# Coordinate measuring machines

CMM coordinate measurements, machine and sensor variants, alignment, performance specifications and task-specific uncertainty.

Reviewed: 2026-10-29

Tags: inspection, metrology, dimensional-measurement

## Identity and measurement principle

A CMM locates sampled points in a coordinate system. The probe, frame, scales and motion establish the measurement chain.

**Illustrative calculation:** an assumed 500 mm length, an assumed coefficient of 10 × 10^-6 /°C and a 2 °C rise give 0.010 mm, or 10 µm, of expansion. This is calculated expansion under a simplified model, not a CMM uncertainty budget or an assigned material property. Temperature gradients and uncertain coefficients are outside this calculation. [Thermal relationship adapted from Mitutoyo, slide 14][S15]

The measured coordinates are inputs to geometric evaluation. Software associates features such as planes, circles and cylinders with sampled surfaces, then calculates relationships such as distances and angles. A reported hole center is therefore a calculated feature location rather than a directly touched point. [Hexagon, measured and constructed features][S2]

The measurand is the quantity intended to be measured. [JCGM VIM 2.3][S17] A bore diameter at one section, its axis location relative to specified datums, and its form deviation are different quantities. **Synthesis:** a report headed "CMM inspection" does not establish which of these quantities was evaluated or whether the evaluation matches the drawing requirement.

## Cartesian coordinates and alignment

A Cartesian CMM represents points by X, Y and Z coordinates along mutually perpendicular axes. The machine coordinate system describes the instrument's axes. A part coordinate system relates coordinates to the workpiece's datum features. Alignment establishes the mathematical relationship between those systems, including origin translation and axis rotation. The workpiece need not be physically parallel to the machine axes for software to express measurements in part coordinates. [Hexagon, coordinate systems and alignment][S2]

Probe qualification is a separate operation. For a spherical contacting tip, measurement of a reference sphere establishes the tip's effective size and location. Probe compensation then relates the tip-center coordinates to the contact surface. Alignment and tip qualification address different relationships. [Hexagon, qualifying probe tips][S2]

**Synthesis:** an arbitrary best fit to a CAD model and an alignment constrained by specified datum features need not produce the same reported deviation. An alignment's usefulness depends on the quantity and datum requirements it represents; small fit residuals alone do not establish conformity.

Coordinates, dimensions and their associated length uncertainties require explicit units, commonly millimetres, micrometres or inches. One micrometre is 0.001 mm. A dimension's numerical value changes with its unit, while the physical length does not. Angles require their own units. An uncertainty stated in micrometres is not directly comparable with an angular tolerance.

## Machine arrangements

Machine arrangement describes the supporting structure and motion. Sensor type and manual or computer-controlled operation are separate distinctions. NIST describes bridge and cantilever frames, translating or rotating tables, and moving bridges. ZEISS's portfolio separately identifies bridge, gantry and horizontal-arm machines. [NIST Technical Note 1400, section 2.3.2.3][S1] [ZEISS CMM portfolio][S3]

| Arrangement | Distinction and bounded application |
| --- | --- |
| Bridge | A bridge structure supports the measuring carriage. A moving bridge is one implementation. The category includes different measuring volumes and performance classes; the name supplies no universal accuracy. [S1] [S3] |
| Gantry | ZEISS groups its large-volume measuring systems here. This is an arrangement for accommodating large workpieces, not a separate sensing principle or a guarantee that every large part can be measured. [S3] |
| Horizontal arm | A projecting arm provides access to workpieces. ZEISS identifies this arrangement with accessible measurement of sheet-metal and other large components. A horizontal arm is distinct from a portable articulated arm. [S3] |
| Articulated arm | A portable jointed mechanism uses rotary encoders in its joints to determine probe position. Its coordinates result from joint-angle measurements rather than three perpendicular linear slides. Hexagon's historical portable-arm guide describes this principle. [S4] |

**Synthesis:** matching a part to a machine requires the usable measurement volume, access paths, probe configuration, fixture clearance and permitted loading. A part fitting inside the nominal travel envelope does not prove that every required surface is reachable. The family names above do not supply model-specific load, clearance or uncertainty limits.

## Contacting and optical sensors

A touch-trigger probe acquires discrete points when contact produces a trigger. A contact scanning probe acquires surface data while the stylus moves along the surface. Renishaw explains that scanning combines continuous stylus-deflection output with machine position. Some scanning probes also acquire discrete points. Scanning therefore describes an acquisition mode, not necessarily an optical process. [Renishaw touch-trigger probes][S5] [Renishaw scanning probes][S6]

Optical sensing uses light without contacting the measured surface. Laser scanners and imaging systems are examples; they do not all share the same measurement geometry or limitations. ZEISS describes multisensor systems combining optical and tactile measurement, as well as optical access limitations at deep bores, pockets and undercuts. Reflective or translucent surfaces can impede optical acquisition, and some applications require surface treatment. [ZEISS tactile and optical comparison][S7]

**Synthesis:** noncontact acquisition can avoid contact loading on a sensitive surface, but it does not remove optical visibility and surface-response limits. A surface treatment introduces a changed measurement condition. Its suitability for the required uncertainty is not established by the untreated-part specification.

Contact scanning can provide more form information than a sparse set of triggered points, but point density alone does not establish correctness. Renishaw identifies sensor control and filtering as parts of scanning evaluation. A tactile probe with an internal optical transducer remains a contacting measurement system. [Renishaw scanning probes][S6]

## Resolution, repeatability and uncertainty

These terms describe different properties.

| Term | Meaning and implication |
| --- | --- |
| Resolution | The smallest measured-quantity change that causes a perceptible change in indication. It can depend on noise and the measured value. Display digits do not establish measurement uncertainty. [JCGM VIM 4.14][S8] |
| Repeatability | Measurement precision under specified repeatability conditions. Those conditions include the same procedure, operators, system, conditions and location over a short period. Repeated readings characterize that setting, not every possible setup. [JCGM VIM 2.20](https://jcgm.bipm.org/vim/en/2.20.html) and [2.21][S9] |
| Measurement uncertainty | A nonnegative parameter describing dispersion of values attributed to the measurand using the available information. It includes contributions associated with systematic effects as well as repeat observations. [JCGM VIM 2.26][S10] |
| Maximum permissible error, or MPE | An extreme error value permitted by a specification or regulation for a measurement or measuring system. [JCGM VIM 4.26][S16] **Synthesis:** an MPE specification is distinct from an observed feature error and from task-specific uncertainty. |

ISO 10360-2:2009 covers acceptance and reverification of Cartesian CMMs measuring linear dimensions with contacting probes in discrete-point mode. Its public scope does not explicitly cover optical or non-Cartesian CMMs. ISO 10360-12:2016 separately addresses articulated-arm CMMs with tactile probes and optional optical distance sensors. Neither scope can be applied to every sensor merely because its host instrument is called a CMM. [ISO part 2 scope][S11] and [part 12 scope][S13]

NIST's 2003 research explains that standardized performance tests on simple artifacts support comparisons but only weakly indicate performance on complex workpiece tasks. It identifies fixturing, workpiece form and point distribution, temperature, contamination, styli and machine dynamics as influences. A simulation also depends on the factors it models and the correctness of its inputs. [NIST task-specific uncertainty paper, sections 1 and 2][S12]

**Synthesis:** a nominal "accuracy" number, fine resolution or tight repeatability cannot by itself establish dimensional conformance. That conclusion needs the measured characteristic, its specification, an applicable uncertainty evaluation and a decision rule. ILAC G8 explains decision rules, uncertainty treatment and the associated risks of false acceptance and rejection. This reference adopts no universal tolerance-to-accuracy ratio or guard band. [ILAC G8:09/2019, sections 1 to 5][S14]

## Environment and workpiece limits

Temperature affects both the machine and workpiece. Mitutoyo's 2018 presentation explains thermal expansion and correct use of temperature compensation. Its CRYSTA-Apex S example associates the stated 16 to 26 °C range with proper compensation; this is a historical product example, not a universal CMM operating range. [Mitutoyo, slides 14 and 22 to 25][S15]

For a uniform temperature and approximately constant coefficient of thermal expansion, the first-order length change relative to 20 °C is:

```text
delta L = L20 × alpha × (T - 20 °C)
```

Here `L20` is the length at 20 °C, `alpha` is the coefficient in inverse degrees Celsius, and `T` is workpiece temperature.

Fixturing, dirt or coolant, workpiece form and thermal conditions can affect results even when the machine passes its performance tests. **Synthesis:** a flexible part measured in a clamped condition can represent a different measurand from the same part in its free state. Probe access, surface condition and the specified restraint condition bound the meaning of the result. [NIST task-specific uncertainty paper, section 2][S12]

## Source provenance and coverage limits

Reviewed 29 October 2026 PDT. This reference covers principles and interpretation, not an inspection program, calibration interval or model selection. It establishes no customer's installed sensors, software options, environmental control or demonstrated capability.

The ISO references below are public catalog scopes and edition information, not the licensed test procedures. The 2003 NIST paper and 2014 Hexagon guide are historical technical sources. Their product descriptions and then-current standards are not presented as current procurement specifications. The undated ZEISS comparison makes broad accuracy and speed claims; those claims are not adopted as universal numerical boundaries here. Public manufacturer text was inspected without login. Some direct downloads returned HTTP 403, while the cited text remained available through the web research service.

| Source | Version and evidence used |
| --- | --- |
| [S1][S1] | NIST Technical Note 1400, *Issues, Concepts, and Standard Techniques in Assessing Accuracy of Coordinate Measuring Machines*, 1993. Section 2.3.2.3 supplies the functional components and structural distinctions. |
| [S2][S2] | Hexagon, *Intro to coordinate metrology*, undated. Coordinate systems, alignment, measured and constructed features, and tip qualification. Its simplified datum terminology is not a replacement for a drawing standard. |
| [S3][S3] | ZEISS, *Coordinate Measuring Machines*, undated portfolio. Machine families and intended applications, not common numerical capability limits. |
| [S4][S4] | Hexagon Metrology, *Portable Arm CMM Buyer's Guide*, Eric Hollenbeck, copyright 2014, page 4. Rotary-encoder principle only. Historical accessory tables are not adopted. |
| [S5][S5], [S6][S6] | Renishaw, *Touch-trigger probes* and *Scanning probes*, undated public explanations. Acquisition principles, not product-independent speed or accuracy guarantees. |
| [S7][S7] | ZEISS, *Tactile and Optical Measurement Technology*, undated. Sensor principles, access and surface limitations. |
| [S8][S8], [S9][S9], [S10][S10], [S16][S16], [S17][S17] | JCGM, online VIM third-edition definitions. Resolution 4.14, repeatability conditions 2.20, repeatability 2.21, uncertainty 2.26, MPE 4.26 and measurand 2.3. |
| [S11][S11], [S13][S13] | ISO 10360-2:2009, edition 3, confirmed 2026, and ISO 10360-12:2016, edition 1, confirmed 2021. Public abstracts only. |
| [S12][S12] | Phillips and coauthors, *The Validation of CMM Task Specific Measurement Uncertainty Software*, ASPE summer topical meeting, 25 to 26 June 2003, six pages. Task dependence and limits of simulation evidence. |
| [S14][S14] | ILAC G8:09/2019, *Guidelines on Decision Rules and Statements of Conformity*. Decision-rule concepts; no example rule is assigned to a customer. |
| [S15][S15] | Jim Salsbury, Mitutoyo America, *Temperature and Dimensional Measurements*, copyright 2018, 26 slides on 13 PDF pages. Thermal model and bounded compensation example. |

## Related references

- [Dimensions, tolerances and specifications](../../parts-and-design/specifications/index.md).
- [Inspection and quality documents](../../sourcing/documents/index.md).
- [Articulated-arm measuring machines](articulated-arm-measuring-machines.md).
- [Measurement uncertainty](../metrology/measurement-uncertainty.md).

[S1]: https://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1400.pdf
[S2]: https://hexagon.com/resources/resource-library/intro-coordinate-metrology
[S3]: https://www.zeiss.com/metrology/en/systems/cmms.html
[S4]: https://hexagon.com/-/media/project/one-web/master-site/mi/pdf/hexagon_metrology_portable_arm_cmm_buyers_guide.ashx?hash=E973184D8EBD51C37937EB98D3D086EC&sc_lang=de
[S5]: https://www.renishaw.com/en/touch-trigger-probes--6652
[S6]: https://www.renishaw.com/en/scanning-probes--6656
[S7]: https://www.zeiss.com/metrology/us/explore/topics/tactile-and-optical-measurement-technology.html
[S8]: https://jcgm.bipm.org/vim/en/4.14.html
[S9]: https://jcgm.bipm.org/vim/en/2.21.html
[S10]: https://jcgm.bipm.org/vim/en/2.26.html
[S11]: https://www.iso.org/standard/40954.html
[S12]: https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=822036
[S13]: https://www.iso.org/standard/63931.html
[S14]: https://ilac.org/?ddownload=122722
[S15]: https://www.mitutoyo.com.mx/webfoo/wp-content/uploads/Temperature_effects_handout.pdf
[S16]: https://jcgm.bipm.org/vim/en/4.26.html
[S17]: https://jcgm.bipm.org/vim/en/2.3.html