Large gap magnetic suspension system with superconducting coils

A magnetic suspension system and a procedure for operating the system employ a superconducting magnet having a lift coil assembly for developing a magnetic field to interact with the magnetic field of an object to be supported about the superconducting magnet. Smaller and larger magnet coils are provided in the superconducting magnet with counter rotating flow of current to introduce a depression in a potential energy surface above the superconducting magnet, this allowing the object to seek a height at the depression for stably locating the object. The system and methodology employs a set of control coils which are energized to orient and to translate the object to maintain a desired position and orientation. Pairs of the control coils are energized to produce a tilting of the object, as in roll or pitch, or a displacement of the object relative to the vertical axis.

BACKGROUND OF THE INVENTION 
This invention relates to the suspension of an object in space by magnetic 
levitation and, more particularly to the use of a set of coil assemblies 
which are symmetrically positioned about a central vertical axis, and are 
selectively energized, for providing both lift and directional stability 
to the object. The object, to be referred to herein as a model, consists 
of permanent magnet material with the magnetization in the direction of 
the vertical axis. The coil assemblies include a main superconducting coil 
assembly for providing lift, and sets of control, or gradient, coils for 
providing positional and directional stability, wherein the control coils 
are constructed in a flat pie form, and also in a circular cylindrical 
form. The control coils are located outside of a superconducting coil of 
the superconducting coil assembly. 
The suspension of objects in free space, distant from any physical support, 
is useful in certain situations for conducting various forms of tests and 
measurements. Of particular interest herein is the suspension of a model 
by magnetic levitation under conditions wherein the model can be held 
essentially motionless and with precise control over the orientation of 
the model. Furthermore, the system of magnets which is to be employed for 
holding and orienting the model is to be located at a distance from the 
model, and below the model, so as to provide unimpeded access to the model 
for the conduction of experiments and measurements. 
A problem arises in that presently available magnetic suspension systems do 
not provide all of the foregoing features. The problem may be appreciated 
from the fact that the laws of physics dictate that one cannot generate a 
field that will keep a permanent magnet, such as that employed in the 
model, stable in all degrees of freedom if the field source is below the 
permanent magnet. Therefore there is a need for active control by use of 
control coils driven with electric currents from a control system. In the 
past, equilibrium has been obtained by suspending an object from a magnet 
coil against the force of gravity with the attendant disadvantage that the 
space above the object is cluttered and may well interfere with 
utilization of the object. 
SUMMARY OF THE INVENTION 
The aforementioned problem is overcome and other advantages are provided by 
a magnetic suspension system employing a superconducting lift coil 
assembly for developing a magnetic field to hold the model above the lift 
coil assembly against the force of gravity. The lift coil assembly 
comprises two superconducting circular cylindrical coils disposed about a 
common central vertical cylindrical axis, with a first of the coils being 
of larger diameter than the second coil. In a preferred embodiment of the 
invention, the smaller-diameter superconducting coil is positioned at a 
higher level than the larger-diameter superconducting coil, however, the 
lift coil assembly is operative even with overlap of the two 
superconducting coils. In the three-axis coordinate system, the Z axis is 
the central vertical axis, while the X axis and the Y axis define a 
horizontal plane. 
Furthermore, in accordance with the invention, there is provided a set of 
assemblies of control, or gradient, coils to provide positional and 
directional stability of the model about all three orthogonal axes of the 
three-axis coordinate system. In the preferred embodiment of the 
invention, the control coils are located outside of the smaller-diameter 
superconducting magnet and above the larger-diameter superconducting coil, 
and are disposed symmetrically about the foregoing central axis. The set 
of control coil assemblies includes a pair of X coils positioned on 
opposite sides of the Z axis and centered on the X-Z plane for developing 
both a displacement force along the X axis, and a tilting force upon the 
model. 
Combination of magnetic fields of these control coils with adjustment of 
direction and intensity of their respective fields produces pure 
translational or pure tilting forces as may be required to adjust the 
position and the orientation of the model. A second pair of Y coils having 
the same construction as the foregoing X coils, is located in the Y-Z 
plane to provide translation of the model in the Y direction and tilt 
about a rotational axis orthogonal to that of the first-mentioned tilt. TO 
facilitate description of the invention, it is presumed that the model is 
aligned along the X axis, and has an elongated form. Thus, a tilt provided 
by the X coils constitutes a pitching of the model, and a tilt provided by 
the Y coils constitutes a rolling of the model. 
The superconducting lift coil assembly establishes a magnetic field which 
is symmetrical about the Z axis, and has a potential energy profile along 
the Z axis with a depression at the location of the model to stabilize the 
Z-axis coordinate of the model's location. The model is stable also in 
roll and in pitch. However, in the X and the Y directions, the equilibrium 
provided by the magnetic field of the superconducting coils is unstable, 
and must be supplemented by the foregoing operation of the control coils 
to attain stability. Also included in the sets of control coils is a 
circular cylindrical coil coaxial to the superconducting coils for 
adjusting the lift of the superconducting coils for fine adjustment of the 
height of the model above the superconducting coils. 
Control of rotation of the model about the Z axis, this being a yaw 
movement of the model, is accomplished by additional assemblies of control 
coils within the set of control coil assemblies. A first of the yaw 
control assemblies (to be referred to as the X.sup.2- Y.sup.2 coil 
assembly) is composed of four flat pie-shaped coils positioned in an array 
which encircles the Z axis, the four coils being arranged in two pairs of 
coils. In one of the two pairs, the coils are disposed symmetrically on 
opposite sides of the Z axis and perpendicular to the X axis. In the 
second of the two pairs, the coils are disposed symmetrically on opposite 
sides of the Z axis and perpendicular to the Y axis. The second yaw 
control coil assembly (to be referred to as the XY coil assembly) has the 
same configuration as the first yaw control assembly, namely, a quadruple 
coil assembly, but is rotated in orientation about the Z axis by 45 
degrees. Energization of the two yaw control assemblies provides a 
magnetic field distribution which torques the model to a desired 
orientation in yaw. 
The model includes magnetic material with magnetization in one direction, 
the vertical direction, to facilitate control of position and orientation 
by use of the control coils. As a further feature of the construction of 
the control coil assembly, it is noted that the control coils are 
positioned near a metallic housing of the superconducting coils, the 
housing forming a part of a cryostat which cools the superconducting 
magnet coils. In order to minimize the generation of eddy currents in the 
housing which might impede rapid changes of magnetic fields of the control 
coils, and thereby interfere with rapid precision control of the model, 
each of the control coil assemblies includes also a shield coil positioned 
alongside the housing to cancel out the eddy currents.

DETAILED DESCRIPTION OF THE INVENTION 
With reference to FIGS. 1 and 2, the invention comprises a superconducting 
magnet 30 having a lower coil 32 and an upper coil 34 which are disposed 
symmetrically about a vertical central axis 36. A set of coordinate axes 
37 is presented with the Z axis coinciding with the central axis 36, and 
with the X and the Y axes being perpendicular to each other and to the Z 
axis. Each of the coils 32 and 34 have a circular cylindrical form, the 
lower coil 32 having a larger diameter than the upper coil 34 and being 
positioned below the upper coil 34. An object to be levitated, namely, a 
model 38, is disposed above the upper coil 34, and is suspended in its 
position by a magnetic field gradient generated by the magnet 30. The 
model 38 may have any desired shape, an elongated cylindrical shape being 
shown in FIG. 1, by way of example. Included within the model 38 is an 
elongated slug 40 of magnetic material with magnetization vector parallel 
to the Z axis. Magnetic flux produced by the magnet 30 flows along an 
interior portion of the magnet 30 parallel to the axis 36, the flux being 
identified by a dashed line 42. 
In accordance with a feature of the invention, the flux field produced by 
counter-rotating currents in the coils 32 and 34 of the magnet 30 is 
structured so as to produce a potential energy surface, shown in the Z 
direction by a graph 43 of the potential energy contour, and in the X and 
the Y directions by a contour 44. The contour 44 has a peak in the center 
along the axis 36. The graph 43 shows an increasing strength of the 
potential energy with increasing distance from the superconducting magnet 
30, except for a depression 45 in the vicinity of the model 38. Due to the 
depression 45 in the Z coordinate of the potential energy field, the model 
38 is urged by the magnetic field to the height of the depression 45 which 
represents a stable position in the Z coordinate of the potential energy 
field. 
The magnetic field from the superconducting coil is designed such that the 
total potential energy of the model U (magnetic and gravitational 
potential energy) satisfy the following conditions at the equilibrium 
point: 
##EQU1## 
These conditions are achieved in practice for small models by designing a 
superconducting coil which produces a first order field gradient in the 
Z-direction which balances the gravitational force of the model thus 
satisfying (1) and a second order field gradient in the Z-direction 
satisfying requirement (2). These two conditions guarantee stable 
equilibrium along the Z-axis. 
In the X and the Y coordinates of the potential energy, the peaking of the 
contour 44 at the central axis 36 introduces an instability at the 
location of the model 38. As a result, upon the slightest offsetting of 
the model 38 from the central axis 36, the model 38 is urged away from the 
desired location at the axis 36 by the magnetic field of the magnet 30 in 
the absence of corrective fields to be introduced by control coils, as 
will be explained hereinafter. 
The counter-rotating currents of the two coils 32 and 34 are accomplished 
by connecting the two coils 32 and 34 in series, as shown in FIG. 2, and 
applying current via a current source 46 through the series circuit of the 
two coils 32 and 34. The directions and magnitudes of the currents are 
selected as a matter of convenience in design of the coils. By way of 
example, the direction of current, as shown in FIGS. 1 and 2, is clockwise 
in the lower coil 32 to provide a magnetic induction vector B1 pointing 
upwards while, in the upper coil 34, a counterclockwise flow of current 
produces a magnetic induction vector B2 which points downward and is of 
larger magnitude than the vector B1 produced by the lower coil 32. The 
number of ampere-turns of the upper coil 34 is greater than that of the 
lower coil 32 for adjusting the relative sizes of the two vectors and the 
magnetic field gradients at the model 38. It is to be understood that the 
representation of the coils in FIG. 2 is schematic only, and that there 
are, typically, many turns of wire in each of the coils 32 and 34. 
In accordance with the invention, and with reference to FIG. 3, control of 
the orientation or attitude of the model 38 at the desired location above 
the magnet 30 is attained by use of an assembly 48 of control coils. To 
facilitate description of the invention, FIG. 3 shows the coordinate axes 
37 having coordinates X, Y and Z of the frame of reference of the magnet 
30, and also shows a further set of coordinate axes 49 having coordinates 
X', Y', and Z' to serve as a frame of reference of the model 38. In the 
first embodiment of the invention, the control-coil assembly 48 is located 
above the lower coil 32 of the magnet 30, and concentrically surrounds the 
upper coil 34 of the magnet 30. The assembly 48 includes numerous sets of 
control coils, as will be described in detail hereinafter, which can be 
energized individually or in concert, and with adjustable amounts of 
current, so as to adjust the configuration of the field of the magnet 30 
for displacing the model 38 along either of the three coordinate axes X, 
Y, and Z as well as for orientating the model 38 by a rolling movement 
about the X' axis and by a pitching movement about the Y' axis. The 
positive Z' direction is vertical and parallel to the axis 36. The X' and 
the Y' directions are horizontal when the model 38 is level, perpendicular 
to each other, and are perpendicular to the Z axis. Roll, pitch and yaw 
are indicated respectively by Greek letters phi, theta and psi. In the use 
of the magnet 30 and the control coils of the assembly 48 for positioning 
and orienting the model 38, if desired, one may employ a safety net 50 
which envelops the model 38 to prevent accidental ejection of the model 38 
by forces of the magnetic field of the magnet 30 in the event of 
accidental dislodgement of the model 38 from its designated location. The 
net 50 may be secured to a frame (not shown) which holds the net away from 
the model 38 and which may be mounted on a floor or other support surface 
which supports the magnet 30 during use of the magnet 30. 
FIG. 4 shows the construction of an enclosure 52 and a frame 54 within the 
enclosure 52 for supporting the coils 32 and 34 of the magnet 30, and for 
providing passages for helium and nitrogen coolant as indicated in FIG. 4. 
A cooled shield, shown diagrammatically in FIG. 4, in cooperation with the 
coolants, provides the necessary low-temperature operating environment as 
is required for operation of the superconducting materials of the coils 32 
and 34 in a superconducting mode. The shield and the enclosure 52 are 
fabricated of a nonmagnetic metal such as aluminum. Also shown in FIG. 4 
is the location of the control coils of the assembly 48. It is noted that 
direct current (DC) is employed in energizing the coils of the magnet 30, 
rather than alternating current (AC), so as to enable construction of the 
shields and the enclosure 52 and the frame 54 of metallic material. The 
entire assembly of the shields and supply of the nitrogen and the helium 
coolants constitutes a cryostat 56. 
With respect to materials used in construction of the invention, the 
electrical conductors of the coils of the magnet 30 may be constructed, by 
way of example, of a superconductor such as niobium-titanium, NbTi. This 
is operative in a bath of liquid helium at one atmosphere pressure and at 
a temperature of 4.2 degrees (K). The superconductor is a NbTi 
multifilamentary wire composite composed of a core of NbTi filaments 
surrounded by a high purity copper shell. The operating current (typically 
400 amperes) produces a magnetic field which is only approximately 
one-third the value of current which produces the critical field; this 
ensures that the magnet 30 is operated well within the superconducting 
region. In a preferred embodiment of the invention, stored energy in the 
magnet 30 is approximately 4.5 megajoules. The frame 54 includes a 
stainless steel, or aluminum, coil form for supporting the radial winding 
pressure in each of the coils 32 and 34. The resulting field of the magnet 
30 is sufficient to space the model 38 at a large gap from the magnet 30, 
the gap being approximately three feet in a preferred embodiment of the 
invention. The control coils of the assembly 48 are located outside of the 
region cooled by the cryostat 56, and are operative at room temperature. 
The magnetic material of the model 38 is an alloy of neodymium-iron-boron. 
A typical weight of the permanent magnet material employed in the model 38 
is in the range of approximately 2-20 pounds. The slug 40 of magnetic 
material of the model 38 is disposed within an outer cylindrical shell and 
is foraged as a set of discs cemented together in a stack approximately 
1.25 inches in diameter and 5.84 inches in length. The overall dimensions 
of the model 38 are approximately 2 inches in diameter by 14 inches in 
length. The vacant spaces at both ends of the stack of magnetic material 
are suitable for housing a payload for conduction of experiments and 
measurements, and may include two electronic sensor packages (not shown) 
by way of example. 
FIG. 5 shows, in accordance with the first embodiment of the invention, the 
arrangement of the various coils which make up the sets of coils in the 
coil assembly 48. The coils include a lift coil Z for raising and lowering 
the model 38 for adjusting its position along the axis 36. Four sets of 
coils are designated as the X1 set of coils, the X2 set of coils, the Y1 
set of coils and the Y2 set of coils which serve to position the model 38 
along the X and the Y coordinates, as well as to introduce pitch and roll 
adjustments to the orientation of the model 38. Two further sets of coils 
are each multiply sectioned, as will be described hereinafter, and serve 
to adjust the orientation of the model 38 in yaw, these additional two 
coils being identified by quadratic terms in X and in Y, namely the XY set 
of coils and the X.sup.2- Y.sup.2 set of coils. 
FIG. 6 shows the arrangement, in plan view, of the control coils described 
above in FIG. 5. The first coil shown at the top of FIG. 6 is the lift (Z) 
coil which is a single coil of circular configuration and encircles the 
upper coil 34 of the magnet 30. The next coil shown is the (X.sup.2- 
Y.sup.2) coil which is composed of four sectors of pie-shaped 
configuration wherein two of the sectors are centered on the YZ plane and 
two of the sections are centered on the XZ plane. Each of the sectors 
includes a first arc segment 58 and a second arc segment 60, the first arc 
segment 58 being an outer arc segment and the second arc segment 60 being 
an inner arc segment. The four coil sectors are positioned symmetrically 
about the Z axis, and lie outside of the upper coil 34 of the magnet 30. 
Arrows indicate direction of current flow in each of the coil sectors. 
Current flow in the loop formed by the arc segments 58 and 60 of one 
sector is in the opposite sense to current flow in the loop of arc 
segments 58 and 60 in the adjacent sector. In the practice of the 
invention, the currents in each of the four sectors are equal, the 
ampere-turns in each of the first arc segments 58 are equal, and the 
ampere-turns in each of the second arc segments 60 are equal. Each sector 
may be energized by connection to a current source to provide the 
requisite current, a series connection being employed in this embodiment 
of the invention. 
The next set of coils depicted is the XY set of coils which is constructed 
of four sectors of coils having the same configurations as the previous 
set of coils, but being rotated in position by 45 degrees about the Z axis 
relative to that of the previous set of coils. Thus, in the XY set of 
coils, one sector is oriented with its center line lying at 45 degrees, 
with the other three sectors being oriented respectively at 135 degrees, 
225 degrees, and 315 degrees. Each sector includes a first arc segment 62 
and a second arc segment 64 wherein the second arc segment 64 is closer to 
the Z axis and the first arc segment 62 is more distant from the Z axis. 
Current flow in the loop formed by the arc segments 62 and 64 of one 
sector is in the opposite sense to current flow in the loop of arc 
segments 62 and 64 in the adjacent sector. 
The fourth coil arrangement shown in FIG. 6 is a composite of two coil 
arrangements, namely, the Y1 set of coils and the X1 set of coils. The 
coils have a flat pie configuration. Each of the sets of coils is divided 
into two sectors. The two sectors of the Y1 set of coils is centered along 
the YZ plane, and the two sectors of the X1 set of coils is centered along 
the XZ plane. There are three arc segments in each section. namely, a 
first arc segment 66, a second arc segment 68, and a third arc segment 70. 
The first arc segment 66 is the outermost arc segment, the third arc 
segment 70 is the innermost arc segment, and the second arc segment 68 is 
disposed at a location between the first and the third arc segments. 
Current direction is indicated by arrows on the respective arc segments. 
In each of the sectors of the Y1 set of coils, which coils are disposed 
diametrically on opposite sides of the Z axis, the current flow in the 
loop of arc segments 66 and 68 of one section is counterclockwise while in 
the other section the current flow in the loop of the arc segments 66 and 
68 is in the opposite sense, namely, clockwise. Similarly, in the case of 
the X1 set of coils, the loop of current in the arc segments 66 and 68 of 
one sector flows in a clockwise direction while the corresponding current 
flow in the opposite sector is counterclockwise. Furthermore, in each 
sector, the current flowing through the third arc segment 70 and the 
second arc segment 68 form a loop having a direction of current 
circulation which is of the opposite sense to that of the loop of arc 
segments 66 and 68. 
The configuration of sets of gradient coils, namely, the X2 set and the Y2 
set at the bottom of FIG. 6 follows the same geometric arrangement of that 
of the preceding configuration of coils. In each sector of the Y2 coils 
and in each sector of the X2 coils, there is a first arc segment 72, a 
second arc segment 74 and a third arc segment 76 wherein the first arc 
segment 72 is the outermost arc segment, the third arc segment 76 is the 
innermost arc segment, and the second arc segment 74 is located at a 
radial distance from the Z axis between the first arc segment 72 and the 
third arc segment 76. The coil sectors have a flat pie configuration. The 
foregoing teachings of direction of coil currents set forth above with 
respect to the X1 and Y1 coil sets applies also to the X2 and the Y2 coil 
sets. The number of ampere-turns in the corresponding coils of the X2 and 
the Y2 coil sets may differ from the number of ampere-turns of the coils 
in the X1 and the Y1 coil sets. Centerlines of the Y2 sectors are parallel 
to the Y axis and centerlines of the X2 sectors are parallel to the X 
axis. 
It is noted also that the innermost arc segments 70 and 76 (FIG. 6) are 
employed for purposes of attenuating any eddy currents which might 
otherwise be developed in the aluminum enclosure 52 (FIG. 4) which 
surrounds the upper coil 34 of the magnet 30, the enclosure extending 
through the center of the array of the control coils of the assembly 48. 
The locations and the number of ampere turns in each of the innermost arc 
segments 70 and 76 are selected for minimization of eddy currents. It is 
noted that, in the case of steady current flow in each of the control 
coils of the assembly 48, that there are no eddy currents. However, any 
type of vibratory or drifting movement of the model 38 will trigger a 
response on the part of a control system, to be described hereinafter, 
which rapidly applies currents, or varies existing currents, to the 
control coils to correct the orientation of the model 38. Such rapid 
changes in current may induce eddy currents in the metallic enclosure 52 
and, accordingly, the arc segments 70 and 76 are employed for minimization 
of these eddy currents. In the X1 and the Y1 coil sets, in each sector of 
coils, the arc segments 66, 68, and 70 are connected in series to ensure 
proper relationship among the magnitudes of the currents in the respective 
arc segments. Similar comments apply to the arc segments 72, 74, and 76 in 
each sector of the X2 and the Y2 coil sets. Maintenance of the requisite 
ratio of current flow in the innermost arc segments 70 and 76 ensures 
minimization of the eddy currents. In the event that the enclosure were 
made of a nonmetallic material, such as plastic, then the innermost arc 
segments 70 and 76 would be reconfigured or eliminated entirely since the 
function of reducing eddy currents is no longer required. 
FIG. 7 shows a control system 80 for applying currents to the control coils 
of the assembly 48 (FIG. 3). The system 80 includes an array of eight 
cameras 82 positioned for viewing the model 38, and outputting electric 
signals via a data bus 84 to a controller 85. Each of the cameras 82 is in 
the nature of a television camera and outputs signals which can be 
combined in the controller 85 to provide data as to the position and the 
orientation of the model 38. Included within the controller 85 are a 
computer 86 and a memory 87 which operate with the camera data and, in 
accordance with well-known programs for coordinate transformnation and 
triangulation, establish the coordinates of the model 38 in terms of the 
X, the Y and the Z coordinates, as well as in terms of angles of pitch, 
roll, and yaw. The controller 85 outputs signals via coil-driver 
amplifiers 88 to individual ones of the sets of coils indicated directly 
in the drawing by the legends X1, X2, Y1, Y2, Z, XY and (X.sup.2-Y.sup.2). 
The memory 87 stores necessary data, which may be entered via a keyboard 
89, and programs for operation of the computer 86 to perform the foregoing 
calculations. 
FIG. 8 shows operation of the controller 85 of FIG. 7. In terms of 
functional operation, the controller 85 may be viewed as comprising a 
position processor 90 and a control signal processor 91. The position 
processor 90 receives the signals from the cameras 82, and computes the 
position of the center of the model 38 in terms of the coordinate axes 37 
of the superconducting magnet 30. The coordinate axes 37 of the 
superconducting magnet 30 may be regarded also a laboratory reference 
frame. The model 38 is provided with coloration or other marking which 
allows the cameras 82 to sense roll about the longitudinal axis X' of the 
model 38. The longitudinal shape of the model 38 allows the cameras 82 to 
sense pitch about the transverse axis Y' of the model 38 and yaw about the 
vertical axis Z of the magnet 30. This information of the model 
orientation is employed by the position processor 90 to compute the values 
of roll, pitch and yaw, and the respective angular velocities. At the 
control signal processor 91, the orientation and position of the model 38 
is compared with a desired value of orientation and a desired value of 
position to develop error signals which represent the difference between 
the desired and actual values of the orientation and the position of the 
model 38. The memory 87 stores values of coil currents to be applied to 
various combinations of the control coils of the coil assembly 48 for 
accomplishing translation of the model 38 along each axis of the 
coordinate axes 37, and rotation of the model 38 about each axis of the 
coordinate axes 49 of the model 38. 
As noted above, the model is inherently stable in the Z direction. The 
model 38 is also inherently stable in pitch and roll. Thus in generating 
servo control signals for positioning the model 38, only damping need be 
used in the correction of vertical position, pitch and roll. For 
correction of displacement in the X and the Y directions, and for 
correction of yaw, feedback is employed in the generation of the requisite 
servo signals. Displacement in a direction inclined to the X and the Y 
axes is accomplished by multiplication of the current values by sine and 
cosine of the angle of inclination to attain the requisite vectorial 
combination of X and Y values of displacement. This multiplication is 
performed by the computer 86. A corresponding use of sines and cosines is 
applied for rotation of the model 38 about an axis inclined to a 
coordinate axis of the coordinate axes 49 of the model 38. The requisite 
control currents are outputted from the control signal processor 91 via 
the amplifiers 88 to the respective control coils as shown in FIG. 8. 
In FIG. 8, the results of combined operation of various combinations of the 
control coils is tabulated in a table 92. Thus, concurrent energization of 
the pair of X1 and the pair of X2 pie coils can produce an X displacement 
force, a pitch torque, or a roll torque. Introduction of cosine of the yaw 
angle and sine of the yaw angle provides for a tilting or rotation of the 
model 38 about a rotational axis. The rotational axis may be inclined to a 
coordinate axis of the coordinate axes 37 of the magnet 30. Thus, 
concurrent energization of the pair of Y1 and the pair of Y2 pie coils can 
produce an Y displacement force, a pitch torque, or a roll torque. 
Introduction of sine of the yaw angle and cosine of the yaw angle provides 
for a tilting or rotation of the model 38 about a rotational axis inclined 
to a coordinate axis of the coordinate axes 37 of the magnet 30. The Z 
coil, by itself, can introduce a vertical force. Concurrent energization 
of the quadrature XY pie-shaped coils and the quadrature (X.sup.2-Y.sup.2) 
pie-shaped coils provides a torque in the yaw direction. 
FIG. 9 shows implementation by the controller 85 of control of currents in 
the X1 and the X2 coil sets operative with power from power supplies 93 to 
produce a resulting magnetic field at 94 for adjustment of the position of 
the model 38. The circuitry of FIG. 9 can be implemented by specific 
circuit components as set forth in FIG. 9, or can be implemented by 
operation of the computer 86. In view of the fact that the operational 
speed of computers is suitable for updating the requisite currents in all 
of the control coils at a rate sufficient for orienting and positioning 
the model 38 with a designated orientation and position, it is the 
practice in a preferred embodiment of the invention to implement the 
circuit functions of FIG. 9 by use of the computer 86. Thus, an arithmetic 
logic unit 96 of the computer 86 outputs a desired value of the X 
component of the model position to a summing circuit at 98 which signifies 
the error between a desired, or reference value of the X position and 
produces an error signal at 100. The reference position is inputted by an 
operator of the equipment by use of the keyboard 89 connected to the 
controller 85 as shown in FIG. 7. Rate-aiding or velocity control, is also 
provided by the computer at block 104 which provides the derivative of 
displacement along the X coordinate, and includes a multiplicative damping 
factor for rate-aiding which is combined at a summing circuit 106 with the 
error signal at line 100. The error signal at line 100 is amplified by 
amplifier 108 prior to being applied to the summing circuit 106, the 
amplifier 108 providing forward loop gain. 
The output signal of the summing circuit 106 is applied to the X1 coil set 
via a summing circuit 110 and an amplifier 112. The summing circuit 110 
incorporates any bias or offset current value with the signal from the 
summing circuit 106. The amplifier 112 provides necessary gain for driving 
the coils of the X1 coil set with the requisite current. A fraction of the 
signal outputted by the summing circuit 106 is extracted at block 114, 
which may be a voltage divider circuit, and is applied via a summing 
circuit 116 and an amplifier 118 for driving current into the coils of the 
X2 coil set. There results a shift of magnetic field strength along the X 
axis with greater field strength being observed to one side of the central 
axis 36 than to the opposite side of the central axis 36. A resulting 
shift in magnetic potential energy is in the nature of the graph depicted 
to the right of the magnetic field 94 (FIG. 9). 
The circuitry of FIG. 10 is the same as that of FIG. 9 and functions in the 
same fashion and, accordingly, need not be described in detail. The result 
is an offsetting of the magnetic field strength along the Y axis in 
response to a difference between a commanded value of the Y coordinate and 
a reference value, Yr, inputted by an operator of the system. 
In FIG. 11, circuitry similar to that disclosed in FIG. 9 is employed to 
operate the Z control coil, the circuitry of FIG. 11 being simplified from 
that in FIG. 9 by the deletion of the components 110, 114, 116 and 118. 
FIG. 12 employs the circuitry of both FIGS. 9 and 10, and outputs a signal 
from the summing circuit 106 via a cosine unit 120 and a sine unit 122 
respectively to the X and the Y sets of control coils. The cosine unit 120 
multiplies the signal of the summing circuit 106 by the cosine of the yaw 
angle. The sine unit 122 multiplies the signal of the summing unit 106 by 
the sine of the yaw angle. The bias or offset currents are also applied as 
indicated via the bias source identification numerals 1-4. There results a 
magnetic field at 124 which tends to offset the field of the magnet 30 to 
induce a pitching movement of the model 38. The resulting configuration of 
the potential energy contour is shown in a graph to the right of the 
magnetic field 124. By introduction of a 90 degree offset to the yaw 
angle, there results an offset of the field of the magnet 30 to induce a 
rolling movement of the model 38. Thereby, the model 38 can be reoriented 
both in pitch and in roll. 
FIG. 13 shows circuit components already presented in FIG. 11 for producing 
coil current; however, in FIG. 13, coil currents are being applied to the 
XY coil set and the X.sup.2- Y.sup.2 coil set. The signal outputted by the 
summing circuit 106 is applied via a cosine unit 126 to the XY coil set , 
and via a sine unit 128 to the X.sup.2- Y.sup.2 coil set. The cosine unit 
126 and the sine unit 128 are coupled via amplifiers 130 and 132 to the 
respective control coil sets, the amplifiers 130 and 132 providing 
suitable power amplification for driving currents in the coils of the 
respective coil sets. The cosine unit 126 multiplies the output signal of 
the summing circuit 106 by the cosine of twice the yaw angle. The sine 
unit 128 multiplies the output signal from the summing circuit 106 by the 
sine of twice the yaw angle. There results a magnetic field outputted by 
the coils at 134 which tends to rotate the model 38 about the yaw angle. 
As indicated in the graph to the right of the magnetic field 134, the 
magnetic potential energy contour introduced by the yaw control is flat, 
except for slight irregularities in the field caused by manufacturing 
tolerances of the superconducting magnet, so as not to introduce any 
pitching or heaving movement to the model 38. 
FIG. 14 shows an insertion/retraction mechanism 136 operative with the 
control system 80 of FIG. 10 for positioning the model 38 at the desired 
location above the magnet 30 and wherein, after appropriate position, 
withdraws from the model 38 to allow the model 38 to be freely suspended 
or leviated within the fields of the superconducting magnet 30 and the 
control coils of the assembly 48. The mechanism 136 is operative with a 
console 138 in a control station 140. The console 138 includes the 
keyboard 89 (FIG. 7) by which the operator enters commands to the 
mechanism 136 includes a carriage 142 for transporting the model 38, the 
carriage 142 terminating in a gripper 144 which engages with the model 38. 
The carriage 142 is held pivotally by a pivot 146 to a swing arm 148 which 
rotates about a post 150 under power of a motor 152. A cable 154 provides 
for transmission of vacuum pressure, as will be described hereinafter, and 
also for transmission of electric signals between the gripper 144 and the 
controller 85 which is located in the console 138. The cable 154 also 
provides power to the motor 152, as well as to motors 156 and 158 which 
serve respectively to pivot the carriage 142 relative to the arm 148 about 
the pivot 146, and to pivot the arm 148 relative to the post 150 about a 
pivot 160. The motor 152 is supported by a base 162 which also supports 
the post 150 rotatably to allow for rotation of the arm 148 and the post 
150 about an axis of the post 150. The motor 156 is supported by the arm 
148 and imparts a pivoting movement to the carriage 142 by rotating a 
shaft 164 of the pivot 146. The motor 158 is supported by the pivot 160 
and imparts a pivoting movement to the arm 148 by rotating a shaft 166 of 
the pivot 160. 
In the operation of the mechanism 136, the arm 148 swings the carriage 142 
to a position above the center of the magnet 30. Height and orientation of 
the carriage is adjusted by the pivots 146 and 160. Thereupon, the gripper 
144 releases the model 38 gradually in the presence of the magnetic field 
of the magnet 30 and the control coils of the assembly 48, so as to 
transfer support of the model 38 from the carriage 142 to the magnetic 
field. Means to facilitate the transfer of the model 38 between the 
carriage 142 and the field will be described hereinafter. Upon completion 
of the transfer, the arm 148 is swung away from the magnet 30 to a point 
of convenience near or at the station 140, as indicated in phantom view. 
Electric current for operation of the control coils of the assembly 48 is 
applied from the console 138 via line 168. 
With reference also to FIGS. 15-17, the gripper 144 comprises a bed 170 for 
engagement with the model 38, and a pair of opposed jaws 172 and 174 which 
serve to maintain the model 38 at or near to the bed 170. Vacuum ports 176 
are located in the bed 170, and connect with a source of vacuum (not 
shown) via a hose 178 to hold the model 38 within the bed 170 under the 
force of vacuum pressure. The hose 178 passes within the cable 154 to the 
station 140 for control of the vacuum pressure. The bed 170 is supported 
by a frame 180 of the gripper 144. The jaws 172 and 174 are mounted 
pivotally by pivots 182 and 184, respectively, to the frame 180. A spring 
186 connects with the jaws 172 and 174 to bias the jaws 172 and 174 via 
spring force in the open position wherein the model 38 is free to approach 
or to leave the bed 170. Application of vacuum pressure via a hose 188 
overcomes the force of the spring 186 to close the jaws 172 and 174 toward 
the model 38. The hose 188 also passes within the cable 154 to the station 
140 for control of the vacuum pressure. In the gripper 144, the hose 188 
connects with a vacuum circuit 190 which operates two pistons 192 and 194 
by displacing the pistons 192 and 194 under vacuum pressure against the 
jaws 172 and 174, thereby to accomplish a desired opening and closing of 
the jaws 172 and 174. Two screws 196 and 198 are carried by the jaws 172 
and 174, respectively, for butting against the bed 170 to serve as stops 
to a closing movement of the jaws 172 and 174. It should be appreciated 
that the gripper insertion tool is formed of non-magnetic material. 
The invention also provides for sensor of force of the magnetic field upon 
the model 38, such as a strain gauge 200 which is located on a connecting 
region 202 of the frame 180 with the carriage 142 to measure changes in 
force directed to the carriage 142 by the model 38 under the influence of 
the magnetic fields of the magnet 30 and the coil assembly 48. Electric 
signals outputted by the strain gauge 200 are transmitted via the cable 
154 to the station 140 to provide data describing an approach of the model 
38 to a stable point in altitude of the potential energy profile along the 
Z axis of the magnet 30. At the stable point, the magnetic field provides 
an upward force which balances the downward force of gravity upon the 
model 38. Thus, the weight of the gripper 144 is the same weight obtained 
for an empty gripper. Away from the stable point, sideways and/or vertical 
forces are sensed which signal the controller 85 as to the requisite 
direction of movement of the model 38 for proper placement at the stable 
point along the vertical dimension of the potential energy profile. 
Thereby, the invention is provided with means for altering the 
configuration of the field of a superconducting magnet so as to permit 
both manual and automatic positioning and orienting of the model freely 
suspended above the superconducting magnet by the magnetic field. 
It is to be understood that the above described embodiment of the invention 
is illustrative only, and that modifications thereof may occur to those 
skilled in the art. Accordingly, this invention is not to be limited to 
the embodiment disclosed herein, but is to be limited only as defined by 
the appended claims.