1) Datum systems are used to precisely locate components relative to each other in assemblies. They introduce constraints to control all six degrees of freedom of movement. 2) Key datum systems include grouped datum planes which control translation and rotation, and grouped datum planes with spigots/recesses or pins/holes which control all degrees of freedom. 3) The accuracy of datum systems depends on factors like flatness of datum planes and fit between mating features like spigots/recesses or pins/holes. Position and geometric tolerances are specified accordingly.

1. Design for Manufacture and Assembly
Datum Systems
235
DATUM SYSTEMS
Design Principles For Locating Components
The movement of any body in space may be resolved into six degrees of freedom
relative to the three co-ordinate axes in figure 1,viz., three of translation in
the directions X, Y and Z and three co-ordination axes OX OY OZ.
Fig.1 Co- ordinate Axes
To fix a body in space relative to any other it is both necessary and sufficient
to introduce 6 constraints. This is the “6 point location principle”.
In figure 2 the block is located precisely in relation to the co-ordinate planes
by 6 hemi-spherical pins, 3 in the base contacting the XOY plane, 2 in the side
contacting the ZOY plane and 1 in the side contacting the ZOY plane.
Fig: 2 “6 point Location Principle” Diagram
Apply these principles in design as far as practicable particularly when precise
location or precise mechanical movements are required.
Note: severe conditions in engineering such as heavy loads, high speeds, etc.,
often necessitate adopting modified principles. An example would be

2. Design for Manufacture and Assembly
Datum Systems
236
substitution of limited areas of contact for the point contact in figure 2 such as
is often adopted in jig and fixture design. the point contact in figure 2 such as
is often adopted in jig and fixture design.
Fig- 3. Datum Spigot and Recess Assembly
When locating one component relative to any other in an assembly, design so
as to confine the need for positional accuracy to the minimum number of
features, consider datum systems.
Function of Datum Systems
To align certain features on two components in accurate geometric relation
when assembled.
In the flange coupling, figure 3, a spigot B and recess A have been introduced
in the design so as to align the respective shafts on assembly.
To locate mating components accurately to finite assembly facilitates
assembly. In figure 3 the datum spigot and recess also facilitates assembly of
the securing bolts.
To set as a convenient base from which to dimension other features. see
surfaces A and D is figure 4

3. Design for Manufacture and Assembly
Datum Systems
237
Fig: 4 Datum Based Dimensioning
Common Datum Systems
Group of two or three datum planes
Function
The system using two co-ordinate planes controls the relative movement of two
components in 5 degrees of freedom, while that using three co-ordinate planes
controls them in all 6 degrees of freedom.
Geometric analysis
Geometry involved is flatness and squareness of the planes.
Location accuracy
This is limited by the tolerances for flatness and squareness. The common is
where one plane, usually in largest , is the principal datum, and in others are
referred to this for squareness. see figure 5 where X is the principal datum.
yy
x z
Fig: 5 Locational Accuracy of Principal Datum(X)
Tolerances
Assign flatness tolerances to each principal datum, and squareness tolerances
to the other datums relative to the principal.
X
Z

4. Design for Manufacture and Assembly
Datum Systems
238
Note: sometimes it may be necessary to assign special requirements to the
flatness tolerance such as “surface must not be convex”, the latter to ensure no
rock when assembled.
Grouped datum plane and spigot assembling
with Grouped datum plane and recess.
Fig: 6 . Positional Datum Groups
Function
This system controls the movement of one component relative to the other in 5
degrees of freedom. The 6th degree not controlled by the system is rotation
about OZ. The two planes control 3 degrees of freedom. Viz., translation in the
Z direction, and rotation about OX and OY; the spigot and recess control 2
degrees of freedom, viz., translation in the X and Y directions. This system is
used as a datum group for position, concentricity or symmetry.
Geometric analysis
The planes are the principal datums with zero position tolerance. The spigot
and recess are the datums with zero position and squareness tolerances all on
MMC, relative to the principal datums. Design the spigot short in length since a
long spigot introduces redundancy by restraining rotational freedom about OX
and OY,which is the function of the planes.
Location accuracy
This is limited only by the fit C between the spigot and recess and the flatness

5. Design for Manufacture and Assembly
Datum Systems
239
DIA
1
Group
No
.001
DIA
Magnitude
Geometry Tols MMC
No of
Features
1B
(a)
Feature
Letter
POSN
&SQ
Type
Datum
Features
A
Y
-0.304
25.4B
O
A
of the planes. _
Take as criterion C=C±k where C is the mean fit and k is the permissible
variation.
Basic size
Choose this from data sheets as appropriate.
Fit, Design sizes and Tolerances
The fit between spigot and recess should be chosen to suit the location
accuracy required. Confine the choice to the fits given in data sheets.
Do not specify flatness tolerances for the planes unless unusually precise
location is required.
Drawing practice
Show the spigot and plane as one geometric group, and the recess and plane as
another. See figure 7 and use tabular method (a) in general; Method (b) may be
used if there is only one positional groups
Geometric Groups and Tolerances

6. Design for Manufacture and Assembly
Datum Systems
240
(b)
Fig: 7 (a) Tabular Method (b) sketch for Using one
positional Groups
Example, figure 6
Design requirements
Location accuracy to be for translation 0.0254mm
Basic size for recess and spigot 25.4mm from data sheet
Fit 1.01H8h8 from data sheet giving
Recess: 25.4+0.0305
And spigot: 25.4-0.0305
Location accuracy is 0.0305± 0.0305
This is close enough to the design requirement to be satisfactory.
Grouped Datum Plane , Spigot and Hole
assembling with Grouped Datum Plane,
Recess and Pin. See figure 8.
Function
This system controls the relative movements of two components in all 6 degrees
of freedom, but rotation about OZ less precisely than the others. This system is
used mainly as a datum group for positional features.
Geometric analysis
The planes are principal datums with zero position tolerances. The spigot and
recess are datums with zero position and squareness
tolerances on MMC relative to the principal datums.

7. Design for Manufacture and Assembly
Datum Systems
241
Fig:8 Spigot & Hole with Recess & Pin Assembly (Grouped
The hole and pin are datums having position and squareness tolerances MMC
relative to the datum spigot and plane and the datum spigot and plane and the
datum recess and plane
Design spigot short in length for the same reason as in 3.22 above.
Location accuracy
Translational movement in the X, Y and Z directions is limited by the fit C
between the spigot and recess and by the flatness of the planes. Take as
before the criterion.
_
C=C±k
Rotation about OX and OY is limited by the flatness of the planes, about OZ by
the fit between the spigot and recess and the hole and pin. The clearance
between the latter including provision for the position tolerances for the
position tolerances for the hole and pin. Take as criterion the mean angular
play.ie, at minimum material conditions with no positional errors present.

8. Design for Manufacture and Assembly
Datum Systems
242
Geometric Groups and Tolerances.
1
Group
No
0.1 dia
O dia
Magnitude
Geometry Tols MMC
No of
Features
1B
C 1
Feature
Letter
POSN
&SQ
POSN
&SQ
Type
Datum
Feature
A
Fig: 9 (a)
9(b) Examples.-Grouped Datum Planes with spigot
and Hole Assembly
Basic Sizes
Choose from data sheets as appropriate.
Fits, design Sizes and Tolerances
The fit between the spigot and recess should be chosen to suit the location
accuracy required. Confine your choice to the fits shown in data sheets 4,5 and
6 for Hole basis; Hole Basis is preferred.
Do not specify flatness tolerances for the planes unless unusually location is
X
Y22.0T.P
A
25.000
5.000 DIA C
+.075
Datum Face A
POSN & SQ TOL O dia MMCdia B
+0.003
POSN & SQ TOL
0.1 dia MMC
Datums Spigot B MMC
& Face A.
5.000 DIA
+.075
22.0T. Y
C
X
+0.003
25.000 dia B
A

9. Design for Manufacture and Assembly
Datum Systems
243
required.
The fit between the hole and pin must satisfy the location accuracy required
and also provide sufficient C min to allow for position tolerances. Confine your
choice of fit to those given for positional fits in data sheets; the shaft basis will
be applicable here.
Drawing practice
Show the plane, spigot and hole as one geometric group, with the plane as
principal datum for the group. See figure 9(a). Similarly the plane would be
shown as principal datum for the recess and the pin in the other component.
The tabular method (a) in figure 9 is preferred in general; method (b) may be
used if there is only one positional group other than the datum group.
Example.
Fig:10.Spigot & Hole with Recess & Pin Assembly
(Grouped Datum Planes)
Design requirements:
Location accuracy to be
For translation 0.03 0.03mm
For rotational 40 minutes of arc
Basic size,
For recess and spigot 25.0mm
For pin and hole 5.0mm

10. Design for Manufacture and Assembly
Datum Systems
244
Both from data sheet
Choose hole basis for both fits.
Assign position tolerances as follows:
For spigot 0 dia MMC
For hole 0.15 dia MMC
For recess 0 dia MMC
For hole for pin 0.15 dia MMC
For concentricity
Of two dies of pins 0.04dia MMC
Cmin for spigot and recess
=0+0.10
=0
For hole and pin = 0.15+0.15+0.04+0.04
= 0.38
Provisional design sizes are as follows:
Recess=25.0: spigot=25.0
Pin = 5.0-0.38: hole = 5.0
=4.62
Choose fits from data sheet as follows:
Spigot and recess = 25.0 H8h9
Giving recess 25.000+0.033
And spigot 25.000-0.033
And hole and pin 5.0 H7h9
Giving hole 5.000+0.075
And pin 4.73-0.03
The location accuracy for translation
=0.033+/-0.033
This is regarded as satisfactory.
The maximum angular play
=(5.075-4.700)+(25.033-24.963)*10800/n
=69 minutes of arc.
Criterion for location accuracy is therefore 35 minutes of arc approximately
and hence is satisfactory.
The position tolerances for the pin and the corresponding hole would be
modified to suit the new Cmin 0.21let position tolerance
For hole =0.1 dia MMC
For pin =0.1 dia MMC
For concentricity of
two diameters of pin= 0.01dia MMC
And let C=0.03
See figure 9
Grouped Datum Plane, Spigot and Tongue,

11. Design for Manufacture and Assembly
Datum Systems
245
Assembling with Grouped Datum Plane,
Recess and Gap. (Fig 11)
Fig: 11. Spigot & Tongue Assembling with Recess
and gap (Grouped Datum Planes)
Function
This system performs a similar function to 3.3 above, except that rotation
about OZ can be more precisely controlled.
Geometric Analysis
For the planes, spigot and recess same remarks apply as in 3.32. The tongue
and gap are also datum related to the other datums, but tolerances are
assigned for symmetrically and squareness instead of for position and
squareness.
Location Accuracy
In principle the same remarks apply as in 3.3.
Basic sizes
Choose from data sheets as appropriate
Fits, Design sizes and Tolerances
In principle the same remarks apply as in 3.3 above, except that the symmetry
tolerance for the tongue relative to the spigot or for the gap relative to the

12. Design for Manufacture and Assembly
Datum Systems
246
recess can be small, even zero on MMC.This requirement is much easier to
attain with this design than with the corresponding position tolerances in
section 3.3. Confine your choice of fit to those given in data sheets for hole
basis; another data sheet for shaft basis; hole basis is preferred
Drawing practice
Show the plane, spigot and tongue as one geometric group with the plane as
principal datum for the group see figure 9(a). Similarly the plane would be
shown as the principal datum for the recess and pin other geometric group.
The tabular method (a) in figure 9 is preferred in general; Method (b) may be
used if there is only one positional group other than the datum group.
.
Fig 12(a)
Fig 12 (b)

13. Design for Manufacture and Assembly
Datum Systems
247
Grouped Datum Plane and Pins assembling
with Grouped Datum Plane and Holes. See
Figure 13
Fig 13 Grouped Datum Plane and Pins assembling with Grouped Datum
Plane and Holes
Function
This system controls the relative movements of the two components in all 6
degrees of freedom and in principle relation as precise as translation. The two
planes control 3 degrees of freedom viz. Translation in X and Y directions and
rotation about OZ.
Datum planes
Datum pins
O
Datum plane
X Y
O
Datum holes
1.2 TP
Y
Z
2 Holes
0.21500±0.0009 dia
X
Z

14. Design for Manufacture and Assembly
Datum Systems
248
Fig :14 Tabular method. Plane as datum for pins
Geometric Analysis
The planes are principal datums with zero position tolerances. The pins and
holes are datums with position and squareness tolerances
on MMC related to their respective principal datums.
Location Accuracy
Translation in the Z direction and rotation about OX and OY is limited by the
flatness of the datum planes. Translation in the X and Y directions and
rotation about OZ is limited by the fit between the holes and pins the
clearance between the later including provision for the position tolerances for
the holes and pins. Take as criterion the mean angular play calculated as half
the maximum angular play ie at minimum material conditions with no
positional errors present.
Magnitude
2 Holes
0.21500±0.0009 dia
1.2 TP
No of
Features
Letter
Group
No
B
1 2
POSN
&SQ
.001
DIA
Geometric Groups & Tolerances
Feature Geometry Tols MMC
Type
2.9 TP
A
1.2 TP
2 Holes
0.21500±0.0009 dia
A
Datum
Feature
2.9 TP
A

15. Design for Manufacture and Assembly
Datum Systems
249
Basic Sizes
Choose from data sheets 2 or 3 as appropriate.
Fits, Design Sizes and Tolerances
Do not specify flatness tolerances for the planes unless unusually precise
location is required.
The fits between the holes and pins must satisfy the location accuracy
required and also provide sufficient Cmin to allow for position tolerances .
Assign the same position tolerances to each pin and to each hole. Confine your
choice to the positional fits in data sheets 4 and the shaft basis may well be
applicable here see data sheet 7.
Drawing practice
Show the plane and the two holes as one geometric group with the plane as
datum for the group. see figure 14similarly the plane would be shown as
datum for the pins in the other geometric group. The tabular method (a)in
Figure 1.14is preferred in general method (b) may be used if there is only one
positional group other than the datum group.
Example, Figure 14
Design Requirement
Location accuracy to be for rotation of 3 minutes of arc
Basic size for pins and holes 6.35mm from data sheet2
Fit (on shaft basis)6.35 h8c9 from data sheet 7
giving pin 6.35 -- .0009
and hole 6.4262 + .0014
Cmin =.003 permitting .0015 dia MMC position tolerances for the pins and
the holes.
The maximum angular play
=(.00531.5) x(10.800/π)
=12 minutes of are approx.
Criterion for location accuracy is 6 minutes of arc and this is too great in
relation to the design requirement.
Choose fit (on shaft basis) as 6.35 h8E8 from data sheet 7
giving pin 6.35 -- .0009
And hole 6.4262 + .0009
The maximum angular play
=(.00281.5) x (10.800/π)
=6.5 minutes of are approx.
Criterion for location accuracy is thus 3.25 minutes of arc and in this case is
regarded as satisfactory.
Cmax = -.001
Position tolerances for strict interchangeability would be .005 dia but are
considered to be too small.
If we choose .001 dia MMC position tolerances for both the pins and the holes
the virtual sizes of pin and hole become secured and then drilled and reamed
for the insertion of dowels, which are normally a press fit.

16. Design for Manufacture and Assembly
Datum Systems
250
If the cover Figure 1.13 were dealt within this way a suitable note would be
inserted on the management drawing such as in figure 1.14. The t chosen here
is 6.35h8s7. The holes B would then not ensure strict interchangeability
between components but is an economical solution for small to medium Pin
.251and Hole .250
Thus theoretically giving interference. However the metal interference will be
only on one side of each pin and hole and will not be greater then .0005 Hence
the fits and tolerances chosen are regarded as satisfactory.
Use of Dowels
This system is similar in design to the datum system of section 3.5 However
the dowels generally play no part in the control during production. Usually the
components are assembled together adjusted quantity production.
Fig 15: Tabular method. Plane as datum for pins
In the datum systems described in section 3 above the principal datum was
invariably the plane or at surface and the spigot was made short in length to
ensure that its function did not conflict with that of the planes. In same cases
however such as in figure 15 the shaft may be used to align the component on
assembly and is then made for the better to achieve this function. The shaft
becomes the principal datum in the datum system and the surface Y is
tolerenced for squareness in relation to Z as shown in figure 15. A shaft washer
is inserted under the head so ads to provide for errors in squareness..
Magnitude
2 Holes
0.21500±0.0009 dia
1.2 TP
No of
Features
Letter
Group
No
B
1 2
POSN
&SQ
.001
DIA
Geometric Groups & Tolerances
Feature Geometry Tols MMC
Type
2.9 TP
A
1.2 TP
2 Holes
0.21500±0.0009 dia
A
Datum
Feature
2.9 TP
A