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Title:
PARALLEL-KINEMATICAL MACHINE WITH AN ACTIVE MEASURING SYSTEM
Document Type and Number:
WIPO Patent Application WO/2006/062466
Kind Code:
A1
Abstract:
A parallel-kinematical machine (1) which has at least three setting device (4.1, 4.2, 4.3) which can be lengthened and shortened individually in their longitudinal direction, wherein each setting device (4.1, 4.2, 4.3) is connected to a positioning head (11) via a first joint, wherein each setting device (4.1, 4.2, 4.3) is connected to a machine base (2) via a universal joint (3.1, 3.2, 3.3), and wherein the positioning head (11) is movable within a working area in response to manoeuvring of the setting devices (4.1, 4.2, 4.3), wherein at least two reinforcing beams (5.1, 5.2, 5.2.1, 5.2.2) are each connected to the positioning head (11) viaa respective beam rotation bearing (10.1, 10.2), wherein each of said beam rotation bearings (10.1, 10.2) has only one degree of freedom, and wherein each of said beam rotation bearings is provided with two angle indicators (5.1a, 5.1b, 5.2a, 5.2b) which are each connected to the beam rotation bearing (10.1, 10.2) so that the measuring points of two angle indicators (5.1a, 5.1b) will each be situated on a respective side of the first beam rotation bearing (10.1) and so that the measuring points of two angle indicators (5.2a, 5.2b) will each be situated on a respective side of the second beam rotation bearing (10.2) so that the angle indicators will firstly register an angle 1, 2, 3, 4 between the positioning head (11) and respective reinforcing beams (5.1, 5.2) and secondly register a first angular difference 1, where 1= 2- 1, between the measuring points of the two angle indicators (5.1a, 5.1b) of the first beam rotation bearing (10.1) and also a second angular difference 2, where 2= 4- 3, between the measuring points of two angle indicators (5.2a, 5.2b) of the second beam rotation bearing (10.2) such as to form an active measuring system (AMS), wherein in the case of a loaded machine each deviation in the value of the angles 1, 2, 3, 4, from a nominal angle value in the case ofa non-loaded machine is adapted to be corrected by manoeuvring the setting devices (4.1, 4.2, 4.3) to a changed working positioning of the positioning head (11).

Inventors:
NEUMANN KARL-ERIK (SE)
Application Number:
PCT/SE2005/001836
Publication Date:
June 15, 2006
Filing Date:
December 05, 2005
Export Citation:
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Assignee:
EXECHON AB (SE)
NEUMANN KARL-ERIK (SE)
International Classes:
B25J17/02; B23Q1/54; B23Q17/22; B25J18/00; G01B5/24; B25J
Foreign References:
US4790718A1988-12-13
US20040027139A12004-02-12
US5616917A1997-04-01
US4329111A1982-05-11
US5189797A1993-03-02
US6587802B12003-07-01
Attorney, Agent or Firm:
Emtedal, Artur (BOX 6107, Stockholm, SE)
Download PDF:
Claims:
CLAIMS
1. A parallelkinematical machine (1) which has at least three setting device (4.1 ,4.2,4.3) which can be lengthened and shortened individually in their longitudinal direction, wherein each setting device (4.1, 4.2, 4.3) is connected to a positioning head (11) via a first joint, wherein each setting device (4.1, 4.2, 4.3) is connected to a machine base (2) via a universal joint (3.1 , 3.2, 3.3), and wherein the positioning head (11) is movable within a working area in response to manoeuvring of the setting devices (4.1 , 4.2, 4.3), characterized in that at least two reinforcing beams (5.1 , 5.2, 5.2.1, 5.2.2) are each connected to the positioning head (11) via a respective beam rotation bearing (10.1 , 10.2), wherein each of said beam rotation bearings (10.1 , 10.2) has only one degree of freedom, and wherein each of said beam rotation bearings is provided with two angle indicators (5.1a, 5.1b, 5.2a, 5.2b) which are each connected to the beam rotation bearing (10.1 , 10.2) so that the measuring points of two angle indicators (5.1 a, 5.1 b) will each be situated on a respective side of the first beam rotation bearing (10.1) and so that the measuring points of two angle indicators (5.2a, 5.2b) wilf each be situated on a respective side of the second beam rotation bearing (10.2) so that the angle indicators will firstly register an angle αi, 0:2, C63, α4 between the positioning head (11) and respective reinforcing beams (5.1 , 5.2) and secondly register a first angular difference βi, where βi=α2 αi, between the measuring points of the two angle indicators (5.1a, 5.1b) of the first beam rotation bearing (10.1) and also a second angular difference β2, where β2=α4 α3,between the measuring points of two angle indicators (5.2a, 5.2b) of the second beam rotation bearing (10.2) such as to form an active measuring system (AMS), wherein in the case of a loaded machine each deviation in the value of the angles αi, ct2, 013, 04, from a nominal angle value in the case of a nonloaded machine is adapted to be corrected by manoeuvring the setting devices (4.1 , 4.2, 4.3) to a changed working positioning of the positioning head (11).
2. A parallelkinematical machine according to claim 1 , characterized in that the angle indicators (5.1a, 5.1b) of the first beam rotation bearing (10.1) are each placed on a respective side of the first reinforcing beam (5.1) and in that the angle indicators (5.2a, 5.2b) of the second beam rotation bearing (10.2) are each placed on a respective side of the reinforcing beam (5.2, 5.2.1 , 5.2.2).
3. A parallelkinematical machine according to any one of claims 12, characterized in that the measuring points of the angle indicators (5.1 a, 5.1 b, 5.2a, 5.2b) are placed in direct connection with the side of a respective reinforcing beam (5.1, 5.2).
4. A parallelkinematical machine according to any one of claims 13, characterized in that each reinforcing beam (5.1 , 5.2, 5.2.1 , 5.2.2) is arranged to slide transversely in a beam bearing (17.1, 17.2.1, 17.2.2) mounted in the machine base (2) when one or more of the setting devices (4.1 , 4.2, 4.3) is lengthened or shortened; and in that each beam bearing (17.1 , 17.2.1, 17.2.2) is connected to the base (2) via a beamuniversal joint (BU1 , BU2); and in that the beam bearing (17.2.1 , 17.2.2) of at least one reinforcing beam (5.2, 5.2.1 , 5.2.2) is rotatable about an axis parallel with the longitudinal axis of the reinforcing beam (5.2., 5.2.1 , 5.2.2).
5. 5 A parallelkinematical machine according to claim 4, characterized in that at least one beam rotation bearing (10.1 , 10.2) consists of the first joint.
6. A parallelkinematical machine according to claim 5, characterized in that at least one beamuniversal joint (BU1 , BU2) consists of a universal joint (3.1 , 3.2, 3.3).
7. A parallelkinematical machine according to any one of claims 16, characterized in that each reinforcing beam (5.1 , 5.2, 5.2.1 , 5.2.2) has in a first direction a flexural rigidity that greatly exceeds its flexural rigidity in a direction perpendicular to said first direction.
8. A parallelkinematical machine according to claim 7, characterized in that each reinforcing beam (5.1 , 5.2, 5.2.1, 5.2.2) has a generally rectangular cross sectional shape.
9. A parallelkinematical machine according to any one of claims 18, characterized in that each angle indicator (5.1a, 5.1b, 5.2a, 5.2b) is placed coaxially with the bearing axis of a respective beam rotation bearing (10.1 , 10.2).
10. A parallelkinematical machine according to any one of claims 19, characterized in that the machine includes three setting devices (4.1 , 4.2, 4.3) each of which is permanently connected to a respective reinforcing beam (5.1, 5.2, 5.2.1, 5.2.2, 5.3) at said first joint at the absence of an intermediate joint.
11. A parallelkinematical machine according to claim 110, characterized in that one of the setting devices (4.2) is provided with an additional reinforcing beam (5.2.1, 5.2.2).
12. A parallelkinematical machine according to any one of claims 111 , characterized in that the beam rotation bearings (10.1 , 10.2) and their angle indicators (5.1a, 5.1b, 5.2a, 5.2b) of at least two reinforcing beams (5.1, 5.2, 5.2.1, 5.2.2) have bearing axles which are orientated perpendicular to one another.
13. A parallelkinematical machine according to claim 12, characterized in that the beam rotation bearings (10.1 , 10.3) and their angle indicators (5.1a, 5.1b, 52a, 5.2b) of at least two reinforcing beams (5.1, 5.3) have bearing axles which are parallel with one another.
Description:
PARALLEL-KINEMATICAL MACHINE WITH AN ACTIVE MEASURING SYSTEM

TECHNICAL FIELD

The present invention relates to the field of machine tools and active measuring systems for such machine tools and then particularly to robots intended for work in the industry.

BACKGROUND OF THE INVENTION

U.S. Patent Specification U.S. 4,732,525 (corresponding to SE 452279) teaches a parallel-kinematical machine in the form of a robot of conventional design. The robot includes three setting devices, which can be lengthened and shortened, in combination with a central tube that carries a positioning head at one end thereof. The central tube is also mounted for movement in its axial direction through the medium of a central bearing in the form of a universal joint, which provides three degrees of freedom in relation to a machine base. Each setting device is connected to the positioning head via a joint that provides three degrees of freedom and. also to the machine base via a joint that has two degrees of freedom, so as to enable the positioning head to move within a limited working range. The setting devices take-up solely tension forces and pressure forces, whereas the central tube takes-up all rotational forces (torque) and bending stresses from loads on the positioning head.

The accuracy of the movements of such a machine depends greatly on its rigidity, which, in turn, depends on the number of bearings/degrees of freedom available and also on the ability of the component materials to minimise torsional stresses and bending stresses in critical directions. For instance, it can be mentioned that large lateral forces in respect of the positioning head result in a tendency of the central tube to bend and/or to be rotated between its gyro bearing in the machine base and its connection with the setting devices.

The rigidity of the described conventional machine thus depends, among other things, on the design of the connection of the setting devices with the positioning head and also on the intrinsic rigidity of the central tube per se. In order to enhance the rigidity of such a conventional machine it is necessary, primarily, to apply stricter tolerances in each joint and, secondarily, to use a more robust central tube therewith adding a weight increase.

The central tube can be made more robust, by using a stiffer material and/or by increasing the thickness of the tube and/or increasing its diameter.

All such improvements in machine rigidity, however, result in higher costs, heavier machines and a reduction in the working area within which the positioning head can be manoeuvred.

With the intention of enhancing the accuracy and the precision of this known machine the machine has been equipped with a control system as taught in patent specification US 6,301,525 (which finds correspondence in SE 512338). However, the sensors of this control system are placed in connection with or in the close vicinity of the machine base, meaning that the system is unable to correct for stresses that cause deformation, down-bending and torsion in the region between the machine base and the positioning head.

Similar parallel-kinematical machines are also known, for instance, from UK Patent Application 8319708 (2,143,498), U.S. 4,569,627 and NO 148216.

However, none of these known machines has a basic construction that permits achievement of the level of rigidity and therewith the level of accuracy to which modern machines aim.

OBJECT OF THE INVENTION

The object of the present invention is to provide for a parallel-kinematical machine an active measuring system that will correct the position of the positioning head of

the machine in response to changes caused by external mechanical and thermal influences.

A further object is to provide such a machine with an active measuring system of the kind that includes a beam rotation bearing which has only one degree of freedom in connection with the positioning head.

It is also an aim of the invention to provide with the aid of such an active measuring system a parallel-kinematical machine that is more rigid and therewith more accurate than earlier known parallel-kinematical machines, which combined with a simple construction contributes towards achieving lower manufacturing costs.

DISCLOSURE OF THE INVENTION

These objects are achieved by means of the present invention as defined in the accompanying independent Claim. Suitable further embodiments of the invention will be apparent from the accompanying dependent Claims.

The invention relates to a parallel-kinematical machine that includes at least three setting devices which can be lengthened and shortened individually in their longitudinal direction and each of which is connected to a positioning head via a first joint. Each setting device is also connected to a machine base via a suitable universal joint, therewith enabling the positioning head to move within a working area when manoeuvring the setting devise. Each of at least two reinforcing beams is connected to the positioning head via a respective beam rotation bearing, each having only one degree of freedom. Each of these beam rotation bearings includes two angle indicators which are each connected to the beam rotation bearing such that the measuring points of the two angle indicators will be located on a respective side of the first beam rotation bearing and so that the measuring points of two angle indicators will be placed on a respective side of the second beam rotation bearing so that the angle indicators will firstly register an angle αi, α 2 , α 3 , α 4 between the positioning head and respective reinforcing beams and secondly

record, on the one hand, a first angular difference, β-i, where βi=α 2 - α-i, between the measuring points of the two angle indicators of the first beam rotation bearing and, on the other hand, a second angular difference β 2 , where β 2 4 - 01 3 , between the measuring points of the two angle indicators of the second beam rotation bearing such as to form an active measuring system AMS. When the machine is loaded, each deviation in the value of the angles α-i, 0: 2 , 00 3 , o^from a nominal angular value in the case of a non-loaded machine is corrected by manoeuvring the setting devices in a manner to change the working position of the positioning head.

In the case of one embodiment of the invention, the angle indicators of the first beam rotation bearing are each placed on a respective side of the first reinforcing beam and the angle indicators of the second beam rotation bearing are each placed on a respective side of the second reinforcing beam.

In the case of a further embodiment of the invention, the measuring points of the angle indicators are placed in direct connection with one side of a respective reinforcing beam.

Each reinforcing beam is arranged to slide transversely in a base-mounted beam bearing in response to lengthening or shortening one ore more setting devices. Moreover, each beam bearing is connected to the machine base via a beam universal joint and the beam bearing of at least one reinforcing beam is pivotal about an axis that extends parallel with the longitudinal axis of the reinforcing beam.

This concept gives rise to a number of conceivable fundamental forms of the relationship between the machine base, the setting devices, the reinforcing beams and the positioning head with regard to the mutual relationship of these components on the one hand and mounting of these components in the machine base and the positioning head on the other hand.

The exemplifying embodiment described in detail hereinafter comprises three setting devices each being connected to a respective reinforcing beam, where the second setting device is also provided with an additional reinforcing beam.

The universal joint includes an outer gyro element which is mounted in the machine base for rotation about an outer gyro axle, and further includes an inner gyro element which is mounted in the outer gyro element for rotation about an inner gyro axle extending at right angles to the outer gyro axle. In this case, the beam bearing is preferably connected to the inner gyro element of the universal joint. In other embodiments, the beam bearing may be separate from the universal joint of the setting device and connected to its own universal joint at a distance to the universal joint of the setting device, although this will require an own beam rotation bearing for connection of the reinforcing beam to the positioning head.

As will be evident from the illustrated embodiment, the first joint shall be formed with only one degree of freedom, therewith giving the machine its rigidity and eliminating the requirement of a central tube.

Each reinforcing beam is adapted to present a bending resistance in a first direction that greatly exceeds its bending resistance in a direction at right angles to said first direction. This enables the reinforcing beam to be given a generally rectangular cross-sectional shape or an elliptical cross-sectional shape. Other cross-sectional shapes, such as the cross-sectional shape of I-beams, are conceivable within the scope of the invention. The reinforcing beam is preferably comprised of composite material reinforced with carbon fibres. The machine according to the illustrated detailed embodiment includes three setting devices each of which is fixedly connected to a reinforcing beam at the first joint. One of the setting devices is also provided with an additional reinforcing beam with the intention of obtaining generally the same degree of stiffness in all directions. As indicated above, the machine may conceivably be provided with only two reinforcing beams orientated at right angles to one another. The beam bearing of at least one reinforcing beam is rotatable about its own longitudinal axis or about an axis which is parallel with said own longitudinal axis in the machine base. In the

case of the illustrated embodiment, the twin reinforcing beams are rotatable about the setting device in the inner gyro element.

Each setting device of the illustrated embodiment has the form of a screw-nut- mechanism whose nut is permanently connected to the inner gyro element. Other machine designs that include setting devices of another kind are fully conceivable within the scope of the invention. For example, linear motors can be used as setting devices instead of the illustrated screw-nut-mechanism. Such a linear motor may even consist of the reinforcing beam or may be comprised of a part thereof.

Two of the first joints at the positioning head have parallel axles whereas the third joint of the first joints at the positioning head has an axle which is perpendicular to the other two axles. Moreover, the inner gyro axis of the universal joint of each setting device is parallel with the axle of the first joint of the setting device in respect of those joints that do not permit tilting, i.e. rotation of the reinforcing beam about an axis parallel with its own symmetrical long axis in the joint.

The exemplifying embodiment described in detail above provides a parallel- kinematical machine whose universal bearings include two joints that each has two degrees of freedom and a joint that has three degrees of freedom with only one degree of freedom for each of the beam rotation bearings of the machine, i.e. at the positioning head.

It will be understood that the number of reinforcing beams provided and their cross-sectional dimensions may be varied. The number of degrees of freedom of the first joint, i.e. the setting device joint in respect of the positioning head, may be varied provided that the beam bearing is not common to the first joint.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in more details with reference to an exemplary embodiment thereof and also with reference to the accompanying drawings, in which

Fig. 1 illustrates a machine embodiment according to the invention;

Fig. 2 illustrates diagrammatically the positions in which the reinforcing beams are orientated at the base on the one hand, and at the positioning head on the other hand, in accordance with the figure 1 embodiment, and

Fig. 3 illustrates diagrammatically a model of the angle indicators according to a general embodiment of the invention.

DESCRIPTION OF THE INVENTION

Figure 1 illustrates an embodiment of a parallel-kinematical machine 1 according to the present invention. Three mutually separate universal joints 3.1 , 3.2, 3.3 are mounted in a machine base 2 in three corresponding through-penetrating openings in the base. Extending through each universal joint is a setting device 4.1, 4.2, 4.3 which can be lengthened and shortened, and a reinforcing beam 5.1 , 5.2.1 , 5.2.2, 5.3. When the universal joint for the setting device does not coincide with the universal joint for the reinforcing beam, the universal joint of the reinforcing beam is designated beam-universal-joint BU1 , BU2, BU3. One end of the setting device is connected to a positioning head 11 in a journal bearing, while its other end is connected to the universal joint. The setting device has the form of a screw-nut-mechanism whose nut is permanently connected to the universal joint. The screw of the setting device is driven by a setting device motor so that manoeuvring of the setting device causes the distance between the universal joint and the positioning head to decease or increase. According to the embodiment of the invention illustrated in figure 1 , this positioning head bearing also functions as a beam rotation bearing 10.1 , 10.2, 10.3 for the reinforcing beam 5.1 , 5.2.1, 5.2.2, 5.3 and therewith acts as a hinge that has only one degree of freedom. A manoeuvring head, a tool head and a tool attachment for movement of a tool within a working area (not shown) are connected to the positioning head 11 in a conventional manner.

Each reinforcing beam 5.1 , 5.2.1 , 5.2.2, 5.3 is intended to slide transversely through a beam bearing 17.1 , 17.2.1, 17.2.2, 17.3 in the machine base 2 when the

setting device 4.1, 4.2, 4.3 is lengthened or shortened. The beam bearing of the figure 1 embodiment is arranged within the beam-universal-joint BU1 , BU2, BU3 that coincides with the universal joints 3.1 , 3.2, 3.3 of the setting devices. Other embodiments within the scope of the present invention are conceivable when these bearings do not coincide.

As will be evident from figure 1 , one of the setting devices, the second setting device 4.2, includes two reinforcing beams 5.2.1, 5.2.2 each being placed on a respective side of the setting device connected to the beams and orientated generally at right angles to the remaining two reinforcing beams 5.1 , 5.3 at the two other setting devices 4.1 , 4.3. The reinforcing beam duplication has been made to allow all reinforcing beams in the machine to have mutually the same dimensions and to take-up forces of the same magnitude.

Each beam rotation bearing includes two angle indicators 5.1a, 5.1b, 5.2a, 5.2b, 5.3a, 5.3b, which are each connected to the beam rotation bearing 10.1 , 10.2, 10.3 so that the measuring points of the two angle indicators 5.1a, 5.1b will be placed on a respective side of the first beam rotation bearing 10.1 , and so that the measuring points of two angle indicators 5.2a, 5.2b will be placed on a respective side of the second beam rotation bearing 10.2 and so that the measuring points of two angle indicators 5.3a, 5.3b will be placed on a respective side of the third beam rotation bearing 10.3. Each angle indicator shall firstly register an angle αi in respect of indicator 5.1a, an angle α 2 in respect of indicator 5.1b, an angle ot 3 in respect of indicator 5.2a, an angle α 4 in respect of indicator 5.2b, an angle α 5 in respect of indicator 5.3a, and an angle αβ in respect of indicator 5.3b, between the positioning head 11 and reinforcing beams 5.1, 5.2, 5.3. Secondly, the angle indicators shall register pairwise a first angular difference βi= α,2- αi between the measuring points of two angle indicators 5.1a, 5.1b of the first beam rotation bearing 10.1 on the one hand and a second angular difference β2= α 4 - 013 between the measuring points of two angle indicators 5.2a, 5.2b of the second beam rotation bearing 10.2 on the other hand and a third angular difference β3= α 6 - as between the measuring point of two angle indicators 5.3a, 5.3b of the third beam rotation bearing 10.3 on the third hand, such as to form an active measuring

system AMS. When the machine is subjected to load, each deviation in the value of the angles α-i, ot2, 0: 3 , α 4 , α 5 , a & in a nominal value of an unloaded machine will be corrected by manoeuvring the setting devices 4.1 , 4.2, 4.3 in a manner to change the working position of the positioning head 11.

It will also be seen from the figure that the universal joints 3.1 , 3.2, 3.3 include an outer gyro element which is mounted for rotation in the base about an outer gyro axle, and an inner gyro element which is mounted for rotation in the outer gyro element about an inner gyro axle. Each reinforcing beam 5.1 , 5.2.1 , 5.2.2, 5.3 is also adapted to slide transversely in the beam bearings 17.1, 17.2.1, 17.2.2, 17.3 in the base 2 in response to lengthening or shortening one or more of the setting devices 4.1, 4.2, 4.3. Each beam bearing 17.1, 17.2.1, 17.2.2, 17.3 is connected to the base 2 two via a beam-universal joint BU1 , BU2, BU3. The beam bearings 17.2.1, 17.2.2 of at least one reinforcing beam 5.2.1, 5.2.2 are also rotatable about an axle which extends generally parallel with the longitudinal axle of the reinforcing beam 5.2.1 , 5.2.2.

In this regard, the setting devices function as tension and pressure transfer elements between the positioning head and the machine base, while the reinforcing beams connected to the setting devices function as elements for taking-up bending stresses and torsion stresses and to transfer laterally acting forces between the positioning head and the machine base.

There now follows according to figure 2 a mathematical model of a machine according to figure.1. The model describes a relationship between an upper fixating platform UP which corresponds to the machine base 2 in figure 1 , and a lower movable platform LP, which corresponds to the positioning head 11 in figure 1.

In one particular configuration set-up of the machine the setting of its lower movable platform LP is somewhat disturbed or deranged with respect to its position or orientation as defined by the illustrated deviation values of the angle indicators.

According to figure 2, the co-ordinate positions of the upper platform UP are:

According to figure 2, the co-ordinate positions in the movable platform LP are:

The frame of the movable platform is:

FO: = Txyz(xO,yO,zO) &* Rx(rx)&*Ry(ry) &* Rz(rz)

FO := matrix([[cos(ry)*cos(rz), -cos(ry)*sin(rz), sin(ry), xθ], [sin(rx)*sin(ry)*cos(rz)+cos(rx)*sin(rz), -sin(rx)*sin(ry)*sin(rz)+cos(rx)*cos(rz), sin(rx)*cos(ry), yθ], [-cos(rx)*sin(ry)*cos(rz)+sin(rx)*sin(rz), cos(rx)*sin(ry)*sin(rz)+sin(rx)*cos(rz), cos(rx)*cos(ry), zθ], [0, 0, 0, 1]])

Axle vectors BA for all angle indicators.

VBA11v := vector([cos(ry)*cos(rz)*Ra2-cos(ιy)*sin(rz)*L+xO-Ra1, (sin(rx)*sin(ry)*cos(rz)+cos(rx)*sin(rz))*Ra2+(- sin(rx)*sin(ry)*sin(rz)+cos(rx)*cos(rz))*L+yO-L, (-

cos(rx)*sin(ry)*cos(rz)+sin(rx)*sin(r2))*Ra2+(cos(rx) * sin(ry)*sin(rz)+sin(rx) * cos(rz))* UzO])

VBA12v := vector([cos(ry)*cos(rz)*Ra2+cos(ry)*sin(rz)*L+xO-Ra1, (sin(rx)*sin(ry) * cos(rz)+cos(rx) * sin(rz)) * Ra2-(- sin(rx) * sin(ry)*sin(rz)+cos(rx)*cos(rz))*L+yO+L, (- cos(rx)*sin(ry)*cos(rz)+sin(rx) * sin(rz))*Ra2- (cos(rx)*sin(ry)*sin(rz)+sin(rx)*cos(rz))*L+zO])

VBA21v := vector([cos(ry)*cos(rz) * L+cos(ry) * sin(rz)*Rb2+sin(ry)*h+xO-L, (sin(rx)*sin(ry)*cos(rz)+cos(rx)*sin(rz))*L-(- sin(rx)*sin(ry) * sin(rz)+cos(rx)*cos(rz))*Rb2-sin(rx)*cos(ry)*h+yO+Rb1 , (- cos(rx)*sin(ry) * cos(rz)+sin(rx)*sin(rz)) * L-

(cos(rx)*sin(ry)*sin(rz)+sin(rx)*cos(rz))*Rb2+cos(rx)*cos (ry)*h+zO])

VBA22v := vector([-cos(ry)*cos(rz) * L+cos(ry)*sin(rz) * Rb2+sin(ry)*h+xO+L, - (sin(rx)*sin(ry)*cos(rz)+cos(rx)*sin(rz))*L-(- sin(rx)*sin(ry)*sin(rz)+cos(rx) * cos(rz))*Rb2-sιn(rx)*cos(ry) !i" h+y0+Rb1, -(- cos(rx)*sin(ry)*cos(rz)+sin(rx)*sin(rz)) * L- (cos(rx)*sin(ry)*sin(rz)+sin(rx)*cos(rz))*Rb2+cos(rx)*cos(ry )*h+zO])

VBA31v := vector([-cos(ry) * cos(rz) * Ra2-cos(ry)*sin(rz)*L+xO+Ra1, - (sin(rx)*sin(ry)*cos(rz)+cos(rx) * sin(rz))*Ra2+(- sin(rx)*sin(ry) * sin(rz)+cos(rx)*cos(rz))*L+yO-L, -(- cos(rx)*sin(ry)*cos(rz)+sin(rx)*sin(rz))*Ra2+(cos(rx) * sin(ry)*sin(rz)+sin(rx)*cos(rz))* L+ZO])

VBA32v := vector([-cos(ry) * cos(rz)*Ra2+cos(ry)*sin(rz)*L+xO+Ra1 , - (sin(rx)*sin(ry)*cos(rz)+cos(rx) * sin(rz))*Ra2-(- sin(rx)*sin(ry)*sin(rz)+cos(rx)*cos(rz))*L+yO+L, -(- cos(rx)*sin(ry)*cos(rz)+sin(rx)*sin(rz))*Ra2- (cos(rx) * sin(ry)*sin(rz)+sin(rx)*cos(rz))*L+zO])

Used reference vectors to measure the values of the angle indicators.

VBH 1 v := vector([cos(ry)*cos(rz), sin(rx)*sin(ry)*cos(rz)+cos(rx)*sin(rz), - cos(rx)*sin(ry)*cos(rz)+sin(rx)*sin(rz)])

VBI12v := vector([cos(ry)*cos(rz), sin(rx)*sin(ry)*cos(rz)+cos(rx)*sin(rz), - cos(rx)*sin(ry)*cos(rz)+sin(rx)*sin(rz)])

VBJ21v := vector([cos(ry)*sin(rz), sin(rx)*sin(ry)*sin(rz)-cos(rx)*cos(rz), - cos(rx)*sin(ry)*sin(rz)-sin(rx)*cos(rz)])

VBJ22v := vector([cos(ty)*sin(rz), sin(rx)*sin(ry)*sin(rz)-cos(rx)*cos(rz), - cos(rx)*sin(ry)*sin(rz)-sin(rx)*cos(rz)])

VBI31v := vector([-cos(ry)*cos(rz), -sin(rx)*sin(ry)*cos(rz)-cos(rx)*sin(rz), cos(rx)*sin(ry)*cos(rz)-sin(rx)*sin(rz)])

VBI32v := vector([-cos(ry)*cos(rz), -sin(rx)*sin(ry)*cos(rz)-cos(rx)*sin(rz), cos(rx)*sin(ry)*cos(rz)-sin(rx)*sin(rz)])

The values shown by the angfe Indicators are the angfes between two vectors and are expressed as:

VBA21 • VBJ21 _ 180

]|raL42l|KR/2l|| π

, VBA32 » VBI32. Λ80 α Λ = arccosGϊ πn a) —

6 Kn VBA32lVBI32ϊ π

Numerical examples.

Geometrical parameters and nominal position:

Figure 3 illustrates diagrammatically a general embodiment of the invention when the machine is equipped solely with two reinforcing beams 5.1 , 5.2 which are each • pivotally mounted and mounted for displacement in a respective beam-universal joint BU1 , BU2 as previously described and which is shown in the figure as an ellipse with two parallel lines, wherein respective ends of the reinforcing beams are each connected to a respective beam rotation bearing 10.1 , 10.2 of which each has only one degree of freedom with regard to the positioning head 11.

Although not shown in figure 3 for the sake of simplicity, the embodiments according to figure 3 are also provided with at least three setting devices which can be lengthened and shortened individually in their longitudinal directions. As

will be seen from the figure, the axles of the two beam rotation bearings 10.1 , 10.2 are generally perpendicular to one another. However, these axles may be generally parallel to one another within the scope of the present invention.

It will also be seen from the figure that the beam rotation bearings 10.1 , 10.2 of the reinforcing beams are placed directly on the positioning head 11 , although these bearings may, alternatively, be connected indirectly to the positioning head within the scope of the present invention. For instance, the bearings may be placed on the setting devices (not shown in figure 3) or caused to coincide with the setting device bearings at the positioning head.

However, each of these beam rotation bearings of all the figure 3 embodiments include two angle indicators 5.1a, 5.1b; 5.2a, 5.2b, each of which is connected to the beam rotation bearing 10.1 , 10.2 so that the measuring points of two angle indicators 5.1a, 5.1b will be situated on a respective side of the beam rotation bearing 10.1 and so that the measuring points of two angle indicators 5.2a, 5.2b will be placed on a respective side of the second beam rotation bearing 10.2 such that each angle indicator will register firstly an angle α-i, 01 2 , 0C 3 , 0:4 between the positioning head 11 and respective reinforcing beams 5.1 , 5.2. Secondly, the angle indicators shall register a first angular difference β-ι=α 2 - αi between the measuring points of two angle indicators 5.1a, 5.1b of the first beam rotation bearing 10.1 and also a second angular difference β2=α 4 - α 3 between the measuring points of two angle indicators 5.2a, 5.2b of the second beam rotation bearing 10.2, so as to form an active measuring system AMS. Thus, the angular differences βi and β 2 denote a measurement of the respective twists of the reinforcing beams i.e. their rotation about an axis generally parallel with their longitudinal axes.

Each deviation in the value of the angles α-i, α 2 , 0, 3 , α 4 from a nominal angular value when the machine is not subjected to load from the angular value of said angles in the case of a loaded machine can be corrected with this general embodiment by manoeuvring the setting devices (not shown in figure 3) to a changed working position of the positioning head 11.

The active measuring system according to the present invention is intended for use together with prior art control systems for these types of parallel-kinematical machines and operates actively with said machines in a more or less continual fashion. The described measuring system therefore constitutes a valuable supplement to these types of machine so as to correct to the greatest possible extent changes in the attitude of the positioning head caused partly by mechanical influences and partly by thermal influences.