WO2012154023A1

WO2012154023A1 - A system and method for assessing the position of a body

Info

Publication number: WO2012154023A1
Application number: PCT/MY2011/000247
Authority: WO
Inventors: Indra Putra Almanar
Original assignee: Universiti Sains Malaysia
Priority date: 2011-05-09
Filing date: 2011-12-27
Publication date: 2012-11-15

Abstract

The present invention provides a system (1 ) and method for assessing the positional errors of an axially moving body on a predefined plane of movement. The system (1 ) comprises of a metrological tool or device (1a) for assessing the measurement errors of the position of a moving body in six degrees of freedom, the device (1a) being adapted for movement with the moving body and is further adapted to receive a beam of electromagnetic radiation (5) and consequently provides an indication of relative movement between the beam (5) and the moving body in one or both of two directions transverse to the beam (5), the directions may be at right angles to each other and/or are at right angles to the beam (5). Aforementioned metrological device (1a) being used in conjunction with a linear scale used to indicate the length of travel of the axially moving body. In addition the system (1 ) further includes an apparatus (25) for monitoring and providing a measure of the pointing instability of a beam (5) of electromagnetic radiation; and an apparatus for monitoring and providing a measure of the of the tilt of aforementioned moving body moving along an axial direction with reference to the plane of movement of the moving body.

Description

A SYSTEM AND METHOD FOR ASSESSING THE POSITION OF A BODY

The present invention relates broadly to the field of metrology. More particularly the present invention relates to a method and apparatus for determining the measurement errors relating to a position of a body.

BACKGROUND TO THE INVENTION

It is known to measure linear and angular positioning errors of a machine tool slide using a laser interferometer. To perform the measurement in X, or V, or Z direction, the slide is moved in the relevant measurement direction.

The laser source system is positioned outside the machine tool and arranged to direct a beam of radiation along the relevant axis, through an interferometer and a Wollaston prism mounted on the slide. The radiated beam from the laser source being directed and transmitted to, a fixed reflector device that is, positioned outside the machine tool. Aforementioned fixed reflector serving to reflect the transmitted beam back, through the interferometer to the laser system. The laser system being equipped to, provide a measurement indication of the position of the received reflected and interfered laser beam and hence the position of the machine tool slide. The slide carrying the interferometer and Wollaston prism is moved in the measurement direction in a series of steps of nominally known length and readings of the corresponding reflected laser beams by the laser system enable a comparison to be made between the nominal position and the actual position to determine the position error.

This technique employs an interference pattern that is produced by splitting a beam of light into two other beams of light that travel along their own separate paths, bouncing the beams back and recombining them. The different paths traversed by the split beams may be of different lengths or the split beams may traverse through different materials along their respective paths to create alternating interference fringes on a back detector. Thus this technique can be used to measure the position errors, linear: dx, dy, and dz, and angular pitch, roll and yaw, in a one by one or incremental manner. Utilizing this approach will take a long period of time to obtain measurements of all linear and angular position errors in one axis of motion, where during this time, temperature and humidity will vary, consequently affecting the individual accuracy of each measurement. A simultaneous measuring technique of the six position errors which are simultaneously compensated for any possible uncertainty which may result from deviations in temperature or humidity is required.

British Patent GB 2162942 (A) filed on 6 August 1985, by Indra Putra Almanar, discloses a technique of reading signals from three quadrant detectors made up of four cells of photosensitive detectors each. As noted therein, a measuring device which consists of two beam splitters and three quadrant detectors has been disclosed. The two beam splitters and three quadrant detectors are configured in an arrangement to capture the relative distances of the three quadrant detectors relative to two parallel reference laser beams. The patent discloses the production of a second laser beam parallel to a first laser beam that is produced through the emission of a low powered laser source with the aid of an optical penta-prism. The penta-prism is mounted outside the machine tool slide, and is placed along the axis of movement of the machine tool slide.

Since the laser beam used is single ended in nature, any slight pointing instability at the source of the beam will be magnified linearly due to the distance between the laser source and the optical penta-prism. The returning beam is then magnified by a factor of two due to the operational nature of the optical penta-prism. This will result in the creation of a systematic uncertainty. However this type of systematic uncertainty can be compensated for by splitting the returning beam from the penta-prism. The transmitted part of the beam is directed to the device mounted on the machine tool slide whereas the reflected part is directed perpendicularly to a photo sensitive quadrant detector fixed on the reflecting half of the penta-prism. Another source of uncertainty is the tilt of the machine where the slide is being measured due to instability of the foundation where the machine is mounted on. By placing horizontally two tilt sensor on the part of the machine, outside the slide being measured, one is parallel to the laser beam used as a reference, and the other one is perpendicular, any unnecessary tilt of the machine in the horizontal plane can be detected and thus be compensated for.

The method and apparatus disclosed in aforementioned British Patent GB 2162942 (A) suffers from the limitation of only being able to provide a measure of positional errors in 5 degrees of freedom out of a total of six degrees of freedom. These including positional errors in the Y-direction, Z-direction, Yaw- angular direction, Pitch-angular direction and Roll-angular direction, if the direction of motion of the body being assessed for positional errors, is along the X-direction. In addition, aforementioned patent does not disclose an apparatus to correct for the inherent pointing instability of a laser beam.

The positional error in the direction of motion dX can also be corrected by considering the yaw angular error and the distance of the measuring device to a linear scale used to detect the axial distance of travel of the slide. Angular errors in the pitch make an insignificant contribution to the overall positional error dX since it is only a cosine error where roll has no influence on the positional error dX due to the fact that it is operational on the same plane as the positional error dX.

Thus, by incorporating one beam-splitter and one quadrant detector to the returning beam of the penta-prism, two tilt-sensors positioned horizontally, parallel and perpendicular to the laser reference system and also by considering the distance between the device to the linear scale used relevant to the motion direction of the slide, the three linear errors and three angular errors in the six degrees of freedom of the machine tool slide in its travel can be detected simultaneously. The measurement obtained is free of errors due to external disturbances that include possible deviations in the accuracy of measurements contributed by tilt of the machinery or apparatus holding the machine tool slide as well as errors due to variations in temperature and humidity. SUMMARY OF THE INVENTION

The following presents a simplified summary of the invention in order to provide a basic understanding of some aspects of the invention. This summary is not an extensive overview of the invention. It is not intended to identify key/critical elements of the invention. Its sole purpose is to present some concepts of the invention in a simplified form as a prelude to the more detailed description that is presented later.

The present invention provides a system and method to assess the position of an axially moving body on a predefined plane of movement.

In one aspect, the system to assess the position of an axially moving body on a predefined plane of movement comprises of: a metrological device for assessing the measurement errors of the position of an axially moving body on a predefined plane of movement that is adapted for movement with the body and adapted to receive a beam of electromagnetic radiation, said device being adapted to produce an indication of relative movement between the beam and the body in one or both of two directions transverse to the beam, the directions may be at right angles to each other and/or are at right angles to the beam; a linear scale and pointer used to indicate the length of travel of the axially moving body on a predefined plane of movement; an apparatus for monitoring and providing a measure of the pointing instability of a beam of electromagnetic radiation that is used in conjunction with aforementioned metrological device for assessing the measurement errors of the position of aforementioned axially moving body; and an apparatus for monitoring and providing a measure of the of the tilt of aforementioned axially moving body moving along an axial direction with reference to the plane of movement of the axially moving body. The metrological device enables assessing the measurement errors of the position of an axially moving body. Aforementioned metrological device being capable of providing a measure of five out of six possible positional measurement errors a body can experience when travelling linearly along an axial direction in space on a predefined plane of movement. An example of the positional measurement errors include linear displacement errors in the y and z directions and angular displacement errors in yaw, pitch and roll if the body whose position errors are being assessed is moving linearly in the x-direction;

The metrological device for assessing the measurement errors of the position of an axially moving body on a predefined plane of movement is adapted to receive a beam of coherent electromagnetic radiation from a source of coherent electromagnetic radiation and comprises of a hollow body that includes: a plurality of bore holes that thus allow it to receive a beam of electromagnetic radiation in a two way direction; a pair of beam splitters oriented such as to enable splitting of a pair of beams of electromagnetic radiation respectively into two orthogonal beams and to further direct the resultant beams of split electromagnetic radiation onto a plurality of radiation sensors; and an optical penta-prism reflector.

The source of coherent electromagnetic radiation and optical penta-prism reflector cooperate to provide a pair of beams of coherent electromagnetic radiation that serve as reference beams to enable the metrological device to provide an indication of measurement errors of the position of the axially moving body.

The apparatus for monitoring and providing a measure of beam pointing instability of the electromagnetic beam is comprised of: a radiation sensor; and a beam splitter oriented such that an impinging electromagnetic radiation is split into two; a transmitted part and a reflected part, the reflected part being directed on to the radiation sensor.

The radiation sensor and beam splitter that make up the apparatus for monitoring and providing a measure of beam pointing instability, are used in conjunction with aforementioned metrological tool or device for assessing the position of a moving body and source of coherent electromagnetic radiation to provide an indication of pointing instability.

The beams that impinge on the surface of the plurality of radiation sensors produce a plurality of electrical voltage and current signals that may be fed back to a computer system that serves as a plant of a control system to thus provide signals to an electromechanical system that is electrically connected to the computer system and electromechanically coupled to the moving body to compensate for errors in the position of the axially moving body.

The apparatus for providing a measure of tilt of an axially moving body comprising of a pair of tilt sensors placed parallel and transverse to the coherent electromagnetic radiation beam emitted from the source of coherent electromagnetic radiation with reference to the plane of movement of said axially moving body. In a preferred embodiment of the present invention, the plurality of radiation sensors utilized by the metrological device for assessing the position of a moving body and the apparatus that provides a measure of pointing instability of a coherent electromagnetic radiation beam include photosensitive quadrant detectors, each photosensitive quadrant detector comprising of four quadrants of a circular area that are coated with photosensitive material and will consequently produce an electrical voltage upon impingement by a source of electromagnetic radiation.

In a preferred embodiment of the present invention, the source of coherent electromagnetic radiation is a laser source and the coherent electromagnetic radiation is a laser beam.

In another aspect, the method to assess the position of a body includes: assessing the positional measurement errors in five degrees of freedom of a body experiencing motion along a linear axis on a predefined plane of movement in space which excludes the positional measurement error in the direction of axial motion of said body, the method comprising the steps of placing aforementioned metrological device for the assessment of the position of a moving body of the present invention onto the moving body whose measurement errors are to be determined; placing a source of electromagnetic radiation at one end facing the metrological device such that a beam of electromagnetic radiation emitted from the source is in alignment with the receiving borehole of the metrological device; and placing a corresponding penta-prism at a symmetrically opposing end to receive a portion of the emitted beam of electromagnetic radiation and consequently redirecting a portion of the emitted beam of electromagnetic radiation to another bore-hole of the device, the emitted beam of electromagnetic radiation and the redirected beam being respectively split by a pair of beam splitters that produce electromagnetic radiation beams that upon hitting the surface of a plurality of radiation sensors of aforementioned metrological device, provide an indication of the measurement errors in at least five degrees of freedom; and detecting measurement error in the direction of motion of a body (the measurement error in the sixth degree of freedom) that is used in conjunction with aforementioned metrological device for assessing the position of a moving body that comprises the step of multiplying the measurement error of Yaw angular displacement obtained with the aid of aforementioned metrological device to the distance between the position of the centre of the metrological tool to the position of a linear scale used to indicate the length of travel of a body whose positional measurement errors are to be determined. BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a diagram illustrating a rigid body moving in the x direction of the three orthogonal axes x, y, z on the x-y plane of movement; Figure 2 is a diagram illustrating a set-up required for measurement of six positioning errors of a machine tool slide using the apparatus for assessment of the position of a moving body of the present invention;

Figure 3 is a diagram illustrating a preferred embodiment of the metrological device for assessing the position of a moving body of the present invention and its corresponding beam locations on a plurality of photosensitive quadrant detectors in the event of positional errors in the dZ and dY directions of a axially moving body, moving along the X-direction; Figure 4 is a diagram illustrating a preferred embodiment of the metrological device for assessing the position of a moving body of the present invention and its corresponding beam locations on the plurality of photosensitive quadrant detector surfaces in the event of positional errors in the Yaw direction of a body moving along the X-direction;

Figure 5 is a diagram illustrating a preferred embodiment of the metrological device for assessing the position of a moving body of the present invention and its corresponding beam locations on the plurality of photosensitive quadrant detector surfaces in the event of positional errors in the Pitch and Roll directions of a moving body moving along the X- direction; Figure 6 is a diagram illustrating the use of a preferred embodiment of the metrological device for assessing the position of a moving body of the present invention to measure the positional error along the X-direction of a machine slide tool or any moving body that moves along the X-direction; and Figure 7 is a diagram illustrating the apparatus used to provide a measure of the pointing instability of a beam of coherent electromagnetic radiation.

DETAILED DESCRIPTION OF THE INVENTION The detailed description set forth below in connection with the appended drawings is intended as a description of an exemplary embodiment and is not intended to represent the only form in which the embodiment may be constructed and/or utilized. The description sets forth the functions and the sequence for constructing the exemplary embodiment. However, it is to be understood that the same or equivalent functions and sequences may be accomplished by different embodiments that are also intended to be encompassed within the scope of this disclosure.

The system 1 and method of assessing the positional errors of a body moving in an axial direction on a predefined plane of movement will now be described with reference to figures 1 to 7.

With reference to figures 1 and 2, if a body moves nominally linearly in a direction, say the X-direction, it is subject to six possible positional or movement errors, namely linear displacement errors δχ, d , dz respectively in the three orthogonal axes x, y, z and angular displacement errors of roll, pitch and yaw respectively about the x, y and z axes. This applies to a free solid body moving in space and, for example to the slide of a machine tool known henceforth as a machine tool slide 2, the machine tool slide 2 moving along a predetermined axis on a pair slide rails 3.

With reference to figure 2, there is illustrated a set up in which the system 1 of the present invention is retrofitted to a machine bed 3 supporting a machine tool slide 2. The machine tool slide 2 being configured to mate with a pair of rails 3 and the machine tool slide 2 hence being, slidably moveable in an axial direction determined by the trajectory of the pair of rails 3. The system 1 for assessing the positional errors of a moving body moving along an axial direction on a predefined plane of movement of the present invention in the set up of figure 2 is used to measure the positional errors of the machine tool slide 2. The plane of movement of the machine tool slide 2 is defined as the plane of the machine bed 4 that faces vertically upward. The system of assessing the positional errors of the machine tool slide 2 comprises of: 1. A metrological tool or device 1a for assessing the measurement errors of the position of a moving body which in accordance to figure 2 is the machine tool slide 2. The metrological device 1a being adapted for movement with the machine tool slide 2 and adapted to receive a beam of electromagnetic radiation 5 from a source 6 of coherent electromagnetic radiation, said device 1a being adapted to produce an indication of relative movement between the beam 5 and the machine tool slide 2 in one or both of two directions transverse to the beam 5, the directions may be at right angles to each other and/or are at right angles to the beam 5;

2. A linear scale 21 and pointer 22 used to provide a measure of the length of travel of the axially moving machine tool slide 2;

3. An apparatus 25 for monitoring and providing a measure of the pointing instability of a beam 5 of electromagnetic radiation that is used in conjunction with aforementioned metrological device 1a for assessing the measurement errors of the position of a moving body moving in an axial direction such as the machine tool slide 2 depicted in figure 2; and 4. An apparatus for monitoring and providing a measure of the tilt of aforementioned machine tool slide 2 moving along an axial direction with reference to the plane of movement of the machine tool slide 2 which is defined by the plane of the machine bed 4 that faces vertically upward.

In a preferred embodiment of the present invention, the source of coherent electromagnetic radiation 6 is a laser source and the coherent electromagnetic radiation is a laser beam. With reference to figure 2, the metrological device 1a is positioned to rest upon the upward facing plane of the machine tool slide 2. The axial or longitudinal motion of the slide 2 is defined by the boundary of the machine bed 4. The axial motion of the machine tool slide 2 is constrained to be within the boundaries of the edges that define the machine bed 3 and is defined for the purposes of this description to be along the x- axis on the x-y plane of movement.

The metrological tool or device 1a for assessing the measurement errors of the position of the axially moving machine tool slide 2 on a predefined plane is adapted to receive a beam of coherent electromagnetic radiation 5 from a source of electromagnetic radiation 6 and comprises of a hollow body that includes a plurality of bore holes 16, 17, 19 that thus allow it to receive a pair of beams of electromagnetic radiation 5, 8 in a two way direction; a pair of beam splitters 14, 15 oriented such as to enable splitting of the pair of beams of electromagnetic radiation 5, 8 into two orthogonal beams 5a, 5b and 8a, 8b respectively and to further direct the resultant beams 5a, 8a, 8b of split electromagnetic radiation onto a first 11 , second 12 and third quadrant detectors 13. The beam 5b is transmitted to the penta-prism reflector 9 as directed by beam splitter 15.

The source of coherent electromagnetic radiation 6 and optical penta-prism reflector 9 cooperating, to provide a pair beams of coherent electromagnetic radiation 5, 8 that serve as reference beams to thus enable the metrological device 1a to provide an indication of measurement errors of the position of the axially moving machine tool slide 2.

With reference to figures 2 to 7, more particularly in the setup illustrated in figure 2, the source of coherent electromagnetic radiation 6 is mounted on a support stand 7, such that the beam of coherent electromagnetic radiation 5 emitted from the source 6 is in alignment with a first bore hole 16, thus enabling the emitted beam of coherent electromagnetic radiation 5 to impinge on a first beam splitter 14, to produce a reflected and a transmitted beam 5a, 5b of coherent electromagnetic radiation respectively. The reflected portion 5a of the original beam 5 emitted from the source 6 impinges upon the surface of the first quadrant detector 11 and the transmitted portion 5b of the original beam 5 of coherent electromagnetic radiation exits the metrological device 1a through a second bore hole 17. The transmitted portion 5b of the original beam emitted 5 from the source 6 is directed to the optical penta-prism reflector 9.

The optical penta-prism reflector 9 is mounted on another support stand 10 such that the transmitted portion 5b of the original beam 5 emitted from the source 6 is reflected by the penta-prism reflector 9, resulting in the transmitted portion 5b of the original beam emitted 5 to be reflected and diverted to the apparatus 25 for monitoring and providing a measure of the pointing instability of the emitted beam 5 of electromagnetic radiation emitted from the source 6 via the penta-prism reflector 9. Thus, aforementioned apparatus 25 for providing a measure of pointing instability is aligned to receive the transmitted portion 5b of the original beam 5 emitted from the source 6. With reference to figure 7, the transmitted portion 5b of the original beam 5 emitted from the source 6 is reflected and diverted to a first bore hole 18a of the apparatus for monitoring and providing a measure of pointing instability of a beam of coherent electromagnetic radiation 25. Upon diversion through the first bore hole 18a, the beam 5b will impinge a beam splitter 24 of the apparatus for monitoring and providing a measure of pointing instability of a beam of coherent electromagnetic radiation 25 thus resulting in a reflected beam 8c and a transmitted beam 8. The resulting reflected beam 8c originating from the optical splitting of beam 5b is diverted to a quadrant detector 23 of said apparatus for providing a measure of pointing instability of a beam of electromagnetic radiation 25. The beam spot that impinges on any one or a combination of any of the four individual quadrants of the quadrant detector 23 of said apparatus 25 thus provides a measure of the pointing instability of the beam 5b and hence beam 5 emitted from the source 6.

The transmitted beam 8 (transmitted from beam splitter 24) i.e. the beam originating from the beam 5b reflected via the optical penta-prism reflector 9, exits the apparatus 25 for providing a measure of pointing instability of a beam of electromagnetic radiation through bore hole 18b. The thus transmitted beam 8, being in alignment with a third bore hole 19 of the metrological device 1a. The transmitted beam 8 (transmitted from beam splitter 24) propagates through the third bore hole 19 and impinges a second beam splitter 15 housed within the body of the metrological device 1a. Upon said beam 8 originating from the optical penta-prism reflector 9, impinging the surface of the second beam splitter 15, a reflected beam 8b and a transmitted beam 8a will be produced. The reflected beam 8b will impinge upon the surface of a second quadrant detector 12 and the transmitted beam 8a will impinge upon a third quadrant detector 13. The quadrant detectors 11 , 12, 13, 23 are photosensitive quadrant detectors, each quadrant detector 11 , 12, 13, 23 comprising of four quadrants (A, B, C and D) of a circular area that are coated with photosensitive material and will consequently produce an electrical voltage upon impingement by a source of electromagnetic radiation 5a, 5b, 8a, 8b.

When the machine tool slide .2 moves axially along the x-axis as defined by the pair of slide rails 3 of the machine bed 4, the positional errors of the machine tool slide 2 in five degrees of freedom which include positional errors in the y-direction, z-direction, pitch angular direction, yaw angular direction and roll angular direction will manifest in the position of the beam spots 29 of the beams 5a, 8a and 8b on the individual quadrant detectors 13,14, 15 respectively of the metrological device 1a. Thus the impingement of the beams 5a, 8a and 8b on the individual quadrant detectors 13, 14, 15 will result in a production of electrical signals which provide a measure of the positional errors of the axially moving machine tool slide 2 moving along the x-axis on the x-y plane of movement.

These electrical signals may be fed back to a computer system (not shown) that serves as a plant of a control system to thus provide signals to an electromechanical system (not shown) that is electrically connected to the computer system and electromechanically coupled (not shown) to the machine tool slide 2 to compensate for errors in the position of the axially moveable machine tool slide 2.

Similarly the quadrant detector 23 of the apparatus 25 for monitoring the pointing instability of the beam of coherent electromagnetic radiation 5 emitted from the source of coherent electromagnetic radiation 6 of the present invention, produces an electrical signal upon impingement of the beam 8c, this electrical signal providing a measure and indication of the pointing instability of the source of coherent electromagnetic radiation. Accordingly, the resulting electrical signal produced may -similarly be fed back to a computer system (not shown) that serves as a plant of a control system. The electrical signal originating from the quadrant detector 23 of the apparatus 25 for providing a measure of beam pointing instability serves to provide feedback to the computer system to thus correct the measure of positional errors in the y-direction, z-direction, yaw- angular direction, pitch angular direction and roll angular direction obtained from the metrological device 1a and thus compensate for any inaccuracies in the measure of positional errors of the machine tool slide 2 due to the pointing instability of the electromagnetic radiation emitted 5 from the source 6.

Apart from the apparatus for providing a measure of the pointing instability of a beam of coherent electromagnetic radiation 5 emitted from a source 6 of electromagnetic radiation and the metrological device 1a, the system 1 for assessing the positional errors of a moving body of the present invention further includes an apparatus that provides a measure of the of the tilt of aforementioned machine tool slide 2 moving along an axial direction with reference to the plane of movement of the machine tool slide 2 which is defined by the plane of the machine bed 4 that faces vertically upward. The apparatus for providing a measure of the tilt of the machine tool slide 2 comprises of two tilt sensors 26,. 27 that are respectively placed parallel and transverse to the coherent electromagnetic radiation beam 5 emitted from the source 6 of coherent electromagnetic radiation with reference to the plane of movement of said machine tool slide 2.

Hence in order to correct inaccuracies of the measure of positional measurement errors obtained from the metrological device 1a that result due to the tilt of the machine tool slide 2, the electrical signals from the pair of tilt sensors 26, 27 are fed back to the computer system to thus compensate for the tilt of said machine tool slide 2.

The metrological device 1a of the system 1 for assessing the positional errors of a moving body of the present invention is only capable of providing a measure of the positional errors in five degrees of freedom. For the purposes of this description in accordance with the setup illustrated in figure 2, the system 1 for assessing the positional errors of a moving body of the present invention is used to asses the positional errors of an axially moving machine tool slide 2 moving along the x-axis on the x-y plane of movement. Hence the positional errors of the five degrees of freedom provided by the metrological device 1a include position errors in the y-direction, z- direction, pitch angular direction, yaw angular direction and roll angular direction.

With reference to figures 3 and 5 the measure of the positional errors in the z-direction and pitch angular-direction of the machine tool slide 2 are as given by the equations below:

{{{[(Z_A1 + ZBI) - (Zci + ZDI)] / (ZAI + ZBI + Z_C1 + Z_D1 )} +

{[(Z_A2 + Z_B2) - (Zc2 + Z_D2)] / (ZA2 + Z_B2 + Zc2 + Z_D2)} +

{[(Z_A3 + Z_B3) - (Zc3 + Z_D3)] / (Z_A3 + Z_B3 + Zc3 + Z_D3)}} / 3} - (Pitch)

Pitch = {{{[(P_Ai + PBI) - (Pci ⁺ PDI)] (PAI + P_B1 + Pci + Pm)} + {[(PA2 + P_B2) - (PC2 + P_D2)] / (PA2 + P_B2 + PC2 + P_D2)}} / 2L} +

{[(PA3 + Pes) - (Pes + P_D3)] (PA3 + P_B3 + Pes + P_D3)} / L}} - (dZ)

Hence to obtain the measure of pitch in terms of the variables "P" and "Z", the following equation is utilized:

Pitch = {{{{[(P_A1 + P_Bi) - (Pci + PDI)] / (PAI + PBI + Pci + Pm)} +

{[(PA2 + P_B2) - (Pc2 + P_D2)] / (P_A2 + P_B2 + P_C2 + P_D2)}} / 2L} +

{[(P_A3 + P_B3) - (PC3 + PD3)] (PAS + P_B3 + P_C3 + P_D3)} / L}} - {{{{[(Z_A1 + ZBI) - (Zc, + Z_D1)] / (ZAI + ZBI + Z_Ci + ¾,)} +

{[(Z_A2 + Z_B2) - (Z_C2 + Z_D2)] / (Z_A2 + Z_B2 + Z_C2 + Z_D2)} +

{[(Z_A3 + Z_B3) - (Zc3 + Z_D3)] / (Z_A3 + Z_B3 + Zc3 + Z_D3)}} / 3}} / 2}

Accordingly, dZ can be calculated as follows: dZ = {{{[(Z_A1 + ZBI) - (¾, + Z_D1)] / (ZAI + ZBI + Z_C1 + Z_D1)} +

{[(ZA2 + Z_B2) - (Z_C2 + Z_D2)] / (ZAS + Z_B2 + Z_C2 + Z_D2)} +

{[(Z_A3 + Z_B3) - (Z_C3 + Z_D3)] / (Z_A3 + Z_B3 + Zc₃ + Z_D3)}} / 3} - {{{{[(PAI + PBI) - (Pci + Pm)] (PAI + PBI + Pci + PDI )} +

{[(ΡΛ2 + P_B2) - (Pc2 + P_D2)] / (PA2 + P_B2 + Pc2 + P_D2)}} / 2L} +

{[(P_A3 + P_B3) - (PC3 + P_D3)] (P_A3 + P_B3 + PC3 + P_D3)} / L}} -

{{{{[(Z_A1 + ZBI) - (Zc, + Z_D1)] / (Z_A1 + Z_B1 + Z_Ci + Z_D1)} +

{[(Z_A2 + Z_B2) - (Z_C2 + Z_D2)] / (ΖΑΣ + Z_B2 + Z_C2 + Z_D2)} +

{[(Z_A3 + Z_B3) - (Z_C3 + Z_D3)] / (Z_A3 + Z_B3 + Z_C3 + Z_D3)}} / 3}} / 2}

With reference to figures 3 to 5, the measure of the positional errors in the y-direction yaw angular direction and roll angular direction of the machine tool slide 2 are given by the following equations: dY = {{{[(YAI + YBI) - (Yci + YDI)] / (YAI ⁺ YBI + Yci + YDI)}} +

{{[(Y_A2 + Y_B2) - (Y_C2 + Y_D2)] / (Y_A + Y_B2 + Y_C2 + Y_D2)}} + {{[(YA3 + Y_B3) - (Yea + YDS)] / (YA3 + YB3 + Yes + YDS)} / 3}} - (Yaw); and

Yaw = {{{[(Yw_Ai + Yw_Bi) - (Yw_Ci + Yw_D1)] / (Yw_Ai + Yw_Bi + Yw_Ci + Yw_Di)} +

{[(YWA2 + Yw_B2) - (Yw_C2 + Yw_D2)] / (YWA2 + Yw_B2 + Ywc2 + Yw_D2)}} /(L 2)} +

{[(YW_A3 + YW_B3) - (YW_C3 + YW_D3)] / (Yw_A3 + Yw_B3 + YW_C3 + YW_D3)} / L}} -

(dY)

Hence the measure of yaw in terms of the variables "Yw" and "Y", the following equation is utilized:

Yaw = {{{[(Yw_Ai + Yw_Bi) - (Yw_Ci + Yw_Di)] / (Yw_Ai + Yw_Bi + Yw_Ci + Yw_D1 )} +

{[(Yw_A2 + Yw_B2) - (Yw_C2 + Yw_D2)] / (YWA2 + Yw_B2 + Yw_C2 + Yw_D2)}} / (L/2)}+ {{[(Yw_A3 + Yw_B3) - (Yw_C3 + Yw_D3)] / (Yw_A3 + Yw_B3 + Yw_C3 + Yw_D3)} / L}} - {{[(YAI + YBI ) - (Yci + YDI)] (YAI + YBI ⁺ Yci + YDI )} +

{[(Y*2 + Y_B2) - (Y_C2 + YD₂)] / (YA2 + _B2 + Yc₂ + Y_D2)} +

{[(Y_A3 + Y_B3) - (Yes + YDS)] / (YA3 + Y_B3 + Y_C3 + Y_D3)} / 3

Similarly,

Roll = {{{{[(R_Ai + REM) - (Rci + RDI)] / (RAI + RBI + Rci ⁺ RDI )} - {[(R_A2 + R_B2) - (R_C2 + R_D2)] / (RA2 + R_B2 + Rc₂ + RD₂)}} / L} + {3{[(R_A3 + R_B3) - (Res + R_D3)] / (RAS + R_B3 + Res + R_D3)} / L}} - (dY)}

Hence the measure of Roll in terms of the variables "R", "Y" and "Yw" is as given by the equation below:-

Roll = {{{[(R_Ai + RBI ) - (Rci + RDI)] / (RAI + RBI + Rci + RDI )} +

{[(R_A2 + R_B2) - (R_C2 + R_D2)] / (RA∑ + R_B2 + R_C2 + R_D2)}} / L} + {3{[(R_A3 + R_B3) - (Res + R_D3)] / (R_A3 + R_B3 + Res + R_D3)} / L}} - {{[(YAI + YBI) - (Yci + YDI)] (Y_A1 ⁺ YBI ⁺ Yci + Ym » +

{[(Y_A2 + Y_B2) - (Y_C2 + Y02)] (Y V2 + _B2 + YC2 + Y_D2)} + {[(YA3 + Yes) - (Yes + YDS)] / (YAS + Y_B3 + Y_C3 + YDS)} / 3} - {{{[(Yw_A1 +

Yaw_Bi) - (Ywci + Yaw_Di)] / (Yw_Ai+ Yw_Bi + Yw_Ci + Yw_Di)} +

{[(YWA2 + YW_B2) - (YWc2 + YW_D2)] / (YWA2 + Yw_B2 + Ywc2 + Yw_D2)}} / (L 2)}+ {{[(YWA3 + Yw_B3) - (Yw_C3 + Yw_D3)] / (Yw_A3 + Yw_B3 + Yw_C3 + Yw_D3)} / L}} - {[(YAI + YBI ) - (Yci + YDI)] / (YAI + YBI + Yci + YDI » +

{[(YA2 + Y_B2) - (Y_C2 + Y_D2)] / (Y_A2 + Y_B2 + Y_C2 + Y_D2)} +

{[(Y_A3 + Y_B3) - (Y_C3 + YDS)] / (Y_A3 + Y_B3 + Yes + YDS)} / 3 The meanings of the variables Z_Ai, Z^, Z_A3, Z_Bi, Z_B2, Z_B3, Z_Ci, Z_C2, Z_C3, Y_Ai, Y_A2, YA3, YBI,

Y_B2, YB3, Yd, Yc₂, Yc3, PA1, PA2, PA₃, PB1_> P_B2, PB3, Pel, PC2, PC3, RA1. RA₂, RA3, RB1. R_B2, B3,

RCI , Rc2, Rc3, Yw_Ai, YW_A2, YWA3, YWBI , YW_B2I YW_B3, YWCI , YWC2, YWC3, dY, dZ, Pitch, Roll, Yaw and L of the various equations listed in the preceding paragraphs of this description are as listed below, where;

Z_Ai, ZA2, ZA3 are measures of electrical signals produced in the A quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as result of positional displacement in the z-direction;

Z_B1, Z_B2, ZB3 are measures of electrical signals produced in the B quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as result of positional displacement in the z-direction;

Zci, Zc2, Zc₃ are measures of electrical signals produced in the C quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the z-direction;

Z_D1, Z_D2, Z_D3 are measures of electrical signals produced in the D quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the z-direction; YAI , YA2, YA3 are measures of electrical signals produced in the A quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the y-direction.; YBI, YB2, YB3 are measures of electrical signals produced in the B quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the y-direction;

Yci, Yc2, c3 are measures of electrical signals produced in the C quadrant of the first 11 , second 12, third 13 quadrant detectors respectively as a result of positional displacement in the y-direction;

YDI , D2, YD3 are measures of electrical signals produced in the D quadrant of the first 11 , second 12, third 13 quadrant detectors respectively as a result of positional displacement in the y- direction;

PAI, PA2, A3 are measures of electrical signals produced in the A quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the pitch angular direction;

PBI, PB2, B3 are measures of electrical signals produced in the B quadrant of the first 1 1 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the pitch angular direction; Pci, Pc2, Pc3 are measures of electrical signals produced in the C quadrant of the first 1 1 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the pitch angular direction; PDI , PD2, D3 are measures of electrical signals produced in the D quadrant of the first 11 , second 12 and third quadrant 13 detectors respectively as a result of positional displacement in the pitch angular direction; R_Ai, RA2, A3 are measures of electrical signals produced in the A quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the roll angular direction;

RBI , RB2, RB3 are measures of electrical signals produced in the B quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the roll angular direction;

Rci- c2, c3 are measures of electrical signals produced in the C quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the roll angular direction; DL RD2, D3 are measures of electrical signals produced in the D quadrant of the first 11 , second 12 and third 13 quadrant detectors respectively as a result of positional displacement in the roll angular direction;

Yw_Ai, YW_A2, YW_A3 are measures of electrical signals produced in the A quadrant of the first 11 , second 12, and third 13 quadrant detectors respectively as a result of positional displacement in yaw angular direction; Yw_Bi, Yw_B2, Yw_B3 are measures of electrical signals produced in the B quadrant of the first 11 , second 12, and third 13 quadrant detectors respectively as a result of positional displacement in yaw angular direction;

Yw_Ci, Yw_C2, Ywc3 are measures of electrical signals produced in the C quadrant of the first 11 , second 12, and third 13 quadrant detectors respectively as a result of positional displacement in yaw angular direction; Yw_Di , Yw_D2, Yw_D3 are measures of electrical signals produced in the D quadrant of the first 11 , second 12, and third 13 quadrant detectors respectively as a result of positional displacement in yaw angular direction; dZ represents the total positional measurement error in the z-direction; dY represents the total positional measurement error in the y-direction;

Pitch represents the total positional measurement error in the pitch angular direction;

Yaw ^ represents the total positional measurement error in the yaw angular direction;

Roll represents the total positional measurement error in the roll angular direction; and

L represents the distance from the centre of the metrological tool 1a to the surface on which the third quadrant detector 13 resides.

Since, the metrological device 1a, can only provide a measure of the positional errors of the axially moving machine tool slide 2 in five degrees of freedom, the system for assessing the positional errors of a moving body of the present invention further includes a linear scale and pointer that provides a measure of the longitudinal linear travel of the machine tool slide 2 along the x-axis, to thus enable the computation of the positional error in the final sixth degree of freedom, which represents the positional error of the machine tool slide 2 along the x-axis.

A measure of the of the positional error of the axially moving machine tool slide 2 along the direction of motion which is the x-axis for the purposes of this description and in accordance with the set-up illustrated in figure 2, is obtained by considering the yaw angular error and the distance of the metrological device 1a to the linear scale used to detect the axial distance of travel of the machine tool slide 2. The angular error in the pitch does not significantly contribute to the positional error along the x-direction. Similarly the angular error in the roll does not significantly contribute to the positional error along the x-direction since it is operational on the same plane (x-y plane) as the axial movement of the machine tool slide 2.

With reference to figure 6, the system for assessing the positional errors of an axially moving body on a predefined plane of movement provides a method for obtaining the positional error in the final sixth degree of freedom, which represents the positional error of the machine tool slide 2 along the x-axis. The method comprises the steps of obtaining a measure of the positional error of the machine tool slide 2 in the yaw angular direction as described in an equation as given in a preceding paragraph of this description and multiplying the result with the distance "L _yaw" 20 measured from the centre of the metrological device 1a to the pointer 22 on the linear scale 21 used to indicate the length of axial travel of said machine tool slide 2. Aforementioned method is embodied by the equation below that enables the provision of the positional measurement error along the x-axis, which is the direction of motion of the axially moving machine tool slide 2. dX (Yaw) x L_yaw

{{{[(Yw_Ai + Yawm) - (Ywci + Yaw_Di)] / (Yw_Ai + Yw_B1 + Yw_Ci + Yw_D1)} + {[(YWA2 + Yw_B2) - (Ywc2 + Yw_D2)] / (YWA2 + Yw_B2 + Ywc2 + Yw_D2)}} / (L/2)}+ {{[(Yw_A3 + Yw_B3) - (Ywc3 + Yw_D3)] / (Yw_A3 + Yw_B3 + Ywc3 + Yw_D3)} / L}} - {{{{[(YAI + YBI) - (Yci + YDI)1 (YAI + YBI + Yci + Ym)} +

{[(YA2 + Y_B2) - (YC2 + Y_D2)] (YA2 + Υβ2 + Y_C2 + Y_D2)} +

{[(YA3 + Y_B3) - (Yes + YDS)] / ( _A3 + YB₃ + Y_C3 + YDS)} / 3} x L_yaw; where; dX represents the positional measurement error in x-direction (which happens to be the direction of motion of the machine tool slide 2); and Lyaw represents the length measured from the centre of the metrological device 1a to the pointer 22 on the linear scale 21 used to indicate the length of axial travel of said machine tool slide 2.

Claims

1. A system (1 ) for assessing the positional measurement errors of an axially moving body on a predefined plane of movement, the system (1 ) being capable of providing a measure of positional errors in six degrees of freedom which include positional measurement error in the direction of axial motion of said axially moving body, characterized in that the system comprises of: a metrological device (1 a) for assessing the measurement errors of the position of an axially moving body on a predefined plane of movement in at least 5 degrees of freedom that is adapted for movement with the body and adapted to receive a beam (5) of electromagnetic radiation from a source (6) of electromagnetic radiation, said device (1a) being adapted to produce an indication of relative movement between the beam (5) and the body in one or both of two directions transverse to the beam (5); a linear scale (21 ) and pointer (22) used to indicate the length of travel of the axially moving body on a predefined plane of movement; an apparatus (25) for monitoring and providing a measure of the pointing instability of a beam (5) of electromagnetic radiation that is used in conjunction with the metrological device (1 a) for assessing the measurement errors of the position of a moving body.; and an apparatus for monitoring and providing a measure of the of the tilt of aforementioned moving body moving along an axial direction with reference to the plane of movement of the body.

2. A system (1 ) according to claim 1 , wherein the metrological device (1a) comprises of a hollow body that includes: a first , second and third bore holes (16, 17, 19) that thus allow the metrological device (1a) to receive a pair of beams of electromagnetic radiation (5, 8) in a two way direction; a first (14) and second (15) beam splitter forming a pair of beam splitters (14, 15) oriented such as to enable splitting of the pair of beams of electromagnetic radiation (5, 8) respectively into two orthogonal beams (5a, 5b) and (8a, 8b) respectively and to further direct the resultant beams (5a, 8a, 8b) of split electromagnetic radiation onto a first, second and third quadrant detectors (1 1 , 12, 13); and an optical penta-prism reflector (9); the source (6) of coherent electromagnetic radiation and optical penta-prism reflector (9) cooperating, to provide a pair beams (5,8) of coherent electromagnetic radiation that serve as reference beams (5,8) to thus enable the metrological device (1 a) to provide an indication of measurement errors of the position of the axially moving body.

3. A system (1 ) according to claim 1 , wherein the apparatus (25) for monitoring and providing a measure of the pointing instability of a beam (5) of electromagnetic radiation that is used in conjunction with the metrological device (1a) for assessing the measurement errors of the position of a moving body comprises of: a quadrant detector (23); and a beam splitter (24) oriented such that an impinging beam of electromagnetic radiation (5b) is split into two; a transmitted portion of the beam (8) and a reflected portion of the beam (8c). The reflected portion of the beam (8c) being directed on to the quadrant detector (23); the quadrant detector (23) and beam splitter (24) are used in conjunction with aforementioned metrological device (1a) for assessing the position of a moving body and source (6) of coherent electromagnetic radiation to provide an indication of the impinging beam (5b) pointing instability.

4. A system (1 ) according to claim 1 , wherein the apparatus for monitoring and providing a measure of the of the tilt of the moving body comprises of a pair of tilt sensors (26, 27) placed parallel and transverse respectively to the beam (5) of electromagnetic radiation emitted from the source (6) with reference to the plane of movement of the axially moving body.

5. A system (1 ) according to claims 2 and 3, wherein the plurality of radiation sensors (1 1 , 12, 13, 23) are quadrant detectors that each comprise of four individual quadrants of a circular area of material that is coated with photosensitive material and consequently produces an electrical voltage upon impingement by a beam (5a, 8a, 8b, 8c) of electromagnetic radiation.

6. A method for providing a measure of the positional measurement errors of an axially moving body moving on a predefined movement plane in 5 degrees of freedom utilizing the system of claim 1 , comprising the steps of: i.) placing the metrological device (1a) on to a surface of the axially moveable body; ii.) aligning a source (6) of electromagnetic radiation, such that the emitted beam (5) of electromagnetic radiation is in alignment with a first bore hole (16) of the metrological device (1a); iii.) splitting the emitted beam (5) of electromagnetic radiation via a first beam splitter (14) into a transmitted portion (5a) and a reflected portion (5b); the reflected portion of the original beam (5) of electromagnetic radiation emitted from the source (6) impinges a first quadrant detector (11 ) of the metrological device (1a); and the transmitted portion (5b) of the original beam (5) is directed to a distant optical penta-prism reflector (9) via a second bore hole (17), the optical pentaprism reflector (9) being in alignment with the transmitted portion of the beam (5b); iv.) redirecting the transmitted portion (5b) of the originally emitted beam of electromagnetic radiation (5) into a receiving bore hole (18a) of the apparatus for providing a measure of the pointing instability of the emitted beam (5); v. ) further splitting the beam (5b) into two orthogonal portions, a transmitted portion (8) and a reflected portion (8c); the reflected portion (8c) of beam (5b) impinges the surface of quadrant detector (23) of the apparatus for providing a measure of the pointing instability of the beam (5b) and hence the originally emitted beam (5); the transmitted portion (8) of beam (5b) is directed to a third bore hole (19) of the metrological device (1a); vi. ) splitting the transmitted portion (8) of beam (5b) further to thus produce a reflected portion (8b) and transmitted portion (8a) that are mutually orthogonal to each other; the reflected portion (8b) of the beam impinging a second quadrant detector (12) of the metrological device (1a); and the transmitted portion (8a) of the beam impinging a third quadrant detector (13) of the metrological device (1a); vii. ) initiating movement of the axially moveable body along a predetermined axis on a predefined plane of movement and capturing the electrical signals produced at the individual quadrant detectors (11 , 12, 13 ,23) of the metrological device (1a) due to the production of beam spots (29) by the impinging beams of electromagnetic radiation (5a, 8a, 8b, 8c); viii. ) capturing the electrical signals produced by the pair of tilt sensor (26, 27) that thus serve to provide a measure of the tilt of the axially moving body moving along a predefined axis of movement with respect to a predefined plane of movement; and ix. ) computing the positional measurement errors in five degrees of freedom that does not include the positional measurement error along the direction of movement of the axially moving body by taking into account the electrical signals produced the quadrant detectors (1 1 , 12, 13) of the metrological device (1a) and compensating the errors of the computed positional measurement error by taking into account the measure of pointing instability of the emitted beam (5) emitted from the source (6) and the tilt of the moving body with respect to its plane of movement.

7. A method for providing a measure of the positional measurement errors in the direction of motion of an axially moving body moving on a predefined movement plane utilizing the system of claim 1 , comprising the steps of: determining a distance "L_yaw", the distance taken from the centre of the metrological device (1 a) to a pointer (22) of a linear scale (21 ) used to indicate the length of axial travel of the axially moving body; and computing the measure of positional measurement error in the yaw angular direction and multiplying the result of the computation with the distance computed in step (i) to obtain a measure of the positional measurement error in the direction of motion of the axially moving body.