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Description  |
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FIELD OF INVENTION
The invention relates to a device for positioning a body in at least one
support direction by means of at least one electromagnet and at least one
position sensor, an electrical output of the position sensor being
connected to an electrical input of an electronic control unit with which
an electric current in the electromagnet is controllable as a function of
a difference between a position of the body relative to the electromagnet
as measured by the position sensor and a desired position.
Of interest are commonly owned copending applications Ser. No. 664,074
entitled "Electromagnetic Support with Unilateral Control Currents" in the
name of Cox et al and Ser. No. 664,075 entitled "Electromagnetic Support
with Current-Independent Characteristics" in the name of van Eijk et al
both filed concurrently with the instant application.
BACKGROUND OF THE INVENTION
Philips Technical Review, vol. 41, no. 11/12, 1983/84, pp. 348-361,
discloses a device of the kind described in the opening paragraph in which
a shaft is supported by five pairs of electromagnets in such a way that
rotation of the shaft is possible only about the centerline of the shaft.
A force exerted on the shaft by an electromagnet is substantially directly
proportional to the square of the value of the current through the
electromagnet and substantially inversely proportional to the square of
the size of an air gap between the electromagnet and the shaft. As a
result of the relation between the electromagnetic force and the size of
the air gap, the position of the shaft relative to the electromagnets is
not stable unless additional measures are taken. To maintain a stable
desired position of the shaft in the known device, the position of the
shaft relative to each pair of electromagnets is measured by means of a
position sensor, and a control current determined from the difference
between the measured and the desired position is passed through the two
electromagnets of the relevant pair. The value of the control current is
thereby determined by means of a control unit having a proportional,
differentiating and integrating action (PID controller). A stable support
is obtained through the electromagnets controlled by the PID controller.
Since there is a non-linear relation between the electromagnetic force and
the size of the air gap and the value of the current, the known device
constitutes a non-linear system. The PID controller used is a linear
control unit which in the known device is optimized for a working point
determined by a desired size h.sub.0 of the air gap and by a basic current
i.sub.0 through the electromagnets. As a result, however, a number of
characteristics of the support which also determine the stability of the
support, such as stiffness and bandwidth, are dependent on the position of
the shaft relative to the electromagnets, whereas the PID controller used
functions optimally only in the case of relatively small displacements of
the shaft from the desired position. It is a disadvantage of the known
device, accordingly, that only one position of the shaft is optimally
stable, whereas any other position of the shaft is less stable, or may
even be unstable. Stability problems can thus occur, especially upon
switching on of the support device.
SUMMARY OF THE INVENTION
The invention has for its object to provide a device for positioning a body
in which the stiffness and bandwidth are independent of the position of
the body relative to the electromagnets, so that the disadvantages
described above are avoided.
The invention is for this purpose characterized in that between an
electrical output of the control unit and the electromagnet controlled by
the control unit an electronic multiplier is connected which is unique to
the relevant electromagnet, an output signal of the multiplier being
determined by the product of a control signal of the control unit and an
output signal of the position sensor.
It is achieved through the use of the electronic multiplier between the
control unit and the electromagnet controlled by the control unit that the
current through the relevant electromagnet is proportional both to the
control signal of the control unit and to the size of the air gap of the
elctromagnet. Thus the force exerted by the relevant electromagnet is
proportional only to the square of the control signal of the control unit
and substantially independent of the size of the air gap of the relevant
electromagnet, so that the stiffness and bandwidth of the device are
independent of the position of the body and the control unit can function
optimally in any position of the body (positional independence of the
control). The invention also achieves that the body to be supported can be
accurately displaced relative to the electromagnet by means of the device.
In a device of the kind described in the opening paragraph, with a control
unit optimized for a working point (h.sub.0, i.sub.0), the stiffness and
bandwidth are also dependent on the value of the basic current i.sub.0,
while the control unit functions optimally only in the case of small loads
on the body, i.e. when the control currents through the electromagnets are
small in relation to the basic current. A particular embodiment of the
device according to the invention is characterized in that an electronic
root extractor is connected between the control unit and the multiplier
connected to the control unit. The use of the electronic root extractor
achieves that the current through the electromagnet controlled by the
control unit is proportional to the square root of the control signal of
the control unit. In this way the force exerted by the relevant
electromagnet is proportional to the value of the control signal, so that
the stiffness and bandwidth of the device are independent of the value of
the current through the electromagnet and the control unit functions
optimally for all loads on the body to be supported (current independence
of the control).
A further embodiment of a device according to the invention, in which
during operation the body is supported in the support direction by means
of a pair of electromagnets which, seen in the support direction, are
located opposite one another, while the currents through the two
electromagnets of the pair are controlled by a control unit which is
common to the two electromagnets of the pair, is characterized in that
between the control unit and each of the two multipliers connected to the
control unit an electronic root extractor is connected which is unique to
the relevant multiplier. This embodiment provides a bilateral support of
the body with a high loading capability in that that electromagnet, whose
air gap has increased as a result of a displacement of the body from the
desired position owing to a static load, is supplied with a control
current having a direction equal to that of the basic current, while the
other electromagnet is supplied with control current having a direction
opposite to that of the basic current. In addition to a
position-independent control, a current-independent control is also
achieved through the use of the said unique root extractors.
A yet further embodiment of a device according to the invention, in which
again a pair of electromagnets and a control unit common to this pair are
used, is characterized in that between the control unit and each of the
two multipliers connected to the control unit an electronic rectifier is
connected which is unique to the relevant multiplier, the two rectifiers
being electrically oppositely directed. In this embodiment the
electromagnets are supplied with a control current only, not with a basic
current. It is achieved through the use of the said rectifiers that, in
the case of a displacement of the body from the desired position owing to
a static load on the body, only that electromagnet is supplied with a
current whose air gap has been increased as a result of this displacement.
The electrical resistance losses of the electromagnets are kept low in
this way.
A further embodiment of a device according to the invention, in which the
rectifiers are connected in an efficient manner relative to the
multipliers, is characterized in that the rectifiers are connected between
the control unit and each of the multipliers connected to the control
unit. It is achieved by this that an input signal of each of the
multipliers always has a same polarity, so that an unstable operation of
the multipliers around the zero crossing of the input signal is avoided.
A special embodiment of a device according to the invention, which provides
a control of the electromagnets which is independent of the current value,
while the rectifiers referred to above are used, is characterized in that
between the control unit and each of the two multipliers connected to the
control unit an electronic root extractor is connected which is unique to
the relevant multiplier. A finite stiffness is obtained also in a no-load
condition of the body through the use of the root extractors.
A further embodiment of a device according to the invention, which provides
a control independent of the value of the current with a simple
construction, while the said rectifiers are used, is characterized in that
between the control unit and the two multipliers connected to the control
unit an electronic root extractor is connected which is common to the two
multipliers.
A still further embodiment of a device according to the invention is
characterized in that a digital memory is connected between each of the
multipliers and the position sensor connected to the relevant multiplier.
The use of a digital memory between the position sensor and the multiplier
can effectively convert the output signal of the position sensor into a
signal whose value is proportional to the size of the air gap between the
body and the electromagnet connected to the relevant multiplier. In
addition, the output signal of the position sensor can be corrected by the
digital memory for non-linear effects such as, for example, magnetic
saturation of the electromagnets or the body to be supported.
IN THE DRAWING
The invention will be explained in more detail with reference to the
drawing, in which:
FIG. 1 is a lateral elevation of a common portion of a first and a second
embodiment of a device according to the invention,
FIG. 2 is a plan view of the common portion according to FIG. 1,
FIG. 3 is a cross-section of the common portion taken on the line III--III
in FIG. 2,
FIG. 4 diagrammatically shows the first embodiment of the device according
to the invention comprising a first electronic control circuit, and
FIG. 5 diagrammatically shows the second embodiment of the device according
to the invention comprising a second electronic control circuit.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The devices illustrated in FIGS. 1 to 5 comprise a straight guide with a
steel guide beam 1 which extends in a horizontal direction parallel to the
x-direction in FIG. 1 and which is mounted to a frame 3 near both its
ends, a table 5 being displaceable in the x-direction along the guide beam
1. An object 7 (shown in dashed lines) fastened to the table 5 can be
positioned in the x-direction by driving means not shown in any detail in
the FIGS.
The table 5 is provided with a round, aerostatically supported foot 9 of a
kind known from Netherlands Patent Application 8902472 which corresponds
to commonly owned copending application Ser. No. 594,519 filed Oct. 4,
1990 in the name of Engelen et al. Of further interest is commonly owned
U.S. Pat. No. 4,737,823. During operation, the foot 9 has its support on a
granite base surface 11 by means of a static gas bearing of a type known
per se pretensioned with an underpressure, which base surface 11 extends
in a horizontal plane parallel to the x-direction and to a horizontal
y-direction which is perpendicular to the x-direction (see FIG. 2). The
use of the aerostatically supported foot 9 in combination with the base
surface 11 prevents a translation of the table 5 in a z-direction
perpendicular to the base surface 11 as well as a rotation of the table 5
about an axis of rotation which extends parallel to the x-direction or
y-direction.
A translation of the table 5 parallel to the y-direction and a rotation of
the table 5 about an axis of rotation parallel to the z-direction are
prevented through the use of two pairs of electromagnets (13, 15) and (17,
19), these two pairs being fastened at some distance from one another in a
bearing block 21 provided between the table 5 and the foot 9 and
surrounding the guide beam 1 (see FIGS. 1 and 2). As can be seen in FIG.
2, the two electromagnets (13, 15) and (17, 19) of each pair are located
opposite one another on either side of the guide beam 1, seen in the
y-direction.
When an electric current is passed through the electromagnets 13, 15, 17,
19, each of the electromagnets 13, 15, 17, 19 will exert an attracting
electromagnetic force on the steel guide beam 1. The extent of this force
is substantially directly proportional to the square of the value of the
current through the relevant electromagnet 13, 15, 17, 19, and
substantially inversely proportional to the square of the size of an air
gap 23 between the relevant electromagnet 13, 15, 17, 19 (see FIG. 2) and
the guide beam 1. As a result of the relation between the electromagnetic
force and the size of the air gap 23, an equilibrium condition, in which
the attracting forces of the two electromagnets of each pair (13, 15) and
(17, 19) are equal, will be unstable if the current through the
electromagnets 13, 15, 17, 19 is a constant, non-controlled current. For,
if the table 5 is displaced from the equilibrium position over a small
distance parallel to the y-direction, the attracting forces of the
electromagnets whose air gaps 23 are made smaller by the displacement will
increase and the attracting forces of the electromagnets whose air gaps 23
are made wider by the displacement will decrease. A resultant force in the
direction of the displacement follows, so that the displacement will be
further increased.
In order to obtain a stable support in the y-direction, the current through
the electromagnets of the pairs (13, 15) and (17, 19) is controlled by
means of respective electronic control circuits 25a and 25b (see FIG. 2).
The control circuits 25a and 25b are identical. Each of the two pairs of
electromagnets (13, 15) and (17, 19) is provided with a contactless
capacitive position sensor 29, 31 of a kind known per se which is fitted
in one of the two electromagnets of the relevant pair (13, 15), (17, 19)
(see FIG. 2). During operation, each of the position sensors 29, 31
measures the size of the air gap 23 between the guide beam 1 and the
electromagnet 13, 17 in which the relevant position sensor 29, 31 is
fitted. The control circuits 25a, 25b compare the measured sizes of the
two air gaps 23 with a desired size and pass control currents through the
electromagnets 13, 15, 17, 19 whose values depend on the difference
between the desired and the measured sizes, so that the measured size
becomes equal to the desired size under the influence of the
electromagnetic forces exerted on the guide beam 1. The operation and
characteristics of the control circuits 25a, 25b will be further explained
below.
FIG. 4 diagrammatically shows a first embodiment of the electronic control
circuit 25a, circuit 25a being representative. An electrical output of the
relevant position sensor 29, 31 in each control circuit 25a, 25b is
connected to a first electrical input of a summation circuit which acts as
a comparator 33. An output signal u.sub.pos (voltage signal) of the
position sensor 29, 31, the value of which depends on the size of the air
gap 23, is compared by the comparator 33 with an input signal u.sub.set of
a second electrical input of the comparator 33, the value of which depends
on the desired size of the air gap 23. An output signal u.sub.com of the
comparator 33 is equal to the difference u.sub.set -u.sub.pos of the two
input signals of the comparator 33. The signal u.sub.com forms an input
signal for an electronic control unit 35. The control unit 35 is a PID
controller which is known per se and which is of a usual type having a
proportional, integrating and differentiating control action, transforming
the signal u.sub.com into a control signal u.sub.pid (voltage signal)
which determines the value of the current through the electromagnets 13
and 15.
Such a PID controller unit is a linear control unit and is accordingly
particularly suitable for use in a linear system. As was stated above, the
electromagnetic force is a non-linear force, so that the support of the
table 5 by means of the electromagnets 13, 15, 17, 19 forms a non-linear
system. In the known device described in the introduction, which forms a
non-linear system for the same reason, the use of a PID controller is made
possible in that the non-linear system is linearized around a working
point which is determined by a desired size h.sub.o of the air gap and a
basic current i.sub.o through the electromagnets. The characteristics of
the support, however, such as the stiffness, the damping and the
bandwidth, are then dependent on h.sub.o and i.sub.o. Therefore, an
optimal position control is obtained with the PID controller used only if
the displacements .DELTA.h are small in relation to h.sub.o and if the
control currents .DELTA.i are small in relation to i.sub.o.
In the control circuit 25a shown in FIG. 4, the control signal u.sub.pid is
applied to an electronic root extractor 37 of a type known per se. An
output signal u.sub.sqr of the root extractor 37 has a value equal to the
square root of the value of the signal u.sub.pid, while the sign
(polarity) of the signal u.sub.sqr is the same as that of the signal
u.sub.pid :
##EQU1##
An electrical output of the root extractor 37 is connected to the
electromagnet 15 via a first branch 39 of the control circuit 25, and to
the electromagnet 13 via a second branch 41 of the control circuit 25. The
branches 39 and 41 are provided with an electronic rectifier 43 and an
electronic rectifier 45, respectively. The rectifiers 43 and 45, which
both operate as diodes, are of a conventional type and may be of analog
design (a comparator circuit with a half-wave rectification action), or of
digital design (a logic circuit). The rectifiers 43 and 45 are
electrically oppositely directed relative to the signal u.sub.sqr, so that
they conduct the signal u.sub.sqr each in a different direction. The
function of the rectifiers 43, 45 in the control circuit 25a will be
further explained below.
The first branch 39 comprises an electronic multiplier 47 of a conventional
kind. A first input of the multiplier 47 is connected to the output of the
root extractor 37 via rectifier 43, while a second input of the multiplier
47 is connected to the output of the position sensor 29 (or 31) via a
feedback line 49 of the control circuit 25. A subtractor circuit 51 is
included in the feedback line 49 with a first electrical input which
receives a constant input signal u.sub.h1 and a second electrical input
which receives the signal u.sub.pos from the position sensor 29 (or 31).
The signal u.sub.h1 in this case is equal to the sum u.sub.0 +u.sub.c1 of
a reference signal u.sub.0, which is proportional to an average size of an
air gap 53 between the guide beam 1 and the electromagnet 15, and a
correction signal u.sub.c1, whose value is determined by a number of
characteristics of the electromagnet 15, such as the magnetic permeability
of the iron used for the electromagnet 15 and the length of the magnet
iron circuit used. An output signal u.sub.dif of the subtractor circuit 51
is a difference u.sub.h1 -u.sub.pos of the two input signals u.sub.h1 and
u.sub.pos of the subtractor circuit 51 and is determined by the size
h.sub.1 of the air gap 53. The signal u.sub.dif is multiplied by the
signal u.sub.sqr in the multiplier 47, so that an output signal u.sub.pr1
of the multiplier 47 is determined by the product u.sub.sqr
.times.u.sub.dif.
The output signal u.sub.pr1 of the multiplier 47 forms an input signal for
an amplifier unit 55 of a type known per se, which is provided with an
operational amplifier 57. The voltage signal u.sub.pr1 is amplified by the
amplifier unit 55 to a control current i.sub.1 through the electromagnet
15.
The second branch 41 of the control circuit 25 comprises an electronic
multiplier 59 with a first input which is connected to the root extractor
37 via the rectifier 45, and with a second input which is connected to the
position sensor 29 (or 31) via a feedback line 61 of the control circuit
25a. The feedback line 61 includes an adder circuit 63 with a first
electrical input receiving a constant input signal u.sub.h2 and a second
electrical input receiving the signal u.sub.pos from the position sensor
29, 31. The signal u.sub.h2 is comparable to the signal u.sub.c1 and is a
correction signal whose value depends on a number of characteristics of
the electromagnet 13, such as the magnetic permeability of the magnet iron
used in the electromagnet 13 and the length of the magnet iron circuit
used. An output signal u.sub.sum of the adder circuit 63 is equal to the
sum u.sub.h2 +u.sub.pos of the two input signals u.sub.h2 and u.sub.pos of
the adder circuit 63 and is determined by the size h.sub.2 of the air gap
23. The signal u.sub.sum is multiplied by the signal u.sub.sqr in the
multiplier 59, so that an output signal u.sub.pr2 of the multiplier 59 is
the result of the multiplication u.sub.sqr .times.u.sub.sum.
The output signal u.sub.pr2 of the multiplier 59 forms an input signal for
an amplifier unit 65 which is of a type similar to the amplifier unit 55
and which is provided with an operational amplifier 67. The voltage signal
u.sub.pr2 is amplified to a control current i.sub.2 through the
electromagnet 13 by the amplifier unit 65.
The approximate values of the forces F.sub.1 and F.sub.2 exerted by the
electromagnets 15 and 13 on the guide beam 1 can be written as follows:
##EQU2##
h.sub.1 and h.sub.2 are the air gaps as shown in FIG. 4 between the
electromagnets and the guide beam 1.
The following holds for the control currents i.sub.1 and i.sub.2 and the
size of the air gaps h.sub.1 and h.sub.2 :
i.sub.1 .about.u.sub.sqr .times.u.sub.dif and h.sub.1 .about.u.sub.dif
i.sub.2 .about.u.sub.sqr .times.u.sub.sum and h.sub.2 .about.u.sub.sum
Accordingly, it is true for the forces F.sub.1 and F.sub.2 :
F.sub.1 .about.u.sup.2.sub.sqr .about.u.sub.pid and F.sub.2
.about.u.sup.2.sub.sqr .about.u.sub.pid
The use of the multipliers 47 and 59 insures that the values of the forces
F.sub.1 and F.sub.2 have become independent of the sizes of the air gaps
h.sub.1 and h.sub.2 and are dependent on the value of the control signal
u.sub.pid only. Thus an optimal position control can be achieved with the
control unit 35 for any size of the air gap 23, so that an optimal
stability is achieved for any position of the guide beam 1 relative to the
electromagnets 13, 15. An advantage of this positional independence of the
control is that starting of the device can take place without problems. In
addition, the control will always provide an optimally stable operation of
the device in the case of sudden, relatively high peak loads on the table
5.
The use of the root extractor 37 in conjunction with the multipliers 47 and
59 insures that the values of the forces F.sub.1 and F.sub.2 are
proportional to the value of the control signal u.sub.pid, so that the
control unit 35 in fact governs a linear system, while also an optimal
position control is achieved by the control unit 35 at any value of the
control currents i.sub.1 and i.sub.2 through the electromagnets 13 and 15.
An advantage of this control is that a basic current through the
electromagnets 13, 15 is unnecessary. The control circuit 25a (and 25b)
shown in FIG. 4 in fact only passes control currents through the
electromagnets 13, 15, (and 17, 19) which renders the use of the
rectifiers 43 and 45 necessary. Indeed, since a force exerted by one of
the two electromagnets 13, 15 on the guide beam 1 is always an attracting
force, irrespective of the direction of the control current through the
relevant electromagnet, the forces of the two electromagnets 13, 15
without the use of the rectifiers 43, 45 would be permanently the same,
and a position control would not be possible. Thanks to the use of the
rectifiers 43, 45, the electromagnet 13 only is provided with a control
current i.sub.2 having a direction as indicated in FIG. 4 in the case of a
static load on the table 5, while i.sub.1 is equal to zero, if the
measured size of the air gap 23 is greater than the desired size. With
such a load, the electromagnet 15 only is provided with a control current
i.sub.1 having a direction as indicated in FIG. 4, while i.sub.2 is equal
to zero, if the measured size of the air gap 23 is smaller than the
desired size. Since a basic current through the electromagnets 13, 15 is
absent, and only one of the electromagnets 13, 15 receives a control
current, the electrical resistance losses of the electromagnets 13, 15 are
low. The resistance losses in a no-load condition of the table 5 are
negligibly small.
FIG. 5 diagrammatically shows a second embodiment of the control circuit
25a. In each control circuit 25a (and 25b) according to FIG. 5, the
subtractor circuit 51 and the adder circuit 63 are replaced by a first
digital memory 69 and a second digital memory 71, respectively. A relation
between the signal u.sub.pos and the signals u.sub.dif and u.sub.sum,
respectively, for a number of consecutive values of u.sub.pos differing by
a step size .DELTA.u.sub.pos is stored in tabular form in the memories 69
and 71. If the step size .DELTA.u.sub.pos is small enough, the functions
of the digital memories 69, 71 in the control circuit according to FIG. 5
approximate the functions of the subtractor circuit 51 and the adder
circuit 63, respectively, in the control circuit according to FIG. 4.
Moreover, the signals u.sub.dif and u.sub.sum are corrected by the
respective digital memories 69, 71 for non-linear characteristics of the
electromagnets 13, 15 and of the guide beam 1, such as, for example,
magnetic saturation.
It should be noted that the devices shown in FIGS. 1, 2 and 3 comprising
control circuits 25a (and 25b) according to FIGS. 4 or 5 are eminently
suitable for application in an optical lithographic positioning device for
the manufacture of masks to be used in the production of integrated
circuits. Dimensional inaccuracies can arise in such positioning devices,
and in other precision machines with electromagnet supports, as a result
of heat generation in the electromagnets. Such inaccuracies can be avoided
through the use of a device according to FIGS. 4 or 5. In addition, very
small air gaps can be used by virtue of the accuracy and the
position-independent characteristics of the said devices, such as
stiffness and bandwidth, which renders possible a reduction in the
required control current values and the accompanying resistance losses.
It should further be noted that the electronic root extractor 37 and the
rectifiers 43 and 45 may be omitted in the control circuits 25a, 25b if no
particular requirements are imposed on the heat generation in the
electromagnets. A position-independent control is then obtained whereby a
basic current with a superimposed control current flows through the
electromagnets. The stiffness and bandwidth are then dependent on the
strength of the basic current.
A still further embodiment is obtained in that only the rectifiers 43, 45
are omitted in the control circuits 25a, 25b. In this embodiment the
electromagnets are also supplied with a basic current, while a root
extractor has to be included in each branch 39, 41 before the relevant
multiplier 47, 59 in order to obtain a control independent of the current
value. The control signal U.sub.pid, which determines the control currents
through the electromagnets 13, 15, should then be added to and subtracted
from a basic signal U.sub.0, which determines the basic current through
the electromagnets, before the relevant root extractor in the branches 39,
41, respectively. In this way a bilateral support with
position-independent and current-independent characteristics is obtained
in the relevant support direction.
It should also be noted that the electronic components shown in FIGS. 4 and
5 may each be replaced by a digital circuit which has a corresponding
operation. Thus, for example, the control unit 35, the root extractor 37
and the two rectifiers 43, 45 may be replaced by an electronic control
unit in which the functions of the control unit 35, the root extractor 37
and the rectifiers 43, 45 are united.
It is pointed out that the devices comprising control circuits 25a, 25b
according to FIGS. 4 or 5 are particularly suitable for use in a
micromanipulator by which the body to be supported can be accurately
displaced over small distances (a few tens of microns). Since such a
device has a position-independent control, an optimal stability is
achieved in every position of the body to be supported.
It is further pointed out that a simple embodiment of the device is
obtained in that only one of the two electromagnets 13, 15 is controlled
in conjunction with a basic current. The other electromagnet in this
embodiment is provided with a basic current only and serves exclusively as
a counterbalancing magnet. A counterbalancing force may also be achieved
by other means such as, for example, vacuum, a permanent magnet, a gas
spring or a mechanical spring. The force of gravity acting on the body to
be supported may also be used as the counterbalancing force. In these
cases only one electromagnet is used in the relevant support direction.
In the device according to FIGS. 1 to 5, the electromagnets 13, 15 are
located opposite one another on either side of the guide beam 1. It is
noted that the electromagnets 13, 15 may also be otherwise located, i.e.
with the U-shaped sides facing away from one another. In the latter case
the pair 13, 15 is located between a first and a second part of the guide
beam, the two parts being parallel.
Finally, it is noted that two degrees of freedom of the table 5 are
suppressed by means of two pairs of electromagnets (13, 15) and (17, 19)
in the device according to FIGS. 1, 2 and 3, viz. a translation parallel
to the y-direction and a rotation about an axis extending parallel to the
z-direction. If more pairs of electromagnets are used in such a device,
more than two degrees of freedom of the body to be supported can also be
suppressed. If a more compact construction of the device is required, the
number of electromagnets used for the support may be reduced. This can be
done, for example, by supporting the body in two directions by means of
three electromagnets positioned at an angle of 120.degree. relative to one
another in a plane which is perpendicular to the said directions. An
adapted control of the electromagnets is necessary for this with
interlinked control circuits.
* * * * *
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