JPH0370196B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to workpiece position control, and in particular to a method and apparatus for centering and leveling a workpiece on a turntable, particularly in a measuring device.

Measuring devices are known in which the size is measured by rotating the turntable while the workpiece is positioned on the turntable and a transducer senses the surface of the workpiece. It is generally necessary to perform an operation known as centering and leveling, in which the turntable is typically displaced horizontally in order to align the desired axis of the workpiece with the axis of rotation of the turntable; and tilted to bring the workpiece to the desired position. Furthermore, it is highly desirable that centering and leveling operations should be performed automatically so that they can be performed efficiently and quickly.

Measuring devices in which centering and leveling can take place automatically are already known and commercially available. In the known device, a circular turntable is mounted on a support structure, which includes a spherical turntable that is on the work surface of the turntable and allows free tilting movement of the turntable around a point in a known horizontal plane. Including bearing surfaces. Two jacks placed below the turntable are spaced 90 degrees from each other.
Provided for providing tilting movement about respective orthogonal axes placed in the horizontal plane. The spring drives the turntable downwardly so that the turntable engages the jack and the spherical bearing surface engages a mating platform that includes a ring of balls set in the support structure in one configuration. The support arrangement is mounted on a spindle for rotating the turntable with further bearings providing for horizontal movement of the support structure, whereby a centering movement can be performed.

In this conventional equipment, the workpiece to be tested is placed on the turntable by first determining the location of the center of that part of the workpiece surface, which is placed in a horizontal plane containing the point at which the turntable can tilt. After placement, centering and leveling is performed. This determination can be made by driving the spindle such that a stylus included in the device contacts the workpiece surface in this horizontal plane and rotates the workpiece about the spindle axis. The degree of eccentricity between the axis of rotation of the workpiece (or axis of the spindle) and the position of the center of the workpiece surface in this plane can then be determined from the signal output by the transducer with which the stylus is associated. The support structure for the turntable is then placed horizontally with respect to the spindle in order to align the determined center of the workpiece surface with the axis of the spindle. The centering operation is thus completed for that plane. Move the stylus to different horizontal planes,
Leveling is accomplished by driving the spindle to rotate the workpiece and determining the eccentricity of the center of the workpiece surface in this horizontal plane with respect to the spindle axis using a signal output by a transducer. After this eccentricity is determined, the center of the workpiece surface in the second horizontal plane is aligned with the rotation axis of the turntable (spindle axis).
The jack is driven as necessary to match the . This completes the leveling operation and thus completes the centering and leveling.

Since the tilting movement of the turntable that occurs during this leveling operation is centered on a point in the first horizontal plane, and this point is brought into alignment with the spindle axis by the centering action, the leveling action does not disrupt this alignment.

This device has many disadvantages. 1st
In some cases, any centering motion must be performed by sensing the workpiece surface located in the same fixed horizontal plane that includes the center of tilt of the turntable, and in some cases The piece has no surface in its plane that can be sensed. This is a considerable disadvantage for complex shaped workpieces such as crankshafts. Second, the center of mass of the workpiece must always be located within the 90° sector of the turntable defined by the positions of the two jacks;
This is because placing the center of mass outside this sector creates a turning moment on the turntable that moves the turntable without contacting these jacks. Third, the spherical bearings that support the turntable are difficult and expensive to manufacture to a certain degree of precision.

This invention provides an apparatus in which one or more of these problems may be eliminated.

In one aspect, the invention provides a workpiece positioning device having a turntable for supporting a workpiece and computer means, which provides for any positioning of the workpiece that occurs as a result of tilting of the turntable for leveling purposes. It is operable to perform centering and leveling operations in which decentering is compensated for. Thus, in a device constructed according to this aspect of the invention, centering and leveling can be performed in any horizontal plane, rather than being restricted to a unique horizontal plane containing the center of tilt of the turntable as in the prior art described above. Regarding, centering and leveling can be performed.

In another aspect, the invention provides a workpiece positioning device having a turntable for a workpiece, the turntable being supported at three points located at the vertices of a triangle, preferably an equilateral triangle; the turntable is centered at, and at least two of said points are adjustable in height;
and the workpiece positioning device is configured to adjust the height of one or more of the points.
It has computer means for performing centering and leveling operations.

In a further aspect, the invention provides a method or apparatus for performing a centering and/or leveling operation, in which the workpiece is sensed by a sensing means and the movement is controlled by an electronic control means according to a predetermined algorithm. It is carried out under

In another aspect, the invention provides an apparatus having a turntable for supporting a workpiece, the turntable being pivoted about a subsurface point or axis thereof to provide leveling, and the apparatus further comprises electronic control means provided for effecting said pivot movement. The point or intersection of the axes is preferably offset from the rotation axis of the turntable.

Other aspects of the invention will be apparent from the following description and claims.

The invention will be further described by way of example with reference to the accompanying drawings, in which: FIG.

Referring to FIG.
It includes a workbench 2 supported by (only the legs of which are visible in Figure 1). The frame 3 holds a turntable 4 on which workpieces can be mounted. The vertical column 6 supports a motor-driven vertically movable carriage 8. The stylus 10 is mounted on the end of a pivot arm 12, which allows the orientation of the stylus to be changed, in turn on the end of a horizontally (radially) movable arm 14 supported by a carriage 8. Retained. The measuring operation on the workpiece is performed by causing the stylus 10 to traverse the surface of the turntable by rotating the turntable and/or by moving the stylus radially and/or by moving the stylus vertically. It is done by twisting.

As shown in FIGS. 2 and 3, the support structure for turntable 4 includes a base 16 held by a disk 18 secured to a motor drive spindle 20. As shown in FIGS. A bearing arrangement 21, shown schematically by dashed lines in FIG. 3, supports the spindle 20 for rotation about its own axis 23, which is vertical. The bearing arrangement 21 is mounted on the frame 3 and is preferably described in British published patent application no. 2178805A. A set of ball bearings 22 in a disc-shaped retainer 24 connect base 16 and disc 18 to provide for horizontal movement of base 16 with respect to disc 18.
caught between. This movement is provided along orthogonal axes x and y by motors 26x, 26y fixed on base 16 and reciprocably movable drive rods via gearboxes 30x and 30y, which may include, for example, worm and wheel assemblies. 28x and 28y, respectively. Drive rods 28x and 28y are driven along the x and y axes, respectively, when their respective motors are driven. Boss 32 is spindle 2
0, projecting through the central opening 34 in the base 16, respectively engaged by the ends of the drive rods 28x and 28y, and lying in planes perpendicular to the x and y axes, respectively. It has 32x and 32y. A tension spring 36 connected to the base 16 at one end and connected to the post 38 at the other end.
, leaving flat surfaces 32x and 32y engaged with opposite ends of respective drive rods 28x and 28y. Thus, with the aid of motors 26x and 26y and under the force of spring 36, base 1
6 can be moved a precisely determined distance in either direction along the x and y axes. Guide plates 40x and 40y, through which drive rods 28x and 28y respectively pass, are connected to gearbox 30.
Guide pin 44 held by x and 30y
It has a slot 42 for receiving.

A ball 46 mounted in a recess at the upper end of the post 38 supports the turntable 4 for free pivoting about point P.

At points A and B, the turntable 4 is supported on the balls 50b and 50b, respectively, via a spacer 52 (FIG. 3 only), which is fixed to the underside of the turntable 4 and on the balls 50a, 5
It is supported by resting on 0b. Lever plates 54a, 54b mounted on bracket 56 for pivoting about a horizontal axis 58 (perpendicular to the plane of the paper in FIG. 3) have recesses 60a, 60b.
, where balls 50a and 50b are each received. The motors 62a, 62b are coupled to jacks 64a, 64b via gearboxes 66a, 66b for pivoting the lever plates 54a, 54b upwardly and downwardly about their pivots 58.
(Figure 3 only). In this way, motor 6
2a causes the turntable to move to points P and B.
and the motor 62
The turntable 4 is moved to points P and A by the drive of b.
Tilt around the axis that joins. These axes pass through the centers of balls 46, 50a and 50b.

Point ABP is placed at the vertex of an equilateral triangle, whose center C coincides with the center of the turntable 4, that is, point ABP is placed symmetrically with respect to point C. This provides the maximum area of the turntable on which workpieces can be placed without causing instability of the turntable. However, as a result the turntable is tiltable axes PA and PB
are 60° from each other.

The tension spring 68 has a spacer 52 connected to the ball 50.
a and 50b, and tension spring 70.
drives lever plates 54a and 54b downwardly so that they remain engaged with jacks 64a, 64b.

The cylindrical wall surface 69 fixed to the disk 18 is
Surrounding the support structure described above.

As shown in the simple block diagram of Figure 4,
Motors 26x, 26y for centering and motors 62a, 62b for leveling are controlled by a computer system 72 which receives input from a transducer 73 responsive to stylus 10. An operator-controlled keyboard 75 is provided for providing commands to the computer system 72. The computer system 72 also has a motor 74 (theta axis) driving the spindle 20 for rotating the turntable, a motor 76 (z axis) for raising and lowering the carriage 8 on the column 6.
shaft), and a motor 78 (r
axis). Further transducers 80, 82 and 84 provide data to computer system 72 representing the angular position of turntable 4, the vertical position of carriage 8 and the radial position of arm 14. VDU 86 and memory 88 are also connected to computer system 72, with memory 88 storing received data and storing programs on which computer system 72 operates. Computer system 72 may include one or more computers.

The movements that the turntable 4 undergoes in achieving centering and leveling of the workpiece can be understood by reference to Figures 5a to 5d. For simplicity, FIG. 5 illustrates a conical workpiece 100 positioned on a turntable 4 within a triangle ABP. The workpiece 100 is located on one end 102, which is assumed to be plane but at a slight angle to the radial plane (more exaggerated in FIG. 5), so that the workpiece The axis 104 of 100 is at an angle with respect to the vertical axis of rotation 23 of the spindle 20. The sequence of steps performed in the centering and leveling operation illustrated in FIG.
8 includes first rotating a turntable 4 arranged to sense the surface of the workpiece 100 at 8. Computer system 72 receives the output from transducers 80, 73, 84 and utilizes a form fitting algorithm to calculate the magnitude and direction of displacement between workpiece center 110 in plane 108 and axis 23. The polarity parameter output by the converter is a conceptual Cartesian system (u,
v) and has coordinates (u _i , v _i ), then the center (u _p , v _p ) and radius R of the surface are summed, i.e. _N 〓 ⁱ⁼¹ [(u _i −u _p ) ² + (v _i −v _p ) ² −R ² ] ² is calculated using a modified least squares error criterion by minimizing 2. Having calculated the center, the computer then calculates the point 1 as shown in Figure 5b.
The motors 26x and 26y are driven as necessary so that the axis 10 is aligned with the axis 23. In the next step, the turntable 4 is rotated with the stylus 10 arranged to sense the surface of the workpiece in different horizontal planes 112 spaced from the plane 108, in this example the plane 112 being above the plane 108. It is in. Again utilizing the form fitting algorithm, computer system 72 determines the location of the workpiece center in plane 112. Thereafter, computer system 72 moves the workpiece from the position shown in Figure 5b to position 5c.
Calculate the angular movement of the turntable 4 and workpiece 100 required to move it to the position shown in the figure, where the workpiece axis 104 is parallel to the spindle axis 23. This calculation is discussed further below. As a result of this angular movement or tilting, point 110 is again displaced from axis 23, as can be seen in FIG. 5c. The final stage is the execution of a second centering movement,
The position of the workpiece axis 104 with respect to the axis 23 is determined again utilizing the form matching algorithm described above and the motors 26x and 2 are activated to align the axis 104 with the axis 23 as shown in Figure 5d.
6y is driven again. Although, for simplicity, the foregoing description of FIG. 5 is based on the various steps being carried out in a particular sequence, this is not essential and in fact the centering and leveling is performed in the position shown in FIG. 5a. Using the workpiece 100 and the turntable 4 in the plane 11
0 and 112, and then motors 26x and 26y and 62a and 62b are driven simultaneously or in any desired sequence, but preferably to center the workpiece, and then the first Level it to achieve the state shown in Figure 5d.

Calculations of the required horizontal and tilt movements to be provided by the turntable 4 to achieve centering and leveling will now be described. In the following description, motors 26x and 26
y is called an x motor and a y motor, and motors 62a and 62b are called an a motor and a b motor. Again for simplicity, the component may have any shape if the surface being assessed has a regular profile, but since the cylindrical axis is easily defined, the fifth It is convenient to consider the case of centering and leveling a cylindrical workpiece, such as the workpiece 100 shown in the figures.

In the following description, all motions are expressed in the right-hand Cartesian coordinate system X, Y with unit vectors i, j, k.
It is convenient to regard it as being at and Z. The origin of the coordinate system is chosen to coincide with a fixed point P, and the X-axis is chosen to bisect the line joining the two points A and B. The coordinate system is shown in FIG. 6, where the Z axis is perpendicular to the plane of the paper and is also shown in FIG.

Centering of the table is achieved by resolving the required motion by the X and Y axes into motions parallel to the lines of action of the x and y motors.

Let the required centering vector be c ₁ i + c ₂ j,
And let e _x and e _y be unit vectors parallel to the lines of action of the x and y motors, respectively. From the geometry, it can then be c ₁ i+c ₂ j=−k[(c ₁ -c ₂ )e _x +(c ₁ +c ₂ )e _y ] (1) where k =2 ^-1/2 .

When describing the leveling of components placed on a table, it is convenient to introduce two more variables θ ₁ and θ ₂ , where θ ₁ is the angle of inclination of the table top about the X axis and , and θ ₂ is the corresponding angle about the Y axis. Thus, the height of any point X ₁ , Y ₁ on the surface of the table, with respect to that height, when the surface is horizontal, can be obtained as follows: Z ₁ = X ₁ tanθ ₁ + Y ₁ tanθ ₂ (2).

Now, the parameters T ₁ and
Introducing T ₂ and the incremental heights of points A and B
If expressed as Z _A and Z _B , this gives the following equations: Z _A = T ₁ tan θ ₁ + T ₂ tan θ ₂ (3a) Z _B = T ₁ tan θ ₁ + T ₂ tan θ ₂ (3b). From these equations it is possible to calculate the incremental heights of A and B on the horizontal plane through P by the angles of inclination θ ₁ and θ ₂ .

As can be seen from Figure 6, the magnitudes of T ₁ and T ₂ are the same as the axis AP and the axis on which the turntable can tilt.
The angle between BP and APB depends. Thus, the calculations performed by computer 72 in performing the leveling operation are dependent on angle APB.

Before continuing, it is necessary to further consider the actual mechanism by which points A and B are moved in the vertical plane by the a and b motors in the preferred embodiment.

As shown in FIG. 7 by way of example, the distance between the shaft 58 and the center 51 of the ball bearing 50a or 50b is 12 mm, and
and the lever 54a of the jack 64a or 64b.
or 36 millimeters between contact point 55 and 54b.

Referring to FIG. 8, if the screw jack 64a
or if 64b is raised by height z, then the center of ball 50a or 50b is at height δz
You can see that it moves through. That is, we know that z=36tanα (4) δz=12sinα, and from there, z=36δz/(12 ² −δz ² ) ^1/2 (5a) or z=3δz+3δz ³ /(2x12 ² )+3 ² δz ⁵ ／(2 ³ x12 ⁴ )＋…
(5b) becomes.

Assuming that the table 4 is initially horizontal and that the cylinder is measured at two heights (z ₁ , z ₂ ), the centers of the two planes are located at (a ₁ , z 2 ) as shown in FIG. b ₁ , z ₁ ) and (a ₂ , b ₂ , z ₂ ). It can be seen that _any point at height Z and on the _cylinder axis has coordinates in the chosen system given by the following _formula , namely: ₁ )]Z+ _a1Y =[( _b2 - _b1 )/( _z2 - _z1 )]z+ _b1 .

Let h=( _z2 - _z1 ) and compare these equations with equation (2).

tanθ ₁ =(a ₂ −a ₁ )/h tanθ ₂ =(b ₂ −b ₁ )/h.

The incremental height _δZA , by which points A and B must be moved to compensate for these angles,
δZ _B is given by equation (3) as follows,
That is, δZ _A =T ₁ tanθ ₁ +T ₂ tanθ ₂ δZ _B =T ₁ tanθ ₁ −T ₂ tanθ ₂ , and from equation (5) the height to which the screw jack must be raised is given as: That is, Z _A = 3δZ _A / (12 ² - δZ _A ² ) ^1/2 Z _B = 3δZ _B / (12 ² - δZ _B ² ) ^1/2 .

Using the binomial expansion of these equations and truncating the series in the second term, we obtain the following equation: Z _A =3δZ _A +PδZ _A ³ Z _B =3δZ _B +PδZ _B ³ , where P = 1.1331161×10 ^-2 ,
and includes corrections for series truncation.

Thus, the number of rotations of the a and b motors required to achieve leveling can be easily determined using the above calculations. Additionally, the number of rotations of the x and y motors required to achieve centering can also be easily calculated. Both calculations are performed by computer system 72 and the results are utilized to drive the a, b, x and y motors.

Thus, the illustrated embodiment has the following substantial advantages: the planes 108 and 11 shown in FIG.
2 may be placed anywhere within the range of motion of transducers 73 and 84, and the workpiece is triangular
It may be positioned with its center of mass anywhere within the ABP, and when it is substantially larger than the corresponding area in prior art devices and symmetrical about the center of the turntable, the Conveniently placed and with 3 turntables
This effectively eliminates the need for the costly large spherical bearings of the prior art, as it is supported at several points, two of which are of adjustable height to provide tilting movement for leveling purposes. It has several advantages.

The above device is characterized in that the centering and leveling movements can be carried out automatically, the mechanical structure of the turntable and its driving means are relatively simple, the turntable has a high degree of stability, and the workpiece that can be assessed is It has the combined advantage of greater variation in the shape of the pieces.

Additionally, aspects of the invention relating to measuring in a plane spaced from the center or axis of the inclination provide that the workpiece is not supported on a worktable, but rather rotates around an axis other than the vertical axis, such as a horizontal axis. It may also be applied to measuring devices held in chucks or the like which can be rotated.

The invention is not limited to sensing external surfaces of workpieces (such as the bearing surfaces of a crankshaft), but internal surfaces (such as the input and output bearing pedestals of a gearbox housing) should also be detected. Applicable in some cases.

In some instances, rather than center aligning two parts of a workpiece (such as the two bearing surfaces of a crankshaft), it is preferable to center a point on the workpiece on the turntable's axis and align it with the axis. It is desirable to level other planar surfaces of the workpiece by making them orthogonal to the surface of the workpiece. For example, it may be desirable for engine pistons to be centered and leveled by centering the piston crown and setting the lower edge of the piston skirt at right angles to the axis. In this case, rather than determining the center of the second part of the workpiece, the slope of the second part of the workpiece or a reference surface resting thereon (such as the turntable surface on which the piston rests) is determined. be done. The determined center can then be centered, the tilt adjusted, and the center re-centered as compensation for any decentering resulting from the tilt adjustment.

The invention is not limited to use with workpieces having circular portions to be sensed, but may also be used with workpieces having other types of portions such as rectangular, triangular, oval, and hexagonal portions to be sensed. May be used.

For example, if the workpiece is cylindrical, 2
It is not necessary to sense the circular profile of the workpiece in two spaced planes, but instead the sensor can be tracked along a helical path with respect to the workpiece surface, and The amount can then be determined.

Preferably, the arrangement of transducer 10, its support structures 12, 14 and the control system shown in FIG. Inventor: HUGH ROGERS
LANE) and PETER DEAN ONYON, a co-pending application which claims priority from UK Patent Application No. 8605324, filed at the same time. In that arrangement, a high resolution transducer with a narrow working range is mounted on a radially movable arm, which is a motor driven under computer control in response to the output of the transducer, thus converting The device is able to automatically follow workpiece surfaces that vary greatly in morphology. In particular, the transducer may have a resolution of up to about 12 nanometers over a range of about 0.4 MM, and the radially movable arm has a range of movement of about 200 MM and a position having a resolution of about 200 nanometers. A sensing system may be provided. This arrangement simplifies centering and leveling operations since it is not necessary to pre-position the workpiece on the turntable accurately by eye, since the transducer system of the above-mentioned co-pending application does not require the use of a turntable. This is because any centering and leveling errors within the range of possible centering and leveling adjustments can be adjusted.

[Brief explanation of drawings]

FIG. 1 is a perspective view of an apparatus implementing the invention. 2 is a perspective view of a support structure for a turntable included in the apparatus of FIG. 1; FIG. Figure 3 shows
The section through the support structure portion of FIG. 2 also shows the turntable. FIG. 4 is a simplified block diagram of the control system included in the apparatus of FIG. Figures 5a-5d diagrammatically illustrate centering and leveling operations. FIGS. 6-9 are drawings to assist in understanding the calculations performed by the control system for performing the centering and leveling operations illustrated in FIG. In the figure, 4 is a turntable, 10 is a stylus, 20 is a spindle, 22 is a bearing,
23 is the axis, 26x, 26y, 62a, 62b, 7
4, 76, 78 are motors, 46, 50a, 50b
is a ball, and 72 is a computer system.

Claims (1)

Claims: 1. An apparatus for performing an operation on a workpiece, comprising a support 20 rotatable about a predetermined axis 23 and a support 20 mounted on said rotatable support 20 for rotation therewith. a mounted workpiece receiving member 4 and first means 46, 50a, 50b for supporting said receiving member and for tilting movement in any direction with respect to said rotatable support 20;
The rotatable support 20 supports the receiving member 4
second means 22 for lateral movement with respect to;
first and second drive means 62a, 62 for effecting said tilting and lateral movement, respectively;
b; 26x, 26y and the rotatable support 20
a third drive means 74 for rotating a surface sensor 10 mounted for movement substantially parallel to and towards and away from said axis 23; said movement of said sensor; and fourth drive means 76, 78 for bringing about the
said surface sensor 10 is adapted to traverse and sense a workpiece surface during relative movement between sensor 10 and the workpiece; and detecting a leveling error and detecting the leveling error of the first and second
drive means 62a, 62b; , B, three supporting elements 46, 50a, 5 that support the receiving member 4 only at three points A, B, P at the vertices of
0b, the first driving means 62a, 62b
are at least two of the support elements 50a, 50b.
so that the adjustment of one of said support elements 50a, 50b is relative to the respective tilt axis PB or PA extending substantially between the other two said elements 46 and 50b or 50a. characterized in that the receiving member 4 is tilted by the programming means depending on the angle PAB between the tilting axes PB, PA, the first drive means 62a,
62b and, depending on any said leveling error, said second drive means 26x, 26y. 2. Device according to claim 1, characterized in that the angle PAB between the tilt axes PA, PB is other than a right angle. 3. Device according to claim 2, characterized in that said points P, A, B are located at the vertices of an equilateral triangle and said angle PAB is thereby 60°. 4. Apparatus according to claim 3, characterized in that said points P, A, B are located symmetrically with respect to the center C of said workpiece receiving member 4. 5 Two of the three support elements 50a, 50b
characterized in that only the third support element 46 is adjustable and the third 46 of said three support elements is fixed,
An apparatus according to claim 4. 6 the first driving means is connected to the first and second driving means;
first and second motors 62 for effecting said tilting relative to each of the tilting axes PB, PA.
6. Device according to claim 5, characterized in that it comprises: a, 62b. 7. Claim 1, characterized in that said second drive means comprises first and second motors 26x, 26y for effecting said lateral movement in respective orthogonal directions x, y. The device according to any one of Items 1 to 6. 8 by a line in which the orthogonal directions x, y are equidistant from the at least two support elements 50a, 50b and pass through the third support element 46;
8. Device according to claim 7, characterized in that it is divided into equal parts. 9. Claims 1 to 8, characterized in that the predetermined axis 23 is vertical.
Apparatus according to any of paragraphs. 10. Apparatus according to claim 9, characterized in that the workpiece receiving member 4 is a turntable. 11 said programming means in said first and second planes 1 at positions perpendicular to and spaced apart from said predetermined axis 23;
Such a centering and leveling correction operation in which the center of the workpiece 100 at 08, 112 is determined and said first and second drive means 62a, 62b; 26x, 26y are driven depending on said determination. 11. Apparatus according to any one of claims 1 to 10, characterized in that it is operable to carry out. 12 a first calculation in which the lateral movement of the workpiece receiving member 4 required for a first of said workpiece centers to coincide with said axis 23 is determined, the line joining said workpiece centers being A member 4 necessary to be parallel to the predetermined axis 23
a second calculation in which the inclination of the workpiece is determined, and a third calculation in which the lateral movement of the member 4 necessary to compensate for the displacement of the center of said first workpiece as a result of said inclination is determined and the first and second driving means 62a, 62b; 26x, 26
Claim 1, characterized in that said programming means are operable to control y.
The device according to item 1. 13 said programming means cause said first calculation to be carried out and said second drive means 26x, 26y to be adapted accordingly such that said first workpiece center coincides with said predetermined axis 23; and then determining the position of the second center, performing the second and third calculations and determining the position of the first center according to the second and third calculations.
and second drive means 62a, 62b; 26
13. Apparatus according to claim 12, characterized in that it is operable to perform a centering and leveling sequence in which the x, 26y are driven. 14. The programming means is arranged such that the second driving means 26x, 26y are driven in accordance with the second calculation following the completion of driving the first driving means 62a, 62b. do,
Apparatus according to claim 13. 15 First driving means 62 according to the second calculation
a, 62b and at the same time the second driving means 2
14. Apparatus according to claim 13, characterized in that the programming means are arranged such that 6x, 26y are driven according to the third calculation. 16 said execution of said first, second and third calculations and said driving of said first and second driving means, so that said first and second driving means 62a, 62b; 26x, 26y
as claimed in claim 13, characterized in that the programming means are arranged such that the two centers of the workpiece are driven simultaneously to align both centers of the workpiece with the predetermined axis (23). Device. 17. said programming means is further arranged to perform a measuring operation on said workpiece by driving said third and fourth drive means 74, 76, 78, thereby causing said sensor to act on said workpiece; 17. A device according to any one of claims 1 to 16, characterized in that the output signal from the sensor is stored to give data about the surface.