Diameter gauge

A diameter gauge is disclosed for measuring the outside diameter of a part having a circular cross section. The gauge comprises two arms converging at right angles to one another within which the part is positioned for measurement.

The present invention relates in general to diameter gauging apparatus and 
in particular to an apparatus and method for determining the outside 
diameter of an object or part having a circular cross section. 
BACKGROUND OF THE INVENTION 
In machine shop practice, it is customary to use a micrometer to measure 
the outside diameter of a part having a circular cross section, e.g. a 
cylindrical shaft, as different steps of the machining process are 
completed. Difficulties may be encountered in accurately and reliably 
placing the micrometer in position on the part to be measured, itself a 
time-consuming procedure, and occasionally errors in measurement occur. 
Furthermore, a particular micrometer can generally only measure a given 
range of cross sectional sizes, so that a number of micrometers must be 
kept on hand for measuring parts of widely different diameters. Such a 
requirement not only increases the amount of capital tied up in equipment, 
but it also necessitates a certain amount of record keeping and equipment 
storage. Finally, the maintenance costs of the shop are increased since 
each micrometer must be periodically re-calibrated. 
OBJECT OF THE INVENTION 
It is therefore a primary object of the present invention to provide a new 
and improved apparatus and method for measuring the outside diameter of a 
part having a circular cross section which are not subject to the 
foregoing disadvantages. 
It is a further object of the present invention to provide an apparatus and 
method for quickly and accurately determining the outside diameter of 
cylindrical parts of widely different cross sections which require only a 
single measuring instrument. 
It is another object of the present invention to provide an apparatus and 
method capable of making diameter measurements of cylindrical parts of 
widely different diameters which will result in a cost saving in capital 
equipment, as well as savings with respect to the maintenance of the 
required equipment, its storage and associated record keeping. 
SUMMARY OF THE INVENTION 
The foregoing objects of the invention are achieved by an apparatus and 
method which make use of the relationship that two tangents of a circle 
which intersect one another at ninety degrees are equal to one half the 
diameter of the circle, as measured from the vertex formed by the 
intersecting tangents to either point of tangency on the circle. The 
principle underlying the invention is implemented by a device comprising a 
pair of mutually perpendicular, linear arms which converge to define a 
line of intersection. Such a device may be applied from any desired 
direction to the part to be measured. In a preferred embodiment, elongate 
resistive means, the resistance of which varies linearly with length, are 
mounted on the arms. In the alternative, they constitute the aforesaid 
arms. The measured resistance of such an arm depends on the length of the 
resistive means between the line of intersection and its point of tangency 
with the part. This length, then, provides a measure of the diameter of 
the cross section. 
These and other objects of the invention, together with the features and 
advantages thereof, will become apparent from the following detailed 
specification when read together with the accompanying drawings in which 
applicable reference numerals have been carried forward.

DETAILED DESCRIPTION OF THE INVENTION 
With reference now to the drawings, FIG. 1 illustrates the geometric 
relationship underlying the present invention. Lines AP and AQ are 
tangents of circle 26 which is representative of a part having a circular 
cross section centered at point O. Lines AP and AQ intersect at right 
angles to form vertex A. The distance between the vertex and one of the 
points of tangency P or Q, is seen to be equal to radius R. By measuring 
this distance, or a quantity representative of the distance, the outer 
diameter of the part represented by the circular cross section can be 
determined. 
FIG. 2 is a partially schematic representation of one embodiment of the 
invention which makes use of the principle explained above by using a 
resistance measurement. A pair of arms 22 and 24 extend outward from a 
support structure 20 at right angles to one another. Arms 22 and 24 have a 
pair of mutually facing planar reference surfaces 23 and 25 respectively, 
which are equivalent to tangents AP and AQ in FIG. 1 with respect to part 
26. For purposes of explanation, reference surfaces 23 and 25 are shown 
extended in phantom outline and define a line of intersection 47 
equivalent to vertex A in FIG. 1. 
Resistive means in the form of a pair of resistor elements 10 and 12, shown 
exaggerated in size for the sake of illustration, extend throughout the 
full length of surfaces 23 and 25 respectively. The surface of each of 
these elements which faces part 26 is referred to as the contact surface 
and makes tangential contact with part 26. Although represented as a 
series of points in FIG. 2, it will be understood that the resistor 
material, e.g. resistive wire, may consist of closely wound turns and will 
in effect present a substantially continuous surface to part 26. Depending 
on the configuration of the contact surfaces (round or flat), and on the 
configuration of part 26 (sphere or cylinder), tangential contact will 
occur either at a point, such as points 28 and 30, or along a line. It 
should be noted that this tangential contact also establishes electrical 
contact between the resistor elements and part 26. For purposes of making 
a diameter measurement, only one of elements 10 and 12 needs to be a 
resistor. Where the other element is omitted, surface 25 functions as the 
second contact surface. 
The resistor elements are of the type wherein resistance increases linearly 
with length, e.g. a wire-wound resistance rod, a composition resistor, or 
a precision film resistor. Conductive composition resistors are preferred 
because of their characteristics of providing essentially infinite 
resolution. The resistance of each of elements 10 and 12 increases from a 
minimum, theoretically located at line 47, to a maximum at points 16 and 
17. In practice, however, the points of minimum resistance are located at 
points 14 and 15 respectively, and these points are connected to an 
ohmmeter 18 by means of a pair of conductors 11 and 13 respectively. 
With the arrangement shown, ohmmeter 18 measures the series combination 
comprising: the resistance of resistor element 10 up to tangency point 28, 
the resistance of that portion of part 26 between tangency points 28 and 
30, resistor element 12 up to tangency point 30, and the negligible 
resistance of conductors 11 and 13. If part 26 has a larger diameter than 
shown in FIG. 2, tangency points 28 and 30 will move closer to points 16 
and 17 respectively, if smaller they will be closer to points 14 and 15 
respectively. Thus, the total resistance of the series combination will 
increase as a function of the part diameter. 
FIG. 3 illustrates in detail a portion of one implementation of the 
apparatus shown in FIG. 2, as viewed from the direction of end surface 16 
of arm 22. In this embodiment of the invention, the measurement taken is 
independent of whether or not the measured part is electrically 
conductive. To implement this type of apparatus, the resistive means 
comprises resistor element 10 paired with a conductor element 34 of equal 
length. As shown, resistor element 10 constitutes a resistance rod of 
circular cross section, although it will be understood that rod 10 may 
also have a flat cross section. Unlike the arrangement of FIG. 2 where 
resistor element 10 is located on reference surface 23, in the present 
embodiment rod 10 is positioned in a groove 38 in surface 23 which runs 
the full length of arm 22 of the support structure. The depth of the 
groove is selected so that rod 10 protrudes above surface 23 of arm 22 by 
some minimum distance F. Two non-conductive, compressible spacers 40 and 
42 flank resistor element 10 at opposite sides of groove 38. As shown, 
each spacer is coextensive in length with resistor element 10, lying 
partly within groove 38 but rising above reference surface 23 by a 
distance B greater than distance F. It will be understood that the spacers 
need not have the round cross section shown in FIG. 3 and that they may be 
disposed on reference surface 23 instead of in groove 38. Further, each 
spacer may consist of a series of successively spaced spacer sections 
rather than being continuous in length. 
In operation, when part 26 is positioned between arms 22 and 24 for a 
diameter measurement, it makes contact with the flat conductive element 34 
along a line of tangency 28L throughout the full width of element 34. As 
shown, spacers 40 and 42 are compressed. Further, depending on the 
construction of element 34, the latter may be flexed toward element 10 by 
the pressure of part 26 on it. Either as a result of spacer compression, 
or as consequence of spacer compression and the flexing of conductor 
element 34 toward element 10, conductor element 34 is moved through a 
distance E toward resistor element 10 and makes electrical contact with 
the latter. In FIG. 3, conductor element 34 is shown broken away in part 
to expose point 27 where electrical contact between the conductor and 
resistor elements occurs. Since the line of tangency 28L and electrical 
contact point 27 are separated only by the thickness of conductor element 
34, contact point 27 is substantially equivalent to tangency point P or Q 
in FIG. 1 and hence an accurate measurement is obtained. It will be clear 
that, instead of protruding above reference surface 23 by a distance F, 
conductor element 10 may also be positioned slightly below the plane of 
surface 23 to accommodate the thickness of the conductor element and to 
place the line of tangency 28L precisely in that plane during a diameter 
measurement. 
As shown in FIG. 3 a pair of tabs 98 and 99 is mounted on reference surface 
23, on opposite sides of groove 38. Another pair of tabs is mounted at the 
opposite end of arm 22, not shown in the drawing. The purpose of tabs 98 
and 99 is to keep spacers 40 and 42 and flexible conductor 34 in place, 
i.e. in alignment with groove 38. 
FIG. 4 is a schematic representation of the resistive means shown in FIG. 3 
and of the series connection which results when part 26 is positioned for 
a diameter measurement. As in FIG. 3, the paired elements of the resistive 
means comprise resistor element 10, which extends between points 14 and 
16, and conductor element 34. The line of tangency 28L between the contact 
surface of element 34 and part 26 is normal to the plane of the drawing. 
Electrical contact between elements 10 and 34 occurs at point 27 and 
establishes a series resistance loop consisting essentially of the 
resistance of element 10 between points 27 and 14 and the negligible 
resistance of conductor element 34. The position of line 28L, and hence of 
point 27, will depend on the diameter of the part under measurement. 
Ohmmeter 18, which is connected between terminals 4 and 14, is calibrated 
to directly provide the diameter of the part. 
As previously explained, a single resistive means, consisting in the 
embodiment under discussion of a resistor element paired with a conductor 
element and placed on one arm of the structure shown in FIG. 2, is 
sufficient to provide the desired diameter measurement. Where both arms 
carry such resistive means, increased measurement accuracy will result if 
a measurement is taken with each and the results are averaged. 
Alternatively, the two series combinations can be connected as a single 
series loop so that a single ohmmeter reading will result from the input 
obtained from both arms. 
As previously explained, the apparatus of FIG. 3 is independent of the 
conductivity of part 26. FIG. 5 illustrates an implementation of the 
apparatus shown in FIG. 2 which similarly makes use of a resistance 
measurement, but which relies on the presence of an electrically 
conductive part. Resistor elements 10 and 12 are positioned respectively 
on mutually perpendicular reference surfaces 23 and 25 of arms 22 and 24, 
at right angles to the line of intersection 47. Resistor element 10 
extends between terminals 14 and 16, while resistor element 12 extends 
between terminals 15 and 17. 
Reference surfaces 23 and 25 further carry conductor elements 7 and 9 
respectively, e.g. copper rods of negligible resistance. Elements 7 and 9 
are positioned parallel to elements 10 and 12 respectively, in close 
proximity thereto but out of contact with the latter. They are the same 
length as elements 10 and 12 and they terminate in terminals 4 and 5 
respectively. Although elements 10, 12, 7 and 9 are shown cylindrical in 
FIG. 5, it will be understood that their configuration may be flat and 
that each may present a substantially planar contact surface to part 26, 
the latter being shown in phantom outline. 
In operation, resistor elements 10 and 12 make electrical contact with part 
26 at tangency points 28 and 30 respectively. These tangency points will 
vary along the length of the resistor elements, depending on the diameter 
of part 26. Ohmmeter 18 is connected between terminals 14 and 15 and 
measures a first series combination comprising the resistance of element 
10 between points 28 and 14, the resistance of part 26 between point 28 
and 30, and the resistance of element 12 between points 30 and 15. To 
determine the joint resistance of elements 10 and 12, the resistance of 
part 26 must be subtracted. This is done by means of conductive elements 7 
and 9, which make electrical contact with part 26 at tangency points 28A 
and 30A, respectively. Thus, conductor elements 7 and 9 and the portions 
of part 26 between points 28A and 30A form a second series combination in 
which the resistance of the conductor element is negligible. Hence, the 
resistance of the second series combination, as measured by ohmmeter 18 
connected across terminals 4 and 5, is essentially the resistance of part 
26 between points 28A and 30A. Because of the close proximity of points 
28A and 30A to points 28 and 30 respectively, the latter resistance value 
is substantially identical to the resistance existing between points 28 
and 30. It is subtracted by programmed device 19 from the measured 
resistance of the first series combination and converted into a measure of 
the diameter of part 26. 
FIG. 6 is a schematic presentation of the resistance measurement of the two 
series combinations described above. Arrows 28, 28A, 30, and 30A represent 
the variable position of the tangency points, as determined by the 
diameter of the part to be measured. Switches 21A and 21B are ganged and 
selectively connect ohmmeter 18 to the first or second series combination. 
The first series combination (shown connected to the ohmmeter), is seen to 
comprise the resistance of element 10 between points 14 and 28, the 
resistance of part 26 between points 28 and 30 and the resistance of 
element 12 between points 30 and 15. The second series combination 
comprises essentially the resistance of part 26 between points 28A and 
30A. 
Another embodiment in accordance with the principles of the present 
invention is shown in FIG. 7 and uses a source of light to determine the 
outer diameter of the cylindrical part. An elongate, distributed light 
source 80 extends along one side of a V-shaped common support structure 41 
and provides a substantially uniform light output throughout its length. 
Structure 41 has a pair of mutually facing, planar reference surfaces 23 
and 25 which also function as the contact surfaces in this embodiment of 
the invention. Surfaces 23 and 25 are located on arms 22 and 24, 
respectively and form a right dihedral angle having a line of intersection 
47. The contact surfaces are oriented to make contact with part 26 at a 
line of tangency on each surface when the part is positioned between arms 
22 and 24 for a diameter measurement. Only one line of tangency is visible 
in FIG. 7 i.e. on contact surface 23 and it is labeled 28L. 
The cross section of part 26 which is co-planar with the planar forward 
surface 82 of structure 41 is designated by the reference numeral 29. As 
shown in the drawing, the portion of part 26 whose diameter is to be 
measured protrudes beyond surface 82 by a distance D. Light source 80, 
which is positioned to one side of the dihedral angle, likewise protrudes 
beyond forward surface 82 and projects light in a plane parallel to the 
latter surface as indicated by arrows 43. Alternatively, the light source 
may be embedded in a slot in surface 23 so as project a plane of light at 
right angles to line 47. 
A light sensing device 48 is positioned adjacent surface 82 on the other 
side of the dihedral angle. Detector 48 is shown affixed to a cable 58 and 
is capable of moving along a straight line path between pulleys 60 and 61, 
driven by a motor 56. An encoder 62 is coupled to motor 56 and is 
calibrated to determine the distance traveled by detector 48 along its 
path, i.e. the distance from one of the ends of the path. The encoder is 
capable of determining the diameter of part 26 from this information. A 
display 64 shows the output of encoder 62. 
Light sensing device 48 is illustrated in greater detail in FIG. 8. The 
light detector comprises a light receiving surface 49, a photodiode 51, 
and associated optics between the latter elements for focusing light. 
Specifically, the optics include a convex len 52 for gathering light, a 
concave len 53 for spreading light and a slit 54 for filtering light. 
These optical elements assure that only light incident at 90 .degree. on 
light receiving surface 49 is capable of reaching photodiode 51. 
In operation, the measuring device is applied to part 26, or the part is 
placed onto the device such that it rests in the dihedral angle formed by 
contact surfaces 23 and 25, as shown in FIG. 7. Part 26 is thus positioned 
between light source 80, and detector 48 and casts a shadow on the latter. 
The lower edge of the shadow, i.e. the boundary between light and 
darkness, is labeled 44 in the drawing. Its location along the path 
traveled by detector 48 is determined by the diameter of part 26, 
specifically by the distance N of part 26 from the line of intersection 
47. Thus, light detector 48 passes from light to darkness, (or vice versa 
depending on its direction of travel), at a point along its path which 
depends on the position of the edge 44 of the shadow cast by part 26. From 
a determination of this point on the path, herein referred to as the 
instantaneous path position, the diameter of part 26 is determinable. 
Referring back to FIG. 1, lines AP and AQ, which are analogous to the right 
dihedral angle shown in FIG. 7, form a square with lines PO and QO. The 
circle has a radius r and the length of AO is 
##EQU1## 
From FIG. 1 it is apparent that the distance and that therefore 
##EQU2## 
Since N is known through the position of detector 48, r and thus the 
diameter of part 26 can be determined. 
Another implementation of the embodiment of the invention which uses a 
light source is illustrated in FIG. 9. This version of the present 
invention includes substantially the same support structure 41 and the 
same detector 48 as in FIG. 7. However, this implementation requires a 
focussed light beam, e.g. a laser beam 70 provided by a laser source 68. 
Laser beam 70 is beamed onto part 26 in a direction perpendicular to the 
line of intersection 47 and it lies in the bisector plane of the dihedral 
angle, the latter plane being normal to the plane of the drawing. In 
practice, part 26 preferably protrudes beyond surface 82 toward the 
viewer. Similarly, the laser source is positioned forward of surface 82. 
In the implementation of the invention shown in FIG. 9, part 26 has a dull 
exterior finish so as to provide diffuse reflections in response to the 
incident laser beam, as schematically indicated at 70A, 70B and 70C. As 
stated above, light detector 48 is substantially like the detector 
discussed in connection with FIG. 8, i.e. it will only sense light which 
is incident at 90.degree. on its light receiving surface. Similarly, the 
mechanism for moving detector 48 along its path may be identical to that 
discussed in connection with FIG. 7. However, in the present embodiment 
detector 48 can also be tilted at an angle with respect to the horizontal 
so as to receive light reflections at a 90.degree. angle of incidence. 
Thus, when reflected beam 70A is sensed, the instantaneous position of the 
detector along its path determines the diameter of part 26, as indicated 
by display 64. 
The geometric relationship for determining the part diameter is the same as 
that underlying the embodiment illustrated in FIG. 7. However, instead of 
detecting the edge 44 of the shadow cast by part 26, the embodiment shown 
in FIG. 9 detects the presence of a reflected beam incident at the 
prescribed angle on the light receiving surface of the light sensing 
means. 
As previously stated, part 26 must have a dull finish so that it will 
reflect light in many directions. Although most of incident beam 70 is 
reflected back to light source 68, some of the reflections are scattered, 
as shown at 70A, 70B and 70C. However, because beam 70 is highly focussed, 
the reflections are sufficiently concentrated to be distinguishable from 
ordinary ambient light. The optical elements of detector 48, ensure that 
only reflections arriving at the proper angle will be detected by light 
detector 48. 
It will be readily apparent to those skilled in the art that the present 
invention is not limited to the embodiments specifically illustrated and 
described above. As has already been stated, the light source in the 
apparatus shown in FIGS. 7 and 9 need not be positioned forward of surface 
82. Similarly the mechanism for moving light detector 48 is illustrative 
only. For example, it will be readily understood that the detector may run 
in a conforming slide on surface 82, or that it may be moved by hand. 
The support structure 20 is illustrated in different configurations for the 
various illustrated embodiments of the invention. It will be understood 
that these configurations are exemplary only and will depend on such 
practical considerations as convenience and the specific use intended. For 
example, as a hand-held gauge for measuring the diameter of a small part 
positioned on a machine tool, the invention will have a different 
configuration from apparatus which is stationary and to which parts are 
brought for measurement. Where the use of the invention as a hand-held 
diameter gauge is contemplated, it is intended that it be capable of being 
applied to the part from any desired angle and not only in the vertical 
position as shown in the drawings. Further, such a gauge must be 
self-contained and portable and hence the encoder and display, or the 
ohmmeter and the programmed device, are preferably incorporated into the 
support structure. 
While the foregoing embodiments of the invention are intended to be 
illustrative only and are offered merely by way of example, it will be 
clear that numerous variations, adaptations, substitutions, changes and 
equivalents will now occur to those skilled in the art without departing 
from the spirit and scope of the invention as defined by the appended 
claims. Accordingly, the invention is intended to be limited only by the 
scope of the appended claims.