Mounted scale bar

A scale-bar artifact can include a base, a structural component, at least two nests disposed on the structural component and configured to receive a spherically shaped object having a center, and at least three mounting assemblies, each mounting assembly including a first portion and a second portion. The second portion of each mounting assembly is coupled to the base. The first portion of each mounting assembly is coupled to the structural component. The first portion and second portion of each mounting assembly are in mutual contact. Each mounting assembly has a center of rotation. The centers of rotation of the three mounting assemblies share a common plane with the centers of the spherically shaped objects.

FIELD OF INVENTION

The present disclosure relates to scale-bar artifacts used in the calibration of dimensional measuring devices.

BACKGROUND

A variety of artifacts are available to measure dimensional measuring devices such as coordinate measuring machines (CMM), articulated arm CMMs, laser trackers, and 3D scanners. Many types of artifacts are available including scale bars, ball bars, gage blocks, step gages, and ball plates.

One type of scale bar includes a bar onto which are mounted two or more nests, each of which can hold an object having a spherical shape. One conventional method to accurately measure the distance between the centers of spheres held in the nests includes using a calibrated interferometer within a laser tracker. A laser tracker is a device that measures the distance and two angles to a retroreflector target, which is usually a spherically mounted retroreflector (SMR). An SMR includes a cube corner retroreflector embedded within a steel sphere with the vertex of the cube corner at the center of the sphere. By lining up the laser tracker with the positions of the SMRs on the scale bar, a very accurate measurement based on tracker interferometer readings can be obtained.

To measure the distance between the centers of the nests on the scale bar, the operator aligns the laser beam with the SMR when mounted on each of the two nests. The operator reads the distance to the SMR at the first nest and then moves the SMR to the second nest without allowing the laser beam to break, which would result in count loss and invalidate the measurement. The operator then reads the distance to the second nest. The difference between the measured distances is the distance between the two nest centers. To make this SMR movement possible, the scale bar is designed to permit the laser beam from the tracker to travel between nest centers without encountering any obstructions.

Most scale bars are designed to sit on kinematic mounts. Kinematic mounts enable the scale bar to be removed and then be reseated in the same position. Conventionally, there are many kinematic mounting methods. One method brings a sphere on a first mount in contact with a plane, a sphere on a second mount in contact with a V-block, and a sphere on a third mount in contact with three smaller spheres located 120 degrees apart. The scale bar can be mounted on a flat surface such as a table. The three larger spheres can be mounted on the bottom of the scale bar and the three complementary surfaces (plane, V-block, 3-sphere structure) can be placed on the table in contact with the larger spheres. A first alternative is to mount the larger spheres on the table and the three complementary surfaces on the bottom of the scale bar. A second alternative is to mount some of the larger spheres on the table and others on the bottom of the scale bar.

Regardless of selected method, the principle involved in kinematically mounting a rigid body is to fully constrain, but not over-constrain, the rigid body. A rigid body—in this case the scale bar—has six degrees of freedom that need to be eliminated to fully constrain without over-constraining. The mount with the three small spheres constrains the larger sphere so that translational motion is not possible at the position of the larger sphere. In other words, three of the six degrees of freedom of the scale bar have been removed. The mount with the V-block constrains the second sphere to move along a straight line, thereby removing two more degrees of freedom. The mount with the flat surface constrains the third sphere to move on a plane, thereby removing one degree of freedom. By using the three mounts together, six degrees of freedom are removed, and the scale bar is fully constrained, but not over-constrained.

Another kinematic mounting method uses three pairs of cylinder, each pair spaced 120 degrees away from the other pairs and each pair pointed toward a central point. Each of the three pairs of cylinders is brought in contact with a sphere. As each cylinder constrains the sphere to move along a straight line, each removes two degrees of freedom, so that the three mounts, when placed between the scale bar and table, fully constrain motion of the scale bar.

Usually the three mounts are placed opposite the side of the scale bar that holds the magnetic nests as described herein. For example, if the mounts are placed on the bottom of the scale bar, the nests are placed on the top of the scale bar. This positioning of the mounts on the side opposite the nests prevents the laser beam from being broken as the SMR is moved from one nest to the other.

However, this placement of the mounts on the side of the scale bar opposite the nests may increase errors in the use of the scale bar. One such error occurs when forces applied to the bar causes the bar to bend. Such forces may be applied by the operator when the operator touches the scale bar with a probe of the instrument under test (for example, the probe on an articulated arm coordinate measuring machine (CMM)). Alternatively, such forces may come from gravity as the scale bar is moved to different orientations, or they may come from thermal expansion of the base element to which the scale bar mounts are attached.

An additional type of error can occur for the case of a scale bar that includes two scale bar segments mounted on a supporting structure. In this case, forces on the structure can cause movement of one of the segments, thereby resulting in a change in the length between the centers of the nests.

There is a need today for an artifact that (1) resists changes in length as forces are applied to it and (2) is free of obstructions, thereby permitting measurement of the distances between nests centers with a laser tracker interferometer.

SUMMARY OF THE INVENTION

Exemplary embodiments include a scale-bar artifact, having a base, a structural component, at least two nests disposed on the structural component and configured to receive a spherically shaped object having a center, and at least three mounting assemblies, each mounting assembly including a first portion and a second portion. The second portion of each mounting assembly is coupled to the base. The first portion of each mounting assembly is coupled to the structural component. The first portion and second portion of each mounting assembly are in mutual contact. Each mounting assembly has a center of rotation. The centers of rotation of the three mounting assemblies share a common plane with the centers of the spherically shaped objects.

Additional exemplary embodiments include a scale-bar artifact having a base, a first structural component section and a second structural component section, at least two nests configured to receive a spherically shaped object having a center, wherein a first of the at least two nests is coupled to the first structural component section and a second of the at least two nests is coupled to the second structural component section, and a first set of at least three mounting assemblies and a second set of at least three mounting assemblies, each mounting assembly including a first portion and a second portion. The second portion of each mounting assembly is coupled to the base. The first portion of each mounting assembly within the first set of three mounting assemblies is coupled to the first structural component section. The first portion of each mounting assembly within the second set of three mounting assemblies is coupled to the second structural component section. The first portion and second portion of each mounting assembly are in mutual contact. Each mounting assembly has a center of rotation. The centers of rotation of the mounting assemblies from among the first set of at least three mounting assemblies and the second set of at least three mounting assemblies and the centers of the spherically shaped objects share a common plane.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Exemplary embodiments include mounted artifacts that resist changes in length as forces are applied to it, thereby greatly reducing Abbe errors, as will be described below. As described herein, alignment of centers of rotations of mounting assemblies with centers of spherically shaped objects reduce Abbe errors as forces are applied to the mounted artifact. The exemplary mounted artifacts described herein are also free of obstructions, thereby providing an unobstructed line of sight thereby permitting measurement of the distances between nests centers with a laser tracker interferometer.

FIG. 1Ashows a schematic view of mounted artifact100, which includes a structural component150, nests110A,110B disposed on the structural component150, mount assemblies120A,120B,120C onto which the structural component150is mounted, and a base160supporting the mount assemblies120A,120B,120C. Each of the mount assemblies120A,120B,120C includes a first portion,121A,121B,121C, and a second portion122A,122B,122C. The first portions121A,121B,121C of each respective mount assembly120A,120B,120C attaches to structural component150. The second portions122A,122B,122C of each respective mount assembly120A,120B,120C attaches to base160. The first portions121A,121B,121C and second portions122A,122B,122C of each assembly120A,120B,120C are in mutual contact.

In addition, each mount assembly120A,120B,120C has a center of rotation123A,123B,123C. The three centers of rotation are not collinear. As described herein, many common types of kinematic mounting structures contain a sphere about which the upper portion and lower portion rotate. For this situation, the center of the sphere is also the center of rotation of the mount assembly. For example, one type of mount assembly described herein contains three small spheres spaced from one another by 120 degrees, upon which a larger sphere is placed. As a particular case, the first portion of the mount assembly might attach to the large sphere and the second portion might attach to the three smaller spheres. With the first and second portions in mutual contact, it would be possible to rotate the first portion or second portion about the other. Regardless, the center of rotation in each case would be the center of the large sphere. As described herein, inFIG. 1Aeach mount assembly120A,120B,120C has a center of rotation123A,123B,123C. However, it is to be appreciated that a mount assembly need not contain a sphere to have a center of rotation. Any rotation about a point, regardless of the mechanism, is regarded as a center of rotation for a mount assembly.

Each of the nests110A,110B is configured to accept a spherically shaped object130A,130B having a center140A,140B. The spherically shaped object130A,130B might be, for example, a steel sphere or a spherically mounted retroreflector (SMR). The nests110A,110B each can include one or more magnets to apply force to hold a ferromagnetic spherically shaped object. The magnets can be integrally included with the nests110A,110B, or can be an additional component of the nests110A,110B.

FIG. 1Bshows a schematic view of the right portion of scale bar100after a force170has been applied. The effect of the force170is to cause a bending of structural component150. As a result of this bending, center140B of spherically shaped object130B moves to new center position140B′, and some of this movement is along the direction of the artifact. This type of error180, which in this case results in a change in distance between sphere centers140A,140B, is often referred to as Abbe error. The purpose of artifact100is to faithfully represent the calibrated reference distance between the centers of the two nests110A,110B. Consequently, the change in the distance, due to the error180, between the nests110A,110B as a result of the applied force170is highly undesirable.

FIG. 2Ashows a schematic view of mounted artifact200, which includes structural components250A,250B, nests210A,210B disposed on the structural components250A,250B, mount assemblies220A,220B,220C,220D,220E,220F, and a base260. As illustrated the structural component250A is mounted on mount assemblies220A,220B,220C and the structural component250B is mounted on mount assemblies220D,220E,220F. Each of the mount assemblies220A,220B,220C,220D,220E,220F includes a first portion,221A,221B,221C,221D,221E,221F, and a second portion222A,222B,222C,222D,222E,222F. The first portion221A,221B,221C,221D,221E,221F of each mount assembly220A,220B,220C,220D,220E,220F attaches to a respective structural component250A,250B. The second portion222A,222B,222C,222D,222E,222F of each mount assembly220A,220B,220C,220D,220E,220F attaches to the base260. The first portion221A,221B,221C,221D,221E,221F and second portion222A,222B,222C,222D,222E,222F of each assembly220A,220B,220C,220D,220E,220F, are in mutual contact. The mount assemblies220A,220B,220C,220D,220E,220F respectively include centers of rotation223A,223B,223C,223D,223E,223F. The centers of rotation223A,223B,223C are not collinear. The centers of rotation223D,223E,223F are not collinear.

Each of the nests210A,210B is configured to accept a spherically shaped object230A,230B, each having a center240A,240B. The spherically shaped object230A,230B can be, for example, a steel sphere or a SMR. The nests210A,210B each can include one or more magnets to apply a force to hold a ferromagnetic spherically shaped object in place. The magnets can be integrally included with the nests210A,210B, or can be an additional component of the nests210A,210B.

FIG. 2Bshows a schematic view of the right portion of mounted artifact200after a force270has been applied to structural component250B. Bending occurs as a result of this force, with some of the resulting movement of spherically shaped object230B to new center position240B′ along the direction of the artifact. This movement produces an error280caused by the change in the distance between sphere centers240A,240B and is another example of Abbe error. As described herein, a purpose of the artifact200is to faithfully represent the calibrated reference distance between the centers of the two nests210A,210B. Once again, the change in the distance, due to the error280, between the nests210A,210B as a result of the applied force270is undesirable.

FIG. 3is a perspective view of an exemplary mounted artifact300, which includes a structural component350, nests310A,310B disposed on the structural component350, mount assemblies320A,320B,320C onto which the structural component350is mounted, and base360. Each of the mount assemblies320A,320B,320C includes a first portion321A,321B,321C, and a second portion,322A,322B,322C. The first portion321A,321B,321C of each mount assembly320A,320B,320C attaches to the structural component350. The second portions322A,322B,322C of each mount assembly320A,320B,320C attaches to base360. The first portions321A,321B,321C and the second portions322A,322B,322C of each mount assembly320A,320B,320C are in mutual contact. The mount assemblies320A,320B,320C include centers of rotation323A,323B,323C.

Each of the nests310A,310B is configured to accept a spherically shaped object.FIG. 3shows the case in which the spherically shaped object is spherically mounted retroreflector (SMR)370. A laser beam380, which may come from a laser tracker, is directed toward SMR center375. To find the distance between the centers of spherically shaped objects mounted on nests310A,310B, the operator first aligns the laser beam380in a straight line that passes through the center of an SMR370when placed in each of the two nests310A,310B. The operator uses the laser tracker to measure the distance from the tracker to SMR center375with the SMR370sitting on nest310B. The operator next moves the laser beam380to nest310A while the laser beam380tracks the position of SMR370. After the SMR370is seated in nest310A, the tracker reads the distance again. The difference in interferometer distance readings at the near and far nests, that is, the nests310A,310B, is an accurate measure of the distance between the centers of two spherically shaped objects mounted on nests310A,310B.

In exemplary embodiments, the structural component350may have any cross section and be made of any material but preferably is a tube of carbon fiber composite material having high stiffness and low coefficient of thermal expansion (CTE). CTE is a measure of the relative change in length of the material per change in temperature. Some carbon fiber composite materials have a CTE less than 10−6/° C. In exemplary embodiments, the nests310A,310B can include a magnet that hold a steel SMR or sphere in place even as the artifact300is tipped. In exemplary embodiments, the nests310A,310B are preferably kinematic so that an SMR370or other desirable spherically shaped object can be removed and repeatedly returned to the same location with very little change in coordinates of the SMR370or sphere center375. A common type of kinematic mount for holding spherical surfaces into a nest is a three point mount. Often, three spheres are mounted in the nest to provide these three points of contact. The spheres can be separated from one another by 120 degrees.

For the embodiment shown inFIG. 3, the first portion321B is combined with the first portion321C in a single structure, and the second portion322B is combined with the second portion322C in a single structure. It is to be appreciated that in other exemplary embodiments, the mount assemblies320B and320C can be separately mounted to structural component350and base360, similar to how mount assembly320A is illustrated inFIG. 3. It is to be appreciated that the mount assemblies320A,320B,320C as illustrated inFIG. 3can be any mounting structure known in the art. In exemplary embodiments the mount assemblies320A,320B,320C are kinematic mounting structures. For example, in the embodiment ofFIG. 3, mount assembly320A can include a large sphere in contact with three small spheres, as known in the art. The mount assembly320B can also include a large sphere in contact with three small spheres, but can further include a ball slide324B. The ball slide324B moves smoothly with low friction along a straight line. Because the ball slide324B is constrained in only two degrees of freedom, while the three point spherical mount is constrained in three degrees of freedom, the mount assembly320B is constrained by two degrees of freedom overall. As such, the mount assembly320B can be equivalent to a V-block mount, which also has two degrees of freedom. The mount assembly320C can include a sphere in contact with a flat. With this combination of mount assemblies, the artifact (i.e., scale bar)300is fully constrained but not over-constrained. Note that since mount assemblies320B and320C are connected, ball slide324B can be placed in contact with the connected structure. As described herein, it is appreciated that any type of mounting structure is contemplated in other exemplary embodiments.

FIGS. 6A,6B schematically illustrate several advantages of the exemplary mounted artifact (i.e., scale bar)300ofFIG. 3. InFIGS. 6A,6B, an exemplary artifact600includes a structural component650, nests610A,610B disposed on the structural component650, mount assemblies620A,620B,620C onto which the structural component650is mounted, and base660. Each of the mount assemblies620A,620B,620C includes a first portion621A,621B,621C, and a second portion,622A,622B,622C. The first portion621A,621B,621C of each mount assembly620A,620B,620C attaches to the structural component650. The second portions622A,622B,622C of each mount assembly620A,620B,620C attaches to base660. The first portions621A,621B,621C and the second portions622A,622B,622C of each mount assembly620A,620B,620C are in mutual contact. The mount assemblies620A,620B,620C include centers of rotation623A,623B,623C. Each of the nests610A,610B is configured to accept a spherically shaped object630A,630B.

InFIGS. 1A,1B, a common plane that holds the centers of rotation123A,123B,123C lies between the center140B of spherically shaped objects130A,130B and base160. In contrast, inFIGS. 6A,6B, a common plane that holds the centers of rotation623A,623B,623C intersects, at least approximately, centers640A,640B, thereby advantageously aligning the centers of rotation623A,623B,623C with the centers640A,640B. When, inFIG. 6B, a force670is applied to the right side of structural component650, the sphere630B moves almost entirely in a vertical direction, causing the sphere center640B to move from position640B to position640B′. This type of change results in an error680in the distance between the centers640B,640A of spherically shaped objects630B,630A. In this case, the error680is mostly a cosine error, defined as the difference in length between a hypotenuse and a side of a triangle. Since the triangle in this case is very long and skinny, defined by center of rotation623C, and centers640B,640B′, the cosine error is negligible. By comparison, the sphere130B inFIG. 1Bmoves partly in the horizontal direction along the structural component150. This type of change results in an Abbe error170in the distance between the centers of spherically shaped objects140B and140A. In exemplary embodiments, by aligning the centers of rotation623A,623B,623C of the mount assemblies620A,620B,620C to coincide with the centers640A,640B of the spherically shaped objects630A,630B, the error in the length between nests610A,610B has been greatly reduced.

FIG. 6Billustrates a placement of the center of rotation623C at such a location that a line connecting the center of rotation623C to the center640B of the spherically shaped object630B is parallel to the structural component650. While this illustration and corresponding discussion is made with respect to reducing the Abbe error, the locations of the centers of rotation623A,623B are pertinent to the discussion. The locations of the centers of rotation623A,623B are not unimportant. Referring again toFIG. 3, which is an embodimentFIG. 6depicts schematically, if the mount assembly320A were replaced with a mount assembly having a pivot point below structural element350, certain differences would result. If force were applied to the right side of structural element350, SMR370(or any other spherically shaped object) would pivot on the plane that connects the three rotation centers about the line that connects the rotation centers323B,323C. Because of the tilt of the plane that connects the rotation centers, SMR370would not rotate straight down, but would instead rotate at an angle. Consequently, the movement of SMR370will have a component along the direction of structural element350, resulting in the unwanted Abbe error. As such, Abbe error is reduced when the centers of spherically shaped objects630A,630B placed in nests610A,610B lie, at least approximately, on a plane that connects the centers of rotation623A,623B,623C of the mount assemblies620A,620B,620C.

FIGS. 6A and 6Bare illustrated as schematic representations of the mounted artifact300ofFIG. 3. It is therefore appreciated that the principles described with respect toFIGS. 6A and 6Bapply to the embodiment ofFIG. 3since the centers of the spherically shaped objects (e.g., the center375of the SMR370) sitting in nests310A,310B coincide, at least approximately, with the plane that holds the centers of rotation323A,323B,323C of the mount assemblies320A,320B,320C.

The exemplary mounted scale bars described herein also do not block the path of the laser beam as an SMR (e.g., SMR375) is moved from nest320B to320A. As such, there are no obstructions in the path between the centers of spherically shaped objects sitting in nests310A,310B. As such, there is an unobstructed line of sight between the spherically shaped objects. In this way, scale bar300can be measured accurately and easily with a laser tracker.

In the exemplary embodiment ofFIG. 3, the centers of rotation of the three mount assemblies320A,320B,320C correspond to the centers of spheres. However, it is possible to construct a kinematic structure using rotating elements such as cylinders rather than spheres. For example, one well known type of kinematic mounting arrangement includes three sets of cylinders each mounted on a pair of spheres. Each set is mounted at 120 degrees with respect to the others. In this case, each cylinder has a line of rotation corresponding to its line of symmetry. However, starting from a resting position of the kinematic structure, infinitesimal movements in two of the cylinders away from their mounts will reveal the center of rotation of the third cylinder. In this way, a center of rotation may be identified for each of the three cylinders within the kinematic mounting arrangement. In other words, each cylinder on its own has a line of symmetry rather than a center (or point) of rotation. However, within the context of the kinematic mounting arrangement, each cylinder also has a center (or point) of rotation. This argument may be applied to any type of mounting structure. Within the context of a mounting arrangement, any kinematic mount assembly, regardless of method of construction, may be considered to have a center of rotation.

FIGS. 4 and 5are perspective and front views, respectively, of a mounted artifact400, a first structural component section450A which includes first nest410A, and a second structural component section450B which includes a second nest410B, a first set of mount assemblies420A,420B,420C supporting the first structural component section450A, a second set of mount assemblies420D,420E,420F supporting the second structural component section450B, and a base460coupled to the mount assemblies420A,420B,420C,420D,420E,420F. Each mount assembly420A,420B,420C,420D,420E,420F includes one of the first portions,421A,421B,421C,421D,421E,421F, and one of the second portions,422A,422B,422C,422D,422E,422F. The first portion421A,421B,421C of each mount assembly in the first set of mount assemblies420A,420B,420C attaches to the first structural component section450A. The first portion421D,421E,421F of each mount assembly in the second set of mount assemblies420D,420E,420F attaches to the second structural component section450B. The second portion422A,422B,422C,422D,422E,422F of each mount assembly420A,420B,420C,420D,420E,420F attaches to base460. The first portion421A,421B,421C,421D,421E,421F and second portion422A,422B,422C,422D,422E,422F of each mount assembly420A,420B,420C,420D,420E,420F are in mutual contact. Each of the mount assemblies420A,420B,420C,420D,420E,420F include centers of rotation423A,423B,423C,423D,423E,423F.

Each of the nests410A,410B is configured to accept a spherically shaped object.FIG. 4shows the case in which the spherically shaped object is spherically mounted retroreflector (SMR)470. A laser beam480, which may come from a laser tracker, is directed toward SMR center475. To find the distance between the centers of spherically shaped objects mounted on nests410A,410B, the operator first aligns the tracker so that its laser beam480travels on a straight line that passes through the centers of the SMR when mounted on the two nests410A,410B. The operator then uses the laser tracker to measure the distance from the tracker to SMR center475with the SMR sitting on nest410B. The operator next moves the laser beam480to nest410A while the laser beam480tracks the position of SMR470. After the SMR470is seated in nest410A, the tracker reads the distance again. The difference in interferometer distance readings at the near and far nests is an accurate measure of the distance between the centers of two spherically shaped objects mounted on nests410A,410B.

In exemplary embodiments, the first structural component section450A and the second structural component section450B may have any cross section and be made of any material but are preferably made of a tubular carbon fiber composite material having high stiffness and low coefficient of thermal expansion (CTE). CTE is a measure of the relative change in length of the material per change in temperature. Some carbon fiber composite materials have a CTE less than 10−6/° C. In exemplary embodiments, the nests410A,410B preferably contain a magnet that holds a steel SMR or sphere in place even as the scale bar is tipped. In exemplary embodiments, the nests are preferably kinematic so that an SMR or sphere can be removed and repeatedly returned to the same location with very little change in coordinates of the SMR470or sphere center475. A common type of kinematic mount for holding spherical surfaces into a nest is a three point mount. Often, three spheres are mounted in the nest to provide these three points of contact. The spheres can be separated from one another by 120 degrees.

For the embodiment shown inFIG. 4, the first portion421A is combined with the first portion421B in a single structure, and the second portion422A is combined with the second portion422B in a single structure. Similarly, the first portion421E is combined with the first portion421F in a single structure, and the second portion422E is combined with the second portion422F in a single structure. It is to be appreciated that in other exemplary embodiments, that the mount assemblies420A and420B could be separately mounted to the first structural component section450A and the base460. Similarly, the mount assemblies420E and420F could be separately mounted to the second structural component section450B and base460. It is to be appreciated that the mount assemblies420A,420B,420C,420D,420E,420F ofFIG. 4can be any mounting structure known in the art. In exemplary embodiments, the mount assemblies420C,420D are kinematic mounting structures. For example, in the embodiment ofFIG. 4, the mount assemblies420C,420D can each include a large truncated sphere in contact with three small spheres, as known in the art. The mount assembly420B can include a large sphere in contact with three small spheres and, in addition, a ball slide424A. The mount assembly420E can include a large sphere in contact with three small spheres and, in addition, a ball slide424B. The ball slides424A,424B move smoothly with low friction along a straight line. Because each ball slide424A,424B is constrained in only two degrees of freedom while the three point mount is constrained in three degrees of freedom, the mount assembly420E is constrained by two degrees of freedom overall. As such, the mount assembly420E is equivalent to a V-block mount, which also has two degrees of freedom. The mount assembly420C can include a sphere in contact with a flat. With this combination of mount assemblies420A,420B,420C,420D,420E,420F, the artifact (i.e., scale bar)400is fully constrained but not over-constrained. Note that since the mount assemblies420B,420C are combined, the ball slide424A can be placed in contact with the connected structure. Similarly, the ball slide424B can be placed in contact with the connected structure that includes420E and420F. As described herein, it is appreciated that any type of mounting structure is contemplated in other exemplary embodiments.

FIG. 4shows that second portions422C and422D are combined in one structure425that mounts to base460. The front view ofFIG. 5shows that structure425includes an extension element433and a support434. The top view of structure425is shown inFIG. 7. The structure425is preferably made of a low CTE metal such as Invar or Super Invar. The structure425attaches rigidly, via the support434, to the base460which can be made of any type of material and is not restricted to low CTE materials. Extensions427C,427D, as shown inFIG. 5, in the first portions421C,421D are disposed through slots426A and426B cut into structure425as shown inFIG. 7, thereby enabling truncated spheres428C,428D to seat on three small spheres, known in the art, disposed around each circular hole429C,429D cut into structure425. The centers of the truncated spheres428C,428D are center points that would have existed for an untruncated sphere. The centers of rotation for mount assemblies420C,420D are the same as the centers of the truncated spheres428C,428D.

The advantage of using truncated spheres in mount assemblies420C,420D is that the centers of rotation remain on the common plane that passes through the centers of spherically shaped objects placed in nests410A,410B without obstructing the path between the nests. As such, there is an unobstructed line of sight between the spherically shaped objects. By eliminating the obstruction, a laser tracker interferometer can accurately measure the distance between nests, as explained previously.

As shown inFIG. 4, ball slides424A,424B allow mounted artifact400to move along a line parallel to the line that connects the centers of spherically shaped objects placed in nests410A,410B. By allowing this free movement, thermal expansion in base460does not cause stresses to develop in mounted artifact400. Such stresses can cause bending of first and second structural elements450A,450B, resulting in changes in the distance between nests410A,410B.

In other exemplary embodiments, the mount assemblies at one end of the base460can be fixed and the other mount assemblies can be allowed to move. For example, combined mount assemblies420A,420B could be fixed to base460, structure425could be put on a ball slide, and combined mount assemblies420E,420F could also be put on a ball slide.

Errors that can occur in a segment containing two structural components have been described herein, as inFIG. 2. By keeping the centers of spherically shaped objects in nests at the same level as the plane that connects the centers of rotation of the mount assemblies, these errors are minimized, as described with respect toFIGS. 1 and 6. In addition, any displacement in the positions of the mount assemblies (resulting, for example, from a compliant base) results in only a cosine error so that the change in the distance between the nests is negligible.

As described herein, there are advantages in having the exemplary scale bars described herein in two segments as shown inFIGS. 4 and 5, rather than one longer segment. First, it is sometimes necessarily to measure one or more scale bar artifacts placed in a variety of positions and orientations. Because of extension element433, for example, it is possible to arrange multiple scale bars placed in different orientations that occupy the same central region in space. Second, it is sometimes necessary to construct very long scale bars. Beyond a certain length, it is difficult to obtain structural components (such as450A,450B) that are stiff enough to avoid problems with excessive bending of the bar. In such cases, it may be better to break the scale bar into two segments as shown inFIGS. 4 and 5.