18-10 Chapter Eighteen
As in the previous examples, the inspector would set up the part, extract the measurements, and
record the data on the Inspection Report as shown in Table 18-3. Note that the report reflects two
allowable tolerances for each hole. The larger tolerance represents tolerance allowed by the upper seg-
ment of the feature control frame, with the smaller tolerance representing the tolerance allowed by the
lower segment of the feature control frame.
Figure 18-8 Four-hole part controlled by composite positional tolerancing
Table 18-3 Inspection Report for composite position verification

+.006

+.005

+.006

+.001
LAYOUT INSPECTION REPORT

NO.

FEATURE

FEATURE SIZE

MMC

ACTUAL

DEV.


±.003

.309

.310

.001

Ø.011

1.500

1.506

2.500

2.503

+.003

2

.312

±.003

.309

.315


4.506

2.500

2.499

-
.001

4

.312

±.003

.309

.312

.003

Ø.013

4.500

4.501

1.000

1.005

of features within the pattern. Verifying a composite positional tolerance using a fixed-limit gage would
require the development of two separate gages, one for each requirement. However, with the paper gage,
both requirements may be easily verified from a single set of measurements. Fig. 18-8 illustrates a compos-
ite position specification for the four-hole part used in previous examples.
Paper Gage Techniques 18-11
.010
.011
.012
.016
.015
.014
.013
GRID LINES = .001 INCH
-X +X
-Y
+Y
GRID LINES = .001 INCH
-X +X
-Y
+Y
0
0
#4
#3
#1
#2
#4
#1
#2
#3

18-12 Chapter Eighteen
With the part locked into the datum reference frame, measurements are made in an “X” and “Y”
direction and the data is recorded on the Inspection Report. The data is then transferred to the coordinate
paper gage grid and converted into a round positional tolerance using the polar overlay. Since the datum
feature has been referenced on an RFS basis, the polar overlay must remain centered on the coordinate
grid to reflect the hole pattern centered on the datum feature, regardless of its produced size.
18.6.2.2 Datum Feature Applied on an MMC Basis
A fixed-limit boundary is used to represent the datum feature, where a datum feature of size is referenced
on an MMC basis. For a primary datum feature of size, the boundary is the MMC size of the datum feature.
For a secondary or tertiary datum feature of size, the boundary is the virtual condition of the datum feature.
These boundaries are easily represented in a functional gage, allowing the datum feature to “rattle”
around inside the boundary if the actual produced feature has departed its MMC or virtual condition size.
Figure 18-11 Datum feature subject to size variation—RFS applied
18.6.2 Capturing Tolerance from Datum Features Subject to Size Variation
In one common assembly application, a pilot hole or diameter is used as a datum feature in locating a
pattern of holes. Paper gaging is extremely useful in capturing dynamic tolerances that cannot be
effectively captured in a typical layout inspection.
18.6.2.1 Datum Feature Applied on an RFS Basis
Verification in relation to a datum feature of size applied on a regardless of feature size (RFS) basis is done
in a similar manner to datum features without size discussed earlier. For the part shown in Fig. 18-11,
locational verification of the hole pattern requires that the inspector establish a datum reference frame
from the high points of datum feature A (primary) and center on the pilot diameter B (secondary) regard-
less of its produced size. Establishing the secondary datum axis requires use of an actual mating envelope
(smallest circumscribed cylinder perpendicular to datum plane A) as the true geometric counterpart for
secondary datum B.
Paper Gage Techniques 18-13
This rattle is commonly referred to as “datum shift” and is allowed to occur every time a datum feature
of size is referenced on an MMC basis. However, unlike “bonus” tolerance, this shift allowance is not
additive to the location tolerance indicated by the feature control frame for the holes. Rather, datum shift
allows the pattern tolerance zone framework to shift off the datum axis (all the holes as a group) to get the

Hole randomly selected to
(antirotate) part
for inspection
Largest gage pin
for produced size for each of
the holes and to aid in
positional verification
Measurement instrument
(
dial indicator for this
Surface table
0

LAYOUT INSPECTION REPORT

NO.

FEATURE

FEATURE SIZE

MMC

ACTUAL

DEV.

ALLOW

TOL.

.002

Ø.009

2.200

2.203

+.003

0

0

0

2

.
482±.002
.480

.483

.003

Ø.010

-
.900

+.003

0

-
.002

-
.002

X

X

X

Paper Gage Techniques 18-15
GRID LINES = .001 INCH
-X
+X
-Y
+Y
0
#3
#1
#2
GRID LINES = .001 INCH
-X
+X
-Y

one on the center of the other (RFS). But the drawing references datum B on an MMC basis requiring that
a fixed-limit, virtual condition cylinder represent the datum. Comparing the actual mating size of datum
feature B to its calculated virtual condition size shows that there is a Ø.004 difference between the two.
This difference reflects the shift tolerance allowed for the datum feature. This allowable shift may be
translated to the hole verification by moving the polar grid such that the center of the coordinate grid
remains inside a Ø.004 zone when measuring the holes as shown in Fig. 18-16.
This movement between the two grids represents the allowable shift derived from the datum feature’s
departure from virtual condition. When shifting the polar grid in this manner, care must be taken to assure
that all of the holes fall within their respective tolerance zones. If the polar grid can be moved to an
optimum position that accepts all of the holes in their tolerance zones without violating the datum shift
tolerance zone, then the hole pattern is accepted as being within tolerance.
18-16 Chapter Eighteen
GRID LINES = .001 INCH
-X +X
-Y
+Y
0
.007
.008
.009
.010
.011
.012
.003
.004
.005
.006
#1
#2
#3


LAYOUT INSPECTION REPORT

NO.

FEATURE

FEATURE SIZE

MMC

ACTUAL

DEV.

ALLOW

TOL.

X LOCATION

DEV

ACCEPT

REJECT

BASIC

ACTUAL

1.250

1.253

+.003

2

.205±.005
.200

.200

0

Ø.010

1.250

1.253
0

+.005

+.005

+.003

3



.205±.005
.200

.200

0

Ø.010

-
1.250

-
1.248

+.002

0

-
.005

-
.005

X

18-18 Chapter Eighteen
GRID LINES = .001 INCH

rotational datum shift
Paper Gage Techniques 18-19
18.6.2.4 Determining the Datum from a Pattern of Features
Where a pattern of features, such as a hole pattern, are used as a datum feature at MMC, the true
geometric counterpart of all holes in the pattern are used in establishing the datum. For the example shown
in Fig. 18-21, the true geometric counterpart for the pattern of three round holes consists of three true
cylinders representing the virtual condition of each hole in the pattern. (Using virtual condition cylinders
compensates for any locational error between the holes.) When referenced on an MMC basis, the axis of
the pattern may shift and/or rotate within the bounds of these cylinders as the holes in the pattern depart
from virtual condition (i.e., they grow larger in size and/or use less positional tolerance).
Figure 18-21 Example of datum established from a hole pattern
These virtual condition “cylinders” may be represented by pins in a functional gage. By simply
dropping the part over the gage pins, the produced hole pattern will average over the pins, relating the
part to datum axis B. But, development of a hard gage is not required to simulate the averaging of the
feature pattern to establish the datum. The drawing in Fig. 18-21 shows a part where the three-hole pattern
will serve as secondary datum feature B at MMC. Since this part will be made in a very small quantity, it
would not be practical or cost effective to build a gage to simulate the datum. Verification of the geometric
tolerances will be done using a conventional layout inspection and paper gaging.
To establish the datum reference frame from a pattern of holes in an open setup or CMM, the hole
pattern must be “averaged” to find a “best fit” center for the pattern. This might be accomplished by
randomly selecting any hole of the pattern from which to start measuring. The remaining holes may be
checked to this “frame of reference” as well as other geometric tolerances related to the datum hole
pattern. Fig. 18-22 illustrates the measurements extracted for the three-hole datum pattern where the
inspector used the top hole as the starting point.
If all tolerances check within their respective zones, then the part is accepted. If the part checks to be
bad, then the inspector may need to paper gage the actual measurements taken for the holes to find the
pattern center. This would be done by plotting the holes on the grid and then graphically “squaring up”
the pattern by rotating the holes about the datum setup hole until they are equally dispersed in relation to
18-20 Chapter Eighteen
the coordinate grid centerlines as illustrated in Fig. 18-23 (left). To square up the pattern for this example,

.252±.004
.250
.250
.250
.002
.002
0 0 0
.625 .630 +.005 -1.315 -1.320 005
Figure 18-22 Inspection Report—hole pattern as a datum
GRID LINES = .001 INCH
-X +X
-Y
+Y
0
#3
#1
#2
GRID LINES = .001 INCH
-X +X
-Y
+Y
0
#3
#1
#2
Approximation of datum
pattern central axis
Figure 18-23 Determining the central datum axis from a hole pattern
Paper Gage Techniques 18-21
GRID LINES = .001 INCH

holes on both grids fall together in a relatively close grouping. The problem for these parts seems to be
that the pattern has drifted off center; one pattern along the X axis (Fig. 18-25a) and the other along the Y
axis (Fig. 18-25b). This may have resulted from movement of the stops used to locate the part in the
machinery. It may have resulted from something preventing the part from coming down fully to the stops,
such as excessive chips on the machine bed. The amount of correction required can be determined by
circumscribing the smallest possible circle about the hole grouping. This roughly approximates the center
of the pattern. By simply counting the grid lines between the center of this circle and the center of the
coordinate grid, the operator may determine the amount of adjustment required to get the pattern back on
center.
18-22 Chapter Eighteen
The coordinate grid shown in Fig. 18-25(c) illustrates a hole pattern that is widely scattered over the
coordinate grid and falls toward the extremes of the tolerance limits. The accuracy of the hole pattern is
poor, and the reliability is questionable since a minor change in the process could result in one or more of
the holes dropping outside their allowable tolerance. This could indicate an unstable or out-of-control
process.
Fig. 18-25(d) illustrates a hole pattern where one of the holes (hole #3) has deviated to an extreme from
the others. The remaining three holes fall as a group relatively close to the grid center, indicating a
generally accurate and reliable process for the majority of the holes. This is a clear indicator that hole #3
deviated due to some special cause. Paper gaging additional parts would help to determine if this were a
single occurrence or an ongoing problem requiring additional corrective action.
GRID LINES = .001 INCH
-X +X
-Y
+Y
0
#4
#3
#1
#2
GRID LINES = .001 INCH

18.7 Summary
Paper gaging is an extremely valuable dimensional analysis tool used in verifying a wide range of geomet-
ric tolerance applications. As illustrated in this chapter, the technique allows for the easy translation of
2-D coordinate measurements extracted from traditional layout inspections into round 3-D tolerance
zones for verifying part conformance. The technique also provides an effective means for capturing
dynamic tolerances, such as datum shift allowance, which cannot be realized in a traditional layout
inspection.
Simplicity of preparation and use, combined with the pictorial form of data presentation, makes a
paper gage extremely easy for the average person to read and understand. When used appropriately, a
paper gage can also save time and money in part inspection through its ability to represent part functional
boundaries without the high cost of designing, building, and maintaining a traditional hard gage.
This chapter has also demonstrated how a paper gage may be used as a manufacturing problem-
solving tool to quickly identify and correct problems during production. Periodic paper gage evaluations,
combined with accepted statistical methods, can greatly aid the operator in keeping the process in control
before bad parts are produced. This can help to lower production costs by raising usable part yield,
lowering scrap rates, and eliminating wasted man-hours attempting to salvage defective product.
18.8 References
1. Foster, Lowell W. 1986. Geometrics II, The Application of Geometric Tolerancing Techniques. Minneapolis,
MN: Addison-Wesley Publishing Company, Inc.
2. Neuman, Alvin G. 1995. Geometric Dimensioning and Tolerancing Workbook. Longboat Key, FL: Technical
Consultants, Inc.
3. Pruitt, George O. 1983. Graphical Inspection Analysis. Doc No. NWC TM 5154. China Lake, CA: U.S. Naval
Weapons Center.
4. The American Society of Mechanical Engineers. 1995. ASME Y14.5M-1994, Dimensioning and Tolerancing.
New York, New York: The American Society of Mechanical Engineers.
19-1
Receiver Gages — Go Gages
and Functional Gages
James D. Meadows
Institute for Engineering & Design, Inc.

doing so, is capable of making a difficult geometric concept easy to understand.
Functional and GO gaging are time-tested tools of 3-dimensional (3-D) measurement that determine
whether or not workpiece features will actually fit into assemblies. They do this without the use of
computers or software. They are reliable and low tech. If used in a well-balanced measurement plan in
conjunction with other measurement tools, they can provide the confidence needed to accept produced
parts on the basis that they will perform their intended function.
Gaging of this variety is sometimes viewed as inappropriate because it produces no variables data
(specifically how a feature has departed from perfect geometric size, form, orientation or location) and is
therefore incapable of assisting in the statistical process control of manufacturing methods. However,
many measurement techniques that do produce variables data are not representative of worst case assem-
bly conditions and collect very little 3-D data concerning worst case feature high point interference
possibilities. The type of data collected by functional and GO gaging is considered attribute (good vs.
bad) information.
Both variables data and attribute data have their place in a well-balanced measurement procedure.
Unfortunately, many measurement professionals are led to believe that only one of the two types of
measurement information is to be used. Therefore, they lose the benefits of the type they do not choose.
19.2 Gaging Fundamentals
In a perfect circumstance, fixed limit gages accept all features that conform to their tolerance specification
and reject all features that do not conform to their tolerance specification. The GO gage and the Functional
Gage should each completely receive the feature it is inspecting.
GO plug gages should enter holes over the full length of the hole when applied by hand without using
extreme force. A GO cylindrical ring gage should pass over the entire length of a shaft when applied by
hand. This inspects not only a violation of the maximum material condition size limit, but also the envelope
of perfect form at maximum material condition that American National Standards require. The rule in ANSI
is that size limits control the surface form of rigid features.
The international rule is not the same. In the International Organization for Standardization (ISO), size
is independent of form. Therefore, according to the ISO policy, unless otherwise specified, size inspection
does not require a full form GO gage. Simple cross-sectional inspection procedures are all that are
necessary to verify size requirements.
In ANSI-approved documents, NOGO gages are designed to inspect violations of the least material

within specification will be accepted by the gage. Most of the parts outside the specification will be
rejected by the gage. A small percentage of parts outside the specifications may be accepted by the gages
or a small percentage of parts that are within the specifications may be rejected by the gages. This policy
may either add or subtract material from the gage MMC boundary or MMC concept virtual condition
boundary since the tolerance is both plus and minus around these boundaries. This means that some of
the gagemaker’s tolerances, the wear allowances, the form tolerances and the measurement uncertainties
reside both within and outside of the workpiece limits of size and geometric control.
Absolute Tolerancing is recommended. This type of gage tolerancing means that gage pins are
toleranced only on the plus side of their MMC concept virtual condition boundary (only allowing them to
grow) and that gage holes are toleranced only on the minus side of their MMC concept virtual condition
boundary (only allowing them to shrink). This has the effect of rejecting all parts not within tolerance and
accepting all parts that are within tolerance except those borderline parts that fall within the range of the
gage tolerance. Part features that are produced within the range of the gage tolerance are rejected as
though they were not in compliance with their geometric tolerance, even though technically they are
within the design specification limits. This is the price we must pay if we choose to accept no parts that
have violated their tolerance.
Absolute Tolerancing is the ANSI-recommended practice of applying gage tolerances so that the gages
will reject all workpiece features that reside outside of their specifications. This is to assure complete random
interchangeability of mating parts in an assembly inspected by these gages. Gagemaker’s tolerances, wear
allowances, form tolerances and measurement uncertainties of the gage are all within the workpiece limits of
size and geometric control. These gage tolerances add material to the gage. The gages are dimensioned at the
MMC limit or MMC concept virtual condition limit of the feature being gaged, then toleranced so that gage
pins can only get larger and gage holes can only get smaller. This policy is based on the gaging premise that
all parts not within tolerance will be rejected, most parts that are within tolerance will be accepted, and a small
percentage of in-tolerance parts that are considered near the borderline between good and bad will be rejected
as though they had violated their tolerance requirements.
19-4 Chapter Nineteen
The ANSI-recommended amount of tolerance is 5% of the tolerance on the feature being gaged plus
an optional 5% of the tolerance allowed for wear allowance. This recommendation is only a place from
which to begin the decision as to what tolerance will be assigned to the gage. Using the Absolute

The fourth and last geometric control shown is to position the two holes in the pattern to one another
and to the three datum planes given by the three highest points of the primary datum feature, the two
highest points of the secondary datum feature with respect to the primary datum plane, and the one
highest point of the tertiary datum feature with respect to the primary datum plane and the secondary
datum plane. Fig. 19-2 shows the gage for Fig. 19-1. The gage has, in order of consideration:
• A primary datum feature that is flat to within 10% of the flatness tolerance given to the primary datum
feature on the workpiece,
• A secondary datum feature that is perpendicular to the primary datum plane to within 10% of the
tolerance given to the secondary datum feature on the workpiece and,
• A tertiary datum feature that is perpendicular to the primary datum plane and the secondary datum
plane to within 10% of the tolerance given to the tertiary datum feature on the workpiece.
Each datum feature simulator on the gage has enough surface area to entirely cover the datum feature
from the workpiece it represents. It must try to hit the highest points of contact on the datum feature to
properly construct the datum plane and unless it has enough surface area, it runs the risk of missing the
appropriate high points and improperly establishing the datums. Too much surface area and the gage runs
a similar risk of establishing nonfunctional and therefore inappropriate datums.
The gage also has two gage pins. Ideally, these gage pins will be at least as long as the holes they are
gaging are deep. If these were simply GO gages meant to gage the maximum material condition of the
holes, they would not be mounted on a plate, would have no relationship to the datum reference frame,
and would be made at the maximum material condition of the holes. But these are Functional Gage pins
meant to gage the positional requirement of the holes, so they are mounted and related to the datums and
dimensioned to be at the virtual condition of the holes they are to inspect.
The size of the gage pins are dimensioned to begin at the virtual condition of the holes being gaged
and go up in size tolerance by 10% of the size tolerance given to those holes. The gage pins also have a
positional control based on 10% of the tolerance given to the holes they are gaging. If the workpiece is
capable of being applied to the gage (as shown in the illustration), while maintaining its appropriate
contact on the datum feature simulators, it is judged to be in compliance with the positional requirement.
The size limits of the holes must be inspected separately.
One of the important requirements of workpieces to be gaged is that they are sufficiently defined to
allow the gage designer/gagemaker to simply follow from control to control using 5%-10% of the toler-

ture and increased geometric tolerance while preserving functionality. The use of the MMC symbol after
the geometric tolerances and also after the datum features of size will make it easy to represent them with
gage pins at their appropriate constant boundary size (their virtual condition size). As in Fig. 19-1, each
size tolerance and geometric tolerance has been mimicked by the gage that uses the same geometric
characteristics and 10% of the tolerance on the workpiece. This geometric tolerance allows the gage pins
to be only larger than the virtual condition boundary of the hole being represented so as to not accept a
workpiece that exceeds its allowed tolerances.
This tolerancing of the gage pins to only get larger than the worst case boundary (and in the case of
gage holes to only get smaller than the worst case boundary) being inspected will make the gages reject
19-8 Chapter Nineteen
a small percentage of technically good parts that are near the borderline between good and bad. This way
the gage doesn’t accept a bad part. One must remember that this absolute tolerancing method is preferred
by ANSI-approved documents, but is not the preferred practice in the ISO-approved documents on
gaging.
The gage in Fig. 19-4 does not show the use of the maximum material condition symbol after the datum
features of size. This will reduce the allowed inaccuracies in the gage, increase the chance of producing a
more accurate gage and will accept more of the produced workpieces. Use of the regardless of feature size
(RFS) concept after datum features of size on the gage design may increase the cost of the gage, but
should more than make up for this additional cost by the gage’s acceptance of a greater number of per-
Figure 19-4 Gage for verifying four-hole pattern in Fig. 19-3
Receiver Gages — Go Gages and Functional Gages 19-9
Figure 19-5 Position and profile using a simultaneous gaging requirement
For example, in a separate gaging requirement, the four-hole pattern could rock on datum A. This
creates a different angle to be accepted than the rocked orientation on datum A used to accept the profile.
Or as the datum pattern B holes grew from their virtual condition boundary toward their least material
condition, the four-hole pattern as a group could shift to the left and the profile could shift to the right and
be accepted. But in a simultaneous gaging requirement this would not be acceptable. Both the four holes
and the profile would have to be accepted by one gage in one rocked orientation, with the four holes and
the profile shifted in the same direction (if rock and shift were to occur).
drawing technically good parts that are inspected by the gage. Even though the gage may use the