Apparatus for measuring the roundness of a surface of an object

The apparatus comprises a bifurcated head rotatably mounted upon a spring loaded arm. The head has two edge plates which can be brought into tangential contact with the periphery of a rotating object. When the head is brought into contact with objects of different diameters, the points of contact with the edge plates progress along location locus lines which, when produced, intersect an an apex. A displacement transducer mounted upon the head has a spring loaded plunger with a probe which is contacted to and detects inaccuracies upon the periphery of the object. In order to accommodate test objects of different diameters, the displacement transducer is bodily movable along an axis of adjustment relative to the head. The point of contact between the probe and test object will, between objects of different diameter, progress along a straight measurement locus line parallel to or coincident with the axis of adjustment. This measurement locus line passes through the apex but does not bisect the included angle between the location locus lines. This arrangement is mechanically simple yet gives unequal angular spacings between the points of contact which do not depend on the diameter of the test object. This facilitates the application of accurate harmonic (Fourier) reconstruction of the roundness profile of the test object. No precision turntable or spindle is required and the method is therefore suitable for in situ measurement. The diameter of the test object need not be known.

This invention relates to an apparatus for measuring the roundness of a 
surface of an object. 
The performance and durability of many industrial products greatly depends 
upon the departures from truly round form of components having nominally 
round e.g. cylindrical and spherical surfaces. In general, for engineering 
components, these departures from roundness are small, or very small, 
compared with the diameter. Devices for the measurement of departures from 
roundness are widely used in industry and elsewhere, and are of various 
forms. 
The subsequent descriptions indicate various known methods of measuring the 
roundness of a cylindrical object (to be termed the test object). The 
measurement of objects having other shapes e.g. spherical are in general 
performed in a like manner. 
Known roundness measurement methods are performed using a displacement 
sensing device, generally termed a displacement transducer. For roundness 
measurement, most such displacement transducers have or are linked to a 
sensing member which is contacted to the surface of the test object. The 
movements of this sensing member with respect to the displacement 
transducer cause changes in the displacement indication from the 
transducer. However, some known displacement transducers have a sensing 
member which does not contact the test object, the displacement indication 
relating instead to the distance of the sensing member from the test 
object surface. The use of this other type of known transducer is not 
described as it is generally used in a like manner. 
One common known method of roundness accuracy measurement involves the use 
of a precision rotary table, upon which the test object is mounted. The 
sensing member of a displacement transducer contacts the periphery of the 
test object, so that as the test object rotates the departures of the test 
object from the round form are measured. This method has several 
limitations. The cylindrical axis of the test object must be approximately 
aligned with the rotational axis of the table. The bearings upon which the 
rotary table is mounted must be of high precision to avoid measurement 
errors, and so are expensive. Moreover, such bearings generally have 
modest load capacities, preventing the roundness measurement of heavy test 
objects. 
An alternative known method involves the use of a precision rotary spindle, 
the test object being mounted on a fixed table, and the axes of the 
spindle and test object being approximately aligned. The spindle has a 
cranked portion on which a displacement transducer is mounted. The sensing 
member of the displacement transducer contacts the periphery of the test 
object and is rotated about the test object. If lengthy test objects are 
to be measured, this method requires a lengthy cranked transducer mounting 
arm which is liable to flexure, and which accentuates spindle bearing 
errors. 
A further known alternative method (to be termed the multiple contact 
method) avoids the need for precision rotary tables or precision spindles 
and can yield useful results even if the test object is rotated upon 
bearings of poor quality. This is a major advantage, as it allows 
roundness measurements to be performed in situ. Components may be measured 
during the manufacturing process without removal from the manufacturing 
machine. Components may also be measured during the servicing of machinery 
without the need for extensive disassembly. A further advantage is that in 
many instances the apparatus may be made smaller and cheaper than that 
required for either of the alternatives described above. The method 
involves the use of a measuring device (to be termed a measuring head) 
which contacts the test object at several locations spaced about its 
periphery, and incorporates one or more displacement transducers. Those 
contacts used for measurement are arranged to lie upon one transverse 
section of the test object. 
In simpler known arrangements, two members (to be termed location members) 
contact the test object and locate the measuring head upon the test 
object. The position of the measuring head is thus sensitive to the 
departures from roundness of the test object at these two contacts (to be 
termed location member contacts) which therefore act as both location and 
measuring contacts. The location members may be of any suitable form, but 
are commonly of part spherical form, or of a form having a straight edge 
which is arranged to make tangential contact with the test object. A 
single displacement transducer upon the head has a sensing member which 
contacts the test object (this contact is to be termed a sensing member 
contact) to give a total of three measuring contacts (such an arrangement 
is to be termed a simple measuring head). As the test object is rotated 
with respect to the measuring head, departures from truly round form 
result in displacements at the transducer corresponding to a weighted 
combination of the departures from roundness at the three measuring 
contacts. These displacements may then be used as an indication of the 
departures of the object from truly round form. However the displacements 
at the transducer do not in general correspond directly to the departure 
of the object from truly round form, as this simple measuring head 
introduces considerable distortion. A skilled operator may be able to 
interpret the transducer displacement indication to give an improved 
estimate of the actual departures from roundness of the test object, but 
often this is unreliable or impossible. 
Alternative known types of measuring head, not of the simple form, may 
introduce less distortion than a simple measuring head. In one such type, 
two location members are again used for location of the measuring head 
upon the test object, and a single displacement transducer is again used. 
However, more than one sensing member is employed, these being contacted 
to the test object at positions spaced around its periphery, and their 
movements being transmitted as a weighted combination to the displacement 
transducer by means of a system of linkages. In another such type, two 
location members are again used for location of the measuring head upon 
the test object, but two or more displacement transducers are used, these 
being linked to sensing members contacted to the test object at positions 
spaced around its periphery. The displacement indications from these 
transducers, which are in the form of electrical signals, are merged 
according to a weighted combination to product a resultant displacement 
indication. A further known alternative merges the electrical signals from 
two simple measuring heads arranged upon one transverse section of the 
test object. All of these alternatives involve undesirable mechanical 
complexity. 
More sophisticated devices use a simple measuring head having three 
measuring contacts, in conjunction with a signal processing technique 
which compensates for, and so largely removes, the distortion (to be 
termed the transfer function distortion) introduced by the measuring head, 
to give a closer indication of the departure of the test object from truly 
round form. The transfer function distortion is calculated, knowing the 
mechanical arrangement of the measuring head, and in particular the 
angular spacing of the measuring contacts with the test object, subtended 
at the centre of the test object. An appropriate inverse distortion is 
then applied to the displacement indication given by the measuring head, 
using the method of inverse filtering, so as largely to remove the 
transfer function distortion. Several methods of applying this inverse 
filtering may be used, including matrix methods, convolution using a 
Finite Impulse Response filter, and fast convolution using Fast Fourier 
transforms. All these examples are digital methods applied to sampled 
data. This approach employs a mechanically simple measuring head, which is 
a considerable advantage. The signal processing required may be 
conveniently performed by a microcomputer. 
In employing this technique, problems are encountered in the design of a 
measuring head which yields accurate results after the inverse filtering 
has been applied, and which is suitable for test objects of different 
diameters. The behaviour of a measuring head in these respects is 
dependent upon the angles subtended by the measuring contacts at the 
centre of the test object, and the manner in which these angles vary with 
test objects of different diameters. Both of these aspects will now be 
considered. 
In attempting to ensure that the predicted departures from roundness 
following the inverse filtering closely reflect the true form of the test 
object, a major consideration is that a simple measuring head will fail to 
detect certain forms of out of roundness in the test object. For these 
forms, the displacements at the measuring contacts effectively cancel each 
other so that the resultant transducer displacements are either very 
small, or indeed zero. This reduces the accuracy of the measurement 
process. Suitable selection of the angles subtended at the centre of the 
test object by the measuring contacts can alleviate this problem, but if 
these angles vary with test object diameter, then this approach is 
difficult. This problem of the insensitivity of the measuring head to 
certain forms of out of roundness is especially marked in those cases 
where the subtended angles are equal. 
With some known designs of simple measuring head, the subtended angles 
ALPHA and BETA between the sensing member contact and the respective 
location member contacts vary with the test object diameter. This is a 
serious disadvantage, as it prevents their advantageous selection to 
alleviate the problem of insensitivity. Furthermore, the inverse filtering 
required is dependent upon the test object diameter, which may not be 
known without separate diametral measurement. This complicates the 
roundness measurement procedure, and places the onus for correct diametral 
measurement upon the operator. In some circumstances, for example when 
only a minor part of the circumference of the test object is accessible, 
such diametral measurement may be difficult or impossible. 
With other possible designs of simple measuring head, the measuring head 
may be adjusted so that the subtended angles remain constant, but in order 
to make the appropriate adjustment, the test object diameter must be 
known. 
Other known designs of simple measuring head ensure that the subtended 
angles are invarient with test object diameter. This is achieved by the 
use of two location members each having a straight edge which is arranged 
to make tangential contact with the test object. The location member 
contacts thus subtend an angle at the centre of the test object which is 
independent of the test object diameter. The sensing member of a 
displacement transducer is arranged to move on a line bisecting this 
subtended angle, so that ALPHA always equals BETA. Thus, the subtended 
angles are invariant, but also equal, this latter being a grave 
disadvantage in that it accentuates the problem of insensitivity. 
A further known design ensures that the subtended angles are invariant with 
test object diameter, and furthermore are unequal. This is achieved by the 
use of two location members each having a straight edge which is arranged 
to make tangential contact with the test object. The location member 
contacts thus subtend an angle at the centre of the test object which is 
independent of the test object diameter. The sensing member also has a 
straight edge which is arranged also to make tangential contact with the 
test object. The orientation of the sensing member is controlled by a 
system of guides so that the included angles ALPHA and BETA remain 
constant. In this design, the contact between the sensing member and the 
test object changes its position upon the sensing member for test objects 
of different diameters. 
This last mentioned arrangement involves considerable mechanical 
complexity. The sensing member must be oriented by a suitable system of 
guides which must maintain the orientation to a high degree of accuracy, 
and which must maintain that same orientation when the sensing member is 
replaced when it has become worn. Furthermore, the sensing member must be 
constrained so that the straight edge of the sensing member is coplanar 
with the straight edges of the location members. Little space may be 
available for such a guide system. 
An alternative possible configuration which would avoid the problem of 
insensitivity encountered in the simple measuring head is the use of a 
measuring head having two or more displacement transducers and sensing 
members, used in conjunction with a modified form of signal processing 
which not only performs the inverse filtering but also merges the signals 
from the transducers into a single signal. If appropriately configured by 
suitable selection of subtended angles, it may be arranged that if one of 
the displacement transducers is insensitive to a given form of out of 
roundness, then at least one other transducer will be sensitive to that 
form of out of roundness. The signal processing takes account of the forms 
to which each transducer is insensitive and for these forms, reliance is 
placed upon the other, sensitive transducer or transducers. The modified 
signal processing thus involves not only the method of inverse filtering, 
but also involves the combination of the signals from two or more 
displacement transducers to give a roundness indication. In order to do 
this, the subtended angles between the measuring contacts must be known. 
Measuring heads for which the sum of the subtended angles between the two 
location member contacts and any sensing member contact is less than 180 
degrees are compact, and may easily be applied to the test object. 
However, if the sum of the subtended angles exceeds 180 degrees, then a 
split design may be needed to allow assembly of the measuring head around 
the test object. An advantage is that the transducer output may be greater 
than in the former case, although the problem of insensitivity to certain 
forms of out of roundness remains. 
Whereas the multiple contact method described above has significant 
advantages when e.g. in situ measurement of the test object is desired 
and/or the test object is long and/or the test object is heavy, it is 
subject to the above drawbacks. 
An aim of the present invention is to overcome the drawbacks of apparatus 
for carrying out the multiple contact method of roundness measurement by 
the provision of apparatus which has an adjustment facility to compensate 
for differences in the diameter of objects being tested. Moreover, the 
design of this adjustment facility is such that without requiring 
knowledge of the diameter of a particular test object, the subtended 
angles will be unequal and substantially invariant, allowing their 
advantageous selection to alleviate the problem of the insensitivity of 
the measuring head to certain types of out of roundness. There will 
therefore be no substantial variation in the accuracy of the test within a 
range of test object diameters. Furthermore, the mechanical arrangement of 
the apparatus of the present invention is simple, convenient and robust in 
comparison with the alternative means of performing this function. 
In accordance with the present invention there is provided apparatus for 
measuring the roundness of a surface of a relatively rotating object, the 
apparatus comprising a head having a pair of location means angularly 
related such that when brought into contact with the peripheries of 
nominally round objects of different diameters points of contact between 
said location means and said objects will progress with respect to the 
head along straight, non-parallel location locus lines tangential to each 
object, means for aligning the head relative to an object to be measured 
such that the location locus lines lie in a common measurement plane to 
which the axis of relative rotation is perpendicular and at least one 
sensing means which is adjustable relative to the head along an axis of 
adjustment in or parallel to the measurement plane, this axis of 
adjustment being transverse to the bisector of the location locus lines, 
the sensing means having a sensing member mounted thereon to detect the 
periphery of an object being measured at a predetermined measurement point 
when the object is in contact with said location means and aligned, the 
arrangement being such that measurement points of objects of different 
diameters progress along a straight measurement locus line parallel to the 
axis of adjustment and passing through the intersection of the location 
locus lines. 
The sensing means may be disposed between the location means within the 
acute or obtuse angle subtended by the location means at the centre of an 
object being measured. 
Preferably the sensing means contacts the object at the measurement point 
and is responsive thereto. 
Preferably the sensing means incorporates a probe which is convex about an 
axis normal to the measurement plane where the probe is adapted to contact 
the object at the measurement point. 
The sensing means may comprise a sensing device on the head supporting a 
sensing member upon a bearing to allow limited reciprocative movement and 
the sensing member may be spring biassed so as, in use, to contact a probe 
of the sensing member to the object. In this arrangement the bearing 
supporting the sensing member may be a linear bearing and the linear axis 
of this bearing may be parallel to the measurement locus line. 
Alternatively, the sensing means may comprise a sensing device linked to a 
sensing member which is mounted upon a linear bearing upon the head to 
allow reciprocative movement in a direction parallel to the measurement 
locus line, this sensing member being spring biassed so as, in use, to 
contact a probe of the sensing member to the object. 
In yet another alternative construction the sensing means may comprise a 
sensing device linked to a sensing member which is mounted upon a bearing 
upon a support member, the support member being adjustable with respect to 
the head along an axis parallel to the measurement locus line, the bearing 
allowing limited reciprocative movement of the sensing member, the sensing 
member being spring biassed so as, in use, to contact a probe of the 
sensing member to the object. 
In a further modification of the invention the sensing means may be 
responsive to the proximity of the measurement point.

Referring first to FIGS. 1-3, a main body 1 of a measuring head is of 
aluminium alloy, upon which are secured edge-plates 2 and 3. Each 
edge-plate has one straight, wear resisting edge, 2A and 3A respectively, 
of semi-circular cross-section and is of tungsten carbide. The centres of 
curvature of these semi-circular edges 2A and 3A lie within the same plane 
M, termed the measurement plane. The measurement plane M intersects the 
semi-circular surfaces of the edges 2A and 3A at two straight lines, JL 
and KN. These two straight lines, representing location locus lines for 
objects of differing diameters, when produced, intersect at an apex A. The 
line which passes through the apex A, lies in the measurement plane M, 
bisects the angle between the lines JA and KA, and lies between the edges 
2A and 3A is herein defined as the centre line 1A of the main body 1. 
A linear variable differential transformer (LVDT) displacement transducer 
has a body 4 of cylindrical form and a cylindrical measuring plunger 6 
which is free to slide axially into the body 4 upon a linear bearing 21 
against a light spring force. Upon the free end of the measuring plunger 6 
is mounted a spherical probe 7 of tungsten carbide. The cylindrical axis 
of the body 4 is colinear with the centre D of the spherical probe 7. The 
displacement indication from the displacement transducer depends upon the 
axial displacement of the spherical probe 7 with respect to the body 4 of 
the transducer. 
The body 4 of the displacement transducer may slide within a close fitting 
bore 5 within the main body 1. Its axial position is controlled by a 
thumbwheel 8 which provides fine positional adjustment by means of a 
threaded rod 9. The body 4 of the displacement transducer may be fixed 
relative to the main body 1 by means of a pinch screw 10. The centre line 
5A of the bore 5 lies within the measurement plane M. 
The main body 1 is rotatably mounted, by ball bearings, upon a support arm 
11 which is in turn rotatably mounted upon a mounting block 12. In 
operation, the mounting block 12 is secured to a suitable fixed support 
adjacent to the test object 30. The support arm 11 is loaded by means of a 
spring 13 so that the edges 2A and 3A are pressed against the test object 
30. The attachment of the mounting block 12 is adjusted so that the 
measurement plane M is perpendicular to the cylindrical axis of the test 
object 30. The body 4 of the displacement transducer is then advanced by 
adjustment of the thumbwheel 8 until the spherical probe 7 is brought into 
contact with the test object 30. Movement of the body 4 is continued 
toward the test object 30 lightly and partially to compress the spring 
loading of the plunger 6 and to bring the displacement transducer into its 
linear working region. The body 4 of the displacement transducer is then 
fixed by means of the pinch screw 10. 
The points of contact between the measuring apparatus and the test object 
30 are B, C and G, which lie within the measurement plane M. Points B and 
C lie within the lines JA and KA respectively. The centre line 1A of the 
main body 1 passes through the centre O of the test object 30 and bisects 
the angle between the radii OB and OC. The centre line 5A of the bore 5 in 
which the transducer 4 slides is not parallel to the centre line 1A of the 
main body 1; rather it is inclined at an angle, indicated as GAMMA, to the 
centre line 1A of the main body 1, so that the angles ALPHA and BETA 
subtended by the arcs BG and GC at the centre O of the test object 30 are 
unequal. The radius OG is inclined at an angle DELTA to the centre line 1A 
of the main body 1. 
The inclination, GAMMA, of the centre line 5A of the bore 5 to the centre 
line 1A of the main body 1 and the location E of the intersection of the 
centre line 5A of the bore 5 with the centre line 1A of the main body 1 
must be appropriately chosen so that DELTA, and thus ALPHA and BETA, 
remain constant over a range of test object diameters. 
The geometrical relationships indicated in FIGS. 1-3 and discussed above 
are those relating to a test object of perfectly cylindrical form. If the 
test object is not of perfectly cylindrical form, these geometrical 
relationships may not be exact. However, if the departures of the test 
object from perfectly cylindrical form are small then their effect upon 
the geometrical relationships, and in particular upon the angular spacing 
of the points of contact, is small. 
In this embodiment, axial movement of the cylindrical body 4 of the 
displacement transducer with respect to the main body 1 of the measuring 
head provides the gross movement required to accommodate test objects of 
various different diameters. The much smaller reciprocative movements of 
the spherical probe 7 with respect to the main body 1 caused by departures 
from roundness in a test object give rise to axial displacement movements 
at the displacement transducer. The colinear arrangement of the body 4 of 
the displacement transducer and the spherical probe 7 obviates the need to 
rotationally align the body 4 of the displacement transducer with the main 
body 1. 
The test object is then rotated about its cylindrical axis, and the output 
from the displacement transducer is recorded, either manually, or 
preferably automatically, at angular intervals. The inverse distortion may 
be applied to the data to provide an indication of the departures from 
roundness of the test object. 
From the foregoing it will be seen that if the linear working region of the 
displacement transducer extends over a considerable distance, then the 
need for positional adjustment of the body 4 of the transducer with 
respect to the main body 1 of the measuring head will be minimised or even 
completely eliminated. 
A second embodiment of the invention will now be described with reference 
to FIG. 4 of the accompanying drawings. Parts like or having a similar 
function to those of the first embodiment have been given like references. 
Referring to FIG. 4, a main body 1 of a measuring head is of aluminium 
alloy, upon which are secured edge-plates, 2 and 3. Each edge-plate has 
one straight wear resisting edge, 2A and 3A respectively, of semi-circular 
cross-section, and is of tungsten carbide. The centres of curvature of 
these semi-circular edges 2A and 3A lie within the same plane, termed the 
measurement plane. The measurement plane intersects the semi-circular 
surfaces of the edges 2A and 3A at two straight lines, JL and KN. These 
two straight lines, representing location locus lines for objects of 
differing diameters, when produced, intersect at an apex A. The line which 
passes through the apex A, lies in the measurement plane, bisects the 
angle between the lines JA and KA, and lies between the edges 2A and 3A is 
herein defined as the centre line 1A of the main body 1. 
A linear variable differential transformer (LVDT) displacement transducer 
has a body 4 of cylindrical form and a cylindrical measuring plunger 36 
which is free to slide axially into the body 4 upon a linear bearing 21 
against a light spring force. Over the free end of the measuring plunger 
36 is a capped tubular thumbwheel 37 upon which is mounted a spherical 
probe 7. The thumbwheel 37 is attached to the measuring plunger 36 by a 
threaded arrangement so that the axial position of the spherical probe 7 
with respect to the measuring plunger 36 may be adjusted by rotation of 
the thumbwheel 37. The cylindrical axis of the body 4 is colinear with the 
centre D of the spherical probe 7. 
The body 4 of the displacement transducer is secured within a close fitting 
bore 5 within the main body 1. The centre line 5A of the bore 5 lies 
within the measurement plane. 
The main body 1 is rotatably mounted, by ball bearings, upon a support arm 
11 which is in turn rotatably mounted upon a mounting block 12. In 
operation, the mounting block 12 is secured to a suitable fixed support 
adjacent to the test object 30. The support arm 11 is loaded by means of a 
spring 13 so that the edges 2A and 3A are pressed against the test object 
30. The attachment of the mounting block 12 is adjusted so that the 
measurement plane is perpendicular to the cylindrical axis of the test 
object 30. The spherical probe 7 is then advanced by adjustment of the 
thumbwheel 37 until the spherical probe 7 is brought into contact with the 
test object 30. Adjustment of the thumbwheel 37 is continued further, 
lightly and partially to compress the spring loading of the measuring 
plunger 36 and to bring the displacement transducer into its linear 
working region. 
The geometrical relationships appertaining to this second embodiment are 
similar to those of the first embodiment. 
In this second embodiment, axial movement of the spherical probe 7 with 
respect to the measuring plunger 36 provides the gross movement required 
to accommodate test objects of various different diameters. The much 
smaller reciprocative movements of the spherical probe 7 with respect to 
the main body 1 caused by departures from roundness in a test object give 
rise to axial displacement movements at the displacement transducer. 
A third embodiment of the invention will now be described with reference to 
FIG. 5 of the accompanying drawings. Parts like or having a similar 
function to those of the first embodiment have been given like references. 
Referring to FIG. 5, a main body 1 of a measuring head is of aluminium 
alloy, upon which are secured edge-plates 2 and 3. Each edge-plate has one 
straight, wear resisting edge, 2A and 3A respectively, of semi-circular 
cross-section, and is of tungsten carbide. The centres of curvature of 
these semi-circular edges 2A and 3A lie within the same plane, termed the 
measurement plane. The measurement plane intersects the semi-circular 
surfaces of the edges 2A and 3A at two straight lines, JL and KN. These 
two straight lines, representing location locus lines for objects of 
differing diameters, when produced, intersect at an apex A. The line which 
passes through the apex A, lies in the measurement plane, bisects the 
angle between the lines JA and KA, and lies between the edges 2A and 3A is 
herein defined as the centre line 1A of the main body 1. 
A cylindrical measuring plunger 40 is mounted upon a linear bearing 41 of 
cylindrical outer form which is located within a bore 5 within the main 
body 1, the arrangement being such that the measuring plunger 40 is free 
to slide into the main body 1. Upon one end of the measuring plunger 40 is 
mounted a spherical probe 7 of tungsten carbide. The centre D of the 
spherical probe 7 lies within the measurement plane and is colinear with 
the centre line 5A of the bore 5. Over the other end of the measuring 
plunger 40 is a tubular thumbwheel 43 having a domed cap 44. The 
thumbwheel 43 is attached to the measuring plunger 40 by a threaded 
arrangement so that the axial position of the domed cap 44 with respect to 
the measuring plunger 40 may be adjusted by rotation of the thumbwheel 43. 
A linear variable differential transformer (LVDT) displacement transducer 
has a body 45 and a measuring arm 46 which is rotatably mounted with 
respect to the body 45, and which is rotationally biassed by a light 
spring torque. The displacement indication from the displacement 
transducer depends upon the angular rotation of the measuring arm 46 with 
respect to the body 45. The body 45 of the displacement transducer is 
secured to the main body 1. The light spring torque causes the measuring 
arm 46 to contact the domed cap 44 and causes the spherical probe 7 to 
extend from the main body 1. 
The main body 1 is rotatably mounted, by ball bearings, upon a support arm 
11 which is in turn rotatably mounted upon a mounting block 12. In 
operation, the mounting block 12 is secured to a suitable fixed support 
adjacent to the test object 30. The support arm 11 is loaded by means of a 
spring 13 so that the edges 2A and 3A are pressed against the test object 
30. The attachment of the mounting block 12 is adjusted so that the 
measurement plane is perpendicular to the cylindrical axis of the test 
object 30. The thumbwheel 43 is then adjusted until the spherical probe 7 
is brought into contact with the test object 30. Adjustment of the 
thumbwheel 43 is continued further, lightly and partially to compress the 
spring loading of the measuring arm 46 and to bring the displacement 
transducer into its linear working region. 
The geometrical relationships appertaining to this third embodiment are 
similar to those of the first embodiment. 
In this third embodiment, axial movement of the domed cap 44 with respect 
to the measuring plunger 40 provides the gross movement required to 
accommodate test objects of various different diameters. The much smaller 
reciprocative movements of the spherical probe 7 with respect to the main 
body 1 caused by departures from roundness in a test object give rise to 
rotational displacement movements at the displacement transducer. 
A fourth embodiment of the invention will now be described with reference 
to FIGS. 6, 7 and 8 of the accompanying drawings. Parts like or having a 
similar function to those of the first embodiment have been given like 
references. 
Referring to FIGS. 6-8, a main body 1 of a measuring head is of aluminium 
alloy, upon which are secured edge-plates, 2 and 3. Each edge-plate has 
one straight, wear resisting edge, 2A and 3A respectively, of 
semi-circular cross-section, and is of tungsten carbide. The centres of 
curvature of these semi-circular edges 2A and 3A lie within the same plane 
M, termed the measurement plane. The measurement plane M intersects the 
semi-circular surfaces of the edges 2A and 3A at two straight lines, JL 
and KN. These two straight lines, representing location locus lines for 
objects of differing diameters, when produced, intersect at an apex A. The 
line which passes through the apex A, lies in the measurement plane M, 
bisects the angle between the lines JA and KA, and lies between the edges 
2A and 3A is herein defined as the centre line 1A of the main body 1. 
A linear variable differential transformer (LVDT) displacement transducer 
has a body 4 of cylindrical form and a cylindrical measuring plunger 6 
which is free to slide axially into the body 4 upon a linear bearing 21 
against a light spring force. Upon the free end of the measuring plunger 6 
is mounted a spherical probe 7 of tungsten carbide. The cylindrical axis 
of the body 4 is colinear with the centre D of the spherical probe 7. The 
displacement indication from the displacement transducer depends upon the 
axial displacement of the spherical probe 7 with respect to the body 4 of 
the transducer. 
The body 4 of the displacement transducer may slide within a close fitting 
bore 5 to which it may be fixed by means of a pinch screw 10. This 
arrangement allows occasional axial movement of the body 4 with respect to 
the bore 5 for calibration purposes. In contrast to the previous 
embodiments, the bore 5 is not in the main body 1 of the head, but in a 
carriage 20 which may slide along a linear bearing 18 in one arm of the 
main body 1. The centre line 5A of the bore 5 lies within the measurement 
plane M. The axial position of the carriage 20 is controlled by a 
thumbwheel 8 which provides fine positional adjustment by means of a 
threaded rod 9. The carriage 20 may be fixed relative to the main body 1 
by means of a pinch screw 15. 
The main body 1 is rotatably mounted, by ball bearings, upon a support arm 
11 which is in turn rotatably mounted upon a mounting block 12. In 
operation, the mounting block 12 is secured to a suitable fixed support 
adjacent to the test object 30. The support arm 11 is loaded by means of a 
spring 13 so that the edges 2A and 3A are pressed against the test object 
30. The attachment of the mounting block 12 is adjusted so that the 
measurement plane M is perpendicular to the cylindrical axis of the test 
object 30. The carriage 20 is then advanced along the translational axis 
of the linear bearing 18 by means of the thumbwheel 8 until the spherical 
probe 7 is brought into contact with the test object 30. Movement of the 
carriage 20 is then continued in the same direction, lightly and partially 
to compress the spring loading of the plunger 6 and to bring the 
displacement transducer to the centre of its linear working region. The 
carriage 20 is then fixed by means of the pinch screw 15. Only during 
calibration is the position of the body 4 of the displacement transducer 
changed with respect to the bore 5. 
The points of contact between the measuring head and the test object 30 are 
B, C and G, which lie within the measurement plane M. Points B and C lie 
within the lines JA and KA respectively. The centre line 1A of the main 
body 1 passes through the centre O of the test object 30 and bisects the 
angle between the radii OB and OC. The translational axis of the linear 
bearing 18 is inclined at an angle indicated as GAMMA to the centre line 
1A of the main body 1. The required angular offset of the point of contact 
G of the spherical probe 7 with respect to the centre line 1A of the main 
body 1 subtended at the centre of the test object 30 is indicated as 
DELTA. The centre line 5A of the bore 5 is inclined at this same angle 
DELTA to the centre line 1A of the main body 1, and lies in the 
measurement plane M. 
The inclination GAMMA of the translational axis of the linear bearing 18 
with respect to the centre line 1A of the main body 1 is determined by the 
following consideration. During calibration, which is described more fully 
in a subsequent paragraph, the measuring head is applied to a calibration 
cylinder, and the carriage 20 is positioned along the translational axis 
of the linear bearing 18 so that the centre line 5A of the bore 5 when 
produced passes through the centre of the calibration cylinder. The body 4 
of the displacement transducer is then positioned and fixed with respect 
to the bore 5 so that the transducer is at the centre of its linear 
working region. To adjust the measuring head to accommodate a test object 
30, the carriage 20 is repositioned along the translational axis of the 
linear bearing 18 so that the displacement transducer returns to the 
centre of its linear working region. The inclination GAMMA must be so 
chosen that when this operation has been performed then the centre line 5A 
of the bore 5 when produced passes through the centre of the test object 
30. 
The geometrical relationships indicated in FIGS. 6-8 and discussed above 
are those relating to a test object of perfectly cylindrical form. If the 
test object is not of perfectly cylindrical form, these geometrical 
relationships may not be exact. However, if the departures of the test 
object from perfectly cylindrical form are small, then their effect upon 
the geometrical relationships, and in particular upon the angular spacing 
of the points of contact, is small. 
In this embodiment, movement of the carriage 20 along the linear bearing 18 
provides the gross movement required to accomodate test objects of various 
different diameters. The much smaller movements of the spherical probe 7 
with respect to the main body 1 caused by the departures from roundness of 
the test object 30 give rise to axial displacement movements at the 
displacement transducer. The colinear arrangement of the cylindrical axis 
of the body 4 and the centre D of the spherical probe 7 obviates the need 
to rotationally align the body 4 of the displacement transducer with the 
main body 1. 
In comparison with the previous embodiments, an advantage of this fourth 
embodiment is that the cylindrical axis of the body 4 of the displacement 
transducer is colinear with the radius OG, and is thus perpendicular to 
the surface of the test object 30 at the point of contact G. Thus, the 
axial displacement of the spherical probe 7 with respect to the body 4 of 
the displacement transducer is largely unaffected by small movements of 
the spherical probe 7 away from a colinear position owing to imperfections 
in the linear bearing 21 which supports the plunger 6. Conversely, a 
disadvantage is that the actual subtended angles ALPHA and BETA are 
dependent upon the position of the carriage 20 with respect to the main 
body 1. Thus the displacement indication from the displacement transducer 
is used to indicate when the carriage 20 has been adjusted to the correct 
position so that the subtended angles are those desired. A calibration 
procedure is required prior to measurement. A specific embodiment of a 
calibration procedure is described, with reference to FIG. 6. 
In this procedure, the measuring head is applied to an available 
calibration cylinder of known diameter. Use is made of the provision, both 
in the carriage 20 and the linear bearing 18, of bores 16 and 17 of equal 
diameter which may be made coaxial by appropriate positioning of the 
carriage 20 with respect to the main body 1 along the axis of the linear 
bearing 18. A close-fitting dowel (not shown) is inserted through both 
bores, 16 and 17, thus locating the carriage 20 so that the cylindrical 
axis 5A of the bore 5 intersects the centre line 1A of the main body 1 at 
a point coincident with the centre of the calibration cylinder. The 
carriage 20 is then fixed by means of the pinch screw 1s. The position of 
the body 4 of the transducer is then adjusted with respect to the bore 5 
until the spherical probe 7 touches the calibration cylinder and the 
displacement transducer is brought to the centre of its linear working 
region. The body 4 of the displacement transducer is then fixed with 
respect to the carriage 20 by means of the pinch screw 10. The dowel and 
calibration cylinder are removed and the pinch screw 15 released. This 
completes the calibration procedure. 
A fifth embodiment of the invention will now be described with reference to 
FIG. 9 of the accompanying drawings. Parts like or having a similar 
function to those of the fourth embodiment have been given like 
references. 
Referring to FIG. 9, a main body 1 of a measuring head is of aluminium 
alloy, upon which are secured edge-plates, 2 and 3. Each edge-plate has 
one straight, wear resisting edge, 2A and 3A respectively, of 
semi-circular cross-section, and is of tungsten carbide. The centres of 
curvature of these semi-circular edges 2A and 3A lie within the same 
plane, termed the measurement plane. The measurement plane intersects the 
semi-circular surfaces of the edges 2A and 3A at two straight lines, JL 
and KN. These two straight lines, representing location locus lines for 
objects of differing diameters, when produced, intersect at an apex A. The 
line which passes through the apex A, lies in the measurement plane, 
bisects the angle between the lines JA and KA, and lies between the edges 
2A and 3A is herein defined as the centre line 1A of the main body 1. 
A linear variable differential transformer (LVDT) displacement transducer 
has a body 50 and a measuring spindle 51 which is rotatably mounted on the 
body 50 and is rotationally biassed by a light spring torque. Upon the 
measuring spindle 51 is a measuring arm 53 which may rotate about the 
measuring spindle 51, to which it may be fixed by means of a pinch screw 
54. Upon the other end of the measuring arm 53 is mounted a spherical 
probe 7. The displacement indication from the displacement transducer 
depends upon the angular rotation of the measuring spindle 51 with respect 
to the body 50. 
The body 50 of the displacement transducer is secured to a carriage 20 
which may slide along a linear bearing 18 in one arm of the main body 1. 
The axial position of the carriage 20 is controlled by a thumbwheel 8 
which provides fine positional adjustment by means of a threaded rod 9. 
The carriage 20 may be fixed relative to the main body 1 by means of a 
pinch screw 15. The centre D of the spherical probe 7 lies in the 
measurement plane. 
The main body 1 is rotatably mounted, by ball bearings, upon a support arm 
11 which is in turn rotatably mounted upon a mounting block 12. In 
operation, the mounting block 12 is secured to a suitable fixed support 
adjacent to the test object 30. The support arm 11 is loaded by means of a 
spring 13 so that the edges 2A and 3A are pressed against the test object 
30. The attachment of the mounting block 12 is adjusted so that the 
measurement plane is perpendicular to the cylindrical axis of the test 
object 30. The carriage 20 is then advanced along the translational axis 
of the linear bearing 18 by means of the thumbwheel 8 until the spherical 
probe 7 is brought into contact with the test object 30. Movement of the 
carriage 20 is then continued in the same direction, lightly and partially 
to compress the spring biassing of the measuring spindle 51 and to bring 
the displacement transducer to the centre of its linear working region. 
The carriage 20 is then fixed by means of the pinch screw 15. Only during 
calibration is the angular position of the measuring arm 53 changed with 
respect to the measuring spindle 51. 
The points of contact between the measuring head and the test object 30 are 
B, C and G, which lie within the measurement plane. Points B and C lie 
within the lines JA and KA respectively. The centre line 1A of the main 
body 1 passes through the centre O of the test object 30 and bisects the 
angle between the radii OB and OC. The translational axis of the linear 
bearing 18 is inclined at an angle indicated as GAMMA to the centre line 
1A of the main body 1. The required angular offset of the point of contact 
G of the spherical probe 53 with respect to the centre line 1A of the main 
body 1 subtended at the centre of the test object 30 is indicated as 
DELTA. 
The inclination GAMMA of the translational axis of the linear bearing 18 
with respect to the centre line 1A of the main body 1 is determined by the 
following consideration. During calibration, which is described more fully 
in a subsequent paragraph, the measuring head is applied to a calibration 
cylinder, and the carriage 20 is positioned along the translational axis 
of the linear bearing 18 so that the rotational axis Q of the measuring 
spindle 51 is at a known position with respect to the main body 1. The 
measuring spindle 51 is then rotationally positioned and fixed with 
respect to the measuring arm 53 so that the spherical probe 7 is contacted 
to the calibration cylinder and the displacement transducer is at the 
centre of its linear working region. The form of the measuring arm 53 and 
spherical probe 7, in particular the diameter of the spherical probe 7 and 
the distance DQ between its centre D and the rotational axis Q of the 
measuring spindle 51 are such that the required angular offset DELTA is 
achieved. To adjust the measuring head to accommodate a test object 30, 
the carriage 20 is repositioned along the translational axis of the linear 
bearing 18 so that the displacement transducer returns to the centre of 
its linear working region. The inclination GAMMA must be so chosen that 
when this operation has been performed then the angular offset remains at 
the required value DELTA. 
The geometrical relationships indicated in FIG. 9 and discussed above are 
those relating to a test object of perfectly cylindrical form. If the test 
object is not of perfectly cylindrical form, these geometrical 
relationships may not be exact. However, if the departures of the test 
object from perfectly cylindrical form are small, then their effect upon 
the geometrical relationships, and in particular upon the angular spacing 
of the points of contact, is small. 
In this embodiment, movement of the carriage 20 along the linear bearing 18 
provides the gross movement required to accomodate test objects of various 
different diameters. The much smaller movements of the spherical probe 7 
with respect to the main body 1 caused by the departures from roundness of 
the test object 30 give rise to rotational displacement movements at the 
displacement transducer. 
A disadvantage of this fifth embodiment, as with the fourth embodiment, is 
that the actual subtended angles ALPHA and BETA are dependent upon the 
position of the carriage 20 with respect to the main body 1. Thus the 
displacement indication from the displacement transducer is used to 
indicate when the carriage 20 has been adjusted to the correct position so 
that the subtended angles are those desired. A calibration procedure is 
required prior to measurement. A specific embodiment of a calibration 
procedure is described, with reference to FIG. 9. 
In this procedure, the measuring head is applied to an available 
calibration cylinder of known diameter. Use is made of the provision, both 
in the carriage 20 and the linear bearing 18, of bores 16 and 17 of equal 
diameter which may be made coaxial by appropriate positioning of the 
carriage 20 with respect to the main body 1 along the axis of the linear 
bearing 18. A close-fitting dowel (not shown) is inserted through both 
bores, 16 and 17, thus locating the carriage 20 so that the rotational 
axis Q of the measuring spindle 51 is at a known position with respect to 
the main body 1. The carriage 20 is then fixed by means of the pinch screw 
15. The measuring spindle 51 is then rotationally positioned with respect 
to the measuring arm 53 so that the spherical probe 7 is contacted to the 
calibration cylinder and the displacement transducer is at the centre of 
its linear working region. The measuring spindle 51 is then fixed with 
respect to the measuring arm 53 by means of the pinch screw 54. The dowel 
and calibration cylinder are removed and the pinch screw 15 released. This 
completes the calibration procedure.