upon which a straightness of surfaceelemens could be applied .90. Suppose the circular cross sections of a cylindrical part (Figrue 3a, rear of book) are

critical to a finer degree ttran the size tolerance would control. Wht type of form controlwould be used? Show the proper symbolic conuol on Figure 3 a usinga total olerance of .002.gL. Show below (sketch) how a tolerance zone would appea if the maximum dianer at atctoss-section was .502.

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92. circularity olerancing can be qpecified on any part configruation which isin cross section. T\oofoical part conngruations (other than cylindricar) upon which circu-lariry tolerurce may be specified are93. Refening to Figures 3b and 3c, add to the parr illustrations the requirement of circularitywfthin.001 totat.94. Show below (sketches) how the tolerance zones would appe on the Figrue 3b and 3c parts'

95. Is adarum reference used with circularity olerarrcing?Erplain Your rerson fs this

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96. Assume rtrat composi surface control of the entire cylindrical surface of the part shown inFigure 3d is required- Add to Figure 3d ttre proper specicion to control the cylindricalsurface within .001 total.9'1. Show below (srch) how the tolerance zone is developed- (Assume the ma:rimum producedsize is-502 )

98. Is a daum eference required with cylin&icity tolerancing?\ilhich thee form tolerurce controls are included in composi in cylindricity olerancing?99. Vee block analysis of critical circularity or cylindricity requirements must be wary of theeffect of pafi and vee block angle100. More rccrua analysis methods for decting circularity or cylindriciry requirements utilizetechniqu which simule pan ris criteria; such asmethods.101. Parts which distort due to their weight or flexibility or due to intemal stesses released in

fabricion are known as parts and are subjectWhere contol of this kind is necessary, any daturr and the features in control may require specifi-cation of their allowable orthe naximumforce necessary to each of ttrem to drawing Olerance.

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t02. tolerancing is an effective method of controlling an irregular curve'1c, or other unusual pan surface contour Where total surface control is desied" profrle of aconuol is used. where line element conuol is desired, profile of acontrol is used.

103. A profile toleiance is shown in theprofile appears.

of ttre drawing in which the desired

dimensions.104. The desired profile is dimensioned by105. Profrle of a surface conuol is normally a combination attdcontrol.106. Profile of a line control is normally used as a refinement of othercontrols.LO7. The surface profile on Figure 4 (at rear of book) is to be connolled to a total of .010

equalty dosed about the basic profile berween X and Y and relative datums A, B, andC. Show this on the drawing.

of

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108. Show by hand skerch below how the tolerance zone is dermined in the preceding example.

109. Can aprofile of surface tolerance be modified to MMC?Which of these statements suPPorts your answer?(1) As the pan size varies, ia form variation is affecd-(2) Accuracy of the surface profile and its desied shape is normally not affected by Pansize vaiation.

110. Add to Figure 4 rht the profile line elements shown in the plan (left) view ae to be main-tained m a fine tolerance (of .003) than the total surface profile.111. The profile of any line toleran zone must be contained within the profite of any surfacecontrol shown in Figure 4. Tne False

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tLz. Referring to Figrue 5 ( rear of book), assume ttrat the part diamers o1:a9h end are tomounr into bealngs and the other diamerers arc to be within .002 total (FM) relive tothe part axis of rotationregardless of feanne size'tolerancingshouldbeused.ShowtherequirementsonFigure5.113. A nrnout tolerance relas srrfaces of to a

-These

surfaces may be (cenraVcoaxial) th the datumor (perpendicular/tadiat) to the datumThe condition (RFS/vf C) is always used in runout tolerancing'

lL4. A nnout tolerance establishes a means ef sstrslling the funcdonal relationship of two or rmore feares of a part This type of tolerance is a (complex/composite) ryPe urd may be applied one of vo different t1ryes of nrnoul These two tyPesnnout, and nrnouLa-) Total runout includes such form errors Also,when applied to surfaces constncted at right

ngles (or other) rc a danrm aris.b.) Circula nrnout includes such form errors as

-'nd circular of the srrface when applied to surfaces consmcd atright angles to a daom ris.l 15. Runout tolerance is considered as a unique category of geometrical dimensioning andtolerance but is u.tuJrv -tnui*tion r ' - , mdtolerance controls.

A darum a,xis for a nrnout tolerance may be established by a diamer (cylinder) of con-116. siderable lengfh, wo diameters having a,xial separion' or a diameter and awhich is at a angle to it

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L77. Referring to Figue 6 (at rear of book), assume ttrat the left face of rhe part (left end of.700 dim) is to be the primary datum and the .4995 rlimg is to be the secondary datumand provide the a,ris of rotation. The pan mounts into a bearing. Specfy the datums withproperprecedenceandthe .890 and1.030diamerswirhintotalrunoutof .001 withrcspect to the darum axis.118. Assume ttr ttre circular elements of the 45o angular surface of Figure 6 are required to becontolled in rotation within .0005 total. Add ttris requirement to Figure 6.

119. If it was desired that the.001 total runout on the .890 diamer w required only for.150 from the right face of the 1.0300 diamer, how would this be indicad bysymbology? Add to figure 6.L20. Referring to ttre .376 hole of Figure t held in perpendiculariry of .003 to danrm A (see

question 65), whatis the virrual condition of the hole? The virnalcondition of a feane is the size of the boundary that must be considered in der-mining clearance between ming par or features.Size + form, orientation or location error = (shafrThole) vimral conditionsize - form, orientation or locaon error = (shaffiole) virrual condition

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IOCANON TOI.ERNCINGyou have now successfully progressed ttEough the series of questions -9.-:**ples of Form'orientation, profiIe and Rrurout torerance controls. Ir is now time to ..sr your ability in using thesebic fundamentals as exnded to Location tolerance'

ise yoru knowtedge in selection ofIn addition, an emPhasis

lzl. Tolerances of locion involve the use of geometric characristics122. Locadon tolerances involve feanues of andbetween two or more features. At least one of the featues must be a -feature.L23. I-ocation tolerances rela tofeatues.

and

of

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L24. Where function or inrchangeability of ming part features is involve4 the principles of,,and tolerancing may be ued.The principle ensures interchangeabiJity and provides gea,test tolerance advan-tages.L25. Position olerancing is a method used to sPecify the location of anof a featue in relationship to a danm reference or other feature.L26. A position tolerurce is the perrrissible variation in the locion of afeature about its desired or exrct (tue) posion.Ln. For cylindrical feanres (e.g. holes and bosses), the position tolerance is theof the tolerance zone within which the of the feanue must lie. Theshape of the tolerance zone is specified wittl the symbol128. For noncylindrical features (e.g. sloa and tabs) the position tolerance is theof the tolerance zone within which the center plane of the featuremust lie. The shape of the tolerance zone is implied as lotal wide in the absence of thesymbot and by the placement of the dimension line andin the desired direction.129. Position tolerance is a cumulive/non-cumulive (which?) methodof control in which each feanne reles to its own desired exrict (me) position130. A position tolerance is based on the size of the concerned feaure

as it relas to the size of the mating part feature.

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131. When position tolerance on an MMC basis is applied to a feue, the tolerance on theactually produced fearure (increases/deeases)ing size depans from MMC size. as the acftal mat-L32. Posirion rolerance (at MMC) is ideally suid to multiple muing pan cylindrical fearues inapanern. True False133. Which rwo of the thee staments below mosr support the answer to question 132.(1) Position tolerancing recognizes the permissible vaiion of a cylindrical feanelocion in 360o of movemenl(2) Position tolerurcing is a more convenient way rela mating feanres than plus andminus coordina tolerancing.(3) The position tolerance is developed directly from the relationship of the mating feanueMMC sizes.134. In this drawing, what is the MMC size of tl.250 holes? Specify onthe drawing that ttre four .250 holes are to be loced within a positional tolerance of .010 diam-

eter at MMC.

2t


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135. On the figrre shown under question 134, what is the position tolerurce of the hole if it isproduced at.247? at.253?L36. On this layout of the part under question 134, skerch in the position tolerance zones atMMC size of the hole and at I{C size of the hole.

137. Dum fearures or surfaces the basis for position relationships should be-on the drawing.138. On the below part, suppose that the upper surface on the front view is the mounting surfaceand the other two surfaces are important to ttre hole patrn positional tolerance, add threedatums with precedence indicated.

.tso 1.005.oto @

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139. Make a skerch below showing the inrpretation of the paft under the preceding question asbed uPon Your answer.

140. Now ren'n to Figure 1 and revise ttre specifications on the .376 hole to show it located at

(venicl) and -940 (horizontal) basic dimensions'

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l4l. Assume th these rwo parts are ming paru with the fou holes in each to coincide so thatfou.138 screws (floing fasners) will assemble. Calcula the position olerances andcomple the position dimensioning and tolerancing on the npo pars. Disregard hole Pauernlocion with reqpect to ouaide surfaces for this example; this will be taken up in succeed-ing exanples. However, select appropria primay (orientation) datum ferues the Part'scorreqponding inrface srrfaces.

4X . t5 I 1.003

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142. These two pafs are ming Pfts, to be assembled with vo '1 n thetwo dowel bosses and mating holes. This is a "fxed fastenef" be-come fixed in their location sembly. Calcula ttre positio the , I 1position dimensioning ad tolerancing, in toCing establishing thee danrms' ' I ? 5-6qP rnlS

< J25 :.33? --:;fi' i''@l{E] lltR,#!) ?'152X . 138 -32 UNC-28 ---------)

t.400

r.250

.3 00

r. t30.600

2X . r48:'3?

,oo G) ,416 (-

.3501 .003

.?J--'--=Jt I___J II-- -J II

.zg!'onon

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L43. Unless otherwise specifie{ the position tolerance zone exnds to thqof the feanre.I44. In the exarrple shown unde question 142, could the distribution of the position toleranceon each part have been different? To suppon your a$wer, whichof the below staments is most appropria?

a-) Position tolerance is calculed on the basis of relationship of size of the correspondingmating paft featres.b.) The total position tolerance calculad may be distributed as desired beveen thecorresponding ming part featues.

145. Referring to the "answer" illustration of question L42,whis ttre position toleance of the.L25 boss if produced at actual mating size of .L235?The . 148 hole if produced ar .L51?Why is the position rolerance of the .138 thrcaded hole different in this regard? Select mostappropria answer:a) Tped holes usually have close size tolerances.b.) Tbe cenring effect of the inserd screw may negarc added tolerance due to sizedeviation from MMC.

146. As an exercise in position tolerance principles, make an analysis of the part shown on thenextpage, given the following measurements from the specified danm surfaces and the holesizes. Make the necessary calculations and plot (use doa) the results on the graph usingthe zero (0) point as ttre rre (exact) posion and origin for the X and Y differentials.Imagine the concentric circles as a transparcnt overlay chart of the sane scale as the graphand as applied after plouing the hole centers or shown as concentic circles on the FaptL.The graph scale is I square = .001 inch. Number the holes #1 (upper lefr),fit2 (lower ft),#3 (upper right), and #4 Qower righ.

Hole #1Hole #2Hole #3Hole #4

Measurement X Direction.749.7522.746

2.7454

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ft C-TU + coc -.u--re -- I iC ? S ''= \gOr/S T"L,J,

4x .300:333) .o1o @ A B c

Q 'aaLS, O 1D--:d0 s---Fas, t oC tQ4 M\-t L.014 .013 .6.soe.OtZ r.011

.010

HOLE NO., ACTUAL LOC., SIZE, POS., TOLt#.7 ,so :fa X= o.7q 7 Y= Z.ztzJ S-O roL- .le1cco.,.t-.r-@ \= . 7-12 srzE-ostzE-a

srzE-o@ *= l:t{g--:t--, oo ft@ X = Z,7rs/ Y= ' 7fS Z@l(x) ) so


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I47. From the analvsis made on the part shown under question 146, has hole #1 met therequirements? Has hole #2?148. What consideration was given to some holes to make the determination of question 147?Which is the most appropriate answer?(1) All holes in the pattern may shift together within the position tolerance assigned.(2) Actual hole size deparnre from MMC adds position tolerance for that hole equal tothe the departure.r49. Is tlre part analyzed under questions 146 and 147 acceptable?(a) Using your calculator*, confrm your aswer to question 146 mathematicatly. Fillin the derived diametical (cytindrical) values calculad for each hole (show at leastto the fifth decimal place).Hole #1Hole #2Hole #3Hole #4

xlf no calculator is available to you,do the best you can with the tables,graphs, and calculation methods shownin your reference materials.)(b) Using-ody your calculator*, dermine from the inspection results of another part(produced to the same drawing as shown under question 146) if the part isacceptable.

Hole #1Hole #2Hole #3Hole #4

MeasurementY Direction2.248.752) )\..746

HoleSize.302.30t.303.303FI in the derived diametrical (cylindrical) values calculad for each hole (show atleast to the fifth decimal place)- Indicate at right acceptnce or rejection of each hole.(yes or no)Hole #1 Hole #3Hole #2- Hole #4

(c) Is the part acceptable?150. Under the function and advantages of position tolerancing, what further determinationscould be made? (Write an answer.)

151. Has the part now met the position requirements in terms of the design specifications?Has it met the production requiremens within tolerance?Are the quality control or inspection requirements clearlystated?

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2. Refecing to this figure, note that a featrre of size (a hole) has been used as a datm. Thedaun hote has been locad by position tolerance with its orientaion, orlrrpendiculariry,refined to a sser tolerance.a)b)c)d)e)s)h)

Whu is the daun hole position tolerance MMC size?Whu is the datum hole position tolerance LMC stz?Wh is the daum hole perpendicularity tolerance at MMC size?What is the daum hole perpendicularity tolerace LMC size?Wh is the . 380 hole position tolerance at MMC size?Wha is e virnal condition of the ' ,380 holes? -Wh is the virnal condition of the daum D hole?Wh is the resulant condition of the -380 hole if profuccd to acualmatine sze of .382?

4x .380:'m8

:560 !.OO52.75 !.O1.5oo:.913o .014 @ A B cI .0 @ A

D153. In the prcceding figu, if the daam D feane is produced at acnal mating slzn, of,502, whatpositional tolerance strift of the hole panem (as a unit) exiss? Is this ahole-ho added orance?I54. In the preceding figure, which dailms does the datrm D hole toca from? ke oieutation (squareness) from? Which dauns does the .380 holes loca: take orienution from?

o .o1o @ A D@ B1.75+.01

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155. If a functional gage were desired to evaluate the locion of the datum D hole of the figureshown under question 152 which danms would be picked up and in what precedence?Would MMC be applicable to the daums?In the functional gage, what would the size of the gage pin be? \ryhawould the gage pin size be for the perpendiculariry requirement?156. Functional gFng can also be used to evaluue the position of the .380 hole patrn under

question 152. Add the nominal gage pin sizes to this illustation of apin gage. Disregadconsideation of gage tolerances and the relionship to darui B for purposes of ttrisquestion. Erplain how you derived the gage pin sizes.Gage pin size for .380 holes = .How derived?Gage pin size for .500 daum *Do'hole = How derived?

157. Can position tolerancing be applied on an RfS basis? Can an MMCposition toleranced paern of feares be relad to an RFS daarm?Show the feare control frame stffing this requirement here:This is based upon which rule?

158. If a nctional gage similar to tbat shown under question 156 were to be use( but wherethe daum is on an RFS basis and the feaues in conrol remain on an MMC basis, whdifference would exist generally in ttre gage desig, and frnction? (Descdbe in words or byskerch below.)

159. Can functional gaging of ttre variety rlisstssed in questions 156 though l5g be used wheeboth datum and featrues in control are on an RFS basis?3


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160. position olerancing may be used on functional or assemblabiliry requirements of noncylin-ical feues. On this prtt, rp.ofy th the .501 slot is to be locad al tne position (atMMC) wittr respect to the 1.L20 width (at MMC) within -005 wide tolerance'

161. Skerch below the parr shown unde question 160 (above) and show the positional toleranceme.

1.120 1.003

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L62. Posirion tolerancing may be applied to relate noncylindrical featues of mating pans. Estalish position tolerances on the mating pans shown below. Also calculate the ma:cimumpermissible production tolerance that could be permitd on each part if its feanre anddatum actual mating envelope sizes were both to depan from MMC size to LMC size.

PART #1 PART +2

Total oleance at LMC size offlatanddarum = Total olerance a LMC size ofslot and danm =MMC Size SIot(Part#2) =MMC Size Fl (Pan *t = 1-MMC Size Daom Slot @an#Z) =MMC Size Danm Flat (Part#1) = (-)

NOTE: For the pu4)oses of this example andfor simpliciry of principles, geometrical tolerancebenveen the danms A and B on both parts has not been made a pan of the calculations. If you wish tocorsider ttris additionally an optional exercise, add here an explanation of the steps necessfy:

.503 *.9?

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t63. Posirion tolerancing may be used on mctional or assemblability requirements of coaxialfeatures. On this parl specify that the .305 fearre is to be locad at tne position (atMMC) wittr respect to the .500 featrre (at MMC) within .003 tolerance zone.

1&. Sketch below the parrshown rnder quesion 163 and show the positional tolerance zone. .305 t.o01

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L65. Position olerancing may be applied to rela coa,xial features of mating parrs. Establishposition tolerances on the rnating parts shown below. Also calculate the ftximum perrris-sible production tolerance that could be permitd on each part if its feanlre and datum rctualmating envelope sizes were bottr to depart from MMC size to LMC size.PART f 1 PART +2

1.300 t .oos.75'l:33

.6r4:'333

.sto1.881.7 4s::33

Total tolerance IfC size ofshaftanddanm =MMC Size Hole (Part*t =MMC Size Shaft (Paf2) - (-)MMC Size Datum Hole @art #1) -MMC Size Danm Shaft (Part f2) = (-)

NOTE: For the purposes of this example and for simplicity of principleS, geometrical tolerancebetween the dums A and B on both parts has not been made a part of the calculations. If you wish toconsider this additionally as an optional exercise, add here an explanation of the steps necessrrry:

ln-.r'ul:BBTotal tolerance at LMC size ofhole and datum =

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166. Where erors of form and location are considered on the basis of displacement of axis of twoor more basically coaxial feaes, which control is used? Establishnecessary danms and comple the featue control frame for the part below. Assume thatttre nvo diamers (.605 and .500) are to establish ttre a:cis of rotation of ttre part withttre 1.000 diamerrelative to that atds, within .003 tolerance, RFS.1.000 1.005

.605 t.OOl .soo t.ool167. Using conventional FIM methods of evaluion, if the pan checked at .003 FIM, has itmet the concentricity requirement? Which of the answers below is most logicat?(1) Yes, if the surface of rotation has been sufciently sampled for mcimum error.Q) No, because the axis of the feature has not been dermined.168. If ttre pan error exceeds the stated tolerance when the FIM method is use{ does this mean

ttre pan has not met the concentricity requirement?Which statement supports yolr nswer most approprialy?(1) The surface may be out-of-circularity, erc., which will influence the reading, but doesnot conclusively prove center (axis) dlacement or eror.Q) Concentricity is a variety of locational tolerance control, and the resultant error' detected must compared to the cylindrical tolerance zone.

169. Before a concentricity olerance is specifred, which other chaacristics should be con-sidered first if possible?Which statement suppsrts your answer most appropriately?(1) Concenricity requirements ate encountered less frequently.Q) MMC methods or conventional surface criria controls are more readily producibleand economical.

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170. Skeh below the part shown under question 166 and show the concentricity tolerance zone arda representation as to how an acnrally produced dia. would be dermined if in compliance wittthe requirement or DoL

l7l. Specfy th ttre .501 widttr of ttris symmetrical part is to be locad using a syrnmetry tolerancewith reqpect to the 1.120 widttr wirhin .005 wide total tolerance, RFS.

1.120 ! .OO3

+.003

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L72- Skerch below ttre part shown under question 171, and show ttre symmetry tolerance zone anda representation as to how an actually produced slot would be dermined if in compliance withthe requirement or not.

173. If this part had been indicad as a positional tolerance, RFS, wh would the difference in meaning be? Explain briefly.

L74. Dum targets have been panially shown on the part on ttre followingpage. Noting thefeaore connol frames and their specified datums, select ttre tagets which approprielyoonstruct these designated datum planes. Then comple the danrm uget symbols andidentify the targets according to your own selection.

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7X.138 - 32 UNC - 28174.

.020 is used for the relar.ionshipof the patt.ern relative o the9u!e! exErernity datum references,A,B,C. A refinement of .0I0t.olerance in the pattern reLaciveEo datum D is used.

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175. In the space below design or srch your own pan using datum Egets. Use a part similar toone from your own experience or esablish an imaginary one. Establish the dum rgets'danm planes, and show some feanre relationships (e.g. hole pattern) with respect to thetfgets.

176. On the below part, add or modify with the necessary symbology to indicate that the tolerancezone is projected above the part for .310.4X.190-32

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I77. On the following casting, establish ttre datum planes for the parallelism and positional controlrelationships by dahrms and datum targets from the part surfaces. Select your own target loca-tions as seems appropriate. Add any necessary views to show your requirements. Show the targetlocations using proper methodology but disregard determining the values; or, if you wish, inserthypothetical values.

8X .164 - 32

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17g. On the following part (shown twice) select the best methods to control the five hole pattems(.430 ,o,d.z}iiroles) relarive to the danm feattues D and E. There are a number of possibili-ties but make your choice by adding in the appropriate modifiers in the feature control frames tobest achieve the following:Add material condition modifiers to relate to the danm features D and E on a functional (virnralcondition) basis on the following figure.

l.oos ( lA lB lc

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179. lition indication to relate to the datum features. also ensure closer compatibility betweenethods.

2X .250+'0^0-?

.o+'90-!

4x .205+'991

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lg0. Indica on the below part that the 4 holes are located at tne position within .010 diameter atLMC with respect to dnm A (the bottom face of the part). Disregard the pattern location fromthe outside edges for purposes of this example'

4X .151 +.003

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ure Proper inrface. Make the necessary determina-calculations and complete the drawings below'

fr,

6X.190 - 32 UNF - 28\f .550 t.OtS

6x .210:'.33;

51

.7gg 1.005


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(NOTE: Question 182 is optional for those inrested in gagrng).182. Design (skeh) a functional gage for the small part (one with clearance holes), to verify the in-the-paern location controls only, as developed under question 181. You need only develop thenominal gage sizes, but show the gage constnction as based upon your answer to question 181.

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183. From the below drawing (similar to one under Questions 181, 182) and given information,determine whether a produced part with the following measured results is acceptable to thepositional .010 at MMC requirement. Hole #1, the lower left hole, has been used as the originof the X and Y meastuements; the pattem has been squared-up with hole #3. The remainingholes, 2,4,5 and 6 have been measured from holes I and 3. Use the graphic analysis apergaging) method. Graph paper and tracing paper with overlay circles to the graPh Paper scale, aresuppled. Use a scale of .001 equals 2 squares. (See pages 57 and 55).

squue-uP

origrn O

Hole 1Hole 2Hole 3HoIe 4oJ.e )HoIe 6holeholeholeholeholehole

inX0(- ) .0040

1 .003L.0032.995Yese22ee,

inY0!,1+9252,996

( - ). ooo51 .48982,9947

No

Actual hole sizeT/.2!zf .ztz5l.zt3l.zt35/.ztzPersrissible position tol on holefsIsTqIsIsIs

#t#2#3#4fr>#6

goodgoodgoodgood.goodgood.Is the part good ?

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-FOR NOTES OR CALCULATIONS -

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61/8255


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- FOR NOTES OR CALCULATTONS -

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REH0lfB FR,@fl EOO'K FOi USE 0N QIJESTIONS(For use on Questlons lg3 & lg6 )

o.35-o.33o.3 Io.29oi,27o,25

0.32o.30o.2a

o.26

0.0 5( Datun Bonus ToQuestlon 186 )

5?


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184. Veri$ yoru answer to question 183 mathematically with a computer or Programmed calculator.Determine the smallest circle (tolerance zone) which will encompass all the measured holecenters (axes) simultaneously. Disregard the hole sizes (assume them RFS) for the initial calcula-tion but consider their sizes as necessary (i.e. departure from MMC as bonus tolerance) in yourfinal derminations to verify the question 183 gaPhic analysis-The smallest circle (tolerance zone) sizn, is: (For information, optimumposition of all 6 holes (centroid) is in X: and inY:'With reference to the above answer, write in your own words how you dermined the partacceptable (or not) from your calculated results.

185. Verify your answer to question 183 mathematically with a computer or programmed calculator.Determine the smallest circle (tolerance zone) which will encompass all the measured holecenters (a,xes), including the holes size departure from MMC (bonus tolerance), in your calcula-tions. The result of this calculation should give a diect answer as to the accePtance of all theholes or noLThe smallest circle (tolerance zone) size, compensating for the MMC deparflue @onus tolerance)on all individual holes, is: @ . (For information, optimum position of all 6 holes(cenroid) is in: X: and inWith reference to the above answer, wri in your own words how you dermined the partacceptable (or not) from yotu calculated results.

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186. From the below data given from an inspection process (i.e. coordinate measuring) on this part,determine if it has met the positional tolerance requirements on the .380 holes and the patternrelationship to the .5N dam hole. Use graphic (paper gagmg) methods. (Graph paper andoverlay .010, etc. supplied). Use scale .001=2 squares. (Use page 57 overlay).+.0034X .38O _.oooe .010 6i A D \il) B

1.75 t.01

.560 +.0052.75 t.O1.500+'991

HoleI2J4Danrm

inX.9948.994.9953.99450

inY.3715.377r.3726.376/.0

ActualHole size.382.3825.382s.383.502Has the part met the .380 hole to hole requirements relative to the tnre position ofeach hole?Has the .380 four-hole pattern met its requirement relative to the datumD .500 hole?

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t9i-'r- i--l -'i--i-;--l--l-

r-ri;;-i-;_--r--_1--i-f-r *i--, :-f-.:-F----t__-+-++-+'-:-r-lri I t I i'

1..' j.-L;:-!:-..:l-. -.:'-*i; -.- ., . !...;-+-.---:.--i:-j-+-i.:..:...i-...-:-;-i-r-: J-.: : : l-:+-i.i..,---:*--;---.--;.-:-..,t;::':::l;l:: I::: :,.......r_i_r:i__:_i -__;_ :- : _:_ ; ., . I _.1 _:_.:_...,_-...,__'_ - .

-r-i ,--:-lLlll_.i-l -r;:_li---r;-----]-a-j-t--.-rr-t-_l_i.ri;J+_.1_


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- FOR NOTES OR CALCTILATTONS -

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tg?. From ttre data given under question 186, verify your answer to question 186 mathematically witha computer or programmed calculator.

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FIGURES

Figures 1 through 6 may be removed for convenience in doing the workshop exercises.

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FIGITRESFigrues 1 through 6 may be removed if desired for convenience in doing work on the relatedquesdons. +.002.376

\ t+

B

/-t'(Lh-4-t //-(1.500 +.005tr@tFt(r-,rr \-r-i-o .bt ^ E

1.610 t.005

.500 r.005

W,*zW/ , o2 r-

Fig.rre I

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.eoo_';;; ,goo3

/. org

.oool'!fo.

\(VIRTUAL CONDITION)-)

69

Figun 2


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.500 t .005

.soo t.oo3Figurc 3dl

7l


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1a


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1.0300 t .0005

.Asss rFlgure 6

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GDT Workbook Questions

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