CALIBRATING CAMERAS USED IN ALIGNMENT OF WHEELS

Abstract: Apparatus for use in calibrating an opto-electric alignment system used to align motor vehicle wheels the apparatus including first (162) and second (164) targets rigidly affixed to a beam (160). During calibration both targets are viewed by a first inspection device when the beam is placed normal to the imaginary line connecting the first inspection device and a second inspection device of the alignment system. Then the beam is moved parallel to the imaginary line and the first target is viewed by the first optical inspection device and the second target is viewed by the second inspection device.

Description: SPECIFICATION CALIBRATING CAMERAS USED IN ALIGNMENT OF WHEELS BACKGROUND OF THE INVENTION Field of the Invention This invention relates generally to a method and apparatus for calibrating electronic cameras, and more particularly to a method and apparatus for determining the spatial position and relative orientation of a pair of electronic cameras used to optically determine the alignment of motor vehicle wheels. Reference to Related Applications This application is a continuation- in-part of U.S. Patent Application Serial No. 08/544,378 filed October 10, 1995, which is a continuation-in-part of U.S. Patent Application Serial No. 08/122,550 filed September 29, 1993 (now U.S. Patent No. 5,535,522) , both of which are entitled "Method and Apparatus for Determining the Alignment of Motor Vehicle Wheels" and assigned to the assignee of the present invention. This application is also related to U.S. Patent Application Serial No. 07/940,935 filed September 4, 1992 (abandoned), and International Application No. PCT/US93/08333 filed September 3, 1993, both of which are entitled "Method and Apparatus for Determining the Alignment of Motor Vehicle Wheels" and assigned to the assignee of the present invention. Terms and Definitions In the vehicle wheel alignment industry the following terms, with corresponding definitions, are commonly used: Camber is the angle representing the inward or outward tilt from true vertical of the wheel and is positive if the top of the wheel tilts outward. Caster is the angle representing the forward or rearward tilt from true vertical of the steering axis. When a wheel is viewed from the side, the angle is positive when the upper ball joint (or top of king pin, or upper mount of a McPherson strut) is rearward of the lower ball joint (or bottom of the king pin, or lower mount of a McPherson strut) . Thrust Line (T/L) is a line that bisects the angle formed by the rear toe lines. Lines and angles measured clockwise from the 12:00 axis are positive. Geometric Center Line, is the line that runs from a point on the rear axle midway between the rear wheels to a point on the front axle midway between the front wheels. Individual Toe is the angle formed by a fron -to-back line through the wheel compared to the geometric center line. Angles pertaining to the left side are positive when clockwise of the thrust line and angles pertaining to the right side are positive when counterclockwise of the thrust line. Offset is the amount that a front wheel and its corresponding rear wheel are out of line with each other. If there is no offset,, the rear wheel is directly behind the front wheel . Setback is the amount that one wheel on one side of the vehicle is displaced back from its corresponding wheel on the other side of the vehicle. Steering Axiβ is a line projected from the upper pivot point of the upper ball joint or top of kingpin, or McPherson strut, through the lower ball joint. Steering Axis Inclination (SAI) is the angle between the steering axis and true vertical. If the steering axis appears to tilt inward at the bottom of the wheel (as viewed from the driver position), the SAI is positive. SAI also is also known as kingpin inclination (KPI) . Thrust Angle (T/A) is the angle between the thrust line and the geometric center line. Angles measured clockwise from the geometric center line are positive. Total Toe is the sum of individual, side-by-side toe measurements. If lines projected parallel to the primary planes of the wheels intersect at a point ahead of the side-by-side wheels, the angle is positive (toe in) . If the lines would intersect behind the side to side wheels, the angle is negative (toe out) . If the projected lines are parallel, the toe is zero . Traditionally, the Camber and Toe measurements for each wheel of the vehicle are relative measurements i.e. relative to a vertical plane or to another wheel and these measurements are therefore made when the wheels are stationary. On the other hand, the calculation of Caster and SAI is a dynamic procedure and entails determining how the Camber of the front wheels changes with respect to a change in steering angle. This is usually done by swinging the front wheels from left to right through an angle of between 10° and 30°, or vice versa,, while determining the resultant changes in Camber of the wheel with steering angle changes. From these determinations the Caster and SAI are determined by methods well known in the wheel alignment industry. Similarly, once Camber, Toe, Caster and SAI have been measured, all other relevant wheel alignment parameters can be calculated by methods and formulations well known in the industry. Brief Description of the Prior Art The wheels of a motor vehicle need to be periodically checked to determine whether or not they are in alignment with each other because, if any of the wheels are out of alignment, this can result in excessive or uneven wear of the tires of the vehicle and/or adversely affect the handling and stability of the vehicle . The typical steps of determining and correcting the alignment of a vehicle's wheels are as follows: 1. The vehicle is driven onto a test bed or rack which has previously been levelled to ensure a level base for the vehicle . 2. Some components of the alignment determination apparatus are mounted onto the wheels of the vehicle. These components are not necessarily accurately placed with respect to the wheel axis. The extent of the inaccuracy by which these components are mounted is called the "mounting error" . 3. A "runout" calculation is done by jacking the vehicle up and rotating each wheel and taking measurements of the orientation of that wheel at different positions. These measurements are then used to calculate a correction factor to compensate for the "mounting error" and actual rim run-out. 4. A determination of the alignment of each of the wheels is done. The results of these determinations are compared to the specifications of alignment parameters for the vehicle being tested. 5. The operator then adjusts the various linkages of each wheel to correct for the misalignment, if any, of the wheels. 6. Steps 4 and 5 are repeated until the alignment is up to standard and/or is within manufacturer's specifications. A large variety of devices for measuring the alignment of a motor vehicle's wheels exist. Many of these use optical instrumentation and/or light beams to determine the alignment of the wheels. Examples can be found in United States Patent Nos . 3,951,551 (Macpherson) ; 4,150,897 (Roberts); 4,154,531 (Roberts); 4,249,824 (Weiderrich) ; 4,302,104 (Hunter) 4,311,386 (Coetsier) ; 4,338,027 (Eck) ; 4,349,965 (Alsina) ; 4,803,785 (Reilly) and 5,048,954 (Madey) . All these devices operate with an apparatus which is mounted onto the wheel of a vehicle and which emits or reflects a light beam to illuminate an area on some form of reference such as a reference grid. As the position of the area illuminated by the beam on the reference is a function of the deflection of the beam, which in turn is a function of the orientation of the wheel, the alignment of the wheel can be calculated from the positioning of the illuminated area on the reference . Other devices utilize a measuring head mounted onto each wheel of the vehicle. These heads typically include gravity gauges that are either connected to adjacent heads by means of cords or wires under tension or, alternatively, configured with beams of light shining between adjacent heads. The measuring heads, which must be maintained level, are then able to measure the relative angles between adjacent cords/beams of light as well as the angles between each wheel and its adjacent cord/beam of light and, from these measurements, calculate the alignment of the wheels. Another type of alignment device is illustrated in United States Patents 4,899,218 (Waldecker) and 4,745,469 (Waldecker et al) . This device operates by projecting structured light _ onto a wheel of the motor vehicle so that at least two contour lines on the surface of the wheel are illuminated. These contour lines are then read by video cameras which are positioned offset from the optical plane of the structured light and which are connected to a processor which calculates the spatial position of the contour lines (and therefore that of the wheel) by means of triangulation. Generally, the heads used in the above described wheel alignment devices are delicate and expensive, complicated to use and must be carefully set up. Furthermore, certain of these devices rely on the accurate placing of optical or other measuring devices either on or in a set position relative to the wheels of the vehicle. This can be time consuming and complicated for the technicians operating the alignment determination apparatus. Such equipment also has the disadvantage that components which are carelessly , lef -secured to the wheels when the vehicle is moved from the test area can very easily be damaged. Such damage, particularly in the case of sophisticated equipment, can be costly. German patent application DE 29 48 573 in the name of Siemens Aktiengesellschaft discloses an apparatus which can be used to determine both the orientation and the spatial position of the plane of the wheel of a motor vehicle as well as the three-dimensional position of the steering axis of this wheel. The application discloses a method whereby a television camera takes an image of the rim on the wheel from two different known height positions. These images are fed into a processor which relates them to the known coordinates and viewing angles of the camera at its two height positions and determines the three- dimensional position of the rim. In a similar way, a number of images of each wheel, in different steering, positions, are taken to determine a three- dimensional solid of revolution for the wheel. From the axis of this solid of revolution the steering axis of the wheel under investigation can be determined. As a result, the three- dimensional position of both the steering axis and the center point of the plane defined by the rim of the wheel is determined. In addition to the fact that little indication is given as to how the above values are determined, the method and apparatus of the described application has the disadvantage that, because a triangulation technique is used, at least two images (from different cameras or from a single camera viewing along different axes) of the wheel must be taken. Furthermore, both the coordinated three-dimensional position for each point from where an image of the wheel is taken as well as the orientation of each of the view paths must be accurately known. This is a major disadvantage of this invention because the accurate determination of the three dimensional positions and the orientation of the view paths, requires sophisticated equipment which can easily go out of calibration due to temperature changes, vibration, ground movement, etc. A further disadvantage is that the method does not indicate how it makes allowances for the perspective distortion of the image of the rim of the wheel. This perspective distortion causes the image of the rim to be in the form of a distorted ellipse with the edge of the ellipse closest to the television camera appearing larger and the image of the edge farthest from the camera appearing smaller. If allowance for this distortion is not made, inaccuracies can result. The need therefore still exists for an optical wheel alignment apparatus which is simple and easy to use, which has its sophisticated alignment detection components remote from the wheels of the motor vehicle, and which can provide reliably accurate alignment measurements over a large range of rim diameters, track widths and wheel bases. A need also exists for a method and apparatus, for facilitating the calibration of the optical sensing devices used to determine wheel alignment and the like . SUMMARY OF THE INVENTION Objects of the Invention It is therefore an object of this invention to provide a calibration method and apparatus which is simple, easy and quick to use. Another object of this invention is to provide a method and apparatus for calibrating wheel alignment apparatus that uses an opto-electronic image detection device to determine the alignment of vehicle wheels. A further object of the present invention is to provide a rigid target structure that can be variously positioned in front of a dual camera image detection apparatus and " used in association therewith to determine the spatial . posit-ion and relative orientations of the cameras. Summary Briefly a presently preferred embodiment of this invention includes a rigid frame to which is mounted a pair of specially configured targets. The assembly is adapted for placement within the field (s) of view of at least one of a pair of electronic cameras forming a part of an opto-electronic alignment system. The viewing camera (s) forms perspective images of each target, and electronic signals corresponding to each of the images are transferred to an electronic processing means which correlates the perspective image of each of the targets with the true shape of each target. In so doing, the processor relates the dimensions of certain known geometric elements of the target with the dimensions of corresponding elements in the perspective image and by performing certain trigonometric calculations (or by any other suitable mathematical or numerical methods) , calculates the position of each target relative to the viewing camera (s) . By first positioning the assembly with both targets within the field of view of a single camera, and then positioning the assembly such that one of the targets is within the field of view of each camera, the processing means can determine the position and orientation of each camera relative to the other. With such information recorded, the system is "calibrated". DESCRIPTION OF THE DRAWINGS FIGS. 1 (a) - (c) are diagrams illustrating three different images of a circle resulting from various degrees of rotation about different axes; FIG. 2 is a schematic representation illustrating a single camera system used to inspect the alignment of motor vehicle wheels,- FIG. 2a is an illustration of a quasi three-dimensional representation of a type that may be generated on a system display screen to report detected alignment and to guide the technician in making appropriate vehicle adjustments; FIG. 2b is a cross-section through a pan-and-tilt mirror used in one illustrated target embodiment; FIG. 3 is a representation of an exemplary target face design that can be used with the apparatus in FIG. 2; FIG. 4 is a schematic representation of an alternative embodiment of a single camera apparatus; FIG. 5 is a perspective view of an alternative target design mounted on a vehicle wheel; FIG. 6 is a schematic representation of an image of the targets illustrated in FIG. 5 formed using the optical system of FIG. 4; FIG. 7 illustrates one method of how the apparatus calculates the run out factor of the wheel; FIGS. 8a-8c illustrate certain aspects of the matheπTatics performed in the method and apparatus; FIG. 9 is a diagram schematically illustrating a dual camera embodiment of an alignment system of the type described; FIG. 10 illustrates details of the camera/light subsystem of FIG. 9; FIG. 11 illustrates an alternative embodiment of a target array; FIGS. 12a-12d are respectively side, top, front and back views of a target assembly in accordance with the present invention; and FIGS. 13 and 14 are perspective views showing the positioning of the assembly of FIGS. 12a-12d relative to dual cameras in implementing the method of the present invention. DETAILED DESCRIPTION Basic Theory of Alignment System This system is based on the fact that the image " of a body varies according to the perspective from which _such -body is viewed and that the variation in the image is directly related to and determinable from the perspective angle of the view path along which the body is viewed. Furthermore it is known that it is possible to determine the perspective angles at which an object is viewed merely by relating the perspective image of that object with a true non- perspective image thereof. Conversely put, it is possible to determine the angles at which an object is orientated to a view path (or a plane perpendicular thereto) by comparing a perspective image of an object with a non-perspective image thereof . This is illustrated in FIGS. 1(a) -(c) with reference to a circle 10, shown as it would appear if viewed from three different perspectives. In FIG. 1 (a) the circle 10 is illustrated as it would appear if it were viewed along an axis perpendicular to its primary plane which, in this case, is in the plane of the paper. If this circle is rotated through an angle θ, being less than 90°, about the y-axis 12 and viewed along the same view path, the image of the circle 10 will be that of an ellipse as shown in FIG. 1(b) . Similarly, if the circle is rotated about both the x and the y-axes, 12 and 14 respectively, through angles θ and φ respectively, the image of the circle (the ellipse) will be as shown in FIG. 1(c) , in which the major axis 16 of the ellipse is shown to be angled relative to both the x and y-axes. It will, however, be realized that the ellipses here are idealized in that they make no allowance for the distortion which results in an image when it is viewed from a perspective angle. This distortion is illustrated by the broken lines 11 in FIGS. 1(b) and (c) . As can be seen from these Figures, the edge of the ellipse 11, which is closer to the viewer, appears larger while the edge 11, which is farther from the viewer, appears smaller. The resulting image 11 is thus a distorted ellipse. Returning to the idealized conditions shown in these figures, and assuming the angles θ and φ are not known, it is possible to determine the orientation of the primary plane of the ellipse illustrated in FIG. 1(c) by relating the image of the ellipse to the circle 10 in FIG. 1(a) . This is usually done by relating the geometric characteristics (e.g. dimension) of at least one element of the ellipse (e.g. the major and minor axes 16, 18 thereof) to characteristics of corresponding elements (the diameters) of the circle in FIG. 1(a) . Under idealized conditions, these orientation calculations are done by applying trigonometric functions or any other mathematical/numerical methods to the ratios between the minor and/or major axis and the diameter. In addition, the angles of the minor and major axes to the horizontal (x-) axis or vertical (y-) axis can be calculated. Once all these angles have been determined, the orientation in space of the primary plane of the ellipse will be determined. Although not illustrated, it is also possible to determine the position in space of the circle 10. This will, however, be demonstrated below with reference to FIG. 8. The performance of the above illustrated calculations is complicated by the real-life perspective distortion of the image, as illustrated by the broken lines 11. How this foreshortening is allowed for will, once again, be discussed with reference to the mathematics illustrated in FIG. 8. Brief Description of One Embodiment of the Alignment Apparatus The apparatus with which this theory is applied is illustrated in the schematic representation in FIG. 2 : In this figure a motor vehicle 20, on which a wheel alignment is to be performed, is represented by a schematic illustration of its chassis and is shown to include two front wheels 22L and 22R and two rear wheels 24L and 24R. The vehicle 20 is shown positioned on a conventional wheel alignment test bed 26, indicated in dotted lines, which does not form part of this invention. The alignment apparatus is shown to be constituted by a video camera 30 which is in electrical communication with an electronic processing means such as a computer 32 which, in operation, displays results and calculations on a visual display unit 34. In addition, the apparatus includes a keyboard 36 (or some other suitable means) for inputting data and relevant information into the computer 32. It will, of course, be appreciated that display and keyboard entry could be provided by a remote unit which communicates with the computer through a cable, lightwave or radio link. In accordance with an exemplary embodiment and as illustrated in FIG. 2a, a computer-generated quasi three- dimensional representation of the wheels being aligned may be depicted on the display unit 34 along with suitable indicia evidencing the detected alignment. In addition, alphanumeric and/or pictorial hints or suggestions may be depicted to guide the technician in adjusting the various vehicle parameters as required to bring the alignment into conformance with predetermined specifications. The video camera 30 sights onto the wheels 22L, 22R, 24L and 24R along a view path 38 which passes through a lens 40 and onto a beam splitter 42. The beam splitter 42 splits the view path 38 into two components 38L and 38R, respectively. As is apparent from this figure, the left hand component 38L of the view path 38 is reflected perpendicularly to the initial view path by the beam splitter 42 while the right hand component 38R is reflected perpendicularly to the initial view path by a mirror or prism 44 mounted adjacent to the beam splitter. The apparatus also includes a housing 48 into which the beam splitter 42, mirror 44 and at least two pan-and-tilt mirrors, 46L and 46R, are mounted. From this point onwards the respective components of the apparatus and the view path are identical for both the left and right side of the motor vehicle and therefore a description of only one side will suffice. The left hand component of the view path 38L is reflected onto the wheels 22L and 24L by the left side pan-and-tilt mirror 46L which is movable to allow the video camera 30 to consecutively view the front wheel 22L and the rear wheel 24L of the vehicle 20. In some embodiments of this invention the pan- and-tilt mirror 46L can be configured so that both the front and rear wheels of the motor vehicle can be viewed simultaneously. In this embodiment, the view path 38L passes from the pan- and-tilt mirror 46L through an aperture 50L in the wall of the housing 48 and onto the respective wheels 22L and 24L. A shutter 52L is positioned so that it can be operated to close the aperture 50L thereby effectively blocking the view path 38L and allowing the video camera 30 to sight onto the right-hand side of the vehicle 20 only. Alternatively, shutters could be placed at the locations 53L and 53R and/or an electronic shutter within the camera 30 could be synchronized with one or more strobed light sources to permit capture of an image only when a particular target or targets are illuminated. Operation of the Alignment Apparatus In a typical operation, the apparatus of this embodiment of the invention works as follows: The vehicle 20 is driven onto the test bed 26 which basically consists of two parallel metal strips on which the wheels of the vehicle rest. Under the test bed, a lift mechanism is located (but not shown) which acts to lift the metal strips and the vehicle to allow the wheel alignment technician to access the wheel mountings to correct misalignment of the wheels. In addition, a rotationally mounted circular plate commonly called a turnplate (not shown) , is located under each front wheel of the vehicle. The turnplates allow the front wheels to be pivoted about their steering axes relatively easily. This facilitates the procedure involved during the calculation of caster and other angles determined dynamically. The rear wheels are positioned on elongate, rectangular, smooth metal plates mounted on the metal strips. These plates are usually termed skid plates and allow the rear wheels to be adjusted by a technician once the rear wheel mountings have been loosened. Such plates also prevent preload to wheels tending to affect their angular position. In addition, as in some sophisticated alignment machines, the vehicle make and model year can be entered into the apparatus at some time early on in the procedure, and this information is used by the apparatus to determine the alignment parameters, for the vehicle concerned, from previously programmed lookup tables within the computer 32. Furthermore, from the vehicle's make and model year, the track width and wheelbase dimensions can be determined by retrieving the .data from memory. These can be used to drive the mirrors of the alignment apparatus to "home" in on the wheels of the vehicle more accurately. Alternatively, previous operational history information can be used to select likely wheel location. Still another possibility is to cause the mirrors to sweep a particular pattern. Once the vehicle 20 has been driven onto the test bed 26, a target 54 is mounted onto each wheel . The shape and configuration of the target will be described later with reference to FIG. 3. The apparatus first makes a "run-out" factor calculation according to the method that will more fully be described with reference to FIG. 7. Once the "run-out" factor has been calculated, the alignment apparatus forms an image (a detected image) of each of the targets 54 on the wheels of the motor vehicle 20. These detected images are processed in the electronic processing means/computer 32 which calculates, using the method of the invention as will be more fully described, the orientation of each of the targets to the respective view paths 38L, 38R. The computer 32 then takes into account the "run-out" factors mentioned above to calculate the true orientation of the wheels relative to the respective view paths. Thereafter the apparatus makes allowance for the orientation of the pan-and-tilt mirrors 46L, 46R to calculate the actual orientation of the primary planes of each of the wheels. Upon this being done, the results of the computation are displayed on the display 34 which gives the operator the required instructions as to which corrections need to be made to, for example, adjustments to the steerage linkages 60 of the front wheels 22L and 22R to correct the detected misalignment of the wheels of the vehicle. Orientation Calculations The computer 32 does all the required calculations using a computer program such as IMAGE ANALYST, which is capable of analyzing images and values associated therewith. Typically, IMAGE ANALYST produces values for the center points of these images in coordinates relating to the pixels on the screen of the video camera. These values are then processed by software which incorporates the later-to-be-described mathematics illustrated with respect to FIG. 8. Although software such as IMAGE ANALYST may have many features, in this application it is apparent that the main features utilized in this application is that of being able to provide screen coordinates for the images detected by the video camera. It is, therefore, possible for software other than IMAGE ANALYST to be used with this method ,.-_„ . , 98/12503 and apparatus. IMAGE ANALYST is supplied by AUTOMATIX, INC. of 755 Middlesex Turnpike, Billerca, MA 01821. Orientation of the Pan-and-Tilt Mirrors In the above-described method it is evident that knowledge of the orientation of the pan-and-tilt mirrors 46L, 46R is required for the effective calculation of the relative alignment of the wheels of the vehicle 20 to each other. The orientation of these mirrors 46L, 46R can be determined in one of two ways. One way of determining the orientation is by linking the mirrors 46L, 46R to a sensitive tracking and orientation determination device which outputs data to the computer 32 which, in turn, calculates the orientation of the mirrors in three-dimensional space. Alternatively, and preferably, the face of each mirror includes a clearly defined pattern, usually in the form of a number of small, spaced-apart dots, which define an identifiable pattern that can be detected by the video camera 30 as it sights onto the wheels of the motor vehicle 20. Once the video camera 30 has detected the pattern on the mirrors 46L, 46R it can form an image thereof; an image which, because of the orientation of the mirrors, will be a perspective image, and which can then be electronically fed into the computer which, in turn, _ can calculate the minor orientation in three-dimensional space along the same lines as the orientation of the wheels of the vehicle 20 are calculated. This second alternative is preferable because it does not require sophisticated and expensive electronic tracking and orientation determination equipment. One way of implementing this second, preferable alternative, is to incorporate a lens 40 into the apparatus. The lens has a focal length such that it projects an adequately clear image of both the targets and the mirrors onto the camera 30. In FIG. 2b, one way of enhancing the images of the dots on the pan-and-tilt mirrors is illustrated. This figure 98/12503 illustrates a cross-section through a pan-and-tilt mirror 46L with two dots 41 shown formed on its upper surface. A planoconvex lens 43 is located on top of each dot. The focal length of each of these lenses is such that, together with the lens 40, they form a clear image of the dots in the video camera 30. Although this figure illustrates two individual plano-convex lenses 43, it will be evident that a single lens spanning two or more dots could be used. Similarly, other optical methods can be used to accomplish this. Orientation of the Targets An example of a typical target 54 that can be used on the wheels of the vehicle 20 is illustrated in FIG. 3. As can be seen from this figure, the target consists of a flat plate with a pattern of two differently sized circles 62, 63 marked in a pre-determined format thereon. Although a specific pattern is shown in this figure, it will be evident that a large number of different patterns can be used on the target 54. For example, the target need not be circular, a larger or smaller number of dots may be included. Moreover, other sizes and shapes can be used for the dots. In addition, multifaceted plates or objects can also be used for the targets. In practice, a mathematical representation, or data corresponding to a true image (i.e. an image taken by viewing the target perpendicularly to its primary plane) and the dimensions of the target are preprogrammed into the memory of the computer 32 so that, during the alignment process, the computer has a reference image to which the viewed perspective images of the targets can be compared. The way that the computer calculates the orientation of the target 54 is to identify certain geometric characteristics on the target 54, take perspective measurements of these and compare these measurements with the true image previously preprogrammed into the memory of the computer. The apparatus could, for example, calculate the center of each of the circles 62a, 62b by means of, say, a method called centroiding. This is a method commonly used by image- analysis computers to determine the positioning of the center point or center line of an object. Once the center points of the two circles 62a, 62b have been determined, the distance between the two can be measured. This process is then repeated for other circles in the pattern on the target 54. These distances can then be compared to the true distances (i.e. non-perspective distances) between the respective centers. Similarly, the angle to the horizontal (or vertical) of the line joining the two centers can be determined. Once allowance has been made for the effect of the focal length of the lens 40 and other optical characteristics of the components, such as beam splitter 42, mirror 44 and mirrors 46L, 46R, are considered, a calculation can be made as to what the orientation of the target 54 is. This calculation can be done by using trigonometric functions or other suitable mathematical or numerical methods. As explained above, this will also yield the orientation of the primary plane of the wheel of the vehicle. Although the above describes one method of calculating the orientation of the target 54, it will be evident that other methods are also available. For example, the apparatus could sight onto only one of the circles, say the circle 63, and by using the perspective image thereof (the distorted ellipse) calculate, in very much the same way as described with reference to FIG. 1, the orientation of that circle and, therefore, the orientation of the target 54. Another example is to take two images rotated about 60° relative to each other and use such information to calculate the orientation of the target with respect to its axis of rotation. Note that only two images are required so long as the wheel axle does not change its axial orientation. In addition, it is envisaged that in sophisticated alignment systems more than one calculation will be completed for each target and that the different results of these calculations will be compared to each other to ensure the required accuracy. Furthermore, as the true dimensions of the target are preprogrammed into the memory of the computer 32, the method and apparatus of this invention can be used to determine the exact position of the wheels in three-dimensional space. This can be done by firstly determining the perspective image of certain of the elements of the pattern on the target (for example, the distances between circles) and comparing the dimensions of this image to the true dimensions of those elements. This will yield the distance that the element and, accordingly, the target 54 is from the video camera. As the processes described above have already yielded the orientation of target 54 with respect to the view path and/or some other reference plane, this result can be combined with the calculated distance and the geometric coordinates of the alignment apparatus to yield a position of the target 54 relative to the alignment apparatus. During this comparison process, the effect of the focal length of the lens 40, as well as the optical characteristics of the beam splitter 42, mirror 44 and the pan-and-tilt mirrors 46L and 46R must also be taken into consideration. Typically, these characteristics would be input into the computer by direct entry or, preferably, by calibration techniques. In this way the exact positioning of each of the wheels of the vehicle 20 can be calculated. Brief Description of an Alternative Embodiment of the Alignment Apparatus It will be evident to one skilled in the art that a number of different configurations of lens, beam splitter and mirrors (i.e. the optical system) are possible to achieve the desired result with the illustrated method and apparatus. One such configuration is illustrated in FIG. 4 of the accompanying drawings . In this figure the equipment is shown to be suspended over the motor vehicle 20 and includes a video camera 30., computer 32 with associated display 34 and data entry keyboard 36 as well as lens 40 similar to those illustrated in FIG. 2. As with the configuration in FIG. 2, the view path or optical center line of the video camera 30 is deflected into two directions 38L and 38R by a combination of beam splitter 42 and plane mirror 44. This configuration also includes two pan-and-tilt mirrors 70L, 72L, located on the left side of the apparatus and two pan- and-tilt mirrors 70R and 72R located on the right side of the apparatus. The mirrors 70L, 72L are arranged to view the left front and left rear wheels 22L, 24L, respectively and the mirrors 70R, 72R are arranged to view the right wheels 22R, 24R respectively. As the mirrors 70L, 72L, 70R, 72R are pan-and- tilt mirrors, they can be moved to view the wheels on the vehicle 20 even though the vehicle is not accurately centered below the apparatus. These mirrors are also useful in making allowance for vehicles of different lengths of wheelbase and track width. A further modification of this apparatus would include the replacement of the beam splitter 42 and the plane mirror 44 with a single reflecting prism. The prism has the advantage over the beam splitter combination in that more light is reflected from the prism into the camera 30. This results in a brighter image of the target 54 being formed by the camera 30. Target and Target Image Details With the apparatus as illustrated in this figure, as with the other illustrated apparatus, a modification of the target, as indicated in FIG. 5, can be used. In this figure the target, generally indicated as 80, is shown to include a flat, rectangular plate 82 which is clamped to the rim 84 of a wheel 86 by means of a clamping mechanism 88. It will be evident from FIG. 5 that the plate 82 is angled relative to the primary plane of the wheel 86 as well as to its axis of rotation 89 ' . The precise orientation of this plate 82 relative to the wheel axis is, however, not known and will, as is described later, be computed with respect to the wheel axis by the determination of a run-out factor for this wheel. The general orientation of the plate 82 is, however, chosen so that it can be adequately viewed by the video camera 30 as it sights onto it. Finally, plate 82 includes a plurality of dots 90 which, as shown, constitute a pattern not unlike that on the target illustrated in FIG. 3. With targets of this nature, the images formed by the video cameras 30, when used together with the apparatus illustrated in FIG. 4, will be something like that illustrated in FIG. 6. In this figure, it is apparent that four discrete images 92, 94, 96, 98 are formed to make up the complete image, generally indicated as 99, formed by the video camera 30. Each of the four images that make up the complete image 99 is an image of one of the rectangular plates 82, respectively disposed o ' n the four wheels of the motor vehicle. For example, the image $2 at the top of the picture 100 could correspond to the plate 82 on the right rear wheel 24R of the vehicle 20. Similarly, image 94 could correspond to the right front wheel 22R, image 96 to the left front wheel 22L and image 98 to the left rear wheel 24L. The advantage of the target 80 when used with the apparatus illustrated in FIG. 4 is that a single image can be taken simultaneously of all four wheels. This single image can then be processed, in very much the same way as described above, to yield the orientation and location of all the wheels to each other. More particularly, the relative orientation of the right front wheel to the left front wheel and the right rear wheel to the left rear wheel can be calculated. On either end of the images 92, 94, 96, 98 a pair of dots 100 can be seen. These dots 100 are in fact images of the dots on the respective pan-and-tilt mirrors referred to in the discussion of FIG. 2. As was pointed out in that discussion, these dots are used to calculate the orientation of the pan-and- tilt mirrors to the view path of the camera; a calculation which is essential to determine both the orientation and the location of the primary plane of each of the wheels of the vehicle . In addition, this figure illustrates that the images of the marks 100 can be separated from the images of the patterns on the plate by means of a vertical line 101. This line 101 serves as a demarkation line between the pattern (from which the orientation of the target is calculated) and the image of the dots 100 (from which the orientation of the pan-and-tilt mirrors is calculated) . Runout Factor Calculations In FIG. 7 of the drawings, a method of calculating the runout factor for a target 104 mounted in a slightly different way on a wheel 103 is illustrated. In this method, the wheel 103.is slowly rotated while a number of different images of the target 104 are taken. This target is, for the sake of clarity, off-set fairly substantially from the center of the wheel. In practice, however, the target may be mounted closer to the center, much like the target illustrated in FIG. 5. For each image, the inclination of the plane of the target, as well as its location in space is calculated. Once these have been determined for each image, they are integrated to define a surface of revolution 106. This surface of revolution 106 will represent the path which the target 104 tracks as the wheel is rotated about its axis, and the axis of rotation 108 thereof is the same as the axis of rotation of the wheel. This means that a plane perpendicular to the axis of rotation 108 of the surface of revolution 106 will be parallel to the primary plane of the wheel 106. As the surface of revolution 106 is determined, its axis of rotation 108 is determined and, therefore, the orientation and position in space of the primary, plane of the wheel of the vehicle can be determined. From these results, the run-out factor can be determined by calculating the angle between the plane of the target and the primary plane of the wheel. This run-out factor is then stored in the computer 32 and used when the alignment of the wheel is calculated from a single image of the target . The calculation of the run-out factor can also be used to determine whether or not the suspension of the vehicle is badly worn. Using the method of the invention an apparent run-out factor (i.e., the orientation of the target with respect to the wheel) can be determined for each image which is taken of the target. From this group of individual run-out factors a mean value can be calculated (which will represent the true "run-out" factor) as well as the extent of the deviation from the mean of the individual factors. If this deviation is above a certain tolerance, this indicates that the suspension of the motor vehicle is worn so badly that it needs to be attended to. " Accuracy Determination Turning once again to the targets, it should be realized that an important feature of the target illustrated either in FIG. 3 or 5 (or any other target for that matter) is that it should have sufficient data points to allow redundant calculations to be made using different sets of data points. This will yield multiple wheel alignment angles which can be averaged out to improve the accuracy of the final measurement. In addition, a statistical distribution of the different alignment angles calculated for each wheel can be used as a measurement of accuracy of the operation of the apparatus. If a suitable check is built into the computer 32, a statistical distribution such as this can enable the computer 32 to determine whether or not sufficient accuracies exist and, if not, to produce a signal which can alert an operator to this fact . Similarly, if the above checking indicates that one or more of the targets used yield (s) unacceptably poor results while the remaining target (s) yield acceptable results, it can be assumed that some of the targets being used are unacceptable. The computer can give an indication to this effect and the operator can, for example, be instructed to remove, clean or repair the offending target (s). A further benefit derived from forming suitable multiple images and computing a statistical analysis, is that the computer 32 can determine whether or not enough images have been taken to suitably ensure the required accuracy of the alignment measuring process. If insufficient readings exist, the computer can direct the apparatus to take further readings which, although sacrificing speed, would result in improved accuracy of the measurement. Furthermore, the target could include a machine-readable, e.g. a bar code or the like, which can be used " for identification, target tracking, intensity threshold measurement, evaluation of illumination quality, and encoding of defects to allow the use of cheap targets. For example, if the target was twisted and the amount of twist was encoded in the bar code, then the computer could compensate for the twist. Another important feature of the target is that the pattern thereon should allow very quick and accurate location of the pattern to an accuracy approaching substantially less than a camera pixel. To achieve this the pattern should exhibit a high contrast and be of a configuration which allows the specific apparatus used to achieve the required speed and accuracy. In one embodiment, retro-reflective materials are used for the dots, and a color that is absorptive of the particular light used is chosen for the background. This apparatus also allows for calibration, " which is important as all optical systems have some geometric distortion. The total image area of the apparatus could, for example, be calculated using a perfect target and the result used to determine correction values that can be stored for use when operating the system in alignment procedures. The absolute accuracy of the apparatus can be checked or calibrated by using a simple 2-sided flat plate target which is placed so that the apparatus views both sides simultaneously. As the plate is flat, the net angle (relative alignment) between the two planes of the target should be zero. If not, a suitable correction factor can be stored in the computer. Alternatively, two views of the same side of the target taken from different angles could be used for this purpose. Mathematical Algorithms Used This section provides the mathematics necessary to reduce measurements made • by the video camera to wheel positions in space using instantaneous measurement. Assumptions The camera system can be defined to include two planes positioned arbitrarily (within reasonable constraints of visibility) with respect to one another. One is the image plane, which maps what is "seen" by the camera and the other is the object plane, which contains three-dimensional, essentially point targets. Based on this, the assumptions made are: (i) the camera principal axis is normal to the image plane (most cameras are built this way) ; (ii) there exists, at a known distance of / (i.e. the imaging system's focal length when set at infinity) from the image plane, along the camera principal axis, a point called the center of perspectivity (CP) such that the behavior of the camera is that the image of a viewed point anywhere in the camera's field of view is to project it onto the image plane by moving it along a line passing both through the viewed point in space and the CP; (iii) the origin of the coordinate system fixed in the image plane is located at the center of perspectivity, with z unit vector directed toward camera along its principal axis,- and (iv) the units of the image plane measurements are the same as those of the object plane measurements. These assumptions are commonplace in the visual sciences. Overview For this configuration, mathematics can be provided to determine the relative orientations and positions of the object and image planes. - This mathematics can be used in 2 ways: (i) during calibration, to find the position oξ. the image plane with respect to the location of an object plane of known position of a calibration target ; and (ii) during the alignment process, to find the position and orientation of the primary plane of the target mounted on the wheels of the vehicle. It is essential in this step that the known coordinate system is fixed in space, and that it remains the same for all four wheels of the car. As has been described above, once the location of the target planes on the wheels is known, by rotating the wheels, the axis of rotation of the wheels can be determined, and from there, the alignment of the wheels. Main Algorithm It should be noted that this main algorithm presents no treatment of the various pan-and-tilt mirrors; this is done later . The main algorithm requires the following inputs: (i) A list of points expressed in object plane coordinates . °q j = (x-, y. j ) , j = 1, n / n > 4 These are actually three-dimensional points, but the object plane coordinate system can always be chosen so that the third coordinate z. = 0. (ii) A corresponding list of image plane point coordinates "q. = (u_, v..) , j = 1, n. For these inputs, the algorithm produces an output which is a homogeneous coordinate transform matrix expressing the center of perspectivity and unit vectors fixed with respect to the principal axes of the image plane. This matrix will normally be inverted, and then applied to transform the viewed points " into image system coordinates. Step 1 : Determine a Collineation Convert all the two-dimensional input coordinates to affine form and find a 3x3 transformation matrix T such that: (l) for i = 1, n and where the ki are arbitrary scalar constants. One way in which the transformation matrix T can be determined is given below. Step 2: Determine transforms of key points and invariants . The transform matrix T will transform points in the object plane to points in the image plane under the projectivity whose center is the center of perspectivity (CP) . When, inverted, it will also perform the reverse transformation, viz: (2) It will be noted that the whole equation may be multiplied by an arbitrary scalar and still remain true. The value m. is such a scalar, and is required to permit normalization of (u. v. l) τ so that its third coordinate is a unit. The matrix T is also useful for transforming lines, which are dual to points on the projective plane. The equation of a line m the projective plane is : (3) [ l C 2 C 3 ] = 0 X = 0 X Where c is the coordinate vector of the line and X is the specimen vector. Any homogeneous representation of a point which satisfies equation 3 lies on the line. Suppose that an object co-ordinate °c lies on a line, then: (4) [ ° C ] is the equation of a line in the object plane, expressed in object plane coordinates. Using equation 2 we can transform to image plane co-ordinates: [ ° c ) 7" L x (5) or = 0 Therefore is the way to transform line coordinates from the object plane to the image plane and (7) "c = T τ *c is the way to perform the inverse transformation. Note that the projective plane differs from the non- projective plane in that it includes points at infinity whose projective coordinate is 0. These points together constitute a line at infinity, whose coordinates are [0,0,1] viz. (8) x y [0 01] w w = o 8/12503 This is illustrated in FIG. 8a which represents a side view of an object plane OP and image plane IP positioned non-parallel to each other at some angle θ . The object plane OP intersects a plane parallel, to the image plane IP but passing through the center of perspectivity CP . This plane is called the view image plane VIP and intersects the object plane OP at the "vanishing line" mapped to the object plane, shown as point VLO . Similarly, the figure shows a plane parallel to the object plane called the viewed object plane VOP which intersects the image plane IP at a "vanishing line" mapped to the image plane, shown as point VLI . As VIP is parallel to IP they intersect at infinity. The collineation matrix T can therefore be used to map the line at infinity of the image to its transformed position in the object plane as follows: VLO (9) and likewise: ;ιo. VLI s By the assumptions stated above with respect to the camera system, the coordinates of the principal point of the image PPI are: (11) PPI The coordinates of the principal point of the object PPO are ; ( 12 ) PPO Step 3 : Complete Remaining Inclination Values The minimum distance between a line in a projective plane with line coordinates l z 1 z 2 z 3 ] τ and a point with coordinates [p 1 p 2 p 3 ] τ is given by (13) This makes it possible to solve for DI , θ and DO: (14) a3 DI / + a, (15) θ = arctan Step 4 : Compute Pan Values FIG. 8b illustrates a plan view of the object plane, looking down from the center of perspectivity. We have :i7) φ = arctan . ' 18. Let = sgn (S x PPO) x -sgn ^1 C 1 + ^2 C 2 + ^3 3 b l C 3 :i9) y t = sgn (S y - PPO) . °p. Step 5 : Solve for Remaining Unknowns Referring to FIGS. 8a and 8b together; (20) DCP = I DO . sin θ I (21) Oi PPI = "PPO + DCP." z i + DCP ° z. (22) This is the origin of the image plane coordinate system expressed in object plane coordinates. It is located at CP . ° x and 0^ the remaining unit vectors can be computed by transformation of the corresponding unit vectors. in the image plane, and subsequent orthogonalization with respect to z 1 . (23) Let :24: Then X. X-, X-, can be orthogonalized with respect to z. (25) X< °z ) and renormalized (26) = X< (27) Similarly, let (28) Then 3 (29) y_ ?! 7_ and :30) y. ? ?ι (3i; Finally Vx o . ' F, = Frames transform from image space to object space is the frame to return, and to express points given in the object plane coordinates in terms of the coordinate system fixed with respect to the image plane, we note (32) and (33) ( k) Q k *F y k o V 1/ That is the general case, but there is also the special case when the object and image planes are parallel. This is detectable when VLO or VLI (equations 9 or 10) turn out to lie at infinity themselves (meaning their first two coordinates lie sufficiently close to 0) . In this case, (34) and the distance DCP can be determined by taking any point in the object plane (x k , y k ) whose corresponding (u k , v k ) is not zero and calculating according to the diagram in FIG. 8(c): (35) Let χ l y l (36) (37) DCP = —2 / and then proceeding as from equation (22) . This concludes the description of the main algorithm to determine plane displacements. 9.4 Determination of Transform Matrix This section illustrates how to calculate the transform matrix T used in equation (1) . The method presented here is an analytic method which maps between only 4 coplanar points and is based on the fundamental theorem of projective geometry which tells us that given four points in the projective plane: constants c l t c 2 and c 3 can be found such that P . = c,p 1( + c 2 p 2 + c 3 p 3 ( 3 9 ) When this is represented in matrix form: ( 40 ) then the matrix M consisting of ( 41 ) will transform the ideal points origin and unit points as follows : (42) (unit x vector) (unit y vector) (origin) (unit point) Therefore, to construct a transform which maps four arbitrary points P j , p 2 , p 3 , p 4 to four arbitrary other points q 1# q 2 , q 3 , q 4 , two transforms must be constructed: M, , 143 ) U → p 4 u → q 4 and then M , such that q_ = P_ M ( 44 ) is given by M = M.- 1 M 2 (45) Note that in this section, the p's and q's are now vectors. In the main section, column vectors are used, so T = M τ (46) Finally, another method (not illustrated here) accepts more than four points and does a least-squares approximation using pseudo- inverses . This second method can be used in the case where the number of points measured has been increased to compensate for expected errors. Allowance for Pan-and-Tilt Mirrors After the imaged data points have been converted back to three-dimensional points given in image plane coordinates, it remains to make allowance for reflections by the beam splitter assembly and the pan-and-tilt mirrors. If x is a point to be reflected, and x n is a unit-length normal to the plane of reflection, 1 x 0 is a point in the plane of reflection (all expressed in image-plane coordinates) then x x r , its reflection is given by (47) The matrix above is a standard displacement style transform which may be inverted using standard methods though there is no need to do so in the present application. These matrices may also be cascaded as usual from right to left, to deal first with the beam-splitter and then with the pan-and-tilt mirror, but the reflection plane point 1 x 0 and normal 1 n for the pan-and-tilt mirror must first be transformed by the beam-splitter reflection matrix before the pan-and-tilt mirror reflection matrix is formed from them. Finally, it should be noted that when the main algorithm is used to find the position of the pan-and-tilt mirror, once these have been reflected through the beam splitter. * z and λ 0 0 are directly usable as normal and point in the reflection plane directly. A subsequent use of an iterative fitting procedure may result in improved accuracies. Other mathematical processes can also be used to process the images detected using the apparatus. Alternative Two-Camera Embodiment In Fig. 9 of the drawing, an alternative embodiment of the alignment apparatus utilizing a pair of fixed, spaced-apart cameras is depicted at 110. A four-wheeled vehicle positioned on a lift ramp 111 for wheel alignment is suggested by the four wheels 112, 113, 114, and 115. In the usual case, the rack 111 will include pivot plates (not shown) to facilitate direction change of at least the front wheels. In this embodiment a camera supporting suprastructure includes a horizontally extending beam 116 affixed to a cabinet 117. The cabinet 117 may include a plurality of drawers 118 for containing tools, manuals, parts, etc., and may also form a support for a video monitor 119 and input keyboard 120. Mounted at each end of the beam 116 is a camera and light source subsystem respectively designated 122 and 124. The length of beam 116 is chosen so as to be long enough to position the camera/light subsystems outboard of the sides of any vehicle to be aligned by the system. The beam and camera/light subsystems 122, 124 are positioned high enough above the shop floor 125 to ensure that the two targets on the left side of the vehicle are both within the field of view of camera assembly 122, and the two targets on the right side of the vehi ' cle are both within the field of view of camera assembly 124. In other words, the cameras are positioned high enough that their line of view of a rear target is over the top of a front target. This can, of course, also be accomplished by choosing the length of beam 116 such that the cameras are outside of the front targets and have a clear view of the rear targets. Details of the camera/light subsystems 122, 124 are discussed below with respect to Fig. 10. In accordance with this embodiment, a target device 126, including a rim-clamp apparatus 128 and a target object 130, is attached to each wheel. A suitable rim-clamp mechanism is discussed in U.S. Patent No. 5,024,001 entitled "Wheel Alignment Rim Clamp Claw" . As will be described in more detail below, the preferred target object has at least one planar, light- reflective surface with a plurality of visually perceptible, geometrically configured, retro-reflective target elements 132 formed thereon. Such target surfaces may be formed on one -or more sides of the target object. In use, each target must be positioned on a vehicle wheel with an orientation such that the target elements are within the field of view of at least one of the camera/light subsystems . In Fig. 10 of the drawing, further detail of the camera and lighting components is illustrated. Mounted within the partially broken-away end of beam 120, the subsystem 122 is shown to include a lighting unit 140, comprised of a plurality of light emitting diode (LED) light sources 142 arrayed about an aperture 144 through which the input optics 146 of a suitable video camera 148 is projected. The light array in the preferred embodiment includes 64 LEDs (a lesser number being shown for simplicity of illustration) which provide a high- intensity source of on-axis illumination surrounding the camera lens, to ensure that maximum light is retro-reflected from the targets. In order to discriminate against other possible sources of light input to the camera 148, a narrow band filter matched to the light spectrum of the LEDs may be positioned in front of the lens 146. Although any suitable type of video camera can be utilized, in accordance with the preferred embodiment a CCD device, such as the manufactured by Phillips is utilized. This camera has a resolving power suitable for the present application. In Fig. 11, an example of a target in accordance with a preferred embodiment is depicted and includes a plurality of light-reflective, circular target elements or dots of light- colored or white retro-reflective material disposed in an array over a less reflective or dark-colored surface of a rigid substrate. Suitable retro-reflective materials include Nikkali te™ 1053 sold by Nippon Carbide Industries USA, Scotchli te™ 7610 sold by 3M Company, and D66-15xx m sold by Reflexite, Inc. The target includes multiple circular dots so as to ensure that sufficient data input may be grabbed by the camera even in the case that several of the target elements have been smudged by handling or are otherwise not fully detectable. In accordance with the preferred embodiment a well defined target includes approximately 30 circular dots very accurately positioned (within 0.0002") with respect to each other. By way of specific example, the target illustrated in Fig. 11 might include 28 circular dots of 1" diameter very accurately positioned on a 2" x 2 " grid, with four l 1 /" dots and a single 1 " diameter dot strategically positioned within the array. By mathematically moving the mathematical image of a target until the mathematical position and orientation of the dots line up with the dots of the real target in the real image, position and orientation information can be obtained. This mathematical manipulation of a well defined target until it is oriented the same way as the image is called "fitting the target." Once the fitting is accomplished, the position and orientation' of the target is very accurately known (to within 0.05" and 0.005°) . Such accuracy is obtainable because the target is made to very strict tolerances and because the design enables measurement of many points (1,500 measured points, i.e. 30 or so fiducials (dots) each with detected 50 edge points) . Furthermore, the use of subpixel interpolation enhances the accuracy of measurement to beyond the pixel resolution of the CCD cameras. The target is typically manufactured using a photolithographic process to define the dot boundaries and ensure sharp-edge transition between light and dark areas, as well as accurate and repeatable positioning of the several target elements on the target face. The target face may also be covered with a glass or other protective layer. Note that since all information obtained from a particular target is unique to that target, the several targets used to align a vehicle need not be identical and can in fact be of different makeup and size. For example, it is convenient to use larger rear targets to compensate for the difference in distance to the camera. In order to accurately determine the position between the wheels on one side of the vehicle and the wheels on the other side of the vehicle, the system must know where one camera is positioned with respect to the other camera. This is accomplished during a calibration and set up operation wherein, as depicted in Fig. 9, a larger target 150 (presently 3' x 3') is positioned in the field of view of both cameras, typically along the centerline of the rack 111, and the approximately 30 feet away from the cameras. Information obtained from each camera is then used to determine the relative positions and orientations of the cameras. More specifically, since each camera will indicate where the target is with respect to itself, and since each is viewing the same target, the system can calculate where each camera is located and oriented with respect to the other. This is called a relative camera position (RCP) calibration. Such calibration allows the results -obtained from one side of the vehicle to be compared to the other. Thus, by mounting the two cameras rigidly with respect to each other and them performing an RCP calibration, the system can be used to locate the wheels on one side of the vehicle with respect to the other side from that point on. This is to say that the RCP transfer function is used to convert one camera's coordinate system into the other camera's coordinate system so that a target viewed by one camera can be directly related to a target viewed by the other camera. The illustrated inspection process is monocular, meaning that by using one camera in one position, the position and orientation of a target with respect to the camera can be determined. This, of course, requires that the target be in view of the camera to accomplish the measurement. But since one camera can only conveniently view one side of the vehicle at a time without using reflectors as earlier described above, two spatially related cameras must be used to view both sides. The RCP transfer function then allows the information obtained by the two cameras to be coordinated and have the same effect as if all of the information had been obtained by a single camera. An advantage of the use of such a system is that, since each wheel is independently inspected and merely related back to the others, the system is independent of level and does not require leveling of the vehicle support rack or floor. Moreover, it is not necessary that the axles of all wheels be at the same height, i.e., differences in tire sizes or inflation will not adversely affect measurement. In operation, once the system has been calibrated using the calibration target 150 as illustrated in Fig. 9, a vehicle may be driven onto the rack 133, and, if desired, the vehicle lifted to an appropriate repair elevation. The target assemblies 126 are then attached to the wheel rims and manually oriented so that the target surfaces face the respective camera/light subsystems. The vehicle and model year are then " entered into the keyboard 120 along with other relevant information which may include the vehicle VIN number, license number, owner name, etc. The system database includes specifications for each model that might be inspected, and upon identification of the particular vehicle under inspection extracts such information to assist in quickly locating the target images. Alternatively, previous inspection history can be used to indicate likely target location . The targets are highly accurate and their position and orientation relative to the rim of the wheel to which they are attached is known to an accuracy of 0.01" and 0.001°. If each wheel was perfect and the clamp was perfectly mounted one could argue that the wheel axle would be normal (90° in all directions) to the wheel plane determined by the rim edge. However, since wheels are normally not perfect and targets are not always perfectly mounted, such information would only indicate orientation and position of the wheel plane and not necessarily provide accurate information as to the orientation of the wheel axis. Such assumption is thus not made. However, by rolling the wheel from one position to another a new image can be taken, and from the position and orientation of the target in the two positions, the actual position and orientation of the wheel axis can be calculated. Similarly, to calculate the steering axle (about which the wheels turn when the steering wheel is turned) two target positions are again compared, one with the wheels turned to one side and one with the wheels turned to the other side. Calculation of the axis about which the targets must have been moved thus identifies the position and orientation of the steering axis. Now knowing where each wheel axle is located and how it is oriented, where the steering axles are located and how they are oriented, the vehicle can be mathematically modeled in three dimensions, and the alignment values in toe, camber, 'caster, thrust angle, etc. can be displayed with respect to the vehicle itself . Once the targets are installed on each wheel and the system is energized, enough information is available to generate an image such as that depicted in Fig. 2a. However, as pointed out above, because the rotational axis of the wheels may not be exactly normal to the wheel plane as defined by the outside perimeter of the rim to which the target assembly is attached, the system operator will be instructed to move the vehicle forward or aft 6 or 8 inches so as to rotate the wheels through about 30 of rotation. With measurements taken of at least two different wheel positions, the system can optically obtain enough information to accurately determine true axle position and orientation for each wheel. Highly accurate computations can then be made and displayed on an updated screen, as depicted in Fig. 2a. At this point, the actual operator alignment procedure can proceed, and since the inspection is continuous, the results of each adjustment will be reflected on the system video screen. In the preferred embodiment of the present invention, the operator can select various levels of assistance, including actual depictions of the location and parts to be adjusted to provide corrective action. Such information can even include the appropriate choice of tool to be used. As pointed out above, since each camera is referenced to the other, it is not necessary that the supporting rack be level or even that all wheels lie within the same plane. However, although each wheel inspection is independent of the others, a reference plane must be identified. This can be accomplished by defining a reference plane that passes through the axles. But since one of the axles may not lie in the plane defined by the other three, some liberties must be taken. For example, for the purpose of aligning the front wheels, one might use the plane defined by the front axles and the average of the rear axles. A similar procedure might be used with respect to the rear wheels, etc. Wheel alignment would then be referenced to such a plane or planes. In addition, wheel position and thrust line measurements would also be referenced to such a plane or planes. Moreover, because of the independence of measurement, once a reference plane is defined, should one of the targets be blocked from view or become loose or even dislodged from a wheel, it will not necessarily affect measurements associated with other wheels . Use of a single calibration target such as that illustrated at 150 in FIG. 9 may, however, in some respects be problematic. For example, the orientation of the two cameras 122, 124 must be set up so that both cameras can see the same target; that is, the fields of view of the cameras must overlap at the position of the target 150. Since it is desirable that the cameras have as narrow a field of view as possible, e . g. , to optimize sensitivity and reduce optical distortion, the single target may have to be positioned a fairly substantial distance from the cameras so as to lie within the fields of view of both cameras. Therefore, it may be necessary to make the target large, unwieldy and expensive . However, according to the present invention, the above- described single target calibration disadvantages can be overcome through use of a calibration target assembly such as that depicted at 160 in FIGS. 12a-12d. The illustrated assembly is comprised of a front target 162 and a rear target 164, respectively mounted in cantilevered fashion to opposite ends of a suitably configured rigid support structure formed by a two- piece telescoping beam 166, 167 mounted to upstanding support legs 168 and 169 rigidly affixed thereto. The beam parts 166 and 167 may be rigidly locked together at a desired extension by a suitable screw-clamp 165 or the like. The lower end of leg 168 is provided with a base 170 extending laterally to one side of the leg. Base 170 is provided with a supporting pad 171 disposed beneath its distal end. The lower end of leg 169 is provided with a base 172 that extends to both sides of leg 169 and has a support pad 173 disposed beneath one end thereof and a two position tilt mechanism 174 affixed to the other end. As will be discussed below, the tilt mechanism 174 is a simple repositionable support that in one position causes the base 172 to lie horizontal, and in a second position causes the entire assembly to be tilted slightly into a new orientation to allow the checking of a previously calculated calibration. Note that since targets 162 and 164 both extend laterally to the same side of beam 166, 167, the center of gravity of the structure is to one side of the beam 166, 167. Accordingly, the three supports 171, 173 and 174 are positioned in unbalanced relationship to the beam centerline so as to counter the unbalance caused by the side-mounted targets. Although the targets 162 and 164 are for simplicity shown with plain faces, it will be understood that they are actually provided with optically detectable geometric designs of the type described above. The target faces are angularly disposed at typically 45° relative to the longitudinal axis of beam 166, 167 for reasons which will be discussed below. Note that rear target 164 is somewhat larger than front target 162 to compensate for the difference in distance to the camera. Also affixed to beam part 167 are simple C-shaped handles 176 and 177 that may be used to lift the assembly to carry or move it from one position to another. In use, the assembly is normally extended as illustrated in FIG. 12a by the solid lines; however, as suggested by the dashed lines, by releasing the clamp 165, beam part 166 may be telescoped into beam part 167 to present a more compact assembly for transport or storage. Turning now to FIGS. 13 and 14, the improved calibration method of the present invention will be described using the assembly 160. With the auto lift rack 180 raised to a typical inspection level, and with the assembly 160 positioned as indicated on the left rack track or rail 181, both the front target 162 and rear target 164 will be within the field of view of camera 122. Neither target will necessarily lie within the field of view of the other camera 124. Since the targets 162 and 164 are now in positions similar to those of the left side targets previously disclosed with reference to FIG. 9, it will be appreciated that camera 122 can optically illuminate and detect the positions and orientations of the targets relative to its own position and optical axis, as well as to each other, by using the techniques described above. But at this point, the system is not yet "calibrated" because the precise position and orientation of camera 124 relative to camera 122 is not yet known. However, now that the separation between targets 162 and 164 is now known and their angular relationship to each other is known, by simply lifting the assembly 160 and placing it in bridging relationship across the rack tracks 181 and 182 as illustrated in FIG. 14, so that target 164 now lies within the field of view of camera 122, and target 162 lies within the field of view of camera 124, the two cameras can respectively determine their position and orientation relative to the targets 164 and 162. And since, as indicated above, the separation and relative orientation of the targets is both known and fixed, the system can accurately compute the orientation and position of camera 124 relative to camera 122. The system is thus now calibrated. However, as a check the technician can simply reposition or reorient the assembly 160 on rack 180 and cause the system to recompute the relative camera positions. One way to accomplish such reorientation is to simply extend or retract the tilt 'mechanism 174 into its other position; another is to move the assembly back a foot or so on the rack. If there is no change in camera position computation, the calibration may be considered accurately accomplished. This also insures that the assembly has remained rigid and dimensionally unchanged during its repositioning. Among the advantages of using this calibration method and apparatus are as follows: (1) Smaller targets can be used (as compared to the previously described single target procedure) . (2) The calibration targets can be located closer to the cameras, thereby improving the accuracy of the process. (3) The camera fields of view do not have to overlap. (4) The assembly need only be held rigid during the calibration operation; thereafter it can be collapsed into a smaller configuration. (5) The assembly need not be built and maintained to a high tolerance on relative target orientation and position; the structure's relative target position is field calibrated. Although the targets illustrated in FIGS. 12-14 are depicted as planar in configuration, it is to be understood that any other suitable target design could likewise be used so long as it includes features which enable the position and orientation of the target to be optically determined by the cameras 122, 124 or other optical inspection means. Moreover, the targets need not necessarily be mounted to one side of the beam 160. For example, they could be mounted above or below the beam in any suitable manner that allows unobstructed viewing by the cameras when the assembly is disposed in the calibrating positions described above. However, one benefit of the disclosed structure is that the same targets, or type of targets, used in the subsequent wheel alignment operations can be affixed to the beam 160 in the same manner and using the same fastening techniques used to mount the targets to the auto wheels . Having now described several embodiments of opto-electronic apparatus suitable for use in aligning the wheels of a vehicle, and having pointed out that the position and orientation of each target and associated wheel may be determined independently of the other targets (and wheels) , it will be appreciated by those skilled in the art that by modifying the target attachment structure to enable the targets to be affixed to other particular points on the vehicle, or to another type of structure, such as, for example, a building structure, an article of manufacture, a robot arm, or even territorial space, the same system can be used to measure relative spatial location or alignment of the several points to which the targets are affixed. For example, in the case of an automotive vehicle or the like, one might use the described system to measure vehicle chassis or body alignment, or perhaps ride height. And because the data is updated at a high rate, "jounce" measurements (i.e. , a measurement of suspension dynamics) can be made. In the case of articles of manufacture, one might wish to embody a target in the form of a label and affix the label to parts on an assembly line, and then use the apparatus to track the position and/or orientation of the article as it moves down the line. In the case of a robot arm, one or more targets affixed to various moving parts could be used to accurately follow the motion of the arm as objects are carried thereby. In the case of building structures, one might use a system in accordance with the present invention to determine or maintain alignment of various points on the structure relative to other points. In the case of territorial space, one might use the system to develop topological surveys of ground surface contours . It will also be apparent that more than two cameras could be used to inspect objects or fields of view not readily inspectable with one or two cameras. In such case an RCP transfer function calibration procedure similar to that described above would be followed. Additional Features As indicated above, this apparatus can also be used to determine the condition of the shock absorbers of the vehicle. This is done by firstly "jouncing" the vehicle. Jouncing a vehicle is a normal step in alignment procedures, or, for that matter, checking the shock absorbers, and entails applying a single vertical force to the vehicle by, eg. pushing down onto the hood of the vehicle and releasing the vehicle, to cause it to oscillate up and down. Secondly, as the vehicle oscillates up and down, the apparatus of the invention takes readings of the targets on each of the wheels. In so doing, the movement of the targets, which will define a dampened waveform, can be monitored to determine the extent of the dampening. If the dampening is not sufficient (i.e. the up and down movement or rocking of the vehicle does not stop soon enough) this indicates that the shock absorbers are faulty. This method is particularly advantageous in that a determination can be made as to the soundness of a specific shock absorber; a result which can be indicated to the operator of the alignment apparatus by means of the computer 32. It will be evident that in the determination of the condition of the shock absorbers of the vehicle, any suitable portion of the body of the motor vehicle can be selected to monitor the oscillation of the vehicle. So, for example, the apparatus can focus on the edge of the wheel housing or, alternatively, a small target placed on a convenient position on the body work of the motor vehicle . In addition, this apparatus can be used to calculate the ride height of the motor vehicle. This parameter is particularly important in the determination of the alignment of the wheels of vehicles such as pick-ups which, in operation, may carry a load. This load would have the effect of lowering the vehicle and it is, therefore, preferable to make allowance for this during alignment procedures. Traditionally, the ride height, or height of the chassis of the vehicle from the floor, is determined by physically measuring it with an instrument such as a tape measure. This measurement is then compared to standard tables which yield a compensation factor for the vehicle concerned. The described method and apparatus can, however, make this measurement directly by viewing an appropriate portion of the body and determining its height from the test bed on which the vehicle rests. Once this height has been determined it can be compared to standard look-up tables stored within the computer which can, in turn, produce the compensation factor. Advantages A general advantage of the above-described apparatus is that it is relatively simple to use as no delicate mechanical or electronic equipment need be attached to the wheels of the motor vehicle concerned. As the sensitive and delicate equipment is mounted within a housing which stands independent and distant from the motor vehicle being tested, no damage can be caused to it if the motor vehicle were, for example, to be driven off the wheel guides . Whereas prior art heads can be knocked out of calibration by simple jarring or dropping, it takes major damage to the wheel-mounted components to affect the calculated results . Another advantage is that the equipment requires very few operator commands and could readily be made hands free with simple auditory outputs and equally simple voice recognition means to receive and/or record operator responses and/or commands . The described system has the further advantage that alignment determinations can be done relatively quickly. This allows a higher turn around rate within the business conducting the alignment determinations. A still further advantage of this apparatus is that it can be placed, as is illustrated in FIG. 4, above and out of the way of the motor vehicle being tested. This has the distinct advantage that the chances of damaging the sensitive alignment determining apparatus is substantially reduced as the apparatus is out of the way of the motor vehicle. Another advantage of this configuration is that the measuring apparatus uses minimal floor space and has no equipment blocking access to the front of the motor vehicle. Furthermore, as the vehicle can be backed up and driven forward, this apparatus has the advantage that it is unnecessary to jack the vehicle up to make the required calculations for "run-out". In addition, this apparatus can be used to determine information other than the relative alignment of the wheels. For example, the alignment apparatus, if equipped with a suitable character recognition capability, could be used to read the license plate of the motor vehicle which could, in turn, yield information such as the make and model of the vehicle and its service history (if available) and, therefore, the required alignment parameters of such vehicle. This would save the operator from entering the motor vehicle's details into the apparatus. As more manufacturers are adding bar codes to the VIN number plates, similar information can also be obtained by optically viewing and processing the bar-coded plate. In addition, it would also be possible to optically identify the vehicle type by comparing certain features of the body or trim thereof to database information. Yet another advantage of the system is that no wires, cords or beams of light pass in front of the vehicle being tested. As most alignment correction is made by accessing the wheels of the car from the front, wires, cords or beams passing in front of the vehicle tend to get in the way of the technician. Often these wires, cords or beams are sensitive to being interfered with and so their absence makes alignment correction work much easier . Related to this advantage is the fact that there are no cords or wires passing between the targets on the wheels, nor are there any wires supplying power to the targets from a remote power source. This absence of wires or cords once again makes work on the vehicle easier. In addition, as the targets are not interlinked or interdependent, after initial capture of target images, it is possible to block off one of the targets from the camera's view without interfering with the orientation calculations for the other wheels. In the prior art devices described earlier, all the test heads are interdependent and cannot function if one of the heads is "blocked" out. It will be evident to those skilled in the art that the concept of this system can be applied in many different ways to determine the alignment of the wheels of a motor vehicle. So, for example, the apparatus could define a reference point for each wheel with the referent point being located at, say, the intersection of the axis of rotation of the wheel, with that wheel. These points can then be processed to define an approximately horizontal reference plane, relative to which the alignment of the wheels can be calculated. This method has the particular advantage that the rack on which the vehicle is being supported does not have to be levelled, a process which requires expensive apparatus and which is necessary to define a horizontal reference plane and which is used in prior art alignment devices. While the present invention has been particularly shown and described above with reference to a preferred embodiment, it will be understood by those skilled in the art that various alterations and modifications in form and in detail may be made therein. Accordingly, it is intended that the following claims be interpreted as covering all such alterations and modifications as may fall within the true spirit and scope of the invention. What is claimed is:

Claims: CLAIMS 1. Apparatus for use in calibrating an opto-electronic alignment system including at least first and second fixed and spaced apart optical inspection devices and an associated data processor adapted to optically inspect and determine the position and orientation relative to said inspection devices of targets affixed to objects such as vehicle wheels to be aligned, and from such determination to infer the position and orientation of the objects to which the targets are affixed, comprising : means forming an elongated beam; support means for supporting said beam at a predetermined elevation above a work surface; and first and second target means rigidly affixed to said beam at spaced apart locations, each said target means having predetermined geometric target features formed on a target face thereof, said target faces being oriented at predetermined fixed angles relative to the length of said beam such that when the length of said beam is disposed to extend generally normal to an imaginary line connecting said first and second inspection devices, said first and second target faces lie within the field of view of said first inspection device, and when the length of said beam is disposed to extend generally parallel to said line, said first target face lies within the field of view of said first inspection device and said second target face lies within the field of view of said second inspection device. 2. Apparatus as recited in claim 1 wherein said target faces are generally planar and are oriented at predetermined angles relative to the length of said beam. 3. Apparatus as recited in claim 2 wherein each said target face is oriented at an angle of substantially 45° relative to the length of said beam. 4. Apparatus as recited in claim 1 wherein said support means includes a pair of vertically oriented support legs having one end rigidly affixed to said beam and opposite ends affixed to base means adapted to support said beam and the affixed target means . 5. Apparatus as recited in claim 1 wherein said first and second target means are both disposed on one side of said beam. 6. Apparatus as recited in claim 1 wherein said beam is a two- part mechanism having one part telescopically receivable within the other so as to be telescopically collapsible for storage and telescopically extendible for calibration use. 7. A method of calibrating an opto-electronic alignment system including at least first and second spaced apart optical inspection devices and an associated data processor adapted to inspect and determine the position and orientation relative to said inspection devices of targets affixed to objects such as vehicle wheels to be aligned, and from such determination to infer the position and orientation of the objects to which the targets are affixed, comprising the steps of: providing first and second target means; providing a means for supporting said first and second target means in rigid disposition relative to each other and at a predetermined fixed distance from each other; disposing said supporting means relative to a work surface such that both said first and second target means lie within the field of view of said first inspection device; optically inspecting said fir'st and second target means to obtain first optical information useful to determine the position and orientation of each said target means relative to said first inspection device,- reorienting said supporting means such that said first target means lies within the field of view of said first inspection device and said second target means lies within the field of view of said second inspection device, and again optically inspecting said first and second target means to obtain second optical information useful to determine the present position and orientation of said first target means relative to said first inspection device and the present position and orientation of said second target means relative to said second inspection device; and using the first and second optical information to compute the precise position and orientation of said second inspection device relative to said first inspection means. 8. A method as recited in claim 7 wherein said first and second target means have target faces that are generally planar and have predetermined angular orientation relative to said supporting means. 9. A method as recited in claim 8 wherein each said target face is oriented at substantially 45° relative to an imaginary line connecting said first and second target means. 10. Apparatus for calibrating an opto-electronic alignment system including at least first and second spaced apart optical inspection devices and an associated data processor adapted to inspect and determine the position and orientation relative to said inspection devices of targets affixed to objects such as vehicle wheels to be aligned, and from such determination to infer the position and orientation of the objects to which the targets are affixed, comprising: first and second targets each having predetermined geometric attributes that can be optically detracted; a support for supporting said first and second targets in rigid disposition relative to each other and at a predetermined fixed distance from each other so that when said support is disposed relative to a work surface such that both said first and second targets lie within the field of view of said first inspection device, the targets can be optically inspected by the alignment system to obtain first optical information useful to determine the position and orientation of each said target relative to said first inspection device, and when said support is reoriented such that said first target lies within the field of view of said first inspection device and said second target lies within the field of view of said second inspection device, the targets can be optically inspected by the alignment system to obtain second optical information useful to determine the present position and orientation of said first target relative to said first inspection device and the present position and orientation of said second target relative to said second inspection device, and the first and second optical information can be used to compute the precise position and orientation of said second inspection device relative to said first inspection device . 11. Apparatus as recited in claim 10 wherein said first and second targets have target faces that are generally planar and have predetermined angular orientation relative to said support. 12. Apparatus as recited in claim 11 wherein each said target face is oriented at substantially 45 relative to an imaginary line connecting said first and second targets.

Inventors: GLICKMAN STEVE L, JACKSON DAVID A, GLICKMAN, STEVE, L., JACKSON, DAVID, A.
Applicants: SNAP ON TECH INC, SNAP-ON TECHNOLOGIES, INC.
Application year: 1997
Main classification: G01B11
IPC codes: G01B11, G01M17