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Based on the ASME Y14.5MBased on the ASME Y14.5M--

1994 Dimensioning and1994 Dimensioning and

Tolerancing StandardTolerancing Standard

DIMENSIONALENGINEERING

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Tolerances

of Form

Straightness Flatness

Circularity Cylindricity

(ASME Y14.5M-1994, 6.4.1)

(ASME Y14.5M-1994, 6.4.3)

(ASME Y14.5M-1994, 6.4.2)

(ASME Y14.5M-1994, 6.4.4)

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25 +/-0.25

0.1 Tolerance

0.5 Tolerance

Straightness is the condition where an element of asurface or an axis is a straight line

Straightness(Flat Surfaces)

0.5 0.1

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Straightness(Flat Surfaces)

24.75 min25.25 max

0.5 Tolerance Zone

0.1 Tolerance Zone

The straightness tolerance is applied in the view where the

elements to be controlled are represented by a straight line

In this example each line element of the surface must lie

within a tolerance zone defined by two parallel linesseparated by the specified tolerance value applied to eachview. All points on the surface must lie within the limits ofsize and the applicable straightness limit.

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Straightness(Surface Elements)

MMC

0.1 Tolerance Zone

0.1

MMC

0.1 Tolerance Zone

MMC

0.1 Tolerance Zone

In this example each longitudinal element of the surface mustlie within a tolerance zone defined by two parallel linesseparated by the specified tolerance value. The feature mustbe within the limits of size and the boundary of perfect form atMMC. Any barreling or waisting of the feature must notexceed the size limits of the feature.

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Straightness (RFS)

0.1

Outer Boundary (Max)

MMC

0.1 DiameterTolerance Zone

Outer Boundary = Actual Feature Size + Straightness Tolerance

In this example the derived median line of the features actual local size

must lie within a tolerance zone defined by a cylinder whose diameter isequal to the specified tolerance value regardless of the feature size.Each circular element of the feature must be within the specified limits ofsize. However, the boundary of perfect form at MMC can be violated upto the maximum outer boundary or virtual condition diameter.

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Straightness (MMC)1514.85

15.1 Virtual Condition

15(MMC)


15.1 Virtual Condition

14.85(LMC)


Virtual Condition = MMC Feature Size + Straightness Tolerance

In this example the derived median line of the features actual local size

must lie within a tolerance zone defined by a cylinder whose diameter isequal to the specified tolerance value at MMC. As each circular elementof the feature departs from MMC, the diameter of the tolerance cylinderis allowed to increase by an amount equal to the departure from the localMMC size. Each circular element of the feature must be within thespecified limits of size. However, the boundary of perfect form at MMC

can be violated up to the virtual condition diameter.

0.1 M

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Flatness

Flatness is the condition of a surface having all elements inone plane. Flatness must fall within the limits of size. Theflatness tolerance must be less than the size tolerance.

25 +/-0.25

24.75 min25.25 max

0.1

0.1 Tolerance Zone

0.1 Tolerance Zone

In this example the entire surface must lie within a tolerancezone defined by two parallel planes separated by the specifiedtolerance value. All points on the surface must lie within the

limits of size and the flatness limit.

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Circularity is the condition of a surface where all points of thesurface intersected by any plane perpendicular to a commonaxis are equidistant from that axis. The circularity tolerance

must be less than the size tolerance

90

90

0.1

0.1 Wide Tolerance Zone

Circularity(Roundness)

In this example each circular element of the surface must lie within atolerance zone defined by two concentric circles separated by the

specified tolerance value. All points on the surface must lie within thelimits of size and the circularity limit.

0.1

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Cylindricity

Cylindricity is the condition of a surface of revolution in whichall points are equidistant from a common axis. Cylindricity is acomposite control of form which includes circularity

(roundness), straightness, and taper of a cylindrical feature.

0.1 Tolerance Zone

MMC

0.1

In this example the entire surface must lie within a tolerance zonedefined by two concentric cylinders separated by the specifiedtolerance value. All points on the surface must lie within the limits of

size and the cylindricity limit.

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____________ and___________ are individual line or circularelement (2-D) controls.

Form Control Quiz

The four form controls are____________,________,

___________, and____________.

Rule #1 states that unless otherwise specified a feature of

size must have____________at MMC.

________ and____________are surface (3-D) controls.

Circularity can be applied to both________and_______ cylindricalparts.

1.

2.

3.

4.

5.

Form controls require a datum reference.

Form controls do not directly control a features size.

A features form tolerance must be less than its size

tolerance.

Flatness controls the orientation of a feature.

Size limits implicitly control a features form.

6.

7.

8.

9.

10.

Questions #1-5 Fill in blanks (choose from below)

straightness

flatness

circularity

cylindricity

perfect form

straight tapered profile

true position

angularity

Answer questions #6-10 True or False

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Tolerances of

Orientation

Angularity

Perpendicularity

Parallelism

(ASME Y14.5M-1994 ,6.6.2)

(ASME Y14.5M-1994 ,6.6.4)

(ASME Y14.5M-1994 ,6.6.3)

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Angularity(Feature Surface to Datum Surface)

Angularity is the condition of the planar feature surface at aspecified angle (other than 90 degrees) to the datumreference plane, within the specified tolerance zone.

A

20 +/-0.5

30 o

A

19.5 min

0.3 WideTolerance

Zone

30 o

A

20.5 max

0.3 WideTolerance

Zone

30 o

The tolerance zone in this example is defined

by two parallel planes oriented at thespecified angle to the datum reference plane.

0.3 A

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Angularity is the condition of the feature axis at a specifiedangle (other than 90 degrees) to the datum reference plane,within the specified tolerance zone.

A

0.3 A

A

60 o

The tolerance zone in this example is defined by a

cylinder equal to the length of the feature, orientedat the specified angle to the datum reference plane.

0.3 CircularTolerance Zone


Angularity(Feature Axis to Datum Surface)

NOTE: Tolerance appliesto feature at RFS

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NOTE: Tolerance

applies to feature

at RFS

Angularity is the condition of the feature axis at a specifiedangle (other than 90 degrees) to the datum reference axis,within the specified tolerance zone.


A

Datum Axis A

Angularity(Feature Axis to Datum Axis)

The tolerance zone in this example is defined by acylinder equal to the length of the feature, oriented

at the specified angle to the datum reference axis.

NOTE: Feature axis must liewithin tolerance zone cylinder

0.3 A

o45

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0.3 A

A

0.3 WideTolerance Zone

A A

Perpendicularity is the condition of the planar featuresurface at a right angle to the datum reference plane, within

the specified tolerance zone.

Perpendicularity(Feature Surface to Datum Surface)


The tolerance zone in this example is

defined by two parallel planes orientedperpendicular to the datum referenceplane.

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C

Perpendicularity is the condition of the feature axis at a rightangle to the datum reference plane, within the specifiedtolerance zone.

Perpendicularity(Feature Axis to Datum Surface)

0.3 C






defined by a cylinder equal to the length ofthe feature, oriented perpendicular to thedatum reference plane.

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Perpendicularity(Feature Axis to Datum Axis)


The tolerance zone in this example isdefined by two parallel planes oriented

perpendicular to the datum reference axis.

Perpendicularity is the condition of the feature axis at a rightangle to the datum reference axis, within the specifiedtolerance zone.


A

Datum Axis A

0.3 A

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0.3 A

A

25 +/-0.5

25.5 max


A

24.5 min


A

Parallelism is the condition of the planar feature surfaceequidistant at all points from the datum reference plane,within the specified tolerance zone.

Parallelism(Feature Surface to Datum Surface)

The tolerance zone in this exampleis defined by two parallel planesoriented parallel to the datumreference plane.

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A


Parallelism(Feature Axis to Datum Surface)

0.3 A

A

NOTE: The specified tolerance

does not apply to the orientationof the feature axis in this direction

Parallelism is the condition of the feature axis equidistantalong its length from the datum reference plane, within thespecified tolerance zone.

The tolerance zone in this exampleis defined by two parallel planes

oriented parallel to the datumreference plane.


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A

B

Parallelism(Feature Axis to Datum Surfaces)

A

B




Parallelism is the condition of the feature axis equidistantalong its length from the two datum reference planes, withinthe specified tolerance zone.


defined by a cylinder equal to thelength of the feature, oriented parallelto the datum reference planes.

NOTE: Tolerance applies

to feature at RFS

0.3 A B

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Parallelism(Feature Axis to Datum Axis)

Parallelism is the condition of the feature axis equidistant alongits length from the datum reference axis, within the specified

tolerance zone.

A

0.1 A


0.1 Circular

Tolerance Zone

Datum Axis A

The tolerance zone in this example isdefined by a cylinder equal to thelength of the feature, oriented

parallel to the datum reference axis.


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Orientation Control Quiz

The three orientation controls are__________,___________,and________________.

1.

2.

3.

4.

5.

A_______________ is always required when applying any ofthe orientation controls.

________________ is the appropriate geometric tolerance when

controlling the orientation of a feature at right angles to a datumreference.

Orientation tolerances indirectly control a features form.

Mathematically all three orientation tolerances are_________.

Orientation tolerances do not control the________ of a feature.

6.

Orientation tolerance zones can be cylindrical.

Parallelism tolerances do not apply to features of size.

To apply an angularity tolerance the desired angle must

be indicated as a basic dimension.

7.

8.

9.

10.

To apply a perpendicularity tolerance the desired anglemust be indicated as a basic dimension.


angularity

perpendicularity

parallelism

datum reference

identical

location

profile

datum feature

datum target


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Tolerances

of Profile

Profile of a Line

Profile of a Surface

(ASME Y14.5M-1994, 6.5.2b)

(ASME Y14.5M-1994, 6.5.2a)

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18 Max

Profile of a Line

2 Wide SizeTolerance Zone

1 A B C

A

17 +/- 1

1 Wide ProfileTolerance Zone

C

A1

20 X 20

A2

20 X 20

A3

20 X 20

B

The profile tolerance zone in this example is defined by twoparallel lines oriented with respect to the datum referenceframe. The profile tolerance zone is free to float within thelarger size tolerance and applies only to the form and

orientation of any individual line element along the entiresurface.

Profile of a Line is a two-dimensional tolerance that can be applied to a

part feature in situations where the control of the entire feature surface asa single entity is not required or desired. The tolerance applies to the lineelement of the surface at each individual cross section indicated on the

drawing.

16 Min.

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Profile of a Surface is a three-dimensional tolerance that can be applied

to a part feature in situations where the control of the entire featuresurface as a single entity is desired. The tolerance applies to the entiresurface and can be used to control size, location, form and/or orientation

of a feature surface.


2 Wide Tolerance ZoneSize, Form and Orientation

A

A1

20 X 20

A2

20 X 20

A3

20 X 20

C 2 A B C

23.5

23.5 NominalLocation

The profile tolerance zone in this example is defined by two parallelplanes oriented with respect to the datum reference frame. The profiletolerance zone is located and aligned in a way that enables the partsurface to vary equally about the true profile of the feature.

B

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A1

20 X 20

A2

20 X 20

A3

20 X 20

B

C

50

B

C

50

1 Wide TotalTolerance Zone

(Bilateral Tolerance)

The tolerance zone in this example is defined by two parallel planes

oriented with respect to the datum reference frame. The profile tolerancezone is located and aligned in a way that enables the part surface tovary equally about the true profile of the trim.

1 A B C

Nominal Location

0.5 Inboard

0.5 Outboard

Profile of a Surface when applied to trim edges of sheet metal parts will controlthe location, form and orientation of the entire trimmed surface. When abilateral value is specified, the tolerance zone allows the trim edge variationand/or locational error to be on both sides of the true profile. The tolerance

applies to the entire edge surface.

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A1

20 X 20

A2

20 X 20

A3

20 X 20

B

C

50

B

C

50

0.5 Wide TotalTolerance Zone

(Unilateral Tolerance)

Profile of a Surface when applied to trim edges of sheet metal parts will controlthe location, form and orientation of the entire trimmed surface. When aunilateral value is specified, the tolerance zone limits the trim edge variationand/or locational error to one side of the true profile. The tolerance applies to

the entire edge surface.


oriented with respect to the datum reference frame. The profile tolerancezone is located and aligned in a way that allows the trim surface to varyfrom the true profile only in the inboard direction.

0.5 A B C

Nominal Location

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A1

20 X 20

A2

20 X 20

A3

20 X 20

B

C

50

1.2 A B C

B

C

50

0.5 Inboard

0.7 Outboard

1.2 Wide TotalTolerance Zone

(Unequal Bilateral Tolerance)

Profile of a Surface when applied to trim edges of sheet metal parts will controlthe location, form and orientation of the entire trimmed surface. Typically whenunequal values are specified, the tolerance zone will represent the actualmeasured trim edge variation and/or locational error. The tolerance applies to

the entire edge surface.


oriented with respect to the datum reference frame. The profile tolerancezone is located and aligned in a way that enables the part surface tovary from the true profile more in one direction (outboard) than in theother (inboard).

0.5

Nominal Location

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A

25

A0.5

0.1

25.2524.75


A

Composite Profile of Two Coplanar

Surfaces w/o Orientation Refinement


Form Only

Location &

Orientation

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25.25

24.75

A

A

A

25

A0.5

A0.1 Form & Orientation

Composite Profile of Two Coplanar

Surfaces With Orientation Refinement


Location

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6.

Profile Control Quiz

Profile tolerances always require a datum reference.


1.

Profile of a surface tolerance is a 2-dimensional control.

Profile of a line tolerances should be applied at MMC.

Profile tolerances can be applied to features of size.

2.

3.

4.

5.

Profile of a surface tolerance should be used to control

trim edges on sheet metal parts.

Profile tolerances can be combined with other geometric

controls such as flatness to control a feature.

Profile of a line tolerances apply to an entire surface.7.

Profile of a line controls apply to individual line elements.8.

Profile tolerances only control the location of a surface.9.

Composite profile controls should be avoided because

they are more restrictive and very difficult to check.10.

Profile tolerances can be applied either bilateral or

unilateral to a feature.

11.

Profile tolerances can be applied in both freestate and

restrained datum conditions.12.

Tolerances shown in the lower segment of a composite

profile feature control frame control the location of afeature to the specified datums.

13.

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In composite profile applications, the tolerance shown in the upper

segment of the feature control frame applies only to the________ ofthe feature.


The two types of profile tolerances are_________________,

and____________________.1.

2.

3.

4.

5.

Profile tolerances can be used to control the________,____,

___________ , and sometimes size of a feature.

Profile tolerances can be applied_________ or__________.

_________________ tolerances are 2-dimensional controls.

____________________ tolerances are 3-dimensional controls.


6._________________ can be used when different tolerances arerequired for location and form and/or orientation.

7. When using profile tolerances to control the location and/or orientation of

a feature, a_______________ must be includedin the feature control frame.

8. When using profile tolerances to control form only, a______

__________ is not required in the feature control frame.

9.

profile of a linedatum reference

composite profile bilateral

location form

primary datum

true geometric counterpart

orientationprofile of a surface

unilateral

virtual condition

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Tolerances

of Location

True Position

Concentricity

Symmetry

(ASME Y14.5M-1994, 5.2)

(ASME Y14.5M-1994, 5.12)

(ASME Y14.5M-1994, 5.13)

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Notes

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10.25 +/- 0.5

10.25 +/- 0.5

8.5 +/- 0.1

RectangularTolerance Zone

10.25

10.25

8.5 +/- 0.1

Circular ToleranceZone

B

A

C

Coordinate vs Geometric

Tolerancing Methods

Coordinate Dimensioning Geometric Dimensioning

Rectangular Tolerance Zone Circular Tolerance Zone

1.4

+/- 0.5

+/- 0.5

57% Larger

Tolerance Zone

Circular Tolerance Zone

Rectangular Tolerance Zone

Increased Effective Tolerance

1.4 A B C

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Formula to determine the actual radialposition of a feature using measuredcoordinate values (RFS)

Z positional tolerance /2

X2 Y2+Z =

X =2

Y =

2

X

Y

Z

Feature axis actuallocation (measured)

Positional

tolerance zonecylinder

Feature axis true

position (designed)

Positional Tolerance Verification

Z = total radial deviation

X measured deviation

Y measured deviation

Actual feature

boundary

(Applies when a circular tolerance is indicated)

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Formula to determine the actual radialposition of a feature using measuredcoordinate values (MMC)

Z

X2 Y2+Z =

X =2

Y =2

X

Y

Z

Feature axis actuallocation (measured)

Positional

tolerance zonecylinder

Feature axis true

position (designed)

Positional Tolerance Verification

Z = total radial deviation

X measured deviation

Y measured deviation

Actual feature

boundary

+( actual - MMC)

2

= positional tolerance

(Applies when a circular tolerance is indicated)

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Bi-directional True PositionRectangular Coordinate Method

3510

10

AC

B

1.5 A B C

0.5 A B C2X

2X

10 35

1.5 Wide

Tolerance

Zone


True Position Relatedto Datum Reference Frame

10B

C

Each axis must lie within the 1.5 X 0.5 rectangular tolerance zone

basically located to the datum reference frame

As Shown

on Drawing

Means This:

2X 6 +/-0.25

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Bi-directional True PositionMultiple Single-Segment Method

3510

10

AC

B

10 35

1.5 Wide

Tolerance

Zone


True Position Relatedto Datum Reference Frame

10B

C

Each axis must lie within the 1.5 X 0.5 rectangular tolerance zone

basically located to the datum reference frame

As Shown

on Drawing

Means This:

2X 6 +/-0.25

1.5 A B C0.5 A B

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3510

10

AC

B As Shown

on Drawing

Means This:

1.5 A B C 0.5 A B CBOUNDARY BOUNDARY

10 3510

B

C

2X 13 +/-0.25 2X 6 +/-0.25

12.75 MMC width of slot-1.50 Position tolerance

11.25 Maximum boundary

Both holes must be within the size limits and noportion of their surfaces may lie within the areadescribed by the 11.25 x 5.25 maximumboundaries when the part is positioned withrespect to the datum reference frame. Theboundary concept can only be applied on anMMC basis.

o90

True position boundary related

to datum reference frame

A

Bi-directional True PositionNoncylndrical Features (Boundary Concept)

MM

5.75 MMC length of slot-0.50 Position tolerance

5.25 maximum boundary

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Composite True PositionWithout Pattern Orientation Control

3510

10

AC

B

10 35

True Position Related

to Datum ReferenceFrame

10B

C

Each axis must lie within each tolerance zone simultaneously

As Shown

on Drawing

Means This:

2X 6 +/-0.25

1.5 A B C0.5 A

0.5 Feature-RelatingTolerance Zone Cylinder

1.5 Pattern-LocatingTolerance Zone Cylinder

patternlocationrelative

to Datums A, B, and Cpatternorientationrelative to

Datum A only (perpendicularity)

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Composite True PositionWith Pattern Orientation Control

3510

10

AC

B

10 35

True Position Related

to Datum Reference

Frame

10B

C

Each axis must lie within each tolerance zone simultaneously

As Shown

on Drawing

Means This:

2X 6 +/-0.25

0.5 Feature-Relating

Tolerance Zone Cylinder

1.5 Pattern-LocatingTolerance Zone Cylinder

patternlocationrelative

to Datums A, B, and C

patternorientationrelative to

Datums A and B

1.5 A B C0.5 A B

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Location (Concentricity)Datum Features at RFS

A

15.95

15.90

As Shown on Drawing

Derived Median Points ofDiametrically Opposed Elements

Axis of DatumFeature AMeans This:

Within the limits of size and regardless of feature size, all median points ofdiametrically opposed elements must lie within a 0.5 cylindricaltolerance zone. The axis of the tolerance zone coincides with the axis ofdatum feature A. Concentricity can only be applied on an RFS basis.

0.5 A

6.35 +/- 0.05

0.5 CoaxialTolerance Zone

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Location (Symmetry)Datum Features at RFS

A

15.95

15.90

0.5 A

6.35 +/- 0.05

Derived MedianPoints

Center Plane ofDatum Feature A

0.5 WideTolerance ZoneMeans This:

Within the limits of size and regardless of feature size, all median pointsof opposed elements must lie between two parallel planes equallydisposed about datum plane A, 0.5 apart. Symmetry can only beapplied on an RFS basis.

As Shown on Drawing

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True Position Quiz


Positional tolerances are applied to individual or patterns

of features of size.1.

Cylindrical tolerance zones more closely represent the

functional requirements of a pattern of clearance holes.

True position tolerances can control a features size.

Positional tolerances are applied on an MMC, LMC, orRFS basis.

2.

3.

4.

5.

True position tolerance values are used to calculate the

minimum size of a feature required for assembly.

6. Composite true position tolerances should be avoidedbecause it is overly restrictive and difficult to check.

Composite true position tolerances can only be applied

to patterns of related features.7.

The tolerance value shown in the upper segment of a

composite true position feature control frame applies

to the location of a pattern of features to the specifieddatums.

8.

Positional tolerances can be used to control circularity

9.

10.

11.

The tolerance value shown in the lower segment of acomposite true position feature control frame applies


True position tolerances can be used to control center

distance relationships between features of size.

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Positional tolerance zones can be___________,___________,or spherical

1.

2.

3.

4.

5.

________________ are used to establish the true (theoreticallyexact) position of a feature from specified datums.

Positional tolerancing is a_____________ control.

Positional tolerance can apply to the____ or________________ ofa feature.

_____ and________ fastener equations are used to determineappropriate clearance hole sizes for mating details

6.

7.

_________ tolerance zones are recommended to prevent fastenerinterference in mating details.

8.

projected3-dimensional

surface boundary floating

location fixed

basic dimensions

maximum material

cylindricalpattern-locating rectangular

feature-relating

True Position Quiz


The tolerance shown in the upper segment of a composite trueposition feature control frame is called the________________tolerance zone.

The tolerance shown in the lower segment of a composite true

position feature control frame is called the________________tolerance zone.

9. Functional gaging principles can be applied when__________________ condition is specified

axis

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Tolerances

of Runout

Circular Runout

(ASME Y14.5M-1994, 6.7.1.2.1)

Total Runout

(ASME Y14.5M-1994 ,6.7.1.2.2)

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Datum feature

Datum axis (establishedfrom datum feature

Angled surfacesconstructed arounda datum axis

External surfacesconstructed around

a datum axis

Internal surfacesconstructed around adatum axis

Surfaces constructed

perpendicular to adatum axis

Features Applicableto Runout Tolerancing

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0+ -

Full IndicatorMovement

Maximum Minimum

Total

Tolerance

MaximumReading

MinimumReading

Full PartRotation

Measuring position #1(circular element #1)

Circular Runout

When measuring circular runout, the indicator must be reset to zero at each measuring positionalong the feature surface. Each individual circular element of the surface is independentlyallowed the full specified tolerance. In this example, circular runout can be used to detect 2-dimensional wobble (orientation) and waviness (form), but not 3-dimensional characteristicssuch as surface profile (overall form) or surface wobble (overall orientation).

Measuring position #2(circular element #2)

Circular runout can only be applied on an

RFS basis and cannot be modified toMMC or LMC.

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o360 PartRotation

50 +/- 2o o

As Shownon Drawing

Means This:

Datum axis A

Single circularelement

Circular Runout(Angled Surface to Datum Axis)

0.75 A

A

50 +/-0.25

0+-

NOTE: Circular runout in this example onlycontrols the 2-dimensional circular elements(circularity and coaxiality) of the angled featuresurface not the entire angled feature surface

Full IndicatorMovement( )

The tolerance zone for any individual circularelement is equal to the total allowable movementof a dial indicator fixed in a position normal to thetrue geometric shape of the feature surface whenthe part is rotated 360 degrees about the datumaxis. The tolerance limit is applied independentlyto each individual measuring position along thefeature surface.

Allowable indicatorreading = 0.75 max.

When measuring circularrunout, the indicator mustbe reset when repositionedalong the feature surface.

Collet or Chuck

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As Shownon Drawing

50 +/-0.25

0.75 A

Circular Runout(Surface Perpendicular to Datum Axis)

o360 Part

Rotation

0+-

Datum axis A

Single circularelement

NOTE: Circular runout in this example willonly control variation in the 2-dimensional

circular elements of the planar surface (wobbleand waviness) not the entire feature surface

The tolerance zone for any individual circularelement is equal to the total allowable movementof a dial indicator fixed in a position normal to thetrue geometric shape of the feature surface whenthe part is rotated 360 degrees about the datumaxis. The tolerance limit is applied independentlyto each individual measuring position along thefeature surface.

Means This:

Allowable indicator

reading = 0.75 max.

When measuring circular runout, the indicator mustbe reset when repositioned along the feature surface.

A

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0+ -


Single circular element

o360 PartRotation

Means This:

As Shownon Drawing

50 +/-0.25

0.75 A

Datum axis A

When measuring circular runout,the indicator must be reset whenrepositioned along the featuresurface.

Circular Runout(Surface Coaxial to Datum Axis)

The tolerance zone for any individual circular element is equalto the total allowable movement of a dial indicator fixed in aposition normal to the true geometric shape of the featuresurface when the part is rotated 360 degrees about the datum

axis. The tolerance limit is applied independently to eachindividual measuring position along the feature surface.

NOTE: Circular runout in this example willonly control variation in the 2-dimensionalcircular elements of the surface (circularity and

coaxiality) not the entire feature surface

A

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0+ -



o360 PartRotation

Means This:

As Shownon Drawing

0.75 A-B

Datum axis A-B

When measuring circular runout,the indicator must be reset whenrepositioned along the featuresurface.

Circular Runout(Surface Coaxial to Datum Axis)

The tolerance zone for any individual circular element is equalto the total allowable movement of a dial indicator fixed in aposition normal to the true geometric shape of the featuresurface when the part is rotated 360 degrees about the datum

axis. The tolerance limit is applied independently to eachindividual measuring position along the feature surface.

NOTE: Circular runout in this example willonly control variation in the 2-dimensionalcircular elements of the surface (circularity and

coaxiality) not the entire feature surface

Machinecenter

Machinecenter

BA

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As Shownon Drawing

50 +/-0.25

Circular Runout(Surface Related to Datum Surface and Axis)

o360 Part

Rotation

0+ -

Datum axis B


The tolerance zone for any individual circular element isequal to the total allowable movement of a dial indicator fixedin a position normal to the true geometric shape of thefeature surface when the part is located against the datum

surface and rotated 360 degrees about the datum axis. Thetolerance limit is applied independently to each individual

measuring position along the feature surface.

Means This:

A


When measuring circular runout,the indicator must be reset whenrepositioned along the feature

surface.

Collet or Chuck

Stop collar

0.75 A B

Datum plane A

B

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0+

Full IndicatorMovement

Total

Tolerance

MaximumReading

MinimumReading

Full PartRotation

-

0+ -

Total Runout

Maximum Minimum

When measuring total runout, the indicator is moved in a straight line along the feature surfacewhile the part is rotated about the datum axis. It is also acceptable to measure total runout byevaluating an appropriate number of individual circular elements along the surface while the partis rotated about the datum axis. Because the tolerance value is applied to the entire surface, theindicator must not be reset to zero when moved to each measuring position. In this example,total runout can be used to measure surface profile (overall form) and surface wobble (overallorientation).

IndicatorPath

Total runout can only be applied on an

RFS basis and cannot be modified toMMC or LMC.

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Full PartRotation

50 +/- 2o o

As Shownon Drawing

A

50 +/-0.25

0.75 A

Means This:

Datum axis A

0+-

The tolerance zone for the entire angled surface isequal to the total allowable movement of a dialindicator positioned normal to the true geometricshape of the feature surface when the part is

rotated about the datum axis and the indicator ismoved along the entire length of the feature

surface.0

+-

NOTE: Unlike circular runout, the use of total runoutwill provide 3-dimensional composite control of thecumulative variations of circularity, coaxiality,

angularity, taper and profile of the angled surface

Total Runout(Angled Surface to Datum Axis)

Collet or Chuck

When measuring total runout, theindicator must not be reset whenrepositioned along the featuresurface.

(applies to the entire feature surface)Allowable indicator reading = 0.75 max.

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0+-

Total Runout(Surface Perpendicular to Datum Axis)

As Shownon Drawing

A

50 +/-0.25

0.75 A

35

10

0+-

Datum axis AFull Part

Rotation

35

10

Means This:

NOTE: The use of total runout in this examplewill provide composite control of the cumulativevariations of perpendicularity (wobble) andflatness (concavity or convexity) of the featuresurface.

The tolerance zone for the portion of the feature surfaceindicated is equal to the total allowable movement of a dialindicator positioned normal to the true geometric shape of thefeature surface when the part is rotated about the datum axisand the indicator is moved along the portion of the featuresurface within the area described by the basic dimensions.

When measuring total runout, the indicatormust not be reset when repositioned along thefeature surface.

(applies to portion of feature surface indicated)

Allowable indicator reading = 0.75 max.

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Runout Control Quiz


Total runout is a 2-dimensional control.1.

Runout tolerances are used on rotating parts.

Total runout tolerances should be applied at MMC.

Runout tolerances can be applied to surfaces at right

angles to the datum reference.

2.

3.

4.

5.

Circular runout tolerances apply to single elements .

6. Circular runout tolerances are used to control an entirefeature surface.

Runout tolerances always require a datum reference.7.

Circular runout and total runout both control axis to

surface relationships.8.

Circular runout can be applied to control taper of a part.9.

Total runout tolerances are an appropriate way to limit

wobble of a rotating surface.10.

Runout tolerances are used to control a features size.11.

Total runout can control circularity, straightness, taper,

coaxiality, angularity and any other surface variation.12.

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Notes

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Notes

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Fixed andFloating

FastenerExercises

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2x M10 X 1.5(Reference)

BA

?.?

2x 10.50 +/- 0.25

M Calculate Required

Positional Tolerance

0.5

2x ??.?? +/- 0.25

M

CalculateNominal Size

A

B

T = H - FH = Minimum Hole Size = 10.25F = Max. Fastener Size = 10

T = 10.25 -10T = ______

Floating Fasteners

H = F +TF = Max. Fastener Size = 10

T = Positional Tolerance = 0.50

H = 10 + 0.50H = ______

In applications where two or more mating details are assembled, and all parts

have clearance holes for the fasteners, the floating fastener formulashownbelow can be used to calculate the appropriate hole sizes or positional tolerance

requirements to ensure assembly. The formula will provide a zero-interference fit

when the features are at MMC and at their extreme of positional tolerance

H= Min. diameter of clearance hole

F= Maximum diameter of fastenerT= Positional tolerance diameter

H=F+T or T=H-F

General Equation Applies toEach Part Individually

remember: the size tolerance must beadded to the calculated MMC hole size toobtain the correct nominal value.

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BA

0.25

2x 10.50 +/- 0.25

M

0.5

2x 10.75 +/- 0.25

M

A

B

Floating Fasteners

REMEMBER!!! All Calculations Apply at MMC



H=F+T or T=H-F

General Equation Applies toEach Part Individually

T = H - FH = Minimum Hole Size = 10.25F = Max. Fastener Size = 10

T = 10.25 -10T = 0.25

Calculate Required

Positional Tolerance

F = Max. Fastener Size = 10


H = 10 + .5H = 10.5 Minimum

H = F +T

In applications where two or more mating details are assembled, and all parts

have clearance holes for the fasteners, the floating fastener formulashownbelow can be used to calculate the appropriate hole sizes or positional tolerance

requirements to ensure assembly. The formula will provide a zero-interference fit

when the features are at MMC and at their extreme of positional tolerance


CalculateNominal Size

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F = Max. Fastener Size = 10.00



B

A

0.8

2x ??.?? +/- 0.25

M

Calculate RequiredClearance Hole Size.

2X M10 X 1.5

A

B

Fixed Fasteners

H = 10.00 + 2(0.8)H = _____



H=F+2T or T=(H-F)/2

General Equation Used When

Positional Tolerances Are Equal

In fixed fastenerapplications where two mating details have equal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerance required to

ensure assembly. The formula provides a zero-interference fit when the features

are at MMC and at their extreme of positional tolerance. (Note that in this example

the positional tolerances indicated are the same for both parts.)

0.8 M 10P

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS USED

Nominal Size

(MMC For Calculations)

H = F + 2T

remember: the size tolerancemust be added to the calculatedMMC size to obtain the correct

nominal value.

10

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B

A

2x 11.85 +/- 0.25

0.8 M


A

B





Fixed Fasteners

H = F + 2TF = Max. Fastener Size = 10.00


H = 10.00 + 2(0.8)H = 11.60 Minimum



H=F+2T or T=(H-F)/2



0.8 M 10P


2X M10 X 1.5Nominal Size



nominal value.


10

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B

A

2x 11.85 +/- 0.25

0.8 M


A

B





Fixed Fasteners

H = F + 2TF = Max. Fastener Size = 10


H = 10 + 2(0.8)H = 11.6 Minimum



H=F+2T or T=(H-F)/2



0.8 M 10P





nominal value.


10

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B

A

0.5

2x 11.25 +/- 0.25

M Calculate RequiredPositional Tolerance .(Both Parts)

A

B

In applications where two mating details are assembled, and one part hasrestrained fasteners, the fixed fastener formulashown below can be used tocalculate appropriate hole sizes and/or positional tolerances required to ensure

assembly. The formula will provide a zero-interference fit when the features are

at MMC and at their extreme of positional tolerance. (Note: in this example the

resultant positional tolerance is applied to both parts equally.)

Fixed Fasteners

T = (H - F)/2H = Minimum Hole Size = 11


T = (11 - 10)/2T = 0.50



H=F+2T or T=(H-F)/2



2X M10 X 1.5

0.5 M 10P


Nominal Size



10

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B

A

0.5

2x ??.?? +/- 0.25

M


A

B

Fixed Fasteners

H = Min. diameter of clearance hole

F = Maximum diameter of fastener

T1= Positional tolerance (Part A) T2=Positional tolerance (Part B)

H=F+(T1 + T2)

General Equation Used WhenPositional Tolerances Are Not Equal


T1 = Positional Tol. (A) = 0.50

T2 = Positional Tol. (B) = 1

H = 10+ (0.5 + 1)H = ____

H=F+(T1 + T2)

In fixed fastener applications where two mating details have unequal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerances required to



the positional tolerances indicated are not equal.)





10

1 M 10P

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B

A

0.5

2x 11.75 +/- 0.25

M


A

B

In fixed fastener applications where two mating details have unequal positionaltolerances, the fixed fastener formulashown below can be used to calculate theappropriate minimum clearance hole size and/or positional tolerances required to



the positional tolerances indicated are not equal.)

Fixed Fasteners


T1 = Positional Tol. (A) = 0.5

T2 = Positional Tol. (B) = 1

H = 10 + (0.5 + 1)H = 11.5 Minimum


H = Min. diameter of clearance hole

F = Maximum diameter of fastener

T1= Positional tolerance (Part A) T2=Positional tolerance (Part B)

H= F+(T1 + T2)

General Equation Used WhenPositional Tolerances Are Not Equal

H=F+(T1 + T2)

1 M 10P





10

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D

P

H F

A

B

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS NOT USED

2x 10.05 +/-0.05

B

A

0.5 M2x ??.?? +/-0.25Calculate

Nominal Size

0.5 M

In applications where a projected tolerance zone is notindicated, it isnecessary to select a positional tolerance and minimum clearance hole sizecombination that will allow for any out-of-squareness of the feature containing the

fastener. The modified fixed fastener formulashown below can be used to

calculate the appropriate minimum clearance hole size required to ensure

assembly. The formula provides a zero-interference fit when the features are atMMC and at the extreme positional tolerance.

Fixed Fasteners

H = 10.00 + 0.5 + 0.5(1 + 2(15/20))

H = __________

H= F + T1 + T2 (1+(2P/D))

remember: the size tolerance must be

added to the calculated MMC hole size toobtain the correct nominal value.

H= Min. diameter of clearance holeF= Maximum diameter of pinT1= Positional tolerance (Part A)

T2= Positional tolerance (Part B)

D= Min. depth of pin (Part A)P= Maximum projection of pin

F = Max. pin size = 10

T1 = Positional Tol. (A) = 0.5T2 = Positional Tol. (B) = 0.5 D

= Min. pin depth = 20. P= Max. pin projection = 15

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D

P

H F

A

B

H= Min. diameter of clearance holeF= Maximum diameter of pinT1= Positional tolerance (Part A)

T2= Positional tolerance (Part B)

D= Min. depth of pin (Part A)P= Maximum projection of pin

APPLIES WHEN A PROJECTED TOLERANCE ZONE IS NOT USED

2x 10.05 +/-0.05

B

A

0.5 M2x 12 +/-0.25Calculate

Nominal Size

0.5 M

F = Max. pin size = 10

T1 = Positional tol. (A) = 0.5T2 = Positional tol. (B) = 0.5 D

= Min. pin depth = 20 P= Max. pin projection = 15

H= F + T1 + T2 (1+(2P/D))

H = 10 + 0.5 + 0.5(1 + 2(15/20))

H = 11.75 Minimum

In applications where a projected tolerance zone is notindicated, it isnecessary to select a positional tolerance and minimum clearance hole sizecombination that will allow for any out-of-squareness of the feature containing the

fastener. The modified fixed fastener formulashown below can be used to

calculate the appropriate minimum clearance hole size required to ensure

assembly. The formula provides a zero-interference fit when the features are atMMC and at the extreme positional tolerance.

Fixed Fasteners

H= F + T1 + T2 (1+(2P/D))


remember: the size tolerance must be

added to the calculated MMC hole size toobtain the correct nominal value.

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Answers to Quizzesand Exercises

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Rules and Definitions Quiz

1. Tight tolerances ensure high quality and performance.

2. The use of GD&T improves productivity.

3. Size tolerances control both orientation and position.

4. Unless otherwise specified size tolerances control form.

5. A material modifier symbol is not required for RFS.

6. A material modifier symbol is not required for MMC.

7. Title block default tolerances apply to basic dimensions.

8. A surface on a part is considered a feature.

9. Bilateral tolerances allow variation in two directions.

10. A free state modifier can only be applied to a tolerance.

11. A free state datum modifier applies to assists & rests.

12. Virtual condition applies regardless of feature size.

FALSE

TRUE

FALSE

TRUE

TRUE

FALSE

FALSE

TRUE

TRUE

TRUE

FALSE

FALSE

Questions #1-12 True or False

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Material Condition Quiz

Internal Features MMC LMC

External Features MMC LMC

.890

.885

.895

.890

23.45 +0.05/-0.25

10.75 +0.25/-0

123. 5 +/-0.1

23.45 +0.05/-0.25

10.75 +0/-0.25

123. 5 +/-0.1

Calculate appropriate values

Fill in blanks

10.75 11

23.2 23.5

123.4 123.6

.890 .895

10.75 10.5

23.5 23.2

123.6 123.4

.890 .885

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1. Datum target areas are theoretically exact.

2. Datum features are imaginary.

3. Primary datums have only three points of contact.

4. The 6 Degrees of Freedom are U/D, F/A, & C/C.

5. Datum simulators are part of the gage or tool.

6. Datum simulators are used to represent datums.

8. All datum features must be dimensionally stable.

9. Datum planes constrain degrees of freedom.

10. Tertiary datums are not always required.

12. Datums should represent functional features.

Datum Quiz

11. All tooling locators (CDs) are used as datums.

Questions #1-12 True or False

7. Datums are actual part features.

FALSE

FALSE

FALSE

FALSE

TRUE

TRUE

FALSE

TRUE

TRUE

TRUE

FALSE

TRUE

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Datum Quiz

The three planes that make up a basic datum reference

frame are called primary, secondary, and tertiary.

An unrestrained part will exhibit 3-linearand 3-rotationaldegreesof freedom.

A planar primary datum plane will restrain 1-linearand 2-rotationaldegrees of freedom.

The primary and secondary datum planes together will restrain fivedegreesof freedom.

The primary, secondary and tertiary datum planes together will

restrain all sixdegrees of freedom.

The purpose of a datum reference frame is to restrain movementof a part in a gage or tool.

A datum must be functional, repeatable, and coordinated.

A datum featureis an actual feature on a part.

A datumis a theoretically exact point, axis or plane.

A datum simulatoris a precise surface used to establish asimulated datum.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


primary

secondary

tertiary 3-rotational

3-linear

2-rotational

datum

three

two

one

six

functional

restrain movement coordinated

datum simulator

datum feature

repeatablefive

1-linear

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Straightnessand circularityare individual line or circularelement (2-D) controls.

Form Control Quiz

The four form controls are straightness, flatness,circularity, and cylindricity.

Rule #1 states that unless otherwise specified a feature of

size must have perfect format MMC.

Flatnessand cylindricityare surface (3-D) controls.

Circularity can be applied to both straightand taperedcylindricalparts.

1.

2.

3.

4.

5.

Form controls require a datum reference.

Form controls do not directly control a features size.

A features form tolerance must be less than its size

tolerance.

Flatness controls the orientation of a feature.

Size limits implicitly control a features form.

6.

7.

8.

9.

10.

FALSE

TRUE

TRUE

TRUE

FALSE



straightness

flatness

circularity

cylindricity

perfect form

straight tapered profile

true position

angularity

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Orientation Control Quiz

The three orientation controls are angularity, parallelism,and perpendicularity.

1.

2.

3.

4.

5.

A datum referenceis always required when applying any ofthe orientation controls.

Perpendicularityis the appropriate geometric tolerance when

controlling the orientation of a feature at right angles to a datumreference.

Orientation tolerances indirectly control a features form.

Mathematically all three orientation tolerances are identical.

Orientation tolerances do not control the locationof a feature.


6. TRUE

Orientation tolerance zones can be cylindrical.

Parallelism tolerances do not apply to features of size.

To apply an angularity tolerance the desired angle must

be indicated as a basic dimension.

7.

8.

9.

10.

TRUE

FALSE

FALSE

TRUE

To apply a perpendicularity tolerance the desired anglemust be indicated as a basic dimension.


angularity

perpendicularity

parallelism

datum reference

identical

location

profile

datum feature

datum target

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Runout Control Quiz


TRUE

Total runout is a 2-dimensional control.1.

Runout tolerances are used on rotating parts.

Total runout tolerances should be applied at MMC.

Runout tolerances can be applied to surfaces at right

angles to the datum reference.

2.

3.

4.

5.

FALSE

Circular runout tolerances apply to single elements .

FALSE

TRUE

TRUE

6. Circular runout tolerances are used to control an entirefeature surface.

Runout tolerances always require a datum reference.7.

Circular runout and total runout both control axis to

surface relationships.8. TRUE

Circular runout can be applied to control taper of a part.9. FALSE

Total runout tolerances are an appropriate way to limit

wobble of a rotating surface.10.

Runout tolerances are used to control a features size.11.

Total runout can control circularity, straightness, taper,

coaxiality, angularity and any other surface variation.12. TRUE

FALSE

TRUE

TRUE

FALSE

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In composite profile applications, the tolerance shown in the upper

segment of the feature control frame applies only to the locationof thefeature.


The two types of profile tolerances are profile of a line, and

profile of a surface.1.

2.

3.

4.

5.

Profile tolerances can be used to control the location, form,orientation, and sometimes size of a feature.

Profile tolerances can be applied bilateralor unilateral.

Profile of a linetolerances are 2-dimensional controls.

Profile of a surfacetolerances are 3-dimensional controls.


6. Composite Profilecan be used when different tolerances arerequired for location and form and/or orientation.

7. When using profile tolerances to control the location and/or orientation of

a feature, a datum referencemust be included in the feature controlframe.

8. When using profile tolerances to control form only, a datumreferenceis not required in the feature control frame.

9.

profile of a linedatum reference

composite profile bilateral

location form

primary datum

true geometric counterpart

orientationprofile of a surface

unilateral

virtual condition

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6.


Profile tolerances always require a datum reference.


1.

Profile of a surface tolerance is a 2-dimensional control.

Profile of a line tolerances should be applied at MMC.

Profile tolerances can be applied to features of size.

2.

3.

4.

5.

Profile of a surface tolerance should be used to control

trim edges on sheet metal parts.

Profile tolerances can be combined with other geometric

controls such as flatness to control a feature.

Profile of a line tolerances apply to an entire surface.7.

Profile of a line controls apply to individual line elements.8.

Profile tolerances only control the location of a surface.9.

Composite profile controls should be avoided because

they are more restrictive and very difficult to check.10.

Profile tolerances can be applied either bilateral or

unilateral to a feature.

11.

Profile tolerances can be applied in both freestate and

restrained datum conditions.12.

Tolerances shown in the lower segment of a composite

profile feature control frame control the location of afeature to the specified datums.

13.

TRUE

FALSE

FALSE

FALSE

TRUE

TRUE

TRUE

FALSE

FALSE

FALSE

TRUE

TRUE

FALSE

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True Position Quiz


TRUE

Positional tolerances are applied to individual or patterns

of features of size.1.

Cylindrical tolerance zones more closely represent the

functional requirements of a pattern of clearance holes.

True position tolerances can control a features size.

Positional tolerances are applied on an MMC, LMC, orRFS basis.

2.

3.

4.

5.

FALSE

True position tolerance values are used to calculate the

minimum size of a feature required for assembly.

TRUE

TRUE

6. Composite true position tolerances should be avoidedbecause it is overly restrictive and difficult to check.

Composite true position tolerances can only be applied

to patterns of related features.7.

The tolerance value shown in the upper segment of a

composite true position feature control frame applies


8. TRUE

Positional tolerances can be used to control circularity

9. FALSE

10.

11. TRUE

FALSE

TRUE

FALSE

TRUE

The tolerance value shown in the lower segment of acomposite true position feature control frame applies


True position tolerances can be used to control center

distance relationships between features of size.

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Positional tolerance zones can be rectangular, cylindrical,or spherical

1.

2.

3.

4.

5.

Basic dimensionsare used to establish the true (theoreticallyexact) position of a feature from specified datums.

Positional tolerancing is a 3-dimensionalcontrol.

Positional tolerance can apply to the axisor surface boundaryof a feature.

Fixedand floatingfastener equations are used to determineappropriate clearance hole sizes for mating details

6.

7.

Projectedtolerance zones are recommended to prevent fastenerinterference in mating details.

8.

projected3-dimensional

surface boundary floating

location fixed

basic dimensions

maximum material

cylindricalpattern-locating rectangular

feature-relating

True Position Quiz


The tolerance shown in the upper segment of a composite trueposition feature control frame is called the pattern-locatingtolerance zone.

The tolerance shown in the lower segment of a composite true

position feature control frame is called the feature-relatingtolerance zone.

9. Functional gaging principles can be applied when maximummaterialcondition is specified

axis

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Virtual andResultant

ConditionBoundaries

Internal and ExternalFeatures (MMC Concept)

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Virtual Condition BoundaryInternal Feature (MMC Concept)

12.5 Virtual Condition Boundary

13.5 MMC Size of Feature

1 Applicable Geometric Tolerance

Calculating Virtual Condition

1 A B CM

14 +/- 0.5

C

BXX.X

XX.X

A

As Shown on Drawing

Axis Location ofMMC Hole Shownat Extreme Limit

Boundary of MMC HoleShown at Extreme Limit

1 PositionalTolerance Zone at

MMC

True (Basic)Position of Hole


Other PossibleExtreme Locations

Virtual ConditionInner Boundary

Maximum Inscribed

Diameter( )

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Resultant Condition BoundaryInternal Feature (MMC Concept)

1 A B CM

14 +/- 0.5

C

BXX.X

XX.X

A

16.5 Resultant Condition Boundary

14.5 LMC Size of Feature

2 Geometric Tolerance (at LMC)

Calculating Resultant Condition (Internal Feature)

As Shown on Drawing

Axis Location ofLMC Hole Shownat Extreme Limit

Boundary of LMC HoleShown at Extreme Limit


LMC




Resultant ConditionOuter Boundary

Minimum CircumscribedDiameter( )

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Virtual Condition BoundaryExternal Feature (MMC Concept)

15.5 Virtual Condition Boundary

14.5 MMC Size of Feature

1 Applicable Geometric Tolerance

Calculating Virtual Condition

1 A B CM

14 +/- 0.5

C

BXX.X

XX.XX

A

As Shown on Drawing

Axis Location ofMMC Feature Shownat Extreme Limit

Boundary of MMC FeatureShown at Extreme Limit


MMC

True (Basic)Position of Feature



Virtual ConditionOuter Boundary

Minimum CircumscribedDiameter( )

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Resultant Condition BoundaryExternal Feature (MMC Concept)

1 A B CM

14 +/- 0.5

C

BXX.X

XX.X

A

11.5 Resultant Condition Boundary

13.5 LMC Size of Feature

2 Geometric Tolerance (at LMC)

Calculating Resultant Condition (External Feature)

As Shown on Drawing

Axis Location ofLMC Feature Shownat Extreme Limit

Boundary of LMC featureShown at Extreme Limit


LMC


True (Basic)

Position of Feature


Resultant ConditionInner Boundary

Maximum Inscribed

Diameter( )

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Extreme Variations of Form

Allowed By Size Tolerance25.125

25(MMC)

25.1(LMC)

25.1(LMC)

25(MMC)

25.1(LMC)

MMC PerfectForm Boundary

Internal Feature of Size

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Allowed By Size Tolerance25

24.9

25

(MMC)24.9(LMC)

24.9(LMC)


25

(MMC)

24.9(LMC)

External Feature of Size

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Allowed By Size Tolerance25.1

25

25

24.9

25(MMC)

25.1

(LMC)

25.1

(LMC)

25

(MMC)24.9

(LMC)

24.9

(LMC)

25(MMC)

25.1

(LMC)


25(MMC)

24.9

(LMC)

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EN

D

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Notes

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Notes

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Notes

2-gd & t

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