BENT TUBE MEASUREMENT USING A VIRTUAL SHARP

An apparatus for determining the location of features in a bent element having at least two straight portions and at least one bend between the two straight portions includes a first rail, a second rail, a third rail, a first rotary coupling rotationally coupling the first rail to the second rail and operatively coupling to a first rotary encoder, a second rotary coupling rotationally coupling the second rail to the third rail and operatively coupling to a second rotary encoder, and a linear encoder configured and arranged to determine the location of the second rotary coupling on the second rail.

BACKGROUND OF THE DISCLOSURE

Field of the Disclosure

The present disclosure relates to the field of fluid communication, more specifically to the fabrication of fluid circuits using tubing, and still more specifically to the repeatable fabrication of bent tubing, and the measurement, inspection, and documenting of the bends and lengths of the tubing.

Description of the Related Art

Tubings are used to allow fluid tight, from the exterior thereof, flows of fluids from a source location to a destination location. Herein, the tubings are discussed with respect to the use of the tubing in an enclosure, but the methods and apparati discussed herein are applicable to the precision fabrication of rigid bent tubing for any applications. The tubings may be incorporated into an enclosure, which provides a contained environment for the tubings. For example, one such enclosure is a gas panel, which is a term in the art of semiconductor fabrication equipment, within which, on the exterior of which, or both, tubings are connected to allow contained fluid flow from a gas source to a desired destination for that gas. A desired destination would be, for example, a semiconductor processing chamber using one or more gases to process a substrate therein. A single gas panel commonly includes a plurality of leak tight fluid circuits therein, which include components such as mass flow controllers or other components configured to controllably flow fluids therethrough, valves for switching the flow of gas to or through the flow control components, flow meters configured to measure the flow of gas though an individual flow line, and other components such as fittings for connection of a tubing to a gas panel component, heaters, chillers, and the like. Additionally, different fluids may flow through different ones of the flow control circuits in the gas panel. These fluids may be toxic, corrosive, flammable or explosive if exposed to the local ambient environment, in other words, to air.

Commonly the rigid tubings have connectors or fittings affixed to the opposed ends thereof for connection to the fluid source, to the fluid use location, or interconnections to additional components, such as additional tubing(s), therebetween. The connectors on the tubing ends are connectable to mating connectors, either on another tubing, a flow component, or on or in a gas panel.

The enclosure is a volume in three-dimensional space, within which connection locations for the tubings are provided. To fit multiple independent fluid flow paths through a single enclosure while minimizing the size of the enclosure, the location of the centerline of a fluid inlet connector to connect to an inlet connector on the fluid inlet end of a tubing is often not collinearly aligned with the centerline of a fluid outlet connector provided to connect to a fluid outlet connector on the outlet end of a connector on a tubing. Additionally, to fit all of the tubings required within the enclosure, the fluid connection design may require tubings be bent in two dimensions, for example in the x and y directions of a Cartesian coordinate system, or in three dimensions, for example the x, y and z directions of Cartesian coordinate system. Thus to interconnect two different connections in the enclosure with rigid tubing, lengths of rigid tubing are commonly bent, to align the inlet connector connected at the inlet end thereof with a gas source connector location within the enclosure, and the gas outlet connector at the gas outlet end thereof with the location of the desired outlet connector of the enclosure therefor. The lengths of the tubing between the bends, between a bend and an adjacent end of the tubing, and the angles of the bends are specified by the enclosure designer. However, the inspection of the bent tubings is problematic, as the actual location of a bend in the tubing and its radius are not easily measured using rigid tools, for example a tape measure, ruler, etc. Thus, a comparator having a moving support table to hold the bent tubing, a camera or optical imaging system to image the tubing on the table, and a mechanism for measuring the travel of the table as the tubing is scanned under the imaging system to determine the location of the beginning and ends of each bend, and the corresponding length of the straight lengths of the tubing extending from the bends. This is both time consuming and expensive, and thus not acceptable in a high volume production environment.

As shown inFIG.1, a length of tubing10is shown having a single bend12therein. Thus, the tubing is composed of a first straight (unbent) length14extending from a first open end18thereof, a second straight (unbent) length16extending from a second open end20thereof, and a curved (bent) portion22of the tubing10fluidly interconnecting the end of the first length14distal of the first open end18and the end of the second length16distal to the second open end20. Here, as the tubing10includes only a single bend22, it can be considered to extend in two dimensions, for example the x and y directions. Because the tubing10is rigid, the bend22therein must extend along a radius R about a center point C, and typically, because of the physical limits of the material of the tubing to deform, that center point C is not located within the envelope of the tubing10, in other words, the center of the bend22is spaced outwardly of the outer surface of the tubing10. Here, the radius of the surface of the tubing10furthest from the center point C of the bend22, in other words, the outer bent surface, is denoted Ro, the radius of the inner surface of the bend in the tubing or the surface closest to the center point C of the bend is denoted Ri, and the radius of the centerline extending along the interior of the bend in the tubing is denoted Rm. As a general approximation, Rm=Ri+ (Ro−Ri)/2 Additionally, the intersection of the projection of the centerline CL1of the first length14through the curved portion12and the centerline CL2of the second length16through the curved portion12intersect at a point VScis likewise not overlying any portion of the length of tubing10, and is on the opposed side of the bent portion (bend22) from the center C of the curve the curved portion22extends along. This (point VSc) is the virtual meeting point, or virtual sharp, of the intersection of the centerlines of the straight first and second lengths14,16of the bent tubing10. A second virtual sharp VSois a point location where extension lines extending along and from the outer surface of the first and second lengths14,16of the bent tubing furthest from the center point C about which the curved portion22extends intersect. A third virtual sharp VSiis a point location where extension lines extending along and from the inner, center point C facing surface of the first and second lengths14,16of the bent tubing intersect.

The specification of, i.e., of the dimensions of the lengths of the straight sections of the tubings, and the dimensions are angle of the curved sections of the tubings, is problematic. This is a result of a number of factors, including the proper measurement of the lengths of the straight portions of the tubing, in particular determining when a straight portion ends and the curved portion begins. Referring again toFIG.1, here the location where the first length14of the tubing10meets the curved section thereof is shown as where the radius26from the center C passes across the tubing10, and the location where the second length16of the tubing10meets the curved section is shown as where the radius28from the center C passes across the tubing10, these radii being disposed a number of degrees apart about angle24about center C. However, in an actual length of bent tubing, it is often difficult, using simple eyesight or rigid tooling, to determine where curve of the curved portion22ends and the length of the straight first and second lengths12,14end.

If the length Li of the first length14of tubing10extending between first (open) end18and radius26is too long or too short, the second (open) end20of the second length16will not be properly aligned with the destination location to which it will be connected. Likewise, if the second length16of tubing10between the second (open) end20and radius28is too long or too short, the first (open) end18of the first length14will not be properly aligned with the destination location to which it will be connected.

SUMMARY OF THE DISCLOSURE

In one aspect, there is provided herein an inspection or measurement device configured to rapidly measure the bend angle(s), and the lengths of the straight portions, of bent tubing in a repeatable manner. The device includes at least two straight portions and at least one bend between the two straight portions includes a first rail, a second rail, a third rail, a first rotary coupling rotationally coupling the first rail to the second rail and operatively coupling to a first rotary encoder, a second rotary coupling rotationally coupling the second rail to the third rail and operatively coupling to a second rotary////encoder, and a linear encoder configured and arranged to determine the location of the second rotary coupling on the second rail.

In another aspect, the location of the virtual sharp and the length of at least one straight length of bent tubing is determined by placing a length of straight tubing against a first engagement surface of a first rail, and a second length of bent tubing against an engagement surface of a second rail pivotably connected to the first rail, while actuating the second or first rail, or both, with respect to a pivot point to bring the surface of the first length of tubing against the first face of the first rail and the surface of the second length of tubing into contact with the second face of the second rail. A third length of straight tubing, extending from a second bend in the tubing between the second length and the third length may be brought into contact with a third face of a third rail, by moving the second rails pivotably with respect to one another. The third rail may also move along the length direction of the second rail. A first rotary decoder is used to determine the angle between the first rail in contact with the first length of tubing and the second rail in contact with the second length of straight tubing, and thereby determine the angle therebetween. A projection of the plane of the first engagement surface and the second engagement surface intersect at a virtual sharp location. Using the bend angle and the specified angle of curvature of the curved portion, the locations and orientations in space of open ends of the tubing can be determined using a programmable device running algebraic and geometric calculations, to determine whether the bent tubing meets a desired design specification thereof.

In another aspect, a method of evaluating dimensions of a rigid bent tube includes providing a first rail having a first surface, providing a second rail having a second surface, providing a third rail having a third surface, providing a first rotary coupling rotationally coupling the first rail to the second rail and operatively coupling to a first rotary encoder, providing a second rotary coupling rotationally coupling the second rail to the third rail and operatively coupling to a second rotary encoder, providing a linear encoder configured and arranged to determine the location of the second rotary coupling on the second rail, positioning a first straight portion of a bent tubing against a first surface of the first rail, positioning a second straight portion of a bent tubing against a second surface of the second rail, wherein the first and second straight portions are interconnected at a bend, and measuring the angle between the first rail and the second rail using the first rotary encoder.

DETAILED DESCRIPTION

Referring toFIG.2, there is shown a schematic isometric view of an inspection and measuring device48hereof. Here, the measuring and inspection device48includes a base50, on which is mounted a first rail52which is affixed to the base50such as by a plurality of threaded fasteners extending through openings in the first rail52and inwardly of mating threaded holes in the base50. A second rail54is here, at a first end56thereof, rotationally connected to the first rail52at a coupling end58thereof, which coupling here includes a first rotary encoder196(FIG.7). Second rail54is freely slidable over and along the upper surface of the base50. First rotary encoder196is configured to detect the angular position of the second rail54with respect to the first rail52. Here, the coupling end58to the second rail end of the first rail52includes a first cutout62extending inwardly of the coupling end58thereof, which allows the second rail54to be positioned relative to the first rail52such that the centerline64of the second rail54in the x-y direction ofFIG.2and the and the centerline66of the first rail52in the x-y direction ofFIG.2can be positioned in parallel with each other, and within limits of the tolerance of the parts, extend collinearly. The second rail54is also moveable along an arc68centered at the first rotational coupling60to a position where the centerlines64,66of the first rails52and the second rail54intersect at an angle as great as, or even greater than, ninety degrees.

Here, second rail54is configured as a rod or as a rod like element having a circular or partially circular cross section in the z-x plane, having the first end56thereof, an opposed second end70, and an outer circumferential surface72. Here, for example, the rod like element forming the second rail54has, in cross section, a truncated circular shape having a flat74(FIG.6) extending along one side thereof. Flat74provides a generally planar surface against which the side of a straight length of tubing can be abutted, and thus a reference surface at the same distance from the centerline64of the second rail regardless of the diameter of the abutting tubing. Here, a third rail76is also rotationally interconnected to the second rail54, through a second rotational coupling78which also serves as a portion of a second rotary encoder198(FIG.6). Additionally, the second rotary coupling198includes an inner slide member82(FIG.6) though which the second rail54slidingly extends. Here, inner slide member82, in cooperation with the second rail54, also provides a linear encoder84(FIG.6). Second rail54is here configured to extend through a slot or second cutout86extending inwardly of the first end wall92of the third rail76, such that the relative positions thereof can be moved through a second arc90centered on the second rotational coupling78. The length of the third rail76is bounded by opposed first and second end walls92,94, and the depth of the second cutout86inwardly of the first end wall92is sized to allow the angle of intersection between the third rail centerline96and the centerline64of the second rail54to extend between greater than zero, to at least ninety or more degrees.

Each of the first through third rails52,54and76include a generally flat or extending in a plane engagement surface against which the outer wall or end wall of a bent length of tubing can be positioned. Here, first rail52includes a generally planar first engagement surface118, and third rail76includes a third engagement surface122. Additionally, where a flat74is provided on the rod forming the second rail54, the flat74forms the second engagement surface120of the second rail54.

Inspection and measuring device48is useful to measure the bending angles and lengths of the straight sections of a length of tubing, in particular bent rigid tubing. For example, as shown inFIGS.3and4, the inspection and measuring device48is employed to measure the angles and virtual sharp locations in a length of bent tubing, inFIG.3a length of tubing having two bends and three straight length sections.

Here, the location of the virtual sharp can be used to locate the center of the bend in the length of tubing, for virtual sharps for a first bend112and a second bend116ofFIG.3, and thereby infer the locations of the centerline of the tubing in the straight or unbent portions thereof.

InFIG.3, the inspection and measuring device48is shown in use to identify the location of a first virtual sharp VSo1adjacent to the outer wall of the bent tubing100, here adjacent to the first bend112of the bent tubing100located between a first straight length102section and second straight length104section thereof. In this example, the bent tubing100includes two bends, the first bend112between a first straight length102of a bent tubing100and a second straight length section104of the bent tubing100, and a second bend116between the second straight length section112and the third straight length section116of the bent tubing100. Here, the outer surface of the bent tubing100contacting the second and third engagement surfaces120,122and the circumferential wall124of the first open end108of the bent tubing100are used as reference locations on the bent tubing100. To determine the distance from the flat first open end108of the bent tubing100and the virtual sharp VSo1, and the angle between the centerlines of the first and second straight lengths102,104of bent tubing100, the flat open end108of the tubing is contacted against the first engagement surface118of the first rail52while the outer circumferential surface of the first straight length102of the tubing100between the first bend112and the first open end108facing the flat74forming the second engagement surface120of the second rail54are pulled or pushed together. Then, the third rail76is slid in the direction of the first rotational coupling60, until the third engagement surface122thereof is parallel to, and in contact with, the outer surface of the second straight length104of the tubing100extending between the first and second bends112,116. The linear encoder84(FIG.6) provides a signal indicative of the location of the second rotational coupling78on the second rail54, and the second rotary encoder198generates a signal corresponding to the angle between the second rail54and the third rail76. The signal from the linear decoder84indicates the distance126between the first end56of the second rail54and the center of the second rotary coupling78, and the signal from the second rotary encoder198indicates the angle between the second and third rails54,76. As the first open end108of the tubing100is at a right angle to the outer wall thereof, and the circumference of the surface of the first open end108of the tubing100abuts and contacts the first engagement surface118of the first rail52while the outer surface of the first straight length102of the tubing100contacts the second engagement surface120of the second rail54over the length of the first straight length102section, the angle between the first and second rails52,54is ninety degrees, so long as the end face of the first straight length102of tubing100is perpendicular to the centerline of the first straight length102of tubing100. Thus, the location in free space of the first open end108of the tubing is the location of the first end of the second rail less (minus) the width128of the first rail52. The location of the first virtual sharp VS01is at the location of the intersection of a ray R, extending one-half way between a ray r1parallel to the second engagement surface120of the second rail54and a ray r2parallel to the third engagement surface122of the third rail76. As the second rotational coupling78is centered in the width130direction of the third rail76, the location of the virtual sharp VS01is one-half the width130of the second rail from the center of the second rotational coupling78along the ray R. Thus, the distance between the first open end108of the tubing100and the virtual sharp VSo1is:

The distance between the center of the second rotary encoder overlying the second rail54and the end thereof connected to the first rail52(the center of a first rotary encoder196), here distance126;

Less (minus) one half of the width128of the first rail52(the distance from the center of the first rotary encoder196to the first engagement surface118);

Less the length l of line segment136(FIG.4), which is the length between an imaginary line138intersecting the center of the second rotary coupling and normal to the a line segment extending, inFIG.5, to the right hand side of the virtual sharp VSo1from the second engagement surface120where that imaginary line138crosses over or intersects the line segment extending from the second engagement surface120, and the location of the virtual sharp VSo1. Here, ray140extends from the virtual sharp VSo1to the center of the second rotational coupling78. The angle134between the ray140and the imaginary line138is the value of 90 degrees less (minus) the value of the angle130a, which also corresponds to the bend angle.

Therefore, the length of the line segment136is equal to:

where W is the length of the imaginary line138which is the distance between the centerline of the second rail54and the flat74, B is the angle134which is 90 degrees less (minus) measured bend angle130abetween the first and second rails52,54, and I is the distance between the location where the imaginary line138passes over or intersects the second engagement surface120and the first virtual sharp VSo1. Here, ray140has a length equal to one-half the Thus, using the inspection and measuring device48, a mechanism for accurately determining the relative position of the ends of the tubing with respect to the bend angles, and the thus the lengths of the straight length sections or segments thereof, can be determined.

Referring now toFIG.5, the measurement and inspection device is also useful to evaluate a segment of a straight length of tubing between two bends in the tubing. Here, a span of the first straight length102of tubing100is located against the first engagement surface118of the first rail52, and the second rail54is moved arcuately so that the second engagement surface120thereof abuts the entire length of the outer side of the second straight length104of the tubing100, where the first bend112is positioned with the minimum possible gap between the outer side wall of the tubing and the adjacent intersection of the first and second engagement surfaces118,120. The third rail76is then moved linearly along the second rail54and swung about the second rotational coupling78to abut a span of the third straight length106of the tubing100thereagainst as shown inFIG.5.

The location of the first virtual sharp VS01is then determined algebraically as discussed above based on the measured first bend angle and the span between the center of the first rotational coupling60and the first engagement surface118, as the first virtual sharp VSo1is located where the projections of the first and second engagement surfaces118,120overlap. The distance between the first virtual sharp VSo1of the first bend112and the second virtual sharp VSo2of the second bend116is then determined using the signal from the liner decoder indicative of the distance between the end of the second rail54and the second rotational coupling78, the second bend angle based on the signal of the second rotary decoder198, and the distance between the center of the second rotational coupling78and the third engagement surface122of the third rail76.

The distance between the second virtual sharp VS02and the second open end110of the tubing can be determined using the inspection and measuring device48in the same manner shown inFIG.3, here by abutting the second open end110against the first engagement surface118and the outer wall of the third straight length106of the tubing100against the second engagement surface120, and the outer surface of the first straight length102of tubing against the third engagement surface122.

Using the system of measurement described herein, a fast, repeatable and accurate evaluation of the dimensional correctness of a bent tubing can be made. In contrast to methods of inspection that attempt to judge the length of the straight sections of the tubing by judging where a straight portion ends and a curve begins, here, the virtual sharp is used as the reference point for the bends. This results in more accurate and repeatable evaluation of bent tubing. The locations of each virtual sharp VS0is the location where a projection of the outer surfaces of the two straight lengths of tubing to either side of a bend intersect. Thus, for a given bent tubing layout or design, it is readily calculable if not already present on a drawing of the bent tubing.

Referring now toFIG.6, the pivoting and sliding connection of the second rail54with the third rail is shown. Here, the third rail54is shown partially, and in section, to show the connection of the second rotational coupling78with the third rail and with a slide block150, and the connection of the second rail54through the slide member. Here, the second rotational coupling78is configured to include a first shaft152, a second shaft154, and a slide block150affixed therebetween. The first shaft152is rotatably supported in a first bore160in the third rail76, and the second shaft154is rotatably supported in a second bore162in the third rail76. The first shaft152is configured to cooperate with a second rotary encoder198which extends over the upper end156of the first shaft152of the rotational coupling78. For example, the upper end156of the first shaft152may include an optical gray pattern, and the second rotary encoder198includes an illumination device and a charge coupled device configured to receive a reflected signal from the gray pattern indicative of the rotational position of the first shaft152with respect to the second rotary encoder198.

The slide block150includes a through slide opening164extending therethrough, having the form of a truncated circle in section. The center of a the circular portion of the opening, i.e., the center of a circle which runs along the curved inner wall166of the slide opening164lies upon a center line passing through the centers of the first and second shafts152,154. A flat portion168extends generally parallel to the centerline passing through the centers of the first and second shafts152,154. The cross section of the slide opening164is configured to mimic the outer circumferential profile of the second rail54, with a slight clearance between the outer surface of the second rail54and the inner surface of the slide opening164, which allows the slide block150to slide over the second rail54or vide-versa. The flat portion168is located to serve as a key to properly orient the position of the flat74of the second rail54to face a section of tubing when the inspection and measuring device48is employed to evaluate a bent tubing. The mating contours of the second rail54and the through slide opening164, including the flat74and flat portion168, prevent rotation of the second rail54about its longitudinal axis.

The slide block150includes a linear encoding device170providing the linear encoder84, having a reading side174facing the curved outer surface172of the second rail54. The linear encoding device170encoding device and the curved outer surface172together cooperate as a linear encoder, such that sliding motion of the second rail54(inwardly or outwardly of the page of the Figure) results in the generation of a signal representative of the span of the linear motion of the second rail54within the slide block150. Similarly, to the second rotary encoder198, the linear encoding device170can include an illumination device and a camera, and the facing portion of the outer curved surface172of the second rail54can include a series of spaced markings along it length direction. The illumination device illuminates the facing portion of the outer curved surface172, and the camera detects the markings and the movement of them past the camera as the second rail54moves within the slide block150.

Referring now toFIG.7, the rotational connection of the first rail52to the second rail54is shown. Here, the first rail54is shown partially, and in section, to show the connection of the first rotational coupling60with the second rail54. Here, the first rotational coupling60is configured to include an upper shaft180and a lower shaft182. The upper shaft180is rotationally supported in an upper bore186in the first rail52, and the lower shaft182is rotationally supported in a lower bore188in the first rail52. The ends of the upper and lower shafts180,182projecting inwardly of the first cutout62of the first rail52connect to opposed sides of the second rail54forming the upper and lower bounds of the first cutout62. The upper shaft180is configured to cooperate with the first rotary encoder196that extends over the upper shaft end194of the upper shaft180of the first rotational coupling60. For example, the upper shaft end194of the upper shaft180may include an optical gray pattern, and the first rotary encoder196includes an illumination device and a charge coupled device configured to receive a reflected signal from the gray pattern indicative of the rotational position of the upper shaft180with respect to the encoder. The longitudinal centerlines of the upper and lower shafts180,182are collinear, and the center of a circle that lies upon the curved portion of the outer circumference of the first rail54also lies on an extension of these centerlines.

Here, the rotary encoder and linear encoders are preferably configured as absolute encoders, wherein a zero position is established therefor, and all outputs thereof are read as referenced back to that original zero position.

Referring toFIG.8, a schematic of the connections of the inspection and measuring device48to an aide device are shown. Here, the aide device is a general purpose computer200and optionally a printer and a scanning device such as a scanner204capable of reading identity information, such as a bar code or RFID tag on a length of tubing, the computer connected to each of the first and second rotary encoders196,198and the linear encoder84. Each of the encoders (Linear encoder84, first rotary encoder196and second rotary encoder198) are configured to transmit a signal to the computer200, either through hard wires or a wireless protocol, indicative of the angle between the first rail52and second rail54, the angle between the second rail54and the third rail76, and the relative location of the second rotational coupling78in the second cutout86of the second rail54, which indicates the position of the third rail76along the length direction of the second rail54. The computer200is programmed to, for a given tubing configuration, compare the virtual sharp locations and the lengths of the straight section of the tubing as measured using the methodologies described herein to reference lengths and reference virtual sharps. Thus for any tubing configuration, a user may enter the identity information manually using for example a keyboard, scan a code on the tubing, or another methodology, and the computer accesses its memory to obtain for the reference lengths and reference virtual sharps for that specific tubing configuration among multiple instances of reference data stored for multiple tubing configurations. The reference data may include a single item of data for each reference data, or a range of values. For example, if the signals from the encoders (linear encoder84, first rotary encoder196and second rotary encoder198) indicate that the actual locations of the virtual sharps are within the reference range thereof, and the actual lengths of the straight portions measured are within the reference range therefore, then the bent tubing is considered to be acceptable and can be used for its intended purpose. If any actual length or virtual sharp falls outside of its respective reference range, the bent tubing is considered defective and will not be used.

The computer200then stores the results of the inspection of the tubing corresponding to the identity of the tubing for tracking purposes. For example, if the tubing has a bar code thereon, the scanner204is employed to scan the code. The code identifies, for example, the design of the tubing configuration, and the computer200then uses the design information to fetch the reference data for that design. For example, the information on the bar code may include a part number, and the computer memory stores the reference data with respect to the part number. Then an operator manipulates the measurement and inspection device48and the length of tubing having the just scanned bar code together, as described herein, to allow the encoders (linear encoder84, first rotary encoder196and second rotary encoder198) to deliver actual data regarding the lengths of the straight length portions and the locations of the virtual sharps. The computer then compares that data to the reference data, and if the desired degree of matching, for example the actual lengths and angles, and thus virtual sharps, are within ranges specified for that tubing design, signals that the tubing is usable as that part number. The computer may also be configured to store, in its memory, or on a server connected thereto, the results of the evaluation of the specific tubing. For example, for tracing purposes, each tubing may have a unique identification, for example a numeric or alphanumeric identifier. Where a bar code is employed and affixed to the tubing, the bar code includes that identification information. That identification information can be used, by the computer, to fetch the design information for the tubing, either from its own memory or from a server. The results of the evaluation of the tubing can then be saved in memory or a server, in association with the part number.

The use of the inspection and measuring device48enables the fabrication of bent tubings with a high degree of accuracy and reliability. The desired lengths of the straight lengths of tubing, and the angles between adjacent straight lengths of tubing, are used to determine the location of the virtual sharps corresponding to a correctly fabricated tubing. For example, the widths of the first and third rails52and76and the distance between the flat74and the centerline of the second rail54are known. Using the equation:

where W is the length of the imaginary line138which is the distance between the centerline of the second rail54and the flat74, β is the angle134which is 90 degrees less (minus) measured bend angle130abetween the first and second rails52,54, and I is the distance between the location where the imaginary line138passes over or intersects the second engagement surface120and the first virtual sharp VSo1. Here, ray140has a length equal to one-half the Thus, using the inspection and measuring device48, a mechanism for accurately determining the relative position of the ends of the tubing with respect to the bend angles, and the thus the lengths of the straight length sections or segments thereof, can be determined. Thus, an inspection and measuring device is provided for ensuring repeatable fabrication of bent tubings.

While the foregoing is directed to embodiments of the present disclosure, other and further embodiments of the disclosure may be devised without departing from the basic scope thereof, and the scope of the invention is determined by the claims that follow.