GB2578143A

GB2578143A - Machine tools and calibration thereof

Info

Publication number: GB2578143A
Application number: GB1816987.0A
Authority: GB
Inventors: Bouvier Christophe
Original assignee: Fives Landis Ltd
Current assignee: Fives Landis Ltd
Priority date: 2018-10-18
Filing date: 2018-10-18
Publication date: 2020-04-22
Anticipated expiration: 2038-10-18
Also published as: GB2578143B; GB201816987D0

Abstract

A method for generating calibration data for a multi-axis machine tool 2, 20 and then using said calibration data to calibrate the multi-axis machine tool comprises sensing and recording the location of a reference point on the axis at a plurality of positions using an electronic location sensor 18. A best fit plane with respect to the plurality of recorded positions is calculated using a processor followed by calculating the location of the centre point of a best fit circle lying in the best fit plane with respect to the plurality of recorded positions and a vector normal to the best fit plane. The controller of the machine tool is calibrated with reference to the location of the centre point of the best-fit circle and the vector normal to the best fit plane. The axis to be calibrated may be rotary (B,D, S1, S2) or linear (W, X, Y, Z).

Description

Intellectual Property Office Application No. GII1816987.0 RTM Date:11 April 2019 The following terms are registered trade marks and should be read as such wherever they occur in this document: Nikon', Trimos', 'Faro H exagon' and Cranfield Precision' Intellectual Property Office is an operating name of the Patent Office www.gov.uk /ipo Title: Machine Tools and Calibration thereof

Field of the invention

The present invention relates to machine tools and calibration of the driven axes of the machine.

Background of the invention

Machine tools may include a plurality of machine axes, such as driven linear machine axes in which one portion is moveable relative to another portion along the direction of a linear reference axis or driven rotary machine axes in which one portion is rotatable relative to another portion about a rotational reference axis.

Once a machine tool has been built, it is usually calibrated against a set of orthogonal reference axes. In this process, deviations of the driven machine axes from perpendicularity and straightness of motion are recorded and used to apply compensations to the drive signals sent to the machine axes so that a workpiece can be machined to a higher degree of accuracy than would otherwise be achievable with the uncalibrated machine tool. One existing approach to calibration of machine tools is the use of ball bars as described for example in US 5,259,120 and US 5,812,128.

Summary of the invention

The present invention provides a method for calibrating a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first rotary axis rotatable about a first reference rotational axis, and a controller for controlling the machine axes, wherein the method comprises the steps of: (a) sensing and recording the location of a point on the first rotary axis which is spaced from the first reference rotational axis at a plurality of rotational positions of the first rotary axis using an electronic location sensor; (b) calculating with an electronic processor a best fit plane with respect to the plurality of recorded rotational positions; (c) calculating with the electronic processor the location of the centre point of a best fit circle lying in the best fit plane with respect to the plurality of recorded rotational positions and a vector normal to the best fit plane; and (d) calibrating the controller of the machine tool with reference to the location of the centre point of the best fit circle and the vector normal to the best fit plane.

In a preferred embodiment, in step (a), the plurality of recorded rotational positions are measured with respect to three mutually orthogonal coordinate system reference axes, and in step (c), the centre point of the best fit circle is calculated by: o determining a 3D rotation matrix which rotates the best fit plane to be parallel to two axes of the coordinate system reference axes; applying the 3D rotation matrix to the plurality of recorded rotational positions to generate a set of transformed rotational positions; determining the coordinates of a centre point of a best fit circle for the set of transformed rotational positions; and applying an inverse of the 3D rotation matrix to the coordinates of the centre point of the best fit circle for the set of transformed rotational positions to determine the coordinates of the centre point of the best fit circle for the plurality of recorded rotational positions.

Preferably, in step (c), calculating the vector normal to the best fit plane comprises: determining the mean of each of the coordinates of the plurality of recorded rotational positions to identify a point lying in the best fit plane; centring the plurality of recorded rotational positions on the location of the point lying in the best fit plane; and determining a singular value decomposition of the centred plurality of recorded rotational positions.

The invention further provides a method for calibrating a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first linear axis, and a controller for controlling the machine axes, wherein the method comprises the steps of (i) sensing and recording the location of a point on the first linear axis at a plurality of positions of the first linear axis using an electronic location sensor; (ii) calculating with an electronic processor the location of a point on a best fit line with respect to the plurality of recorded positions; (iii) calculating with the electronic processor a vector in the direction of the best fit line; and (iv) calibrating the controller of the machine tool with reference to the location of the point on the best fit line and the vector in the direction of the best fit line.

o In a preferred embodiment, in step Op, the location of the point on the best fit line is calculated by determining the mean of each of the coordinates of the plurality of recorded positions.

Preferably, in step (Hi), calculating the vector in the direction of the best fit line comprises centring the plurality of recorded positions on the location of the point on the best fit line, and determining a singular value decomposition of the centred plurality of recorded positions.

Methods disclosed herein enable the rotary and/or linear machine axes of a machine tool to be characterised using an electronic location sensor. The location information may be acquired as the machine axis of interest is being moved either continuously or in steps (with the location acquired at each step). This may generate a set of discrete points representing a trajectory followed by a point on the machine axis. Each set of points may subsequently be analysed to generate a geometrical model of each axis.

Preferably, the geometrical information is then used to determine spatial relationships between the axes. The methods described herein may be used during assembly and commissioning of a machine tool and also subsequently as a diagnostic tool to check and adjust alignment of the machine tool.

The present techniques may be applicable to a wide variety of machine tool configurations. They may be particularly advantageous when the configuration does not readily lend itself to the use of existing calibration techniques. For example, in some machine tools, the workzone may be relatively confined, making it difficult to use calibration artefacts such as straight edges and reference squares. In some cases, it may be difficult to access locations suitable for mounting laser calibration mirrors or interferometers which require a constant line of sight with the laser source and a reflector over ranges of motion of the machine tool.

Furthermore, there is a need for an accurate method for calibrating a rotary axis which is more readily carried out successfully than existing approaches such as those using Moore tables or microptic clinometers.

o The calibration methods may involve fitting a best fit circle or best fit line to a set of locations recorded by an electronic location sensor. This averaging or smoothing of the position data may allow the geometrical location of axes to be determined to a precision which may be greater than the "one-point accuracy" of the electronic location sensor.

Preferably, the electronic location sensor is arranged to acquire the measurements for each of the machine axes of a multi-axis machine tool in the same coordinate system. In some embodiments of the invention, the geometrical and spatial relationships between two or more machine axes may be evaluated in a common frame of reference.

In some embodiments, the electronic location sensor includes a light source, such as a source of laser light for example. It may be able to determine the location in space of a point on a machine axis by detecting light reflected back directly from a region of the machine axis. The electronic location sensor may be used in combination with a trackable device which may comprise a reflector or light sensor. The electronic location sensor may be configured to determine the location of a trackable device mounted at a selected point on a machine axis and record the location. Laser tracker systems are marketed for example by Hexagon Manufacturing Intelligence and Faro.

The electronic location sensor may include a contact probe and be able to detect the location in space of a point on a machine axis when the contact probe is brought into contact with the point. The sensor may include an articulated arm on which the contact probe is mounted. Examples of suitable measurement arms are marketed by Nikon, Trimos, Faro and Hexagon Manufacturing Intelligence.

In a preferred embodiment, the machine tool includes a second rotary axis rotatable about a second reference rotational axis, and the method includes the step of carrying out steps (a) to (d) in relation to a point on the second rotary axis.

The machine tool may include at least one rotary axis and at least one linear axis which are calibrated using methods described herein.

Embodiments of the methods may involve a step of calculating the angle defined between first and second rotary axes, a rotary axis and a linear axis, or two linear axes with reference to the calculated respective point locations and vectors.

IS Further embodiments may involve a step of calculating the minimum distance between first and second rotary axes, a rotary axis and a linear axis, or two linear axes with reference to the calculated respective point locations and vectors. More particularly, the distance between the two axes may be calculated in a reference plane. The reference plane may be a plane parallel to a base of the machine. It may be a plane parallel to axes of the machine tool identified as the "X" and "Z" axes.

According to conventional machine tool nomenclature, X and Z axes are mutually perpendicular linear reference axes which may be ascribed as being parallel to the plane of the machine base.

In a preferred implementation, the machine tool includes a machine base, and the first and second rotary axes are rigidly mounted on the base in immovably and unadjustably fixed positions relative to the base, and the first reference rotational axis is parallel to and spaced laterally from the second reference rotational axis.

Prior to the present invention, there was a need for a method to accurately calibrate a machine tool having such a configuration. An example of such a machine tool is the Twin Turret Generator (TTG) offered by Cranfield Precision. The versatility and adaptability of calibration techniques according to examples of the present disclosure mean that they are suitable for application to a wide range of machine tool configurations, including machine tools such as the TTG which are not suited to use of known calibration techniques.

The present invention further provides a system for generating calibration data for a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first rotary axis rotatable about a first reference rotational axis, and a controller for controlling the machine axes, wherein the system comprises: an electronic location sensor for sensing and recording the location of a point on the first rotary axis which is spaced from the first reference rotational axis at a plurality of rotational positions of the first rotary axis; and an electronic processor configured to calculate from the recorded rotational positions a best fit plane with respect to the plurality of recorded rotational positions, and the location of the centre point of a best fit circle lying in the best fit plane with respect to the plurality of recorded rotational positions and a vector normal to the best fit plane, and generate calibration data therefrom for use in calibrating the machine tool.

The present invention further provides a system for generating calibration data for a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first linear axis, and a controller for controlling the machine axes, wherein the system comprises: an electronic location sensor for sensing and recording the location of a point on the first linear axis at a plurality of positions of the first linear axis; and an electronic processor configured to calculate from the recorded positions the location of a point on a best fit line with respect to the plurality of recorded positions, and a vector in the direction of the best fit line, and generate calibration data therefrom for use in calibrating the machine tool.

The present invention additionally provides a multi-axis machine tool comprising a plurality of machine axes, a controller for controlling the machine axes, and an electronic processor configured to receive the calibration data generated by a system for calibrating a multi-axis machine tool as described herein, and calibrate the controller with reference to the calibration data.

The present invention also provides a multi-axis machine tool including a calibration system as described herein, wherein the machine tool is arranged to carry out a calibration method according to an embodiment of the present disclosure.

The machine tool may include a third rotary axis carried by one of the first and second rotary axes. The third rotary axis may be carried in an orientation in which its o reference rotational axis is perpendicular to the reference axis of one of the first and second rotary axes on which it is mounted. Calibration methods as described herein may enable the angle and distance between the third rotary axis and its supporting axis to be determined to improve the accuracy of machining processes carried out by the machine tool.

Similarly, a linear axis may be carried by one of the first and second rotary axes. It may be orientated with its reference axis perpendicular to the reference rotational axis of the rotary axis on which it is carried and a calibration method described herein may be employed to determine the angle and spacing between the linear axis and the supporting rotary axis.

The best fit lines and/or circles and locations calculated to characterise machine axes as described herein may be used to determine the extent to which each axis deviates from its intended location. They may therefore be used to calibrate the controller of the machine tool in order to minimise positioning errors. The machine tool may then be operated under the control of the calibrated controller to process a workpiece.

Brief description of the drawings

Machine configurations and embodiments of the invention will now be described by a way of example and with reference to the accompanying schematic drawings, wherein: Figure 1 is a perspective view of a known horizontal boring machine; Figure 2 is a perspective view of a known twin turret grinding machine, together with a system for generating calibration data; Figure 3 is a diagram showing the spatial relationship between the machine reference axes of the machine shown in Figure 2; Figure 4 is a diagram to illustrate characterisation of a linear axis according to an embodiment of the invention; Figure 5 is a diagram to illustrate characterisation of a rotary axis according to an embodiment of the invention; and Figure 6 is a diagram illustrating calculation of the spatial relationships between two axes in a reference plane according to an embodiment of the invention.

Detailed description of the drawings

A known horizontal boring machine 2 is shown by way of example in Figure 1 to illustrate combination of a plurality of machine axes in a machine tool. A worktable 4 is provided, on which a workpiece (not shown) is mounted during use of the machine. The worktable is rotatable about a reference axis 6 in directions indicated by a double-headed arrow labelled "B". The machine includes a rotary drive for rotating the worktable in directions B about axis 6. This drive is referred to as the "B axis" of the machine. The B axis is in turn carried by a horizontal linear machine axis which is arranged to reciprocate in directions indicated by the double-headed arrow labelled Z. This driven machine axis is referred to as the "Z axis".

A rotatable drive spindle 8 is provided for holding a cutting tool (not shown). The spindle is in turn carried by a vertical linear machine axis, namely the "Y axis". The Y axis is attached to a column 10 which is carried by a horizontal linear machine axis, namely the "X axis". The X, Y and Z axes are arranged to be mutually perpendicular.

During calibration of the machine, deviations from mutual perpendicularity of the axes and straightness of their motion are recorded (for example using geometrically precise artefacts) and used to apply compensations to the positions demanded of the machine by its control system.

A further known machine tool configuration 20 is shown in Figure 2. It includes two vertical rotary machine axes, B and D, which have respective reference axes 34 and 36 that are arranged to be parallel and spaced apart. The rotary axes are mounted to a base 22 of the machine at fixed, unadjustable locations. A workpiece spindle 24 is io provided for holding a workpiece and is able to rotate it about a horizontal reference axis 38 in direction C. The workpiece spindle 24 is mounted on a linear machine axis W which translates along reference axis 39 in a direction perpendicular to the B axis and parallel to the axis 38.

i5 Two tool spindles 26 and 28 are carried on the rotary axis D. They are rotatable about respective reference axes 30, 32 which are perpendicular to the D axis and mutually parallel. They are referred to below as the Si and S2 axes, respectively, of the machine.

Figure 3 is a diagram illustrating the machine axes of the machine tool of Figure 2 to show their spatial relationships.

In order to accurately control relative motions of the tools carried by the tool spindles 26 and 28 and a workpiece mounted in workpiece spindle 24, it is necessary to determine a number of geometrical parameters, namely: (i) the angle and distance between the B and D reference axes (34 and 36); (ii) the angle and distance between the W and B reference axes (39 and 34); (iii) the angle between the W and C reference axes (39 and 38); (iv) the distance between the C and B reference axes (38 and 34); and (v) the angle and distance between the tool spindle reference axes (30, 32) and the D reference axis 36.

Methods for determining the locations in space of the reference axes of linear and rotary machine axes will now be described with reference to Figures 4 to 6. In order to acquire data about the alignment of a machine axis, an electronic location sensor is used to monitor motion of the axis. The sensor may be in the form of a measurement arm including a contact probe that can be used to follow the path of a reference point on the machine axis. Alternatively, a trackable component or device 16 (see Figure 2) may be rigidly mounted at a reference point on a driven part of the axis, and an in electronic location sensor in the form of an electronic device tracker is then used to track the location of the trackable device. The trackable device may be a light reflector trackable using a laser coordinate measuring instalment 18. The location of the reference point is acquired as the axis of interest is moved either continuously or in steps to record a set of spaced apart positions.

As illustrated in Figure 4, in the case of a linear axis, a set of points 40 is acquired along the direction of motion of the axis. The location of each point is recorded in a selected metrology coordinate system, such as a set 42 of three mutually perpendicular axes labelled, X, Y and Z in Figure 4.

In the case of a rotary axis, as illustrated in Figure 5, the location of a reference point is monitored, with the reference point being on a moving part of the rotary machine axis at a position spaced from the reference axis about which the rotary axis is rotatable. A set 50 of measured locations of the device is recorded as the axis rotates, using the same coordinate system 42 as used in relation to other axes of the same machine.

The measured locations are stored in an electronic memory and then retrieved and processed using an electronic processor. The processor used may be included in an electronic location sensor, which may be in the form of a measurement arm or an electronic device tracker, for example. It may instead be a processor provided as part of a machine tool. In a further variation, the electronic processor may be embodied in a computing device separate from the electronic location sensor and machine tool.

The processor may be a number of processors, a multi-processor core, or some other type of processor, depending on the particular implementation. The electronic memory may be any piece of hardware that is capable of storing information, such as, for example, without limitation, data, program code in functional form, and other suitable information either on a temporary basis or a permanent basis. The memory may be, for example, a random access memory or any other suitable volatile or nonvolatile storage device.

As described in further detail below, for a linear axis, a best fit line 44 for the set 40 of measured positions (see Figure 4) is then calculated using an electronic processor. In o the case of a rotary axis, a best fit circle 52 for the set 50 of measured positions (see Figure 5) is calculated using an electronic processor, having a centre at point 54. A vector 56 normal to the plane of this circle and passing through the centre 54 lies along the calculated location of the reference axis of rotation of the rotary axis.

The best fit line for a linear axis may be determined in a vector equation form, such that for any point P on the line: P= t DL + PL where DL is a vector in the direction of the line, PL a point on the line and t a real number. PL and DL are therefore characteristics of the linear axis being evaluated and may be used in calibration of the machine tool, as described below.

Coordinates for PL may be obtained by calculating the mean of each coordinate of the n measured points: Pi, . Pn of set 40: PLx = mean( Pix, Pit\ ) PLY = mean( Ply, P-)y, Pny) PLZ = mean( Piz, P2z, Pnz DL may be obtained by computing the SVD (Singular Value Decomposition) of the set of measured points when centred on PL: svp Pix PLX 12 =UEVT P 1Y PLY PIZ -PLZ Pay -PLY PnZ -PLz1 i where E is a diagonal matrix containing the singular values, U and V are the matrices of left and right singular vectors and DL is the vector of V corresponding to the largest singular value.

Characterization of a rotary axis in accordance with an embodiment of the invention will now be described with reference to Figure 6.

Figure 6 shows a set of data points (Pi, P2...P,1) acquired in relation to a rotary axis V1. V, rotates about a reference rotational axis 64. This set of points is transformed (as described below) using an electronic processor to lie on a horizontal circle 62 by to rotation of the rotary axis through an angle 0 to lie along reference line 66 which is parallel to the Z axis of the metrology coordinate system 42. C, is a point at the centre of a best fit circle 60 for the untransformed set of data points and C' is a point at the centre of circle 62 having radius R. V, is a generic axis (having a reference axis 68) which could represent either a linear or a rotary axis of the same machine tool.

The best fit circle for a set of data points for a rotary axis may be determined by first establishing the best fit plane for the measured data and then calculating the best fit circle in that plane.

zo The best fit plane may be expressed in vector form using the dot product: Np (P -Pp) = 0 where Np is the normal vector to the plane, and Pp a point on the plane.

Similarly to the best fit line estimation above, Pp may be estimated by calculating the mean of each coordinate of the measured points.

A normal Np to the best fit plane may then be evaluated via the same SVD of the mean-centred data as used for the best fit line estimation above, with the difference that Np is the vector of V corresponding to the smallest singular value.

The best fit circle is evaluated in the resulting best fit plane. This is achieved by subjecting the measured points to a rotation about an axis (u in Figure 6) which makes the best fit plane parallel to two axes of the coordinate system reference axes. For example, it may be transformed to be horizontal (that is, such that its normal is parallel to Z). The axis u is defined as the cross product of Np and the Z axis (and o therefore perpendicular to a plane containing both the Np and Z axes): u = Np x [0 0 1] The rotation angle 0 is the angle between Np and Z, which can be estimated from the norm of the cross product: = sin1 ( 1-111 Any point may be chosen as rotation centre and Pp may be selected for that purpose.

Those parameters are used to compute the corresponding 3D rotation matrix R(0,u) and use it to transform the points: P,' = R(0,u) * (P1 -Pp) + Pp The best fit circle is computed by applying a least squares algorithm on the X and Y coordinates of the resulting points to establish the centre C' and radius R minimizing the radial deviations between the transformed measured points and that centre.

The outputs are the best fit circle centre coordinates: Cx' and Cy' in the horizontal plane and its radius.

Since the horizontal plane is obtained by rotation about Pp: Cz' = Ppz The centre point coordinates in the measurement coordinate system are established by performing the inverse of the previously applied transformation: C = R(-e,u) * (C' -Pp) + Pp Centre point C and vector Np characterise the rotary axis being evaluated and may be used in calibration of the machine tool, as described below.

Once the axis position measurements are processed as described above, each machine axis may be characterised by an axis point P and vector V ((Pm VB), (Pw, Vw), (Pc, o Vc) (PD, VD), (Psi, Vs,), ) and their relative positions in space have been defined.

Their spatial relationships can then be further evaluated.

The angle p between axes V, and V, (in particular to assess parallelism and orthogonality) may be estimated using the axes directions dot product: v, Iv, *11\1,11 The distance A between two axes can be estimated as the distance between two parallel planes passing through each axis line.

The cross product of the two direction vectors provides the planes' normal n: n = V, x V, The distance of interest is then the length of the projection onto n of a vector joining points on each line, such as P, and P, n.(P1-P1) This provides the distance between two axes in the mathematical sense, that is, the minimum distance between those two axes. This minimum could occur anywhere along those axes and potentially very far from the region where the machine components attached to those axes are located. In fact, axes such as B and D, expected (ij = COS-to be parallel, might not be perfectly aligned and could actually intersect away from the region where measurement took place and A would then be 0.

Thus, the evaluation of the separation distance 6 between two axes in a reference plane (e.g. machine X-Z plane) can be valuable. It may be computed as the distance between the intersection of each axis with that plane of interest (POI), which is defined by its normal: npoj and a point: Ppo1. For axis i: (pPOI PI) HP01* vi VI lipoi io Then the separation distance between the axes i and j is given by: 2 2)2 Sji = .1(Pri Pnjx) + (Pn--Prijy) + (Pniz Pnjz Although the embodiments according to the present disclosure described with reference to the drawings comprise processes performed by an electronic processor, the present disclosure also extends to computer programs comprising instructions for causing an electronic processor to perform the processes. More particularly, computer programs on or in a transitory or non-transitory recording medium, adapted for putting the disclosure into practice are encompassed by the present disclosure. The program may be in the form of source code, object code, a code intermediate source and object code such as in partially compiled form, or in any other form suitable for use in the implementation of the processes according to the present disclosure. The recording medium may be any entity or device capable of carrying the program.

For example, the recording medium may comprise a storage medium, such as a ROM, for example a CD ROM or a semiconductor ROM, or a magnetic recording medium, for example a floppy disc or hard disk. Alternatively, the carrier may be an integrated circuit in which the program is embedded, the integrated circuit being adapted for performing, or for use in the performance of, the relevant processes. Pfl

Thus, the present disclosure provides a computer program comprising program instructions for causing an electronic processor or a machine tool including such a processor to perform the methods described herein. Furthermore it includes provision of such a computer program on a recording medium, embodied in a record medium, stored in a computer electronic memory, or embodied in a read-only electronic memory.

Aspects of the present disclosure may be embodied as a computer method, computer system, or computer program product. Accordingly, aspects of the present disclosure may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, and the like), or an embodiment combining software and hardware aspects. Furthermore, aspects of the present disclosure may take the form of a computer program product embodied in a computer-readable medium (or media) having computer readable program code/instructions embodied thereon.

It will be appreciated that references herein to perpendicular or parallel relative orientations and the like are to be interpreted as defining substantially perpendicular or parallel relationships between components within practical tolerances.

Claims

Claims 1. A method for calibrating a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first rotary axis rotatable about a first reference rotational axis, and a controller for controlling the machine axes, wherein the method comprises the steps of: (a) sensing and recording the location of a point on the first rotary axis which is spaced from the first reference rotational axis at a plurality of rotational positions of the first rotary axis using an electronic location sensor; (b) calculating with an electronic processor a best fit plane with respect to the plurality of recorded rotational positions; (c) calculating with the electronic processor the location of the centre point of a best fit circle lying in the best fit plane with respect to the plurality of recorded rotational positions and a vector normal to the best fit plane; and (d) calibrating the controller of the machine tool with reference to the location of the centre point of the best fit circle and the vector normal to the best fit plane.
2. A method of claim 1, wherein in step (a), the plurality of recorded rotational positions are measured with respect to three mutually orthogonal coordinate system reference axes, and in step (c), the centre point of the best fit circle is calculated by: determining a 3D rotation matrix which rotates the best fit plane to be parallel to two axes of the coordinate system reference axes; applying the 3D rotation matrix to the plurality of recorded rotational positions to generate a set of transformed rotational positions; determining the coordinates of a centre point of a best fit circle for the set of transformed rotational positions; and applying an inverse of the 3D rotation matrix to the coordinates of the centre point of the best fit circle for the set of transformed rotational positions to determine the coordinates of the centre point of the best fit circle for the plurality of recorded rotational positions.
3. A method of claim 1 or claim 2, wherein in step (c), calculating the vector normal to the best fit plane comprises: determining the mean of each of the coordinates of the plurality of recorded rotational positions to identify a point lying in the best fit plane; centring the plurality of recorded rotational positions on the location of the point lying in the best fit plane; and determining a singular value decomposition on of the centred plurality of recorded rotational positions.
4. A method for calibrating a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first linear axis, and o a controller for controlling the machine axes, wherein the method comprises the steps of: (i) sensing and recording the location of a point on the first linear axis at a plurality of positions of the first linear axis using an electronic location sensor; (ii) calculating with an electronic processor the location of a point on a best fit IS line with respect to the plurality of recorded positions; (iii) calculating with the electronic processor a vector in the direction of the best fit line; and (iv) calibrating the controller of the machine tool with reference to the location of the point on the best fit line and the vector in the direction of the best fit line.
5. A method of claim 4, wherein in step (ii), the location of the point on the best fit line is calculated by determining the mean of each of the coordinates of the plurality of recorded positions.
6. A method of claim 5, wherein in step (iii), calculating the vector in the direction of the best fit line comprises centring the plurality of recorded positions on the location of the point on the best fit line, and determining a singular value decomposition of the centred plurality of recorded positions.
7. A method of any of claims 1 to 3, wherein the machine tool includes a second rotary axis rotatable about a second reference rotational axis, and the method includes the step of carrying out steps (a) to (d) in relation to a point on the second rotary axis.
8. A method of any of claims 1 to 3 or claim 7, wherein the machine tool includes a first linear axis, and the method includes the steps (i) to (iv) of claim 4.
9. A method of any of claims 4 to 6 or claim 8, wherein the machine tool includes a second linear axis, and the method includes the step of carrying out steps (i) to (iv) in relation to a point on the second linear axis.
10. A method of one of claims 7 to 9 including the step of calculating the angle defined between the first and second rotary axes, the first rotary axis and the first to linear axis, or the first and second linear axes, respectively, with reference to the calculated locations and vectors.
11. A method of one of claims 7 to 9 including the step of calculating the minimum distance between the first and second rotary axes, the first rotary axis and the first linear axis, or the first and second linear axes, respectively, with reference to the calculated locations and vectors.
12. A method of claim 11, wherein the minimum distance between the first and second rotary axes, the first rotary axis and the first linear axis, or the first and second linear axes is calculated in a reference plane.
13. A method of claim 7, or one of claims 8 or 9 when dependent on claim 7, wherein the machine tool includes a machine base, and the first and second rotary axes are rigidly mounted on the base in immovably fixed positions relative to the base, and the first reference rotational axis is parallel to and spaced laterally from the second reference rotational axis.
14. A system for generating calibration data for a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first rotary axis rotatable about a first reference rotational axis, and a controller for controlling the machine axes, wherein the system comprises: an electronic location sensor for sensing and recording the location of a point on the first rotary axis which is spaced from the first reference rotational axis at a plurality of rotational positions of the first rotary axis; and an electronic processor configured to calculate from the recorded rotational positions a best fit plane with respect to the plurality of recorded rotational positions, and the location of the centre point of a best fit circle lying in the best fit plane with respect to the plurality of recorded rotational positions and a vector normal to the best fit plane, and generate calibration data therefrom for use in calibrating the machine tool.
15. A system for generating calibration data for a multi-axis machine tool, the machine tool comprising a plurality of machine axes, at least one of which is a first linear axis, and a controller for controlling the machine axes, wherein the system comprises: an electronic location sensor for sensing and recording the location of a point on the first linear axis at a plurality of positions of the first linear axis; and an electronic processor configured to calculate from the recorded positions the location of a point on a best fit line with respect to the plurality of recorded positions, and a vector in the direction of the best fit line, and generate calibration data therefrom for use in calibrating the machine tool.
16. A multi-axis machine tool comprising a plurality of machine axes, a controller for controlling the machine axes, and an electronic processor configured to receive the calibration data generated by a system of claim 14 or claim 15, and calibrate the controller with reference to the calibration data.
17. A multi-axis machine tool including a system of claim 14 or claim 15, wherein the machine tool is arranged to carry out a method of any of claims 1 to 13.
18. A computer-readable medium storing computer executable instructions for causing a machine tool of claim 17 to perform a method of any of claims 1 to 13.
19. An electrical carrier signal carrying computer executable instructions for causing a machine tool of claim 17 to perform a method of any of claims 1 to 13.