GB2505558A

GB2505558A - Calibrating a portable parallel kinematic machine

Info

Publication number: GB2505558A
Application number: GB201312449A
Authority: GB
Inventors: Olarra Urberuaga; Lopez Garcia; Azkorbebeitia Ezenarro
Original assignee: Fundacion Tekniker
Current assignee: Fundacion Tekniker
Priority date: 2012-07-24
Filing date: 2013-07-11
Publication date: 2014-03-05
Anticipated expiration: 2033-07-11
Also published as: GB2505558B; GB201312449D0; ES2448215B1; ES2448215A2; ES2448215R1

Abstract

Calibrating a portable parallel kinematic machine A method for calibrating a portable parallel kinematic machine comprises the steps of: a. placing positioning means (8, 9 figs. 3 & 4), which comprise at least three housings (8', 9' figs. 3 & 4), on a workpiece to be machined, b. positioning a linear measurement device 7 between each one of the housings (8', 9' figs. 3 & 4) of the positioning means (8, 9 figs. 3 & 4) and a bearing support 10 of the machine, c. increasing the length of one leg 3 of the machine by a small distance, d. measuring the elongation of each of the linear measurement devices 7, e. repeating steps c) and d) for all of the legs 3 of the machine, f. determining an approximate position of the machine's fixed ball and socket joints 5 on the basis of the measurements obtained in step e), g. calculating the maximum displacements for each one of the legs 3, h. increasing the length of one leg 3 of the machine by the length calculated in step g, i. measuring the elongation of each one of the linear measurement devices 7, j. repeating steps h) and i) for all of the legs 3 of the machine, k. determining the position of the machine's fixed ball and socket joints 5 on the basis of the measurements obtained in step j. The portable parallel kinematic machine comprises a movable platform or support 1 carrying a tool 2 for machining the workpiece and a series of legs 3 each joined at one end to the support 1 by a ball and socket joint 4 and each joined at the other end by a ball and sockets joint 5 to one of a number of support stands 6 that can rest on and be fastened to the workpiece. The linear measurement device 7 may be a Double Ball Bar (DBB).

Description

Method for Calibrating a Portable Parallel Kinematic Machines

DESCRIPTION

TECHNICAL FIELD

The present invention relates to the field of methods for calibrating parallel kinematic machines and more specifically portable parallel kinematic machines where said machine is placed on the workpiece to be processed.

BACKGROUND OF THE INVENTION

Currently the use of general purpose machining centres is widespread, but there are also special machines, with a specific purpose for execution of a specific task, for example the maintenance and repair operations of large and complex installations (aerospace, power, maritime). Currently, small general purpose portable machines are being developed which are capable of carrying out a large number of machining operations on this type of installation. These are machines that are carried to the workpiece, as opposed to the concept of carrying the workpiece to the machine. In this way, enormous savings are made on the cost of disassembly/assembly, handling, and machining at large machining centres.

A machine of this type is disclosed in patent document US2O1 1/01 94906A1. This relates to a parallel kinematic configuration, similar to a Stewart-Gough platform (in other words, a moveable support or platform which carries the tool and a series of legs joined at one end to the moveable platform by means of moveable ball and socket joints and at the other end to a fixed base by means of fixed ball and socket joints), wherein the fixed platform or base has been entirely eliminated. In this way, each leg of the machine can be positioned individually on the surface of the free form workpieces. The legs are secured to the workpiece, for example, by means of magnets. Hereinafter, this configuration will be referred to as a portable hexapod As in the case of any machine that needs to generate a particular form in a workpiece by means of any process, for example milling, it must be possible to position the portable machine on the workpiece to be processed with a good level of precision.

The positioning of the tool on a parallel kinematic machine depends on several geometric parameters. These parameters are listed below for the case of a Stewart-Gough type platform: the position of the fixed ball and socket joints, the length of each of the arms, the position of the moveable ball and socket joints on the moveable platform and the position of the tool on said moveable platform.

In the case of the portable hexapod described above, greater versatility of use is provided by leaving the fixed ball and socket joints free (by removing the fixed base), for the purpose of adapting to the possibilities offered by the workpiece to be processed. However, this freedom requires that once the hexapod has been secured to the workpiece (by means of the fixed ball and socket joints), the position of said fixed ball and socket joints must be identified.

It is sufficient to know the position of the ball and socket joints in relation to each other. After determining the positions of the fixed ball and socket joints, the hexapod can be positioned with precision and generate arbitrary trajectories such as lines, circles or spirals.

In the case of a "normal" hexapod, the positions of the fixed ball and socket joints, the moveable ball and socket joints and the tool on the moveable platform tend to be "constant" parameters. In order to carry out movements with precision, said parameters are usually identified by means of calibration.

Generally, calibration is used to determine all the geometric parameters listed above.

In contrast with these methodologies, in order to enable precise movement of a portable hexapod once secured, it is sufficient to determine the relative position of the fixed ball and socket joints, the remaining parameters are known by other means. For example, by means of previous calibrations, or by means of a direct measurement, which may be possible using a Coordinate-Measuring Machine given the reduced dimensions of the portable machine.

However, determination of the position of said fixed ball and socket joints must be very robust, due to the fact that the configuration in which the user decides to secure the portable hexapod can vary enormously, herein lies the machine's versatility In contrast with this need, the calibration procedures of "normal" parallel kinematic machines are usually prepared to determine only small errors in relation to a theoretical design.

On a separate note, all machines need to resolve the problem of knowing their position relative to the workpiece that they must process.

In conventional machines, this search for references can be carried out using details in almost any part of the workpiece, which in some way simplifies the centring of the workpiece on the machine.

However, a portable machine only reaches a small zone of the workpiece, the zone on which it must work. This fact makes it considerably difficult to search for references on the basis of which the machine's position in relation to the workpiece can be known.

During the last few years, different calibration procedures for parallel kinematic machines have been developed. The calibration always requires redundant measurements additional to the minimum ones necessary for positioning the machine. Occasionally, the machines have been equipped with redundant measuring systems, but the most common practice is to use measuring systems that are external to the machine.

As an external measuring device, the so-called Double Ball Bar (DBB) has been used for example, which is a linear measurement device provided with ball and socket joints at both ends and which provides the measurement of the relative displacement between both ends. The ball and socket joints are normally implemented by means of balls that rotate inside a housing with three points of contact. The measurement of the distance can be carried out in different ways: LVDTs can be used, linear rulers or laser interferometers. One example of a parallel kinematic machine using DBBs is described in patent document US2006/0254364 Al.

The calibration procedures that use the DBB make use of tools or parts which provide housings for one of the ends of the DBB. The position of these housings is usually known, in other words, has been measured externally, for example, in a coordinates-measuring machine. This type of tools is not appropriate for the portable hexapod's application, due to the fact that it conditions to a great extent the possibilities of using it on workpieces where it is complicated to position the tool.

Therefore, it is necessary to develop methods for calibrating and taking down references of the workpiece in situ for portable hexapods.

DESCRIPTION OF THE INVENTION

The present invention relates to a method for calibrating a portable parallel kinematic machine which comprises a moveable platform or support which carries a tool and a series of legs joined by one of their ends to the aforesaid moveable support by means of ball and socket joints and by their other end, by means of fixed ball and socket joints, to supporting stands that can rest on and be secured to a workpiece to be machined. The method comprises the steps of: a-placing positioning means, which comprise at least three housings, on the workpiece to be machined, b-positioning a linear measurement device between each one of the housings of the positioning means and a support bearing of the machine, c-increasing the length of one leg of the machine by a distance in which no collisions occur between the moveable elements of the machine and between the machine and the workpiece (this distance is a very small distance in respect of the maximum stroke of the legs and may be for example 1mm or less depending on the size of the machine), d-measuring the elongation of each one of the linear measurement devices, e-repeating operations c) and d) for all legs of the machine, f-determining an approximate position of the machine's fixed ball and socket joints on the basis of the measurements obtained in step e), g-calculating maximum displacements for each of the legs (these displacements are limited by interferences between the DBB and the legs or moveable platform, displacement limits of the DBB, displacement limits of the machine's legs, limits on the angular strokes of the machine's ball and socket joints), h-increasing the length of one leg of the machine by the length caicuiated in step g), i-measuring the elongation of each of the linear measurement devices, repeating steps h) and i) for all of the legs of the machine, k-determining the position of the fixed ball and socket joints of the machine on the basis of the measurements obtained in step j).

Steps c), d), e) and f) are necessary in order to carry out step g), in other words maximisation of the machine's displacements during the calibration By maximising said displacements, the step g) parameters can be identified with less uncertainty.

The linear measurement device may comprise an extensible arm and two end supports, for example two balls. The linear measurement device may be a DBB.

The machine's support bearing may comprise bearings for the end supports of the linear measurement devices in such a way that they form a spherical joint, with the position of said bearings being known in respect of the machine's moveable ball and socket joints.

The positioning means may comprise a positioning tool that can rest on the workpiece, the aforesaid tool comprising three housings to house the ends of the linear measurement devices in such a way that they form a spherical joint (between each housing and end of the measurement device), the three housings being disposed in the tool at known distances. Obviously, the dimensions of the tool are known and also the distances between the three housings.

Alternatively and preferably the positioning means may comprise four independent tools or elements, each one of which comprises a housing for one end of a linear measurement device in such a way they form a spherical ball and socket joint (between each housing and each end of a measurement device). In this case, as the distance and position between the different tools is not known, it is necessary to use four tools so that the solution to the calculation formula (described later) has a single solution.

The method of the invention may comprise calculation of the position of the fIxed ball and socket joints in the reference system of the workpiece to be machined. To this effect, the positioning means may have reference elements in order to reference their position in respect of the workpiece to be machined (in respect of known details of the workpiece). These reference elements may be for example centring pins that are housed in determined points of the workpiece or may be flat faces that rest against details of the workpiece (for example walls or corners of the workpiece).

According to the method of the invention, the position of the fixed ball and socket joints is related to the elongation of each one of the linear measurement devices according to the following formula: {dBB} = f({pMAQ}. [jiBE}. {cIL}) where {dBB} is the elongation of the linear measurement devices {dL} is the elongation of the arms of the portable hexapod {pMAQ} are the set of geometric parameters of the machine {pF} are the positions of the fixed ball and socket joints {pM} are the positions of the moveable ball and socket joints {pBB} is the set of geometric parameters of the linear measurement devices {pAF} are the positions of the fixed housings of the linear measurement devices (pAM) are the positions of the moveable housings of the linear measurement devices.

In accordance with the calibration method of the invention, determination of the position of the fixed ball and socket joints of steps f) and k) comprises the determination of the {pF} values according to the following equations: 1 {ApF} {ciBB}= [BSMk{AF} (dBB},IJ,J -{dBB},,, = [BSM]j{ApF} 1{APAF} where the matrix [BSM}, is the Jacobian of previous function f around the positions where the measurements are taken in relation to the parameters to be estimated.

The machine's calibration is performed on the basis of the tool's positioning error measurements. These positioning errors depend on the machine's geometric parameters. To correct them, the mathematical relationship must be found that makes it possible to evaluate the contribution of the error in each parameter to the positioning error of the tool.

In this way, by taking sufficient measurements, it is possible to write a system of equations that allows the errors of identification of each parameter to be obtained.

f measurement4 = p 4 PararneierE,ro, = cahbrationMatgrix -ParwnererError ineacurement / . ParameterError ParameterErrorfi Development of the calibration matrices The calibration matrices make it possible to relate the error in the positioning of the head to the errors of each one of the parameters on which said positioning depends.

Due to the fact that the measurements will be taken with the Ball Bar, the calibration matrices must express the elongation of the Ball Bar, due to a change in the geometric parameters of the machine.

[dParam 1 dBB=[p1... ii

This section develops the analytical formulae that allow the calibration matrices to be obtained.

The influence of the following parameters has been studied: -Position of the fixed ball and socket joints -Position of the moveable ball and socket joints -Offset of the legs Matrix S This is the Jacobian of the lengths of the legs in respect of the position of the tool. To obtain it, equations 1 and 2 are used as a starting point. By distinguishing in respect of the tool's position and orientation, one arrives at: dx 1 0 0 In. lu-i li-il dy di [XJX/?Ii yf-yni1 zJ._Zfl211 0 0!jV dz L 1, 1, j aaj' afll'l yI'l cia 0 0 1 j.v, JVJ dJ3 As can be seen, the relationship between the increase in the length of a leg and the displacement of the tool is a function of the lafter's position and orientation.

This expression must be evaluated for each leg. Resulting in: d11=[51].(dX} *=1 6 Which regrouped and expressed in matrix form gives rise to the sought expression: {ni)s{dr} Ec.

With a view to performing the calibration using the Ball Bar, it is only relevant to know the effect of the variation in the length of the legs on the position of the tool, not on its orientation, such that with {dx}=r' -{dL}

B

reference Slxyz will be given to the sub-matrix of S' which only provides the degrees of freedom of displacement, for a determined increase in the lengths of the legs. Namely, 1x1 civf=slxvz.{dL} Eq.

Matrix M Matrix M relates the increase in the length of each leg due to the increase of the machine's geometric parameters. Next, the different parameters considered are analysed one by one.

> Position of the fixed ball and socket joints Starting out with the expressions shown in equations 1 and 2, after distinguishing in respect of the position of the fixed ball and socket joint, the following is obtained dxf ____ yf1--yrn, __ Expressed more compactly as {dL}=A#f.{anz} > Position of the moveable ball and socket joints Starting out with the same expressions as in the previous case, this time, distinguishing in respect of the position of the moveable ball and socket joint c/u, 1 yf)4111 ZLz1fl]R(fl){(JVf or equally, {dL}=M -{suvw} > OFFSET of the legs The increase in the offset of the legs implies the same increase in their length, therefore, dl, = c/OFFSET3 {O'L} = -{d0FFSET} By grouping the effect of the increase of all the parameters on the length of a leg, one obtains, IthflZl {dL) = [Al1 Mm Mo;FSRTf J{ dUVW = M -{dFaram} tdUIPSETJ Eq.

This is the sought expression.

Matrix B Matrix B relates the increase in the Ball Bar's measurement to the displacements sustained by the tool.

To this effect, a similar expression to the one used in the analysis of the machine leg extension is used as a point of departure = (x-x22)' ÷(y-y23)2 ÷(z-z)2 where fl* the length measured by the Ball Bar Ix -1" lz L: the tool's position xsBB yj8sJ-Zths F the position of the Ball Bar support Distinguishing in respect of the position of the tool, the following is obtained [d [dx

_____ YYRB ___

z cL Eq.

Complete calibration matrices To conclude the development of the calibration matrices shown in this section, it remains for all of them to be integrated into the same expression.

The machine's control calculates the length of the legs in a reference position and uses this length as the basis for calculation of the lengths in the rest of the positions. By modifying the parameters, the lengths calculated in this reference position change and are carried to the calculation of all the rest of the positions-Consequently, the expression that relates the increase in the length of the measurement taken by the Ball Bar and the increase in the different parameters is provided by the following expression: --(slxyz-MI -Slxyz. ). (dRaram) Eq. 6 where

d11 D is the elongation of the Ball Bar due to when the tool is at point P1 and the Ball Bar support is at point sBB.

L Matrix B evaluated for the preceding points SiryzM -L Matrices S and M evaluated at point P1 L Matrices S and M evaluated at the reference position This is the expression that allows us to calculate the calibration matrices.

BRIEF DESCRIPTION OF THE DRAWINGS

To complement the description and with a view to contributing to a better understanding of the characteristics of the invention, according to a preferred example of a practical embodiment thereof, a set of drawings is attached as an integral part of the description, which by way of illustration and not limitation, represent the following: Figure lisa flow chart of the method of the invention.

Figure 2 represents two perspectives of a portable hexapod.

Figures 3A, 3B and 3C represent three embodiments of an individual positioning tool and the corresponding DBB.

Figures 4A, 4B, 4C represent three views of a positioning tool that comprises three housings.

Figure 4D represents a positioning tool that comprises three housings and three DBBs.

Figure 5 represents a portable hexapod with a positioning tool that comprises three housings and the corresponding DBBs.

PREFERRED EMBODIMENT OF THE INVENTION

Figure 2 includes a representation of a portable hexapod on which the calibration method of the present invention can be applied.

The portable hexapod or parallel kinematic machine comprises a moveable platform or support (1) which carries a toot (2) and a series of legs (3) joined by one of their ends to the aforesaid moveable support by means of moveable ball and socket joints (4) and by their other end, by means of fixed ball and socket joints (5), to support stands (6) that can rest on and be secured to a workpiece to be machined, not represented.

In figures 3A, 3B, 3C, 4D and 5 linear measurement devices (7) have been represented, which may comprise one extensible arm (7') and two end supports (7"), for example two balls and which will be used in the calibration of the portable hexapod in accordance with the method of the invention. The represented measurement devices are also known as double ball bars (DBBs).

Figure 5 shows a bearing support (10) of the machine which may comprise bearings for the end supports (7") of the linear measurement devices (7) in such a way that they form a spherical ball and socket joint. As can be seen from the aforesaid figure, the position of said supports is known in respect of the machine's moveable ball and socket joints (4).

In figures 4A, 4B, 4C and 4D positioning means (8,9) have been represented, which consist of a positioning tool (8) that can rest on the workpiece (not shown), said tool comprising three housings (8') to house the end supports (7") of the linear measurement devices (7) in such a way that they form a spherical ball and socket joint (between each housing and the end of the measurement device), the three housings (8') being disposed in the tool (8) at known distances. Obviously, the dimensions of the tool (8) are known in addition to the distances between the three housings (8').

Figures 3A, 3B and 30 represent an alternative and preferred solution for the positioning means (8, 9) which comprises four independent tools or elements (9), each one of which comprises a housing (9') for one end support (7") of a linear measurement device (7) in such a way that they form a spherical ball and socket joint (between each housing and each end of a measurement device).

The positioning means (8, 9) may have reference elements (11, 11') to reference their position in respect of known details of the workpiece. In figures 3B and 4B a centring pin (11) can be seen for example, provided in the lower face (in contact with the workpiece) of the positioning means (8, 9) which will be housed in some hole of the workpiece having a known position The reference elements can also be flat faces (11') of the positioning means (8, 9) which rest against details of the workpiece (for example walls or corners of the workpiece). These flat faces (11) can be seen for example in figure 3A.

The method comprises, as described schematically in the diagram of figure 1: Placing of the bases.

The calibration process determines both the positions of the fixed ball and socket joints (5) of the portable hexapod as well as the positions of the housings (8', 9') of the DBB (7) used during the calibration with a similar uncertainty.

Knowing the positions of the housings (8', 9') of the DBB (7) can be used to determine references in relation to the workpiece on which the portable hexapod has been placed. To do this, it is proposed to use housings (8', 9') like the ones represented in figures 3A, 3B and 4B, provided with reference elements (11,l 1") which allow them to be situated in a manner that is known in relation to small details of the workpiece.

As mentioned, the calibration process determines both the positions of the fixed ball and socket joints (5) of the portable hexapod as well as the positions of the housings (8', 9') of the DBBs (7) used during calibration with similar uncertainty.

The calibration makes use of at least four DBBs (7) simultaneously, or of one DBB or two DBBs (7), provided with various details that allow them to be positioned in reiation to detaiis of the workpiece to be machined as mentioned previously.

The securing of the positioning tools (8, 9) to the workpiece can be carried out by different means. For example, magnetic or adhesive.

Coarse calibration and fine calibration The stages of calibration consist of executing a series of movements and recording measurements and subsequently, estimating geometric parameters.

These stages are described below.

Coarse calibration does not require movements to be calculated. Simply, very small predetermined movements are carried out in order to avoid collisions.

During fine calibration, with a view to maximising said movements, the displacement limits of each leg (3) of the hexapod is calculated with the following conditioning factors: a. Stroke limits of the legs (3) of the portable hexapod.

b. Rotation limits of the ball and socket joints of the legs (3) of the

portable hexapod.

c. Stroke limits of the DBBs (7).

d. Collisions between parts of the portable hexapod.

e. Collisions between the DBB (7) and parts of the portable hexapod.

Execution of movements Measurement of the displacements of each DBB (7) in a set of positions of the portable hexapod.

These movements are carried out in two stages of the calibration process.

During coarse calibration, the movements performed are very small in relation to the machine's work volume, in such a way that there is no risk of collision.

During fine calibration, the movements are more far-reaching, but the collisions are avoided due to the fact that the coarse calibration result allows the limits of said movements to be determined with certainty.

Estimation of geometric parameters The geometric parameters that are estimated are the positions of the fixed ball and socket joints (5) and the positions of the housings (8', 9') of the DBBs (7).

Next is an introduction of the variables that are used in the calibration {dBB} Li elongation of the DBBs {dL} Li elongation of the arms of the portable hexapod {pMAQ}L set of geometric parameters of the machine {pF} Li positions of the fixed ball and socket joints {pM} Li positions of the moveable ball and socket joints {pBB} Li set of geometric parameters of the DBBs {pAF} Lii positions of the fixed housings of the DBBs {pAM} positions of the moveable housings of the DBBs Of these variables, all are assumed to be known except for {pF} and {pAF} All other parameters have been obtained through direct measurement, for example using a coordinates-measuring machine, a relatively practical procedure due to the reduced size of the portable hexapod.

With each displacement of the portable hexapod, each one of the DBBs (7) sustains a determined elongation, which may be stated as follows: (dBB} = f({pAL4 Q}. {pBB}. (c/i}) This function is non-linear in relation to all the variables.

The self-calibration seeks to estimate the unknown parameters, {pF}, based on carrying out some known movements of the arm, {dL}, measuring the resulting elongation of the DBBs, {dBB}.

To do this, the previous f non linear relationship is aligned around a position of the portable hexapod and an assumed disposition of the DBBs (7).

The calibration is reduced to solving the following inverse problem: {dBB}=[BSM1 {ApF} {pAF} {dBB}.SUIS -{ dBB} = [BSM I 1{uhuj 1 p44F}J Matrix [BSMI, is the Jacobian of previous function f around the positions where the measurements are taken in relation to the parameters to be estimated.

Transformation of coordinates Once the position of the housings (8', 9') of the DBBs (7) are known following calibration, it is possible to transfer the reference system of the portable hexapod to a coordinates system linked to the workpiece.

In more detail, the phases of the method would be: A-A phase of placing the bases or positioning means (8, 9) which comprises: a-placing positioning means (8, 9), which comprise at least three housings (8', 9'), on the workpiece to be machined (not represented), b-positioning a linear measurement device (7) between each one of the housings (8',9') of the positioning means (8,9) and a bearing support of the machine, B.-A coarse calibration phase, which is repeated for the six legs of the portable hexapod which comprises executing movements that comprise: c-increasing the length of one leg (3) of the machine by a distance wherein no collisions occur between moveable elements of the machine and between the machine and the workpiece (a very small distance in respect of the machine's work volume, for example 1mm), d-measuring the elongation of each one of the linear measurement devices (7) and making a (coarse) estimate of geometric parameters, which comprises determining an approximate position of the machine's fixed ball and socket joints (5) on the basis of the measurements obtained in step e), C.-A fine calibration which comprises a calculation of movements (of greater displacements) which consists of calculating the maximum displacements, for each one of the legs (3) and an execution of movements which comprises: h-increasing the length of one leg (3) of the machine by the length calculated in step g), i-measuring the elongation of each one of the linear measurement devices (7) j-repeating steps h) and i) for all of the machine's legs (3) and estimating geometric parameters, which comprises determining the position (in precise terms) of the machine's fixed ball and socket joints (5) based on the measurements obtained in step j), D.-A transformation of the coordinates system which comprises calculating the position of the fixed ball and socket joints (5) in the reference system of the workpiece to be machined.

In this text, the word "comprises" and its variants (such as "comprising", etc.,) are not to be interpreted in an excluding manner, in other words, they do not exclude the possibility of what is described including other elements, steps, etc. At the same time, the invention is not limited to the specific embodiments described but also encompasses, for example, variants that could be embodied by the average person skilled in the art (for example, with regard to the choice of materials, dimensions, components, configuration, etc.), within the scope of what is inferred from the claims.