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This news article was originally written in Spanish. It has been automatically translated for your convenience. Reasonable efforts have been made to provide an accurate translation, however, no automated translation is perfect nor is it intended to replace a human translator. The original article in Spanish can be viewed at Máquinas de medir tridimensionales

Three-dimensional measuring machines

Maurizio Ercole - Director of r & d of Brown & Sharpe - dea15/02/2003
Coordinate measuring machines (MMC), as well as well-known companies pioneer of electronics in California (e.g. Hewlett Packard), were born in a garage, this time in Turin. Italy had become the axis Turin / Ivrea in the exporting third country of machine tools, Japan and Germany and leaving behind the United States, France, England, and many others, which was without doubt a breeding ground for the development of precision metrology. Suddenly, Dea became export 75-80% of its production


The position of a point in space is defined, in Cartesian coordinates by the relative values of the three axes X and y Z with respect to a reference system. Using series of dots, it is possible to construct geometric element that passes through them or closer to the maximum.

A three-dimensional measuring machine is capable of defining uniquely and with extreme precision the position of these points in three-dimensional space, and calculate the significant parameters of the geometric figures on which these points have been taken.

A coordinate measurement machine is an instrument of measure absolute precision capable of determining the dimension, shape, position, "attitude" (perpendicular, planarity, etc.) of an object by measuring the position of various points of its own surface.


Coordinate-measuring machines (MMC) are used for the following applications:

  • Control of the correspondence between a physical object with its theoretical specs (expressed in a drawing or a mathematical model) in terms of size, shape, position and attitude.
  • Definition of dimensional geometric characteristics (size, shape, position and attitude) of an object, e.g. a cast whose theoretical characteristics are unknown.


Precision mechanics

A unit's operation manual, or numerical control that is capable of positioning the element sensor at any point in the volume of useful work

Numerical control and computer science

Multiaxiales numerical controls (from 3 to 10 axes), together with a distributed architecture for the control of the dynamics of machines and the necessary development of measurement points

Applications programs

Programs focused on solutions for specific applications, such as gears, bladed turbine, etc.


Devices that scan the coordinates of the points that lie on the surface of the workpiece to be measured, with or without contact with the same.


Usually called "machine" to the mechanical structure, while in reality, the machine is the combination of the four elements listed above. The parameters that characterize the mechanical structure of a MMC are as follows:


Length of the generally Cartesian axes that determine the useful working volume (VUT) mechanical structure. The dimensions vary from 1 dm3 to several tens of3m. It is easy to appreciate how the dimensions of the mechanical structure can strongly influence the other characteristics of the MMC: for example, the behavior variations of ambient temperature and, in particular, those in the space thermal gradients.


The architecture of mechanical structures of measuring machines is already consolidated. Architecture is relative to the dimensions of the mechanical structure and, in general, it is possible to assert that a certain type of architecture tends to find the best compromise between: to) dynamics of the system; (b) its accuracy; (c) ease of access to the piece to be measured.

Currently available architectures are: to) bridge; (b) Gantry; (c) horizontal arm. (See figures 1 and 3).

Fig1.jpg (20395 bytes) Fig2.jpg (8061 bytes) Fig3.jpg (8799 bytes)
Fig. 1 Bridge architecture. The useful workload ranges from 0.3 to 8 m3 Fig. 2 Architecture Gantry. The useful workload ranges between 6 and 100 m3 Fig. 3 Horizontal arm architecture. The useful workload ranges from 0.3 to 100 m3

Recently appeared another configuration for small applications in manual operation: the architecture Scara, already known in the world of robotics.

Useful volumes of work of each of these settings are shown in the table.

Architecture Minimum VUT (3 m) Maximum VUT (3 m)
Bridge 0.3 8
Gantry 6 100
Horizontal arm 0.3 100

Table I.-margin of useful volume of labour according to architecture

Horizontal arm architecture is used in relatively small structures as the measurement of prismatic precision and large bodywork parts.


Historically, the MMC have been installed in venues of metrology thermally controlled. But the impressive development of process automation has generated the need for measurements in the same location in which parts are produced. Precisely there where the environmental conditions and in particular the thermal gradients, spatial and temporal can adversely affect the reliability of the results.

Fig4.gif (20634 bytes) The graph in Figure 4 illustrates the anticipation of the market data according to which the MMC in laboratory tend to decrease, while growing teams in workshop environment.

Fig. 4. Historical evolution and forecasts sales of MMC as their destination is the laboratory (in red) or workshop (in blue). The black line is the sum of the two curves.

To get structures much more inert to the environmental conditions of workshop have developed various solutions:

  • Upgraded protection cabinets.

This solution entails problems of cost and space and does not solve the temperature difference between the piece and the structure.

  • Inert thermal tensile materials (fibre of carbon, ceramic, etc.)

This is also an expensive solution, and brings strong problems of availability of semi-finished products.

  • Rapid updating of the coefficients of its molecular structure materials with regard to thermal variations, analyzed through a programme of compensation.

This last solution turns out to be the most appropriate.

Through the use of special aluminium alloys, it is possible to quickly obtain data from the thermal behaviour of the structure, thus eliminating a large portion of the phenomenon of (significant in large machines due to the spatial gradients) deformation.

Suppose for example that a welded steel bar whose top is located at an altitude of 1,620 mm from the ground and the lower part is 1,370 mm (Figure 5). All this in a thermal environment of the following characteristics:

  • Local temperature to 1,620 mm: 23.16or
  • Local temperature to 1,370 mm: 2300or

The difference in temperature at the ends is therefore of 0.16or. Consider the linear expansion of the steel we have that the expansion in the upper part is:

12 x 0.16 x 1285 = 2.46 µm

What will lead to deformation that shows the same figure. On the other hand, the rate of thermal diffusion of both materials is:

Steel: STDfaith = 1310-6
Aluminum: STDto the = 95.10-6

These ratios show how aluminum alloys react more quickly and evenly to the thermal stresses than other materials. An idea of the relationship is provided by the following expression:

TCCratio = CBTto the / CBTfaith = 178/25 = 7.12
STDrate = STDto the / STDfaith = 95.10-6 / 1310-6 = 7.30

Fig5.jpg (10382 bytes)
Fig. 5 Deformation of the mechanical structure for space thermal gradient

One could speak more of the thermal behavior of materials, but we shall confine ourselves to take note of what has been demonstrated in terms of the speed of adaptation of the aluminium front temperature variations. This is of great importance, for allowing an optimal implementation of the so-called techniques of structural thermal compensation (CTE).

The latest CTE technical (on an industrial scale) is illustrated in the following diagrams. They are mainly based on linear compensation, which allows a more rational approach to deformation.

Fig6b.gif (44562 bytes)
Fig. 6. The structure mechanics, both linear and structural thermal compensation

The compensation system is based, essentially, in the components illustrated in Figure 6:

  • 4 thermal sensors for the temperature of the transducer and the piece to measure
  • 12 thermal sensors to meet variations in mechanical structure
  • A compensation program based on algorithms in the calculation of the transducers and the piece expansion due to temperature variations and structural deformations caused by thermal gradients. From an experimental point of view, see Figure 7.
Fig7.gif (88298 bytes)

Fig. 7 Test of thermal compensation in a M/c bridge (axis and)


To refer to coordinate-measuring machines, the first idea that appears is precisely accurate. But before it is necessary to specify the unit that will be expressed. In fact, the term precision is inaccurate: values declare manufacturers indicate precisely the opposite. We literally translating the German term (Meunsichereit) and establish the significant parameter to judge the accuracy of a MMC is the uncertainty of measurement.

The uncertainty of measurement

The uncertainty of measurement (IM) is the maximum error who can commit a MMC during the measurement of a known length and in the manner established by an international standard. The widely recognized standards currently for the certification of IM a MMC are:

  • The VDI, for Europe and its areas of influence
  • The B89 to the United States and their areas of influence
  • The JIS for some areas of Asia

Recently approved a standard ISO that, for the time being, no is being very used due mainly long requiring trials established.

The IM is the most significant parameter, since it contains all the possible components of error:

  • Geometric errors of mechanical structure
  • Sensor errors
  • Etc.

To find us on European soil, we will use the VDI standard. The IM can be expressed in three different levels:

  • U1, when referring to one only of the axes of the machine (X, and or Z)
  • U2, when referring to two of the axes of the machine (XY, YZ, or ZX)
  • U3, when referring to the three axes.

Generally speaking, the IM is expressed in terms of +/-2, obtained according to the following formula:

to + b L/1,000 (in µm), where:

  • (µm) is the error constant declared by the manufacturer for a specific MMC
  • (b) (µm) is the variable for error depending on the length of the block pattern, declared by the manufacturer for a specific MMC
  • L (mm) is the length of the block pattern
Fig8.gif (2334 bytes) The above formula can be expressed as a graph, as shown in Figure 8. It should be noted that the error does not (obviously) tends to infinity, but becomes asymptotic to a length specified by the manufacturer.
Fig. 8. Uncertainty of measurement

As it has been pointed out, the uncertainty of measurement is closely related to the thermal conditions of the environment. Therefore, the manufacturer is obliged to specify under what conditions of operation has obtained the declared IM, for example in the following way:

  • Ambient temperature in the place of installation: + 20or
  • Space thermal gradient: 1or C/m
  • Maximum time of thermal gradient: 0.5 orC/h and 2orC / 24 h

In short: the volumetric uncertainty of measurement (IVM), U3, corresponds to the difference between the length of the block pattern oriented in space and its corresponding value measured by the MMC.

In order to verify as described here, a set of three blocks should be measured pattern in different areas of the volume and/or orientations of the MMC. The length of these three blocks pattern should roughly correspond to 1/3, 2/3 and 3/4 of the useful travel of the longest axis of the MMC (up to a maximum of 1,000 mm). For practical reasons, the entire blocs pattern are aligned in the center of the volume of measurement of the machine, approximately every one of the diagonals.

The measures of length are measured once every surface using a block pattern. Pattern is measured three times each block. One of the trials consists of nine measures taken on a series of three specific samples in a position and orientation.

For each of the three measures samples, the uncertainty of measurement of length U3 is the absolute value of the distance that exists between the value of the block calibration pattern and the value measured by the MMC. Each test will get three values U3. They depend on the length, and its value cannot exceed the formula U3 = to + bL/1,000, where "a" and "b" are constants specified by the manufacturer.


We understand by dynamic characteristics of acceleration and speed of positioning of a MMC. Of course, they are not only related with mechanical structure but, fundamentally, with associated control and firmware. However, the dynamic benefits are observing the mechanical structure during its operation. The speed and acceleration are important in relation to the sampling frequency that the MMC can reach: the higher these values are greater the number of pieces that can be measured per unit of time.


It is almost always expressed in vector form. The highest speed reached is in the environment of 70 m/min.


It is the most important parameter when considering the productivity of a MMC. Through structures with an optimal relation mass/rigidity and proper control has been accelerations of up to 3 m/s2. He also stressed that the acceleration is the most important parameter in the face of the reduction of the measurement cycle times.


Tasks of the supervisory system

The main task of the control of a machine tool is the Government of the possibly very sophisticated dynamics of the machine and some auxiliary functions. A MMC control system performs the following basic functions:

  1. Control of the dynamic activity of a MMC: management of the operational and mechanical synchronism metrological structure with 3 to 10 axes.
  2. Control of the measurement programme management of the necessary instruction set for automatic execution of the programme of action.
  3. Processing of data of measured points: generation, based on the points taken on the surface of the piece of the geometric element
  4. The man/machine communication management: managing the interaction between the user and the MMC
  5. management of communication with the outside world: communication between MMC and local networks management
  6. Subordination to the measuring cycle: synchronizing the activity of a MMC with external and asynchronous events.
  7. Etc.


Due to the complexity of these calculations, the structure of the systems of control and process data from the MMC multiaxiales articulated at different levels, according to the logical intelligence distributed hierarchically (Figure 9). The system is structured on two levels:

Fig9.gif (67585 bytes)

Level 1: Server (host) system. In this case a W/S Digital equipmentAlphaStation station. Programmes containing performed the following functions:

  1. They manage the communication with the outside world: management of the interface with local networks in order to:

    (a) transmit measurement data to an external hub broadcasts measurement from remote stations of programming
    (b) I/F for remote management of measuring cells

  2. They manage the man/machine communication, in order to:

    (a) carry out the local management of the MMC
    (b) prepare or modify measurement programs
    (c) seek emergency restart
    (d) carry out Diagnostics

  3. Managed piece programme: management of the measurement programme.

    (a) instructions for positioning
    (b) calculation instructions
    (c) packaging instructions
    (d) addressing results

  4. They estimate measured points: estimates from the points taken from:

(a) points, straight lines, surfaces, circles, spheres, cylinders, etc.
(b) colisos (cashiers), also square, special for body elements.

Level 2. In this case, articulated around an Intel 80C187 co-processor, this level has, essentially, three tasks:

  1. Interface with level 1: calculation of the dynamic laws of motion based on positioning commands received from level 1:

    Calculation of the reference trajectory
    Coordination of the axes
    Calculation of control equations
    The position loop management

  2. Level 3 interface (MMC): management of the movement of the axes of the machine based on the theory of motion calculated previously:

Management of the movements
Management of sensors
Management of inputs/outputs of the structure (air, end of career, etc.)
Power management
Emergency management
Management of the local inputs/outputs (e.g., those of feed systems)

System control and data processing, illustrated here from a structural point of view, can be controlled from 3 to 10 axes. In addition, in the case of a horizontal arm architecture, the two sides of the machine can be managed as a single unit with 10 axles (Figure 10) or as two separate each one with 5-axis units (Figure 11).

Fig10.gif (7414 bytes) Figs.. 10 and 11


Applications a machine to measure programs are generated from a set of programs that allow the measurement techniques preset for any type of piece, and an evaluation in real time of the results. A_continuación discuss the technologies currently available in the following fields of activity: to) programming of piece; (b) analysis of the results.

Programming of piece

The programming of piece in an essential phase of preparation for the (automatic or not) implementation of a dimensional inspection cycle. The term "programming piece" means:

  • the definition of the instructions to be executed or performed by the machine (for example: choice of the transducer movement leading to the obtaining of the coordinates of each point, coordinates nominal points to measure and movement of withdrawal at the end)
  • the definition of the sequence of instructions
  • the generation of the programme

Piece programming techniques

There are three basic techniques to make the programming of piece

Programming online ("on line", self-learning)

It is the technique most used, despite the fact that it requires the simultaneous availability of MMC and the piece to be measured and consolidated

Offline programming ("off line").

This technique, although known from years ago, is implementing is currently due to the increasing reliability of technology support. This allows the creation and the simulation of a measuring cycle by means of CAD/CAM Station with dimensional inspection functions.

Automatic offline programming ("Automatic off line programming part").

Unfortunately, this technique no longer exists. The generation of inspection programmes and strategies would be controlled by the own application software

Part online programming

The operator, through the use of basic measurement programs, the drawing of the piece, the physical piece and the MMC generates one to one cycle of inspection instructions. In most cases, especially when the piece is complex, is a long and tedious process.

During the phase of programming of piece, measuring machine can not inspect other piece, which is a strong drawback for installed in line with process machines. The beginning of the programming of piece is always subject to the physical availability of the piece.

Measurement programmes have been developed considerably in an attempt of simplification and reduction of the time, in order to optimize the execution of the inspection cycle.

The best example of progress in this area are "subroutines" or "procedures". They are made through a sequence of predefined instructions that the operator must be completed by inserting the nominal values of each particular element in a preformatted input device. Due to its extreme simplicity, "subroutines" are one of the instruments more valid and widely used for the programming of complex elements.

The examples of the figures show two typical subroutines for the measurement of body elements: "Flush and gap" (opera and capture the difference between the mobile and fixed parts of a body) and "Ratio of the sheet metal curve". The sequence and the mode of measurement are automatically defined by the system: data nominal to introduce by the operator in a particular input device are graphically illustrated in the figures.

Piece offline programming

Offline programming allows the preparation of a programme of inspection previously production itself said of the piece, and does not require the MMC additional tasks which has awarded institutionally: measure.

Fig13.gif (73452 bytes)

Fig. 13-Piece programming scheme out of line

Most CAD/CAM software vendors currently offer metrology-oriented CAM applications. These programmes, to use a mathematical description of the piece (CAD) and emulation of the MMC instruments (CAM oriented) opermiten the definition and simulation on the screen of a full programme of inspection.

The end result in programming piece "off line" consists of a file format DMIS (Dimensional measuring Interface Standard), the standard for the transfer of inspection programmes between CAD/CAM and measurement environments.

Once the DMIS program has been transferred to the machine can be immediately executed. And ideally, in theory! Because in practice, although sunset times in motion have been reduced drastically, it is almost always necessary to carry out local modifications, for example, to add the fastening elements of the piece, that CAD systems rarely provide.

To run a program DMIS is also necessary, in most cases, translate it into understandable language for the measurement programme and and the machine control system. Except in rare cases, measuring only machines are able to interpret themselves and exclusive each manufacturer (propietary) languages.

While the conversion of a language to another presents considerable difficulties, particularly where it passes a language evolved to one that is not so much (think to translate a C program to another in Fortran!), the machines which adopt DMIS as their native language are preferable for this technical "off line".

Another advantage which is derived from the measurement systems that employ DMIS as native language consists of the fact that in the case of being necessary local modifications in the programme of measurement can be written in the same language as source that the CAD/CAM environment of the user. This allows a perfect compatibility and a congruence between the two environments. As a result, at any time, and on both sides, can be made modifications in the programme of action without loss of information. Which is of course impossible with the "owners" languages.

Automatic programming offline

Two piece programming techniques described above have different advantages and disadvantages. In any case, even when the measurement program is generated CAD/CAM or MMC the final result, in terms of cycle times is significantly influenced by the "human factor", for the efficiency of the inspection strategies adopted, etc.

Automatic programming out of line, as we have said, is not currently available, it would:

  • Generate measurement program based CAD/CAM (in a similar way as now occurs)
  • Completely eliminate the variables related to the skills and experience of the operator.
Fig14.gif (80598 bytes)

Fig. 14.-Scheme of automatic programming of piece out of line

From a purely operational point of view, the operator should be able to, simply, of:

  • Choose the mathematical description of the piece to be measured
  • Choose the content of a computer science library, the measurement system which is expected to carry out the inspection (at this level all the characteristics of the chosen system, for example the available probes)
  • Choose the elements to be measured
  • Start the automatic generation of the measurement programme.

Analysis of the results

Still being out of doubt to maintain a quality process under control is essential to measure the produced pieces, it is equally obvious that the measures would not be useful without an assessment of the results obtained. Thus, the analysis of the results should be considered not as an auxiliary to the measuring element, but as an integral part of the same. Traditionally, measurement systems generate a large and comprehensive file of difficult interpretation - even for those who carried out the inspection program.

Fig12a.gif (26670 bytes) Fig12b.gif (23455 bytes)

The objective of an efficient process control is the avoiding and does not monitor the production of pieces outside of tolerances. Above all, it is important to act in time. To this end, the results of the measurements must be:

  • available and ready to be analyzed in real time, for each of the samples
  • consistent security and statistically analyzed in real time

Programs for statistical process control

The SPC (statistical process Control) programs analyze the measurement results to generate statistical reports and real-time control cards; they can easily interpret the measurement results and evaluate trends; control, based on custom and predefined, standard trend of critical parameters, generating alarms when they tend to leave the established margins and associated critical conditions of the piece with abnormalities of the process that has occurred.

SPClr.gif (9687 bytes) Fig. 15 Examples of output of programmes of statistical process control. You can see how the graphics of the examined piece facilitates partnership between the results and the element that has generated

Click here for a higher quality image

The architecture of these programs is based, generally speaking, in a relational database that prepares the data to be analyzed by modular programmes. Each module is designed to make - optimally - a particular type of analysis; the different modules must be integrated among themselves so that the user obtain reports customized to their specific needs.


The transducer

As already indicated, taking the coordinates of the surface of the workpiece to be measured is done using very sophisticated devices, called probes. These probes are strictly connected to the scan mode, which can be of two types:

Point to point: transducer comes into contact with the piece to be measured and, without stopping, generates a signal that allows the acquisition of the coordinates of the point where the transducer has "touched" the piece. This type of transducer is the most used.

Continuous. In this mode, transducer remains in contact with the piece to be measured, taking points to high frequency according to certain acquisition laws. (Submicrométricos) more accurate probes are part of this category.

Regardless of the category, there are two types of transducers:

Touch: in them, both in point mode point-to-point as well as in continuous mode, transducer comes into contact with the piece to allow the acquisition of data.

Sensors for non contact. It probes that allow the acquisition of data without the need for physical contact with the piece to be measured.

Probes touch point to point

As we have said, they are the most common. Although there are various types, most of them are based on the principle illustrated in Figure 16.

The principle of operation is very simple: is based on the adoption of a system isostatic has 3 sets of fields (fixed elements) that host 3 cylinders (moving parts). Each set of fields and their related cylinder are separated between a 120 °

  • When the field comes into contact with the piece, it moves. Just an infinitesimal motion to open the circuit (Figure 16)
  • The system logs (and "freezes" the coordinates of the transducer at the time that it has come into collision with the piece (Figure 17).)
  • At this point, the coordinates of X, and Z "played" piece are available to be processed.

Continuous tactile sensors

In the MMD whose error is less than 2 microns sensor acquires crucial importance, being necessary to further reduce the uncertainty of measurement of the machine. This is especially true in laboratory machines (for example for the other measuring instruments certification: ISO 9000).

Analog sensors in continuous mode are used generally in applications previously mentioned: submicrométricos exploration of high-precision devices. In this type of sensors we describe of deflection, real machines to measure extremely high precision.

Deflection sensors are based on the principle of the elastic deformation of the material. Scan deflection system achieves a very high resolution through differential transducers, and moves parallel along the three Cartesian axes by an elastic parallelogram system. The deflection of the system of exploration is perpendicular to the surface of the piece and, for every point measured normal to the tangent of the measurement surface is also acquired passing through the own point.

The mechanical principle of operation is shown in Figure 19. The parallelogram on the Z axis is "balanced" by a motor so as to avoid gravitational errors.

Triangular probes of no contact

Sensoriality of no contact has undergone a remarkable evolution in recent years, due to the development of assistive technologies such as the miniaturization of compoenntes and high-speed processors and low cost. In dimensional metrology, this type of sensory may acquire great importance, because:

  • allows the measurement of soft surfaces
  • You can reduce cycle measurement through a one-time measurement (single shot) either a continuous high speed acquisition
  • is not subject to mechanical friction

Still considering advances induscutibles that have been occurring, especially through artificial vision, with regard to the measurement of large and medium-sized pieces the solution complete and satisfactory is still touch sensoriality.

Just in this context to analyze the operating principle of the sensor laser triangular (single beam), which are currently the most commonly used. It is necessary to indicate the type of sensor in question presents significant disadvantages to explore points in the interior of hollow elements. The scheme of operation of a triangular single beam laser sensor is shown in Figure 20.

This type of sensor works by diffuse light. The beam laser generated by the diode DL, was brought to the surface of the part that generates the "spot" PI. The resulting diffraction light is then conducted to the PDphotodetector, which consists of a photodiode of large surface area in contact with a highly homogeneous semiconductor (Figure 21). The apparent purpose of this process is to determine, as accurately as possible, the distance X.

The scheme of operation of a triangular typical single beam laser is shown in Figure 13. When PO meets the fotosensor at XO generates a stream. The current flow through X 1 and X 2 and the electrodes C and C1. Passing through (d), closes the circuit.

The sum of the currents I1 and I2 is function of the distances X 1 and X 2. In theory, could be a linear function, but it is not the case because of the imperfect homogeneity of the photodetector. The value of the currents I1 and I2 is not only of XO, but also of PO.

The analog signal of the photodetector is then amplified and filtered; removed you also the influence of PO. After the corresponding analog/digital conversion, each signal undergoes a treatment designed to compensate for linearity by means of a special firmware errors.

From a geometric point of view, the operation of a triangular sensor is very simple: see Figure 22 and its conclusions.

Related Companies or Entities

Hewlett Packard Española, S.L.
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