The Geostep

Geostep History

A brief history of the Geostep Starts with attempts to develop a ball step standard. They failed to perform as a high quality artifact due to variations caused by elastic deformation of the line of balls when the attitude of the artifact was shifted from horizontal to vertical. Even with complex force correcting mechanisms, the artifacts just were not a good answer.

First Geostep
Historical Step in Development of the Geostep ™ (not for sale)
Long Ball Bar Geostep

The approach of mounting a row of balls along a straight edge suffers from large first order errors due to bending of the beam and heavy weight. At the same time that these artifacts were failing, N.I.S.T. began developing a new concept of the ball plate that was more compatible with the long pre-travel required by some American machines. These were very sophisticated devices with large windows around the balls. They were constructed from Super Invar ® with Zerodur ® balls.

A marriage of the elements of the previous designs was prototyped. This became the Geostep program. We distilled all to the good features and culled out all of the bad.

The choice of materials for the Geostep pitted low rates of thermal expansion, against long-term dimensional stability. The addition of about 38 percent nickel to iron or steel brings about a dramatic reduction in the rate of thermal expansion of the resulting alloy. The addition of nickel causes severe dimensional instability of the alloy. Although a high temperature anneal stabilizes the rate of thermal expansion of these materials, it does not do anything to dimensionally stabilize it.

On the other hand, cast iron with carefully controlled chemistry is very dimensionally stable; but has the normal 6.4 microinches per inch per degree Fahrenheit expansion. Until some new developments in metallurgy come along the choice of material is an easy one.

Ball Bar Theory

To fully appreciate the significance of the Geostep's design, we need an in depth understanding of Ball Bar (Dumbbell) theory. A sphere is the only geometry that has a single point that describes its exact position in three-dimensional space. If we mechanically attach two ultra precise spheres, of exactly the same diameter, to the opposite ends of a rather long rigid bar we have the most accurate long artifact that can be produced.

There are no flatness errors, there are no parallel errors, there are no cosine errors and the surface texture of the spheres is a fraction of any other gage geometry. Knowing only the sphericity and common diameters of the spheres a Ball Bar (Dumbbell) will accurately evaluate all of the machines geometry related errors. This is done by simply measuring it in a number of different positions within the machines measuring envelope. This is commonly referred to as the volumetric accuracy of the machine.



The Geostep carries the Ball Bar (Dumbbell) concept to new levels, by expanding its abilities so they include the accurate evaluation of all of the machine's potential error sources. The Geostep is a new concept in Coordinate Measuring Machine calibration. It uses several fundamental concepts of physics to achieve the ultimate in calibration accuracy.

The first advantage is the added length, better facilitates reversal technology. There is mathematical leverage afforded by extra length. Another principal is the unique point axis that so precisely defines the three-axis position of the sphere. The long line of oddly spaced spheres is better at unscrambling systematic errors.

The longer artifact eliminates errors caused by mathematically gluing together multiple fixations made of smaller artifacts. The longer artifact provides more steps to better check the scales. A longer artifact improves evaluation of elastic deflections because it exposes longer under supported portions of the ways. The longer length adds a repeatability test bed to the evaluation. The longer length adds a temperature drift test bed to the evaluation.

Multiple Spheres

It uses multiple spherical artifacts that are of almost perfect geometry and of exactly the same diameter. These spheres are made of high chrome, high carbon stainless steel that is hardened to 58 HRC and thermal cycled for long-term dimensional stability. The nominal diameter of these spherical artifacts is 19 mm or about (3/4 inch) but other sizes have been supplied. The spherical geometry by definition has but one point in three-dimensional space that defines its perfect position.

Vector Forces

Test Probe Against Mounted Ball

The variety of vector forces generated when measuring a sphere applies forces to the test probe and the machines frame from all directions so it truly evaluates the probes performance and bending moments of the frame in all circumstances. Probing a nearly perfect sphere tests the entire machines ability to measure and document its perfect position in the x - y and z coordinates.

By probing spheres that are rigidly mounted at well-known distances apart, the three scales are added to the calibration equation. By carrying this concept further and adding a whole series of balls on the same centerline, additional basic principles of physics apply. As the artifact gets longer, more of the C. M. M.'s error sources begin to show up. Systematic scale errors are made manifest because the line of balls are intentionally spaced varying distances apart. All of the fundamentals of ball bar technology apply to the Geostep.

The simple act of measuring the Geostep in a series of well-chosen positions will check all 21 of the possible geometry and scale errors of a Coordinate Measuring Machine. This is based on the fact that the inter ball dimensions of the Geostep are fixed and calibrated so that any variations from position to position are errors in the measuring machine. The longer geometry lends itself to reversal technology, which enhances the accuracy and could even detect original calibration errors, if they existed.

Monday Morning

First the Geostep is placed in a compound attitude, such as an inclined position across a body diagonal and then it is reversed 180 degrees. This simple test accurately evaluates a whole series of potential scale errors and shows up squareness and straightness errors, if they exist. When the same test is performed on the other body diagonal you have a very quick, interim or Monday morning evaluation of the entire machine.


This is an archival test artifact that requires only an occasional traceable calibration.

Neutral Bending Plane

The line of balls is placed on the neutral bending plane of the extremely rigid beam construction. This reduces small bending moments to second order cosine errors that are of insignificant magnitude. During the eight years of its development many features of this device were perfected.

Three-inch Window

The large three-inch diameter window around the ball provides more than enough pre-travel for accurate, repeatable measurements of each ball's position, by any make of C.M.M.

Ball Mounting

Unlike the ball mounting techniques used on other artifacts the balls of the Geostep retain their almost perfect sphericity and original size. To prevent elastic deflection of the balls true position, by the probing force, during measurements, a deep hole is drilled into the ball and into the post that supports the ball. A solid Tungsten Carbide shaft is used to mount the ball to the body of the Geostep. This gives the ball the same rigidity as the body of the beam itself. Remember that tungsten carbide has a stiffness or Young's modulus of 98,000,000 psi, which is more than four times that of cast iron.

Straight Edge

Side View of Geostep

Although virtual CMM evaluation shows that this device does evaluate straightness of the machine axii, the edges of one side rail can be flat lapped to provide a straight reference datum. This arrangement lends itself to reversal verification of the artifacts straightness.


The body of the Geostep is produced to near net shape by the "stable cast" process, from a special alloy iron to assure long-term dimensional stability.

Hard Metal Coat

The entire body of the artifact is sealed with a hard metal coat that is very corrosive resistant.

6.4 Micro Inches

The thermal coefficient of expansion for the materials that are used to construct the Geostep is 6.4 microinches per inch per degree Fahrenheit, at temperatures near the 68-degree standard. This expansion rate is the same as most steel parts.

Two-Inch Mounting Hole

The device is rigidly supported by a precision honed two-inch diameter hole (50 mm) in the very center of the part. This well-balanced arrangement divides the bending moments in half so any deflections caused by the probing forces are minute. The position of the Geostep is rigidly fixed by clamping two annular flat parallel rings surrounding the two-inch diameter hole. This isolates the clamping force, to prevent distortion of the Geostep

Mounting Hardware

The standard support mechanism allows a full 360-degree of rotation and 120 degrees of articulation. This basically depicts a large spherical shell from each location of the rigid support mechanism on the C.M.M. table.

N. I. S. T. Stand

There is also a N.I.S.T. developed version of the support stand that is somewhat more sophisticated. It will index the Geostep to preselected positions in both planes and can be relocated in the same place on the machine table time after time. Learning procedures can be used so that re-measurements of the artifact can be made automatically.

Trivet, 14 " Indexing

The 14" Indexing Trivet (Part No.: INDTRI14)

This lightweight device, a trivet, is designed to provide precise, repeatable, indexing of the "Geostep" or other C.M.M. calibration devices. Most of the hardware used in this setup are part of our off the shelf line of components. By using these standard components, this rather sophisticated device can be produced for a very modest cost. Our standard "14-inch Trivet" is modified to become the upper rotating half of this Kinematically positioned indexing system. The indexing lever is simply rotated 90°, to raise the "Trivet". The "Trivet" is then indexed to the next position. When the lever is returned to its original position, it lowers the "Trivet" onto the Kinematic spheres of its new orientation and the next measurements can be made. This system provides six precise, repeatable positions. They start at 0° then to 60° then 120° then 180° then 240° then 300° and then back to zero, or 360°.

The calibration device or devices used for the C.M.M. evaluation are held in position at the desired height by using the ideal height of "Anchor" (see the "Anchor" technical data sheet in the C.M.M. catalog, for the standard heights available). To hold the "Geostep" in perfect position, the "Geoclamp" is attached to the top of the "Anchor" and the "Geostep" is installed between the two parallel clamping plates. In order to keep the weight of the "Geoclamp" to a minimum, it is constructed almost entirely of aluminum. The circular base of this system forms a truly Kinematic indexing device. It is constructed of a lightweight, aircraft quality, aluminum casting. Twenty four ( 24 ) very precisely ground and lapped spherical components are rigidly fixed to give precise fifteen degree ( 15° ) increments in the top surface of the base casting. The upper half of the Kinematic indexing system consists of three pair of our standard split Kinematic vee blocks (see Split Vee Blocks technical data sheet under Kinematic products) that are rigidly mounted in three precision-machined trenches in the Trivet.

When working with automatic self-propelled C.M.M.'s, totally automatic measuring of the calibration artifacts can be achieved using the indexing Trivet. With the twenty four spheres on the base ring, every twelfth sphere is 180 degrees apart. By measuring and aligning any two of the Kinematic spheres that are at 180 degrees to each other, with the "X" axis of the C.M.M., the position of the artifact will be aligned well enough for automatic re-measurement. The material chosen for the vees and the spheres of the indexing Trivet is a very high chrome, high carbon, Martensitic stainless steel. This ultra fine-grained material is through hardened to 58 HRC (Hardness on the Rockwell "C" scale) minimum. This indexing Trivet can also be supplied in custom configurations with orthogonal or other angular configurations.

Low Horizontal

Trivet Trivet, Vee Block Trivet Trivet, Rosebud

For a thorough machine evaluation, very low horizontal measurements must be made. For this application, a rugged Kinematically coupled base plate is available. The Geostep is the culmination of eight years of research. It is a simple, single element, calibration device that will give a total calibration of all 21 rigid body errors as well as the myriad of the flexible or elastic errors. The only limitation to the perfection of the Coordinate Measuring Machine evaluation and calibration by the Geostep is the accuracy of the original calibration of the artifact. This device has been commercially available since 2000, and is well on its way of becoming a world standard for C.M.M. calibration.

N. I. S. T. Calibration

N.I.S.T. is providing a calibration service for this artifact that is accurate to less than one part per million.

Three Versions

The full size artifact is 34 inches (860 mm) long with 10 ultra precise spheres placed on a common centerline in an uneven pattern that avoids synchronistic errors. Two shorter versions of the Geostep are available for calibration of smaller machines. A 26 5/8-inch (676 mm) version with 8 spheres and a 16 5/8-inch (424 mm) version with 6 spheres. All three versions are of identical construction. They are one and one half inch (36.1 mm) thick and four inches (10.16 mm) wide.

The large thermal mass of the Geostep makes it insensitive to momentary contact by the calibration technician. A big factor in the function of the Geostep is the things that the Geostep doesn't depend on. There is no laser with its dependency on due point, or barometric pressure; and it requires no power, so it does not generate any heat.

Twenty ( 20 ) Pounds

The device weighs less than 20 pounds, so that a single technician can perform the entire machine calibration. The device is extremely rugged, so it can be safely transported in a simple container. This Geostep costs only a small fraction of any other complete calibration system. It has all of their advantages and none of their limitations.

Thermal Drift

In addition to the routine calibration procedures, this single device is long enough to check thermal drift effect and to perform repeatability tests.


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