Placing Datums

Learning Objectives

After studying this chapter, you will be able to:❍ Explain the purpose of datums.❍ Defi ne common terms related to datum features.❍ Interpret information provided by datum feature symbols.❍ Describe methods for representing datum surfaces on drawings.❍ Explain how to establish datum reference frames.❍ Identify the degrees of freedom of a part.❍ Explain how to establish datum targets.❍ Identify datum target points, areas, and lines.❍ Describe methods for representing datum axes on drawings.❍ Describe methods for representing datum center planes on drawings.

Technical TermsActual mating envelopeCoaxialCoaxial datum featuresCoplanar surfacesDatum axisDatum featureDatum feature simulatorDatum feature symbolDatum planeDatum reference frame (DRF)Datum reference orderDatum target lineDatum targetsDatumsDegrees of freedomHigh pointsNormal

77

Order of precedencePrimary datumPrimary datum planeRotationalSecondary datumSecondary datum planeSimulated datumSimulated datum axisSimulated datum planeTangent planeTertiary datumTertiary datum planeThree degrees of rotationThree degrees of translationTranslational

Datums are considered theoretically perfect planes, surfaces, points, lines, or axes. Datums are placed on drawings as requirements for referencing features of an object. These datums are used by the machinist, toolmaker, or quality control inspector to ensure that the part is in agreement with the drawing.

Datums

Chapter 3

This sample chapter is for review purposes only. Copyright © The Goodheart-Willcox Co., Inc. All rights reserved.

78 Geometric Dimensioning and Tolerancing

This chapter is designed to help you identify and read information related to datums on drawings. This chapter also covers the specifications for properly placing datum-related symbols on drawings. This information is covered without regard to specific inspection and tooling techniques. Advanced instruction is recommended after you gain a solid understanding of the basic fundamentals presented here.

DatumsDatumsDatums are planes, points, lines, or axes from where measurements are made.

A datum is assumed to be exact. A datum feature is an actual feature on a part, such as a surface, that is used to establish a datum. A datum is the true geometric counterpart of a datum feature. Datums are placed on drawings as requirements for referencing features of an object. Location and size dimensions are established from the datum. Examples of datums in manufacturing are machine tables, surface plates, gauge surfaces, surface tables, and specially designed rotation devices. These are referred to as datum feature simulators and are used to contact the datum features and establish what are known as the simulated datums. The datum feature simulator is an imperfect physical feature of adequate accuracy in which the errors are considered irrelevant. A datum feature simulator can be tooling, such as a surface plate or angle block, or a set of points established on the datum feature using a coordinate measuring machine.

There are many concepts to keep in mind when datums are established, including the function of the part or feature, manufacturing processes, methods of inspection, the shape of the part, relationship to other features, assembly considerations, and design requirements. Datum features should be selected to match on mating parts, to be easily accessible, and to be of adequate size to permit control of the datum requirements.

Datum Feature SymbolDatum Feature SymbolThe datum feature symbol is placed on the drawing to identify the features of

the object that are specified as datums and referred to as datum features. The datum feature symbol identifies physical features and shall not be applied to centerlines, center planes, or axes. This symbol is placed in the following locations on a drawing:

• On the outline of a feature surface in the view where the surface appears as an edge.

• On a leader line directed to the surface. The leader line can be shown as a dashed line if the datum feature is not on the visible surface.

• On an extension line projecting from the edge view of a surface, clearly separated from the dimension line.

• On a chain line next to a partial datum surface.

• On the dimension line or an extension of the dimension line of a feature of size when the datum is an axis or center plane.

• On the outline of a cylindrical feature or an extension line of the feature outline, separated from the size dimension, when the datum is an axis.

• Above or below and attached to a feature control frame.

Chapter 3 Datums 79

Datum feature symbols are commonly drawn using thin lines with the symbol size related to the drawing lettering height. The triangular base on the datum feature symbol can be filled or unfilled, depending on the company or school preference. The filled base helps easily locate these symbols on the drawing. Each datum feature on a part requiring identification must be assigned a different datum identification letter. Uppercase letters of the alphabet, except the letters I, O, and Q, are used for datum feature symbol letters. These letters are not used because they can be mistaken for numbers. Example 3-1 shows the specifications for drawing a datum feature symbol.

Symbol Specifications Examples

H = Letter height

2H

2H H

H60°

Anyneededlength

Optional shoulder

Identification letter

Filled Unfilled

Example 3-1. Drawing specifi cations for datum feature symbols.

Datum FeatureDatum FeatureThe datum feature is the actual feature of the part that is used to establish the

datum. When the datum feature is a surface, it is the actual surface of the object that is identified as the datum. Look at the magnified view of a datum feature placed on the simulated datum in Example 3-2. Study the following terms:

Actual mating envelope: The smallest size that can be contracted about an external feature or the largest size that can be expanded within an internal feature.

Datum feature: The actual feature of the part (such as a surface).

Datum feature simulator: The opposite shape of the datum feature. The datum feature simulator is one of two types:

1. The theoretical datum feature simulator is a perfect boundary used to establish a datum from a specifi ed datum feature.

2. The physical datum feature simulator is the physical boundary used to establish a simulated datum from a specifi ed datum feature. The manufacturing inspection equipment associated with the datum feature or features is used as the physical object to establish the simulated datum or datums. Physical datum feature simulators represent the theoretical datum feature simulators during manufacturing and inspection.


A datum feature simulator can be one of the following:

• Maximum material boundary (MMB).

• Least material boundary (LMB).

• The actual mating envelope.

• A tangent plane.

• A mathematically defined contour.

Datum feature simulators shall have the following requirements:

• Perfect form.

• Basic orientation to each other for all the datum references in the feature control frame.

• Basic location relative to other datum feature simulators for all the datum references in the feature control frame, unless a translation modifier or movable datum target symbol is specified.

• Movable location when a translation modifier or movable datum target symbol is specified.

In actual practice, measurements cannot be made from theoretical datum features or datum feature simulators. This is why manufacturing inspection equipment is of the highest quality for making measurements and verifying dimensions even though they are not perfect.

Datum plane: The theoretically exact plane established by the simulated datum of the datum feature.

Simulated datum: A point, axis, line, or plane consistent with or resulting from processing or inspection equipment, such as a surface plate, inspection table, gage surface, or a mandrel. The simulated datum plane in Example 3-2 is the plane derived from the physical datum feature simulator and coincides with the datum plane when the datum plane is in contact with the simulated datum plane.

Surface of manufacturingor verification equipment

Datum planeTheoretical datum feature simulator in

contact with simulated datum plane

Part

Physical datumfeature simulator

Simulated datum planePlane derived from the physicaldatum feature simulator

Datumfeature

Example 3-2. Datum plane, datum feature, and the simulated datum plane. Datums are to be treated as if they are perfect even though they may not be perfect.

Chapter 3 Datums 81

Angled Surface

Datum feature symbolplaced on edge viewof surface or extensionline from edge view

Surface datum feature symbolsmust be clearly separated from

dimension line arrowheads

The Drawing The Meaning The Drawing The Meaning

Example 3-3. Methods for placing datum feature symbols on surface datums. The datum feature symbol is placed on the edge view or on an extension line in the view where the surface appears as a line. The datum feature symbol can also be placed on a leader line directed to the surface. The leader line can be shown as a dashed line if the datum feature is not on the visible surface.

Tangent plane: A plane that contacts the high points of the specified feature surface.

When a surface is used to establish a datum plane on a part, the datum feature symbol is placed on the edge view of the surface or on an extension line in the view where the surface appears as a line. Refer to Example 3-3. A leader line can also be used to connect the datum feature symbol to the view in some applications.


Geometric Control of Datum SurfaceThe datum surface can be controlled by a geometric tolerance such as flatness,

straightness, angularity, perpendicularity, or parallelism. Measurements taken from a datum plane do not take into account any variations of the datum surface from the datum plane. Any geometric tolerance applied to a datum should only be specified if the design requires the control. Example 3-4 shows the feature control frame and datum feature symbol together. Example 3-5 is a magnified representation that shows the meaning of the drawing in Example 3-4.

The geometric tolerance of 0.1 is specified in the feature control frame in Example 3-4. The maximum size that the part can be produced is the upper limit of the dimensional tolerance, or MMC. The MMC is 12.5 + 0.3 = 12.8. The minimum size that the part can be produced is the lower limit of the dimensional tolerance, or LMC. The LMC is 12.5–0.3 = 12.2.

Example 3-4. A feature control frame and datum feature symbol.

12.2minimum

12.8maximum

0.1 geometric tolerance

Datumplane A

Example 3-5. The meaning of the drawing in Example 3-4.

The Datum Reference Frame ConceptThe Datum Reference Frame ConceptDatum features are selected based on their importance to the design of the part.

Generally three datum features are selected that are perpendicular to each other. These three datums are called the datum reference frame (DRF). The datums that make up the datum reference frame are referred to as the primary datum, secondary datum, and tertiary datum. As their names imply, the primary datum is the most important, followed by the other two in order of importance. Refer to Example 3-6and notice how the direction of measurement is projected to various features on the object from the three common perpendicular planes of the datum reference frame. The primary datum must be inspected first, the secondary datum inspected second, and the tertiary datum inspected third regardless of the letters. For example, the letters in the feature control frame might be C, B, A, where C is the primary datum, B is the secondary datum, and A is the tertiary datum.

The datum feature symbols on the drawing relate to the datum features on the part. Notice datum feature symbols A, B, and C as you look at Example 3-7. Also, notice the datum reference order A, B, C in the feature control frame. The datum reference in the feature control frame tells you that Datum A is primary, Datum B is

Chapter 3 Datums 83

Mutuallyperpendicular planes

Direction ofmeasurements

Part

90°

90°

90°

Example 3-6. The datum reference frame.

Example 3-7. The datum feature symbols on the drawing relate to the datum features on the part. Look at this drawing as you refer to Examples 3-8 through 3-10 and the related discussion in the text.

secondary, and Datum C is tertiary. The geometric tolerance that controls a feature or features relative to datums must include one or more datum references, as shown with the position tolerance relating the location of the two holes to Datums A, B, and C in Example 3-7. An explanation of the symbols on the drawing in Example 3-7 follows.


The part is then positioned against the secondary datum, as shown in Example 3-9.With the part held against the primary and secondary datums, dimensions can be verified from the secondary datum inspection table surface to features that are dimensioned from the secondary datum.

Primary datum plane

Example 3-8. The surface of the part labeled as the primary datum is placed on the surface of the inspection table.

Secondary datum plane

90°

Example 3-9. The part is now positioned against the secondary datum.

The surface of the part labeled as the primary datum is placed on the surface of an inspection table or manufacturing inspection equipment, as shown in Example 3-8.Now measurements can be made from the primary datum inspection table surface to features that are dimensioned from the primary datum.

Chapter 3 Datums 85

Tertiary datum plane

90°

90°

Example 3-10. The tertiary datum is established to totally confi ne the part in the datum reference frame.

Finally, the tertiary datum is established to totally confine the part in the datum reference frame, as shown in Example 3-10. Now, with the part totally confined in the datum reference frame, all measurements made from the simulated datum planes to related features on the part are reliable and have the same origin every time.

The surfaces of this inspection equipment are the simulated datums. The datums are the assumed exact planes established by the true geometric counterpart of the datum features. Measurements cannot be made from the datums, because they are only assumed to exist, but do not actually exist. The machine tables, surface plates, or inspection tables are of such high quality that they are used to act as the datums where measurements are taken from and where dimensions are verified. In this way each dimension always originates from the same reliable location. Dimensions are never taken or verified from one surface of the part to another. Dimensions always originate from the datum planes.

Refer again to Example 3-7 for review. Notice again the feature control frame associated with the 2X ∅8.0-8.2 dimension. The last three compartments in the feature control frame provide the datum reference. This is known as the datum order of precedence. The primary datum (A) is given first followed by the secondary (B) and tertiary (C). For instructional purposes, this example labels datum feature symbols conveniently as A, B, and C. In industry and later in this book, other letters are used to identify datums, such as D, E, F, or L, M, N, or X, Y, Z. The letters O, Q, and I are avoided because they may resemble numbers.

As the part is positioned on the datum reference frame, as illustrated in Example 3-8 through Example 3-10, there must be three points anywhere on the primary datum feature in contact with the first datum plane. At least two points of contact are required to establish the secondary datum feature against its datum plane. At least one point must contact the datum plane on the tertiary datum


feature. These points of contact, referred to as high points, take into account possible irregularity in the manufacture of the part within design limits. Positioning the part in the datum reference frame in this manner ensures a common basis for measurements.

Degrees of FreedomAll parts have six degrees of freedom. There are three translational degrees

of freedom and three rotational degrees of freedom. The term degrees of freedommeans the number of coordinates it takes to exclusively control the position of a part. The term translational refers to uniform movement without rotation, and the term rotational refers to movement around an axis.

Considering the datum reference frame in Example 3-11, the part can move without rotation in each of the three directions from the mutually perpendicular planes. This is called the three degrees of translation. The part can also rotate about each of the axes, which is referred to as the three degrees of rotation.

Refer again to Example 3-11 and notice that the three translational degrees of freedom are labeled x, y, and z. The three rotational degrees of freedom are labeled u,v, and w. The following demonstrates the degrees of freedom related to the primary, secondary, and tertiary datums:

The primary datum plane constrains three degrees of freedom:• One translational in z.• One rotational in u.• One rotational in v.

Datum axis

Secondary datumTertiary datum

Primary datum

Datumaxis

Part

Datumaxis

Three Mutually Perpendicular Planes

Example 3-11. All parts have six degrees of freedom. The three translational degrees of freedom for this part are labeled x, y, and z. The three rotational degrees of freedom for this part are labeled u, v, and w.

Chapter 3 Datums 87

The secondary datum plane constrains two degrees of freedom:• One translational in y.• One rotational in w.

The tertiary datum plane constrains one degree of freedom:• One translational in x.

Multiple Datum Reference FramesDepending on the functional requirements of a part, more than one datum

reference frame can be established. In Example 3-12, datums X, Y, and Z constitute one datum reference frame, while datums L, M, and Y establish a second reference frame. The relationship between the two datum reference frames is controlled by the angularity tolerance on datum feature L. Datum M is the axis of the large hole to which the datum feature symbol is connected. Datum axes are discussed later in this chapter.

For parts with inclined datum features, as in Example 3-12, the datum feature simulator plane is oriented at the basic angle of the datum feature. The related datum reference frame plane passes through the vertex of the basic angle and is mutually perpendicular to the other datum planes.

Represents datum axis

Example 3-12. Multiple datum reference frames.


Datum Features Specified IndividuallyWhen multiple datum reference frames exist and features need to be positioned

to different datums individually, then a note can be placed next to the datum feature symbols identifying how many datum features are to be considered separately. For example, if there are two separate datum features that are identified with the same datum identification letter, but they need to be considered individually, the note 2X INDIVIDUALLY is placed next to the datum feature symbols. An example of this can be seen on the SAW GUIDE FIXATION BLOCK drawing in the Prints for Print Reading Exercises section on page 433. This drawing has four holes at different angles. The holes on the right side need to be positioned to different datums than the holes on the left side. Instead of calling out two more datums and having to cut another section to show the holes on the left side, the datums are used individually and the locations of two holes on each side are positioned to the two datums individually. Using this method, only two holes are checked for position at a time to different datums.

Datum Target SymbolsDatum Target SymbolsIn many situations it is not possible to establish an entire surface, or entire

surfaces, as datums. When this happens, datum targets can be used to establish datum planes. Datum targets are designated points, lines, or surface areas that are used to establish the datum reference frame. This procedure is especially useful on parts with surface or contour irregularities, such as some sheet metal, sand cast, or forged parts that are subject to bowing or warpage. However, datum targets can be used on most parts. Use datum targets to minimize the variation in the way features are measured. This method can also be applied to weldments where heat can cause warpage.

The datum target symbol is drawn as a circle using thin lines. The circle is divided into two parts with a horizontal line. The bottom half provides the datum reference letter and the specific datum target number on that datum. The top half is left blank if a datum target point or line is identified. When identifying a datum target area, the top half contains the shape and size of the area. The dimension for the datum target area can be placed outside the datum target symbol with a leader and a dot pointing to the upper half if the dimension is too big to fit inside. See Example 3-13. When the datum target area is circular, a diameter symbol precedes the size value. When the datum target area is square, a square symbol precedes the size value. The datum target area can also be rectangular in shape, which is dimensioned with a length and width value, such as 10 X 25. The rectangular dimension is placed outside the datum target symbol and a leader points to the top half of the datum target symbol. A spherical datum target area can be used by placing the spherical diameter symbol in front of the size value. The spherical diameter is generally placed outside the datum target symbol and a leader points to the top half of the datum target symbol. A movable datum target symbol is used to indicate that the datum target is not fixed at its basic location and is free to translate. Refer to Example 3-13.

Chapter 3 Datums 89

Examples

Datum Target Symbol

Movable Datum Target Symbol

Symbol Specifications

H = Letter height

Datum target symbolwithout area size

Datum target symbolswith circular target area

Datum target symbolwith square target area

Datum target symbol withrectangular target area

Movable datumtarget symbol

without area size

Movable datumtarget symbol with

spherical target area

Datum Target number

Target area size, when used

3.5H

0.8H

60°0.3H

Example 3-13. Drawing specifi cations for datum target symbols and example applications.


Symbol Specifications

H = Letter height

Datum Target Point

Datum Target LineDatum Target Line

Dashed leader indicatesopposite side of part

90°

Target area

Target line

2H

On the drawing, the datum target symbol is connected with a leader to the datum target point, line, or area. This leader line generally has no shoulder or arrowhead associated with leaders. Example applications of datum target points and datum target lines are shown in Example 3-14. Example applications of datum target areas are shown in Example 3-15. Additional uses are provided where they relate to specific applications.

Example 3-14. The datum target point and datum target line and examples of their use.

Chapter 3 Datums 91

Square Datum Target Area Rectangular Datum Target Area

Circular Datum Target AreaCircular Datum Target Area

Area notshown

Areashown

Example 3-15. Example applications of datum target areas.


Datum Target PointsDatum planes are established by the datum points as follows:

The primary datum plane must be established by at least three points on the primary datum surface. These points are used to provide stability on the primary plane, similar to a three-legged stool.

The secondary datum plane must be located by at least two points on the related secondary datum surface. Two points provide the required stability for the secondary plane.

The tertiary datum plane must be located by at least one point on the related tertiary datum surface. One point of contact at the tertiary datum plane is all that is required to complete the datum reference frame and provides complete stability of the part in the datum reference frame.

Baseline or chain dimensioning can be used to locate datum target points. The location dimensions must originate from datums. Datum target points are established on the drawing using basic or tolerance dimensions. Established tooling or gauging tolerances apply when datum targets are located with basic dimensions. Datum targets are established on the part with fixtures and with pins. These pins contact the part where the datum targets are specified. Example 3-16 shows a pictorial drawing of the datum target points on the primary, secondary, and tertiary datums.

Three points of contacton primary datum

One point ofcontact ontertiary datum

Two points of contacton secondary datum

Example 3-16. Datum target points on primary, secondary, and tertiary datums.

Chapter 3 Datums 93

As you have seen, each datum target point is identified with a datum target symbol. The information inside the datum target symbol identifies the datum target point, as shown in Example 3-17.

Example 3-18. Locating datum target points using baseline dimensioning with basic dimensions. Chain dimensions and tolerance dimensions can also be used.

Identifies the specificpoint on the datum

Identifies the datum featurewhere the point is located

Example 3-17. The information inside the datum target symbol identifi es the datum target point, target line, or target area.

The datum target points can be located with basic dimensions or tolerance dimensions. Refer to Example 3-18 for a multiview representation using basic dimensions to locate the datum target points. The datum feature symbols appear on


Example 3-19. The datum target symbol can be placed on an edge when a surface view is not available, such as point Z1 in this drawing. Note: Datum target point Z1 is located at the edge where datum surfaces X and Z meet. Otherwise, there would be a side view and location dimensions provided.

the view where the datum surface is a line and the datum points are located on the surface view of the related datum. The datum target symbol can be placed on the view where the surface appears as an edge if the drawing arrangement dictates such placement, as shown in Example 3-19.

Chapter 3 Datums 95

The Fixture Setup

The Drawing

Locating pins

Datumplane X

Datumfeature

Part

X3

X1,X2

Example 3-20. Datum target points on a drawing and the points established with locating pins.

When datum target points are used on a drawing to identify a datum plane, the datum plane is established by locating pins at the datum tangent points as shown in the magnified representation in Example 3-20. The locating pins are rounded or pointed standard tooling hardware.


Datum Target AreasAreas of contact can also be used to establish datums. When this is done, the

shape of the datum target area is outlined by a phantom line with section lines through the area. Circular areas are dimensioned with basic or tolerance dimensions to locate the center. The diameter of the target area is provided in the upper half of the datum target symbol, as shown in Example 3-21, or with a leader and dot pointing to the upper half. The locating pins for target areas are flat end tooling pins with the pin diameter equal to the specified size of the target area.

The Drawing

The Fixture Setup

Fixture base

3X ∅12locating pins

X1,∅12X3,∅12 X2,∅12

Datumfeature

Part

Datumplane X

Example 3-21. Datum target areas are located to their centers. The locating pins for target areas are fl at end tooling pins with the pin diameter equal to the specifi ed size of the target area.

Chapter 3 Datums 97

When the area is too small to accurately or clearly display on a drawing, then a datum target point is used at the center location. The top half of the datum target symbol identifies the diameter of the target area, as shown in Example 3-22.

Fixture base

The Drawing

The Fixture Setup

3X ∅6locating pins

X3,∅6X2,∅6X1,∅6

Datumfeature

Part

Datumplane X

Example 3-22. When the datum target area is too small to show, the datum target point is used and the target area size is given in the top half of the datum target symbol.


Datum Target LinesA datum target line is indicated by the target point symbol “X” on the edge view

of the surface and by a phantom line on the surface view. Refer to Example 3-23. If the locating pins are cylindrical, then the datum target line is along the tangency where the pins meet the part. The pins can also be knife-edged. A surface is often placed at 90° to the pin to create the datum reference frame.

Fixture base

The Drawing

The Fixture Setup

Part

Locating pin

Example 3-23. Specifying a datum target line.

Partial Datum SurfacePartial Datum SurfaceA portion of a surface can be used as a datum. For example, this can be done

when a part has a hole or group of holes at one end where it is not necessary to establish the entire surface as a datum to effectively locate the features. This can be accomplished on a drawing using a chain line dimensioned with basic dimensions to show the location and extent of the partial datum surface. The chain line dimension is considered a minimum distance. The datum feature symbol is attached to the chain line. The datum plane is then established at the location of the chain line, as shown in Example 3-24.

Chapter 3 Datums 99

The Fixture Setup

The Drawing

Chain line

Datum featurePartSimulated datum

(fixture surface)

Datum plane

Example 3-24. A partial datum surface established with a chain line.

Coplanar Surface DatumsCoplanar Surface DatumsCoplanar surfaces are two or more surfaces that are on the same plane. The

relationship of coplanar datum features establishes the surfaces as one datum plane in correlated feature control frame specifications. A phantom line is placed between the surfaces if a void, such as a slot, exists. The phantom line between surfaces is omitted when the area between the surfaces is higher than the datum features. The surfaces are treated as a single, interrupted surface. The number of surfaces can be specified as continuous by using a note, such as “2 SURFACES,” below the related feature control frame. See Example 3-25A and Example 3-25B. This concept is also discussed in Chapter 9 with an application for profile tolerances of coplanar surfaces.


The Drawing

0.6 tolerance zone

Datum feature MDatum feature L

The MeaningA

The Drawing

0.6 tolerance zone

Datum feature L

The MeaningB

Datum feature M

Example 3-25. Coplanar surface datums represented using a note to indicate the number of coplanar surfaces.

Chapter 3 Datums 101

It is also possible to display multiple coplanar surfaces as a single datum by placing the datum feature symbol on the phantom line, or by attaching the datum feature symbol to a feature control frame that is connected to the phantom line by a leader. In Example 3-26, there are a total of 6 raised surfaces behind the two that can be seen in the front view. This is identified with the note “6 SURFACES” below the feature control frame. In this application, the surfaces are all controlled by a flatness geometric tolerance of 0.05 and they are also Datum D. A top view is also required to provide dimensions to the 6 raised features.

Example 3-26. Specifying multiple coplanar surfaces as a single datum.

Extension lines canbe used or omitted

Example 3-27. Sample drawings using the continuous feature symbol.

For your reference, the continuous feature symbol can be used to identify any group of two or more interrupted features as a single feature. Example 3-27 shows sample drawings using the continuous feature symbol with dimension values.


Datum AxisDatum AxisA cylindrical object can be a datum feature. When the cylindrical datum feature

is used, the center axis is known as the datum axis. There are two theoretical planes intersecting at 90°. These planes are represented by the centerlines of the drawing. Where these planes intersect is referred to as the datum axis. The datum axis is the origin for related dimensions, while the X and Y planes indicate the direction of measurement. A datum plane is added to the end of the object to establish the datum frame, as shown in Example 3-28.

The Drawing

The Meaning

X

Y

Y

Secondarydatum axis

X

Part

Primary datum

Secondarydatum axis

Example 3-28. Datum axis.


Placement of the Datum Feature Symbol for a Datum AxisWhen the datum is an axis, the datum feature symbol can be placed on the

drawing using one of the following methods (also shown in Example 3-29).

Example 3-29. Methods of representing the datum axis.


• The symbol can be placed on the outside surface of a cylindrical feature.• The symbol can be centered on the opposite side of the dimension line

arrowhead, but it must line up and be centered with the arrowhead.• The symbol can replace the dimension line and arrowhead when the

dimension line is placed outside of the extension lines.• The symbol can be placed on the dimension line.• The symbol can be placed on a leader line shoulder.• The symbol can be placed below and attached to the center of a feature

control frame.

Simulated Datum AxisThe simulated datum axis is the axis of a perfectly cylindrical inspection

device that contacts the datum feature surface. For an external datum feature, as shown in Example 3-30, the inspection device is the smallest circumscribed cylinder. The inspection device for an internal datum feature is the largest inscribed cylinder, as shown in Example 3-31. For a review on simulated datums and datum feature simulators, refer to the discussion earlier in this chapter.

Datum feature simulatorDatum axis

Datum feature (part)

Simulated datumSmallest circumscribedcylinder

Example 3-30. Simulated datum axis for an external datum feature.

Datum feature (part)

Datum feature simulator

Datum axis

Simulated datumLargest inscribedcylinder

Example 3-31. Simulated datum axis for an internal datum feature.


Coaxial Datum FeaturesCoaxial means two or more cylindrical shapes that share a common axis.

Coaxial datum features exist when a single datum axis is established by two datum features that are coaxial. When more than one datum feature is used to establish a single datum, the datum reference letters are separated by a dash and placed in one compartment of the feature control frame. These datum reference letters are of equal importance and can be placed in any order. See Example 3-32. A datum axis established by coaxial datum features is normally used as a primary datum.

Simulated pair of coaxialcircumscribed cylinders

Datum feature ADatum feature B

Datum axis A-B

The Drawing

The Meaning

Example 3-32. Coaxial datum features.

The Datum Axis of Screw Threads, Gears, and SplinesWhen a screw thread is used as a datum axis, the datum axis is established from

the pitch cylinder unless otherwise specified. If another feature of the screw thread is desired, then a note such as “MAJOR DIA” or “MINOR DIA” is placed next to the datum feature symbol. For example, the note “MAJOR DIA” is specified when the datum axis is established from the major diameter cylinder.

A specific feature such as the major diameter should be identified when a gear or spline is used as a datum axis. When this is done, the note “MAJOR DIA,” “MINOR DIA,” or “PITCH DIA” is placed next to the datum feature symbol as appropriate. The use of a screw thread, gear, or spline should be avoided for use as a datum axis unless necessary.


Datum Axis Established with Datum Target SymbolsDatum target points, lines, or surface areas can also be used to establish a

datum axis. A primary datum axis can be established by two sets of three equally spaced targets—a set near one end of the cylinder and the other set near the other end, as shown in Example 3-33. Notice the datum target points in the circular view are rotated as needed to align with an imaginary line projected from the center for clarity.

Primarydatum axis

Example 3-33. Establishing a primary datum axis with target points.


When two cylindrical features of different diameters are used to establish a datum axis, then the datum target points are identified in correlation to the adjacent cylindrical datum feature. Refer to Example 3-34.

Example 3-34. Two cylindrical features of different diameters used to establish a datum axis.

Example 3-35. Establishing datum axes with a cylindrical datum target area and a circular datum target line.

Cylindrical datum target areas and circular datum target lines can also be used to establish the datum axis of cylindrical shaped parts, as shown in Example 3-35.In this application, the datum target area is a designated width band that goes all around the part. This datum target area is shown as two phantom lines with section lines between. The datum target line is a phantom line that goes all around the part.


A secondary datum axis can be established by placing three equally spaced targets on the cylindrical surface. Refer to Example 3-36.

Example 3-36. Establishing a secondary datum axis with datum target points.

Movable Datum Target SymbolsMovable Datum Target Symbolsand Datum Target Pointsand Datum Target Points

The movable datum target symbol can be used to indicate movement of the datum feature simulator. When datum targets establish a center point, axis, or center plane on a regardless of material boundary basis, the datum feature simulator moves normal to the true profile and the movable datum target symbol can be used for clarity. The term normal is used in ASME Y14.5 and in mechanical engineering applications to represent a feature that is perpendicular to a plane surface and radial to a curved surface. In Example 3-37, datum C uses movable target symbols. The part is fixed against datum target points A1, A2, and A3 primary, datum target lines B1 and B2 secondary, and datum target points C1 and C2 tertiary. Because datums B and C are referenced in the feature control frame as RMB, the datum simulator makes contact with the part. If the actual part is manufactured to the small size tolerance, then datum target points C1 and C2 are movable in order to contact the feature part. In this case, the movable target points move along the basic 45° angle


Example 3-37. Using movable datum target symbols with datum target points.

Movable Datum Target SymbolsMovable Datum Target Symbolsand Datum Target Spheresand Datum Target Spheres

The movable datum target symbol can be used with a spherical diameter specified for the datum target size, and a circular phantom line is used to represent the spherical datum feature simulator as shown in Example 3-38. The spherical datum feature simulators are used to establish the datum axis in this example. The conical shaped ends on the part allow the spherical datum feature simulators to restrict the movement of the part and define the datum axis. In this example, the spherical datum targets move horizontally normal to the axis to contact the actual surface of the part, with datum A specified at RMB in the feature control frame.

that is attached to the movable datum target symbol C1 until contact is made. This example shows how to define the direction of the movement. When the datum feature simulator is required to move and when the movement is not normal to the true profile, the movable datum target symbol is used and the movement direction is defined. If the 45° basic angle is not given, the datum target can move “normal” to the surface or radial toward the center of the round feature.


The Meaning

The Drawing

Datum plane

Part

Datum axis


Example 3-38. The movable datum target symbol can be used with a spherical diameter specifi ed for the datum target size, and a circular phantom line is used to represent the spherical datum feature simulator.

Datum Center PlaneDatum Center PlaneElements on a rectangular, symmetrical part or feature can be located and

dimensioned in relationship to a datum center plane. Axis and center plane datum feature symbols must align with or replace the dimension line arrowhead or be placed on the feature, leader shoulder, dimension line, or feature control frame. The representation and related meaning of datum center plane symbols are shown in Example 3-39.

Datumcenter plane

Datumcenter plane

Datumcenter plane

Datumcenter plane

Datumcenter plane

Example 3-39. Placement of center plane datum feature symbols.



Be sure you notice the difference between the datum feature symbol associated with the datum axis discussed earlier and the datum center plane. The drawings look similar. The datum axis is on a cylindrical feature such as an external shaft or an internal hole. Look carefully at the drawing views and notice that the cylindrical datum feature is dimensioned with a diameter (refer to Example 3-29). The datum center plane is the plane that splits a symmetrical feature such as a slot or tab. The dimension associated with the center plane datum does not have a diameter symbol because the feature is not round. The datum feature symbol is placed in one of the following ways.

• The symbol is centered on the opposite side of the dimension line arrowhead.

• The symbol replaces the dimension line and arrowhead when the dimension line is placed outside of the extension lines.

• The symbol is placed on a leader shoulder.

• The symbol is placed below and attached to the center of a feature control frame.

Simulated Datum Center PlaneThe simulated datum center plane is the center plane of a perfect rectangular

inspection device that contacts the datum feature surface. For an external datum feature, the datum center plane is established by two parallel planes at minimum separation, as shown in Example 3-40. For an internal datum feature, the datum center plane is established by two parallel planes at maximum separation, as shown in Example 3-41.

Datum centerplane A

Datumfeature A

Datum feature simulatorof datum feature A

Parallel planes at minimumseparation (RMB)


PartDatum feature simulator

Example 3-40. Simulated datum center plane for an external datum feature.


The Center of a Pattern ofThe Center of a Pattern of FeaturesFeaturesas the Datum Axisas the Datum Axis

The center of a pattern of features, such as the holes in the part shown in Example 3-42, can be specified as the datum axis when the datum feature symbol is placed under and attached to the middle of the feature control frame. In this application, the datum axis is the center of the holes as a group. This will be discussed further in Chapter 7 in regard to location tolerances.


Parallel planes at maximumseparation (RMB)

Datum centerplane A


Parallel planes at maximumseparation (RMB)

Part

Datum featureA


Example 3-41. Simulated datum center plane for an internal datum feature.

Datum axis B

Datumaxis B

Example 3-42. The datum axis at the center of a pattern of features as a group.


Applying a Translation ModifierApplying a Translation Modifierto a Datum Referenceto a Datum Reference

The translation modifier is added to the feature control frame following the datum feature reference and any other applicable modifiers. The translation modifier is used to specify that the basic location of the datum feature simulator is unlocked and free to translate within the specified geometric tolerance. Example 3-43 shows the translation modifier used in an application and the resulting datum reference frame.

The Drawing

Translationmodifier

Translationmodifier

Example 3-43. Establishing a datum reference frame with a translation modifi er. (Continued)


The Meaning

Secondary datumfeature B

Adjustable

location

Primary datumfeature A

Tertiary datumfeature C

Datum feature simulatorof datum feature BExpanding cylinderperpendicular to datumplane A


Datum axis B

Datum plane A

Datum axis C

Datum reference frame

Datum feature simulator of datum feature CExpanding cylinder perpendicular to datum plane ALocation distance adjustable from datum axis B

Example 3-43. (Continued)


Using a Contoured Surface as a Datum FeatureUsing a Contoured Surface as a Datum FeatureSome applications require a compound or contoured surface to be identified

as a datum feature. The feature on the part containing the compound surface is defined by a three-dimensional mathematical coordinate system. In this application, the datum feature datum simulator results from the mathematical data and is used to establish the datum reference frame. Aligning the high points of the datum feature with its datum feature simulator restricts movement of the part to the datum reference frame. Example 3-44 shows the use of a contoured surface as a datum feature and the three-dimensional mathematical coordinate system. The phantom oval line is used to define the limit of the datum target area and the hatched area defines datum target area A1. The word TRUE is added before the dimension when the feature displayed on a 2D view is shown foreshortened. In this example, the holes are shown as ellipses and the note TRUE is added before the ∅6.0/6.1 dimension value, as in TRUE ∅6.0/6.1. The 10 mm basic dimension also has the note TRUE before it to clarify that it is the width of the datum target area, because it does not show true width in the displayed view.

The note [BSC] placed in the feature control frames means that datum target area A1 is defined by the 3D CADD model as basic. See note 1 in the example referring to the model for complete product definition. In addition, there are basic dimensions from the origin of the mathematically defined data to locate the hole centers with the x, y, and z axis directions and coordinates. This is an example of using a mathematically defined feature or a contoured surface as a datum feature.

A practical application is when a part is designed to copy the contours of an actual object that has few or no flat surfaces to use as datums. In this approach, a CADD model that defines the basic shape of the plate is used and the engineer applies a profile tolerance on the shape of the plate to control its size. The bottom surface is datum target area A, and the CADD model defines the basic location of the holes in the plate. A position tolerance relative to datum target area A on the holes is used to control the hole locations. This application has many uses for parts that are not square. Chapter 7 explains location tolerances.


8X ∅5.85 (6.0-.15) MMBDatum feature simulator

of datum feature B

Datum feature simulator ofdatum feature A fixed at basicDatum feature A must remainin contact with the simulated

datum feature

10

The Drawing

Basic

All around

Origin ofmathematicallydefined data

The Meaning

Example 3-44. Establishing a contoured surface and a mathematically defi ned feature as a datum feature.


Chapter Test

Name _________________________________

1. Defi ne datum. __________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

2. Defi ne datum feature. ___________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

3. Describe datum feature simulators. Include the term “simulated datums” in your description and give at least three examples of datum feature simulators used in manufacturing. _________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

4. Identify at least fi ve locations where a feature control frame can be placed on a drawing.

1) ____________________________________________________________________

____________________________________________________________________

2) ____________________________________________________________________

____________________________________________________________________

3) ____________________________________________________________________

____________________________________________________________________

4) ____________________________________________________________________

____________________________________________________________________

5) ____________________________________________________________________

____________________________________________________________________

5. Defi ne datum plane. _____________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

3Chapter 3 Datums 119

6. Describe the method used for datum feature identifi cation. Indicate which letters cannot be used for datum identifi cation and explain why they cannot be used. __

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

7. List at least fi ve items that can be considered as datum features on an object or part.

1) ____________________________________________________________________

2) ____________________________________________________________________

3) ____________________________________________________________________

4) ____________________________________________________________________

5) ____________________________________________________________________

8. Identify the datum feature, the part, the simulated datum plane, the physical datum feature simulator, and the datum plane on the following illustration.

C)

E)D)

A)

B)

9. There are two types of datum feature simulators. Name and describe each type.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

10. Name at least four items that can be used as a datum feature simulator.

1) ____________________________________________________________________

2) ____________________________________________________________________

3) ____________________________________________________________________

4) ____________________________________________________________________


11. Identify at least three required conditions for datum feature simulators.

1) ____________________________________________________________________

____________________________________________________________________

2) ____________________________________________________________________

____________________________________________________________________

3) ____________________________________________________________________

____________________________________________________________________

12. Defi ne simulated datum. _________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

13. Defi ne actual mating envelope. ___________________________________________

_______________________________________________________________________

_______________________________________________________________________

14. Defi ne tangent plane. ____________________________________________________

_______________________________________________________________________

_______________________________________________________________________

15. Given the following drawing and related meaning, fi ll in the blanks at Part I A and B and at Part II A, B, C, and D. Provide the actual dimensions as related to the drawing at Part II B, C, and D.

A)

B)

A)

B)

D)

Part I

Part II

C)


16. Name the three datums of a complete datum reference frame. ________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

17. When referring to the datum reference frame in the feature control frame, the ____________ datum is given fi rst followed by the ____________ and ____________ datums. This is known as the datum ____________.

18. Defi ne degrees of freedom. _______________________________________________

_______________________________________________________________________

_______________________________________________________________________

19. Identify how many degrees of freedom are found on every part, and identify how many are translational and how many are rotational. ____________________

_______________________________________________________________________

_______________________________________________________________________

20. Defi ne translational. _____________________________________________________

_______________________________________________________________________

_______________________________________________________________________

21. Defi ne rotational. _______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

22. Defi ne datum targets. ___________________________________________________

_______________________________________________________________________

_______________________________________________________________________

23. The primary datum plane must be established by at least ______ point(s) on the primary datum surface.

24. The secondary datum plane must be established by at least ______ point(s) on the secondary datum surface.

25. The tertiary datum plane must be established by at least ______ point(s) on the tertiary datum surface.

26. How is a datum target area represented on a drawing? _______________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

27. The circular datum target area is dimensioned with ____________ dimensions or ____________ dimensions to locate the ____________ from datums and the diameter of the area is provided in the ____________ half of the datum target symbol.


28. How are datum target areas treated on a drawing when the target area is too small to draw? __________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

29. Describe how to properly display the symbols for a circular datum target area, a square datum target area, a rectangular datum target area, and a spherical datum target area. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

30. What does a movable datum target symbol indicate? ________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

31. How are datum target lines represented on a drawing? ______________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

32. When a portion of a surface is used to establish a single datum, this is referred to as a(n) ____________ datum surface.

33. Two or more surfaces that are on the same plane are referred to as ____________ surfaces.

34. Depending on the functional requirements of a part, more than one datum reference frame can be established. This is referred to as a(n) ____________ datum reference frame.

35. Describe the basic function of the continuous feature symbol. _________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________


36. List at least fi ve ways the datum feature symbol can be placed on the drawing when the datum is an axis.

1) ____________________________________________________________________

2) ____________________________________________________________________

3) ____________________________________________________________________

4) ____________________________________________________________________

5) ____________________________________________________________________

37. Label the elements A, B, C, and D below that represent the fi xture setup for a datum axis. This setup is for a datum feature at regardless of material boundary (RMB).

C)D)

B)

A)

38. A primary datum axis can be established by two sets of three equally spaced target points. True or False?

39. Cylindrical datum target areas and circular datum target lines can be used to establish the datum axis of cylindrical shaped parts. True or False?

40. List at least three ways to place the datum feature symbol on the drawing for a datum center plane.

1) ____________________________________________________________________

2) ____________________________________________________________________

3) ____________________________________________________________________

41. Explain the basic function of the translation modifi er. ________________________

_______________________________________________________________________

_______________________________________________________________________


42. Identify the items in the drawing below labeled A through F.

E)

D)

F)

G)

A)

B)

C)


43. Identify the items in the drawing below labeled A through C.

C)B)

A)


44. For the drawings below, identify on the blank lines (A through G) whether the datum feature symbols represent a datum surface, datum axis, or datum center plane.

A)

B)

E)D)C)

G)

F)


45. Label the elements A, B, C, D, and E below that represent the fi xture setup for a datum center plane. This setup is for a datum feature at regardless of material boundary (RMB).

A)

D)

B)

C)

E)


Print Reading Exercises

Name _________________________________

The following print reading exercises use actual industry prints with related questions that require you to read specifi c dimensioning and geometric tolerancing representations. The answers should be based on previously learned content of this book. The prints used are based on ASME standards. However, company standards can differ slightly. When reading these prints, or any other industry prints, a degree of fl exibility is required to determine how individual applications correlate with the ASME standards.

Refer to the print of the SLEEVE-DEWAR REIMAGING found on page 417.

1. Describe Datum A. ______________________________________________________

_______________________________________________________________________

2. Describe Datum B. ______________________________________________________

_______________________________________________________________________

3. Give the location dimension of the ∅.107±.001 hole from Datum A. ____________

Refer to the print of the BRACKET found on page 418.

4. Identify the datums that make up the primary datum reference frame. _________

_______________________________________________________________________

5. Describe Datum D. ______________________________________________________

_______________________________________________________________________

6. Identify the primary, secondary, and tertiary datum references associated with the positional geometric tolerance placed with the ∅.875±.005 dimension:

Primary _______________________________________________________________

Secondary _____________________________________________________________

Tertiary ________________________________________________________________

7. Give the location dimensions to the three ∅.437±.005 holes from Datum C.

_______________________________________________________________________

8. Give the location dimensions to the three ∅.437±.005 holes from Datum B.

_______________________________________________________________________

9. Give the location dimensions to the four ∅.187±.003 holes from Datum A.

_______________________________________________________________________

10. Give the location dimensions to the four ∅.187±.003 holes from Datum C.

_______________________________________________________________________

11. Are the location dimensions in question 7 placed using baseline or chain dimensioning?

_______________________________________________________________________

3Chapter 3 Datums 129

Refer to the print of the HUB-STATIONARY ATU found on page 419.

12. Describe Datum A. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

13. Describe Datum B. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

14. Describe Datum C. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

15. Give the dimension from Datum A to the left face of the part. _________________

16. Give the horizontal and vertical location dimensions from Datum C to the six ∅.352+.005/–.001 holes. __________________________________________________

_______________________________________________________________________

_______________________________________________________________________

Refer to the print of the PEDAL-ACCELERATOR found on page 420.

17. How many points of contact are used to establish the following datums?

Datum A ______, Datum B ______, Datum C ______.

18. Identify the following items for each of the datum target areas: the datum reference, specifi ed number on the datum, and the area size and shape. ________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

19. What is the distance between datum target points B-1 and B-2? _______________

20. What does the box around the 74.00 dimension mean? _______________________

_______________________________________________________________________

21. Describe Datum D. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

22. Give the location dimensions between the datum target areas A1 and A2.

_______________________________________________________________________

23. Give the location dimensions between the datum target area A1 and datum target point A3. _________________________________________________________

24. Give the location dimensions between the datum target points A3 and C1.

_______________________________________________________________________


25. Give the location dimensions between the datum target points B1, B2, and C1.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

Refer to the print of the DOUBLE V-BLOCK found on page 424.

26. Identify the datum reference frame. _______________________________________

27. Describe Datum D. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

28. Give the dimension from Datum C to the bottom of the 1.60 wide slot.

_______________________________________________________________________

29. Give the location dimension to the ∅12.70/12.65 feature from Datum B.

_______________________________________________________________________

30. Give the location dimension to the ∅12.70/12.65 feature from Datum C.

_______________________________________________________________________

Refer to the print of the BRACKET ASSY-EL GIMBAL found on page 429.

31. Give the location dimension from Datum D to the three ∅.109+.004/–.001 COUNTERSINK ∅.172×100° features. ______________________________________

32. Describe Datum B. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

33. Describe Datum C. ______________________________________________________

_______________________________________________________________________

_______________________________________________________________________

34. What is the wall thickness of the material? _________________________________

35. Give the vertical location dimension from Datum B to the three .086-56UNC-2B features. _______________________________________________________________

_______________________________________________________________________

Refer to the print of the FEMORAL A-P SAW GUIDE STD. found on page 430.

36. Describe Datum A. ______________________________________________________

_______________________________________________________________________

37. Describe Datum B. ______________________________________________________

_______________________________________________________________________

38. Describe Datum C. ______________________________________________________

_______________________________________________________________________


39. What is the relationship between Datums A, B, and C? _______________________

_______________________________________________________________________

_______________________________________________________________________

Refer to the print of the FEMORAL BEVEL CUTTER found on page 431.

40. Describe Datum A. ______________________________________________________

_______________________________________________________________________

41. Describe Datum B. ______________________________________________________

_______________________________________________________________________

Refer to the print of the CEMENT RESTRICTOR found on page 432.

42. Describe Datum A. ______________________________________________________

_______________________________________________________________________

43. Describe Datum B. ______________________________________________________

_______________________________________________________________________

44. Describe Datum C. ______________________________________________________

_______________________________________________________________________

Refer to the print of the SAW GUIDE FIXATION BLOCK found on page 433.

45. Describe Datum A. ______________________________________________________

_______________________________________________________________________

46. Describe Datum B. ______________________________________________________

_______________________________________________________________________

47. Describe Datum C. ______________________________________________________

_______________________________________________________________________

48. Describe Datum D. ______________________________________________________

_______________________________________________________________________

49. Describe Datum E. ______________________________________________________

_______________________________________________________________________

50. Describe the use of the note 2X INDIVIDUALLY placed below the feature control frame for the ∅.193+.005/–.000 feature. _____________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________


Refer to the print of the STANDARD REAMER GUIDE found on page 434.

51. Describe Datum A. ______________________________________________________

_______________________________________________________________________

52. Describe Datum B. ______________________________________________________

_______________________________________________________________________

Documents

Placing Datums