MAGNETIC FIELD GENERATOR

Abstract

A magnetic field generator that comprises at least three groups of magnets, the magnetic moment of each magnet being rotatable about a rotation axis, wherein each group comprises at least two magnets, and each group has an orientation in the sense that the rotation axes of the magnetic moments of the magnets of the same group extend in the group's orientation. The orientations of the different groups are linearly independent.

Claims

1. A magnetic field generator that comprises at least three groups of magnets, the magnetic moment of each magnet being rotatable about a rotation axis, wherein each group comprises at least two magnets, and each group has an orientation in the sense that the rotation axes of the magnetic moments of the magnets of the same group extend in the group's orientation, characterised in that the orientations of the different groups are linearly independent.

2. A magnetic field generator that comprises at least six magnets, and input means for a set of control parameters, wherein the magnetic moment of each magnet is rotatable about a rotation axis such that in a workspace the magnetic fields of the magnets in combination can generate a resulting magnetic field of arbitrary orientation and arbitrary flux density, and wherein the orientation and flux density of the resulting magnetic field is determined by the values of a set of control parameters, characterised in that the set of control parameters comprises less than six control parameters.

3. A magnetic field generator that comprises at least two groups of magnets, the magnetic moment of each magnet being rotatable about a rotation axis, wherein each group comprises at least two magnets, and each group has an orientation in the sense that the rotation axes of the magnetic moments of the magnets of the same group extend in the group's orientation, characterised in that the magnets of the same group are operationally coupled with regard to the rotation of their magnetic moments such that their magnetic moments rotate simultaneously by identical angles about their respective rotation axis.

4. A magnetic field generator that comprises at least two groups of magnets, the magnetic moment of each magnet being rotatable about a rotation axis, wherein each group comprises at least two magnets, and each group has an orientation in the sense that the rotation axes of the magnetic moments of the magnets of the same group extend in the group's orientation, characterised in that the magnets are located essentially on the edges of a parallelepiped, or essentially on intersecting circumferences on an ellipsoid.

5. The magnetic field generator of claim 1, characterised in that the magnets are permanent magnets.

6. The magnetic field generator of claim 1, characterised in that the magnetic moment of at least one magnet forms an angle of more than 80 degrees with the orientation of the rotation axis.

7. The magnetic field generator of claim 1, characterised in that in at least one group of magnets has a hub in the sense that all magnets of this group have the same distance to the group's hub.

8. The magnetic field generator of claim 1, characterised in that the maximum achievable flux density of the resulting magnetic field generated in a workspace by the magnets in combination in each one of the achievable orientations of the resulting magnetic field is larger than 90 Gauss.

9. The magnetic field generator of claim 1, characterised in that by mean of rotating the magnetic moment(s) of one or more of the magnets a spatial gradient of the magnetic flux density of the magnetic field generated in a workspace by the magnets in combination can be changed.

10. The magnetic field generator of claim 1, characterised in that the direction of the resulting magnetic field can be changed at a speed larger than 0.1 degrees per second.

11. A method of changing at least one property of a resulting magnetic field generated by at least three groups of magnets by means of rotating the magnetic moment of each magnet about a rotation axis, wherein each group comprises at least two magnets, and wherein each group has an orientation in the sense that the rotation axes of the magnetic moments of the magnets of the same group extend in the group's orientation, characterised in that the orientations of the different groups are linearly independent.

12. A method of changing at least one property a resulting magnetic field generated by at least six magnets by means of rotating the magnetic moment of each magnet about a rotation axis, wherein the resulting magnetic field can have arbitrary orientation and arbitrary flux density, and wherein the orientation and flux density of the resulting magnetic field is determined by setting the angle of rotation of the magnetic moments about the respective rotational axes to values derived from the values of a set of less than six control parameters.

13. A method of changing at least one property of a resulting magnetic field generated by at least two groups of magnets by means of rotating the magnetic moment of each magnet about a rotation axis, wherein each group comprises at least two magnets, and wherein each group has an orientation in the sense that the rotation axes of the magnetic moments of the magnets of the same group extend in the group's orientation, characterised in that the magnets of the same group rotate simultaneously by identical angles about their respective rotation axis.

14. A method of changing at least one property of a resulting magnetic field generated by at least two groups of magnets by means of rotating the magnetic moment of each magnet about a rotation axis, wherein each group comprises at least two magnets, and wherein each group has an orientation in the sense that the rotation axes the magnetic moments of the magnets of the same group extend in the group's orientation, characterised in that the magnets are located essentially on the edges of a parallelepiped, or essentially on intersecting circumferences on an ellipsoid.

15. Use of the magnetic field generator according to claim 1 for actuating a tethered or untethered device that possesses a magnetic moment.

16. Use of the method according to claim 11 for actuating a tethered or untethered device that possesses a magnetic moment.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In the following, further preferred embodiments of invention are illustrated by means of examples. The invention is not limited to these examples, however.

[0054] The drawings schematically show:

[0055] FIG. 1 A schematic perspective view on a magnetic field generator with cylindrical magnets;

[0056] FIG. 2 A schematic perspective view on a magnetic field generator with cubic magnets;

[0057] FIG. 3 A cross-sectional view through one group of the permanent magnets in the magnetic field generator in FIG. 1; their magnetic moments M.sub.1, M.sub.2, M.sub.3 and M.sub.4 are of the same magnitude within manufacturing errors and all magnetic moments extend in the paper plane. Yet, they have different rotation angles α.sub.1, α.sub.2, α.sub.3, α.sub.4 about their rotation axes, which extend perpendicularly to the paper plane. Moreover, all magnetic moments rotate at the same absolute value of angular velocity |ω| but two magnetic moments rotate clockwise while the other two rotate counter-clockwise;

[0058] FIG. 4 A schematic representation of a magnetic field generator with three groups of magnets actuating a untethered medical device inside the human body; the view on the left side of the top row is a top view, the view on the right side of the top row is a side view, and the view on the bottom is a front view;

[0059] FIG. 5 A schematic representation of a magnetic field generator with three groups of magnets actuating a tethered medical device inside the human body; the view on the left side of the top row is a top view, the view on the right side of the top row is a side view, and the view on the bottom is a front view;

[0060] FIG. 6 The components of a resulting magnetic field as generated by a group of four rotating magnets and measured in the workspace; the magnets are spherical with a diameter of 30 mm and a coercive field strength of approximately 955 kA/m. The resulting magnetic field is a spatially homogeneous field of 20 mT that rotates at 1 Hz starting at about 1 s;

[0061] FIG. 7 The results of measurements of the maximum magnetic field generated by a group of magnets compared with the results of a simulation;

[0062] FIG. 8 The results of a simulation of a resulting magnetic field that oscillates along the z axis;

[0063] FIG. 9 The results of a simulation (“Sim”) and of measurements (“Exp”) of an oscillating resulting magnetic field B (G) with three different orientations within the x-y-plane: (a) α.sub.B=0°. (b) α.sub.B=45°. (c) α.sub.B=90°. The fields' components in x and z direction are labelled as “B.sub.x” and “B.sub.z”, respectively; the curves are results from simulations (labeled as “Sim”) and the markers are experimental results (labeled as “Exp”);

[0064] FIG. 10 (a) a schematic drawing identifying the component vectors B.sub.x, B.sub.y and B.sub.z, of a resulting magnetic field B along the axes of a coordinate system and angles defining the orientation of the magnetic field vector in the coordinate system; and (b) a schematic drawing of the three magnetic fields B.sub.y, B.sub.xz and B.sub.yz, each generated by the magnetic moments of a different one of three groups of magnets; the orientation of the latter three magnetic fields is defined by the angles α.sub.xy, α.sub.xz, and α.sub.yz, respectively;

[0065] FIG. 11 A cross-sectional view in the yz-plane through a group of four permanent magnets that gives rise to a magnetic field B.sub.yz;

[0066] FIG. 12 A cross-section view in the yz-plane through a group of five permanent magnets that gives rise to a magnetic field B.sub.yz (a) in a schematic cross-sectional view (a) Schematic of the geometry; and (b) the results of a numerical simulation that verifies the rotating magnetic field; the arrows in the simulation point at the direction of the magnetic field and the lengths of the arrows correspond to the field strength;

[0067] FIG. 13 An illustration of a magnetic field B rotating about an axis defined by vector û in tree-dimensional space;

[0068] FIG. 14 A schematic perspective view of a magnetic field generator with one group of magnets used for medical applications;

[0069] FIG. 15 A schematic perspective view of a magnetic field generator with six magnets arranged in in three groups with two magnets per group;

[0070] FIG. 16 A schematic perspective view of a human-scale magnetic field generator; top: side view, bottom: front view;

[0071] FIG. 17 The result of a finite element simulation of one group of 18 magnets in a human-scale setup; the arrows represent the direction of the magnetic field, and the grey tone represents the flux density; the length in the figure has a unit of meter and the grey tone scale has a unit of Gauss;

[0072] FIG. 18 A soft miniaturized linear actuators that is wirelessly powered by the magnetic field generator; (a) is a schematic representation of the working principle of the actuation; (b) is a drawing of the actuator where the arrows in the attached magnets indicate their magnetization, and (c) is a photograph of the assembled actuator on a 10-cent coin;

[0073] FIG. 19 Photographic snapshots of a video that shows the movement of the linear actuator of FIG. 1 when operated by a magnetic field generator; The snapshots show the compressed (a), relaxed (b) and elongated (c) states of the soft actuator; and

[0074] FIG. 20 The results of load measurements on the linear actuator of FIGS. 18 and 19; (a) shows a snapshots of the video showing the lift of a load by the actuator powered by the magnetic field generator; and (b) shows the maximal displacement D of the actuator plotted against different loads L and the work W calculated from the load and the displacement.

DETAILED DESCRIPTION OF AN EMBODIMENT OF THE INVENTION

[0075] In the following description of preferred embodiments of the invention, identical reference numerals refer to identical or similar components.

Example: Magnetic Field Generator with 12 Magnets

[0076] The magnetic field generator illustrated in FIGS. 1 to 3 comprises of three groups of permanent magnets 1, and four parallel magnets 1 belong to each group. Each magnet 1 in the drawing is in a cylindrical or cubical shape, yet other shapes would also be possible, for example spherical or cuboid shapes. The permanent magnets 1 have closely matched magnetization and strength and a permanent magnetization direction. They are arranged to be rotated by electrical motors (not shown) around an axis that is perpendicular to the magnets 1 magnetic moment M.sub.i. Combined, the magnets generate resulting a magnetic field 2 with field vector B at the centre of the magnetic field generator where the workspace 3 is located.

[0077] For many applications, it is beneficial to generate a homogeneous magnetic field 2 in a large workspace 3 with negligible magnetic gradient force. In the magnetic field generator of figured 1 to 3, the magnets 1 are arranged equidistantly to their next neighbours and in a circle around a hub that is located in centre of the workspace 3, so as to minimize spatial and temporal gradients of the resulting magnetic field 2. Should the magnets 1 differ in their magnetization, then in principle it is possible to compensate differences in the physical properties by an arrangement of the magnets 1 where these no all longer have the same distance from the hub or are no longer arranged equidistantly from their next neighbours.

[0078] Advantageously, in the arrangement of FIGS. 1 to 3, only three independent angular inputs (labeled as α, β, γ in FIGS. 1 and 2), are needed to change the direction of the field vector B to point in an arbitrary direction in three-dimensional space while also allowing for the adjustment of the B field flux density. The flux density can be zero, but not larger than a maximum achievable flux density specific to the respective orientation of the vector B. Although there are in total 12 magnets (3 groups times 4 magnets per group) in the magnetic field generator shown in FIGS. 1 to 3, only three independent rotational inputs are required, thus only three motors are needed for the setup.

[0079] In each group, there are at least 2 magnets (arranged on opposing sides of the workspace); and there can be more than four magnets 1, as more magnets 1 result in a higher flux density over a larger workspace 3. The mechanical driving mechanism (not shown) of the magnets 1 does not require the direct connection to a particular magnet 1, and can include a belt drive, a gear driven or other means of actuation.

[0080] As the magnets 1 are placed on the edges of a cube, the workspace 3 can be accessed from many directions. Only one rotational degree of freedom is required for each magnet 1, and there is no translational motion of the magnets 1. This design feature allows changes of the magnetic field 2 to be realized; and it also enables long-term accessibility to the workspace 2. Shown as hollow big arrows in FIGS. 1 and 2, the workspace 3 can be accessed from the four sides between the magnets 1, and also from the top and bottom. This is beneficial, for example in the clinical application as shown in FIGS. 4 and 5. A patient 11 can lie on a bed sliding into the magnetic field generator via patient access 16; and anaesthetic tubes, intravenous (IV) injections and electrical sensors 12 can stay connected to the patient 11 during the operation. Moreover, medical imaging modalities (x-ray, computer tomography (CT), ultrasound, optical, etc) are also allowed from the top or side imaging access 13.

[0081] Possible applications of the invention include but are not limited to: (1) driving a propeller or robot to swim or drill through biological fluids or tissues as for example disclosed in the European Patent Applications 17 166 356 and 17 187 924; (2) steering an optical fibre or an electric wire to cut through biological tissues; (3) steering an endoscope or catheter in a body lumen; (3) driving a wireless miniaturized actuator; (4) driving magnetic micro- or nano-particles under the microscope, for biological study or for delivery, eg into a cell, or for a microrheology study; and (5) magnetically steering an electron beams.

Example: Actuation of a Medical Device in a Human Body

[0082] An exemplary application of the disclosed invention is to actuate and steer and control a medical device inside the human body by the generated magnetic field. Two embodiments are shown in FIG. 4 and FIG. 5, to actuate an untethered medical device and a tethered medical instrument respectively. A tethered medical device has a physical material connection leading to the outside of the workspace, such as cable; an untethered medical device does not have such connection.

[0083] In FIG. 4, an untethered medical device 15 is actuated by the magnetic field 2 in the workspace 3. As the device 15 has a finite magnetic moment (eg due to a permanent magnet is attached to the device), it tends to align with the external magnetic field 2 direction. The magnetic field 2 from the magnetic field generator can be used to exert a torque on the medical device 15 and is actuated in this way. The device 15 can have a suitable shape, eg that of a helical propeller, to enable its translational motion during rotation. The device 15 can have multiple segments that have multiple magnetic moments so that the shape of the device is changed under the actuation of the magnetic field 2. For example, the medical device can be a gripper or a stent that opens and closes, a valve that opens and closes, or a pump that moves periodically.

[0084] In FIG. 5, a tethered flexible medical instrument 15 is steered by the magnetic field 2 in the workspace 3. A part of the patient's 11 body (in the example of FIG. 5 the head, for neurosurgery) is placed in the magnetic field generator through one of the open spaces defined as access 16. A surgical tool 15, for instance, can be applied through the workspace via another access 14. As the tip of the tool 15 is equipped with a permanent magnetic moment, which here is assumed to point along the long axis of the instrument 15 (eg due to a permanent magnet encapsulated at the tip), the tip can be made to align with the external magnetic field 2 direction and the orientation of the instrument 15 tip is controlled in this way. Alternately, the flexible instrument 15 steered with the disclosed method can be an endoscope, a catheter, an optical fibre, a bundle of optical fibres, a tube, a wire, a gripper or any other suitable instrument.

[0085] The invention can be used to steer an active device to cut through biological tissues, eg an optical fibre that transmits laser light (for example pulsed laser light) to cut through biological tissue.

[0086] The part of the human or animal body placed in the magnetic field generator can be a head, brain, eye, arm, leg, knee, hand, foot, or any other desired part of the body (whole or in part). The position of the patient 11 relative to the magnetic field generator can be adjusted. The monitoring of the device or instrument 15 in the human body is accomplished by a suitable medical imaging modality. The positional information of the device or the tip of the instrument 15 is can be used as an input signal in a feedback control loop to drive the field generator, and the relative position of the patient 11 and the field generator can be adjusted to keep the device 15 or the tip of the instrument 15 well inside the workspace 3, for example near its centre. In another case, the workspace 3 of the field generator is larger than the required movement range of the device 15, so the position of the patient 11 is fixed relative to the field generator.

[0087] The device or instrument 15 can be actuated or steered in solid or liquid biological tissue, eg brain, liver, prostate, muscle, skin, eye or in an organ, or in a body lumen, such as urinary tract, kidney, urinary bladder, eye, heart, stomach, lung, blood vessel, or any other suitable biological tissue.

[0088] The device may also be steered by means of the magnetic field generator or the method according to the invention while an additional external force is provided to a tethered medical device. In this embodiment the magnetic field generator provides the direction control while the force required to penetrate tissue or other biological material is provided by other means.

[0089] There are several advantages of the magnetic field generator and the method according to the invention: a) it is a potentially wireless approach, thus it allows more dexterity of the medical device 15; b) the workspace 3 is large enough to incorporate the human body or a part of the human body; c) a high magnetic flux density is realized, thus it results in larger actuation force or torque on the device 15; and d) the accesses 16 to the workspace 3 allows the positioning of the patient 11, the connection and inclusion of other medical instruments, e.g. IV tubes 12, anesthesia tubes 12, sensors 12, and the application of medical imaging instrument 13 and surgical tools 14, eg scalpel, scissors, needle.

[0090] Analytical Theory for Generating a Superimposed Magnetic Field

[0091] With the invention, it is possible to generate a controlled magnetic field 2 in both the field strength and the direction in the workspace 3. In order to explain the theory behind the invention, first a situation is discussed in which one group of magnets 1 creates resulting magnetic field 2 with a fixed strength and continuously changing direction. Then, a situation is explained where one group of magnets 1 creates a resulting magnetic field 2 of fixed direction with oscillating strength. Finally, a resulting magnetic field 2 with arbitrary orientation and flux density is discussed.

[0092] Spatially Homogeneous Resulting Field that Rotates

[0093] Four magnets 1 in one group are shown as an example in this embodiment to control the in-plane resulting magnetic field 2. The magnets 1 have the same magnitude of their magnetic moment, and they are distributed equidistantly from their next neighbours and at identical distances from hub of the group. A spatially homogenous field 2 in the workspace that rotates around the x axis is described by the following equations:

B.sub.y=B.sub.0 cos α.sub.B  (1.1)

B.sub.z=B.sub.0 sin α.sub.B  (1.2)

[0094] where B.sub.y and B.sub.z are the component of the magnetic field 2 in y and z direction, respectively, and α.sub.B is the angle between the magnetic field 2 and the y axis as illustrated in FIG. 3.

[0095] Each permanent magnet 1 is a cylindrical or disk-shaped magnet 1 that has a magnetic dipole in the diametric direction, and rotates around its cylindrical axis (which is along x, and which is perpendicular to the dipole moment), as shown in FIG. 3. The magnetization vectors M.sub.i are oriented by an angle α.sub.i in the yz-plane. The magnetic field 2 vector B resulting from the superposition of the magnetic fields generated by the four dipoles at point p is given by:

[00001]$\begin{array}{cc}B\left(p\right)=\underset{i=1}{\overset{4}{.Math.}}\frac{{\mu }_0\left|M_i\right|}{4\pi |r_i{|}^3}\left(3{\hat{r}}_i{\hat{r}}_i^T-1\right){\hat{M}}_i& \left(2\right)\end{array}$

[0096] where μ.sub.0=4π×10.sup.−7 T.Math.m.Math.A.sup.−1 is the permeability of free space, I is the 3×3 identity matrix, r.sub.i is the vector from the magnet 1 i to point p, is the unity vector in the direction of r.sub.i. A maximum combined field strength (ie flux density) in the yz-plane at the hub of the group is found for the orientation:

α.sub.1=α.sub.4=α.sub.0  (3)

α.sub.2=α.sub.3=α.sub.0+π  (4)

[0097] where α.sub.0 is defined as shown in FIG. 3 and is the initial angle for the magnets 2 according to the initial angle of the magnet field α.sub.B0:

[00002]$\begin{array}{cc}{\alpha }_0=\frac{\pi }{2}-{\alpha }_{B0}& \left(5\right)\end{array}$

[0098] It follows that when the magnetic moments of the magnets 1 are aligned pairwise in the diagonal position, ie the pairs M.sub.1 & M.sub.4, and M.sub.2 & M.sub.3, respectively, but they are opposed to each other (180° phase difference) between the two pairs, then a maximum resulting field strength is obtained. This state is taken to be the initial state, and from this state, the magnets 1 are mechanically rotated with the same angular velocity clockwise α.sub.B=α.sub.B0−ωt, so that their magnetic fields rotate with the same angular velocity ω but counter-clockwise, and the rotation angle is φ=ωt:

α.sub.1=α.sub.0+φ  (6)

α.sub.2=α.sub.0+π+φ  (7)

α.sub.3=α.sub.0+π+φ  (8)

α.sub.4=α.sub.0+φ  (9)

[0099] The measured resulting magnetic field 2 follows the theoretical prediction. As shown in FIG. 6, the components in the y and the z directions oscillate with a phase difference of π/2, thus the combined field is constant in strength and rotates around the x axis. The maximal field B.sub.max that can be achieved by the set-up, where the coercive field strength of each spherical magnet with a diameter of 30 mm is approximately 955 kA/m, is also measured as a function of the distance between the magnets, as shown in FIG. 7. The measurement fits the simulation very well, and the maximal strength for the current set-up exceeds 500 G in the current set-up.

[0100] Oscillating Resulting Field Along a Given Axis

[0101] The oscillating resulting magnetic field 2 has a fixed oscillation axis (direction) defined as α.sub.B, which is the angle to the y axis, and a field strength oscillates, which is given by:

|B|=B.sub.max cos φ  (10)

[0102] where B.sub.max is the maximal field strength (ie flux density) that could be achieved by the superposition of the four magnetic dipoles, and φ=ωt is the oscillating angle, and w is the angular velocity.

[0103] The geometry of the set-up and the initial conditions are the same as in Equations (3)-(5). The difference is that two pairs of magnets 1 rotate in opposite directions. Specifically, as illustrated in FIG. 3, M.sub.1 and M.sub.2 rotate clockwise with an angular velocity of −ω, and M.sub.3 and M.sub.4 rotate counter-clockwise with an angular velocity of ω. The oscillating angle is φ=ωt, so the rotational angles of the four magnets 1 are given by:

α.sub.1=α.sub.0−φ  (11)

α.sub.2=α.sub.0+π−φ  (12)

α.sub.3=α.sub.0+π+φ  (13)

α.sub.4=α.sub.0+φ  (14)

[0104] With this approach, two outputs, ie the magnitude and the direction of the resulting magnetic field 2 at the hub of the group of magnets 1, are fully controlled with two independent inputs α.sub.0 and φ.

[0105] The simulation results of the magnetic flux density are shown in FIG. 8. In this embodiment, a resulting magnetic field 2 oscillating in the z direction (α.sub.B=90°) is shown as an example. Simulations also show that the resulting magnetic field 2 increases non-linearly from a maximum of about 374 G at a distance of 120 mm, to a maximum of about 485 G at a distance of 110 mm, to a maximum of about 645 G at 100 mm. This is achieved with the same magnets 2, all having a relatively small diameter of 30 mm. It clearly demonstrates the advantage of the permanent magnet 1 set-up over electromagnetic ones, as the field can easily achieve 3 to 6 times the strength of a common electromagnet, without any special cooling requirement or the need for expensive power amplifier systems. The resulting magnetic field 2 at the hub was measured by a gaussmeter and plotted in FIG. 9. The experimental results fit the simulations very well.

[0106] Resulting Field with Arbitrary Orientation and Flux Density

[0107] The magnetic field generator disclosed here can also generate a magnetic field 2 vector B pointing in any arbitrary direction within the three-dimensional space enclosed by the magnets 1 and the magnitude of the resulting magnetic field 2 can also be controlled. It is The direction and the strength of the resulting magnetic field is fully controlled with only three independent angular control parameters for each group of magnets (labelled as α, β, γ in FIGS. 1 and 2); at the same time, the flux density of the generated B field is tuned in the range from zero to the maximal achievable flux density.

[0108] The desired resulting magnetic field 2 in the workspace is:

B=B.sub.0ŵ=[B.sub.x,B.sub.y,B.sub.z].sup.T=B.sub.0[sin θ.sub.w cos φ.sub.w, sin θ.sub.w sin φ.sub.w, cos φ.sub.w].sup.T  (15)

[0109] where ŵ is the unity vector in the direction of B, B.sub.0 is the field strength (ie the flux density), and θ.sub.w, φ.sub.w are the angles between the vector and the axes, as shown in FIG. 10a. [⋅].sup.T is the transpose symbol.

[0110] The resulting magnetic field 2 is the sum of three magnetic vectors generated by each group of magnets 1 that are orthogonal to each other, thus:

B=B.sub.xz+B.sub.yz+B.sub.xy  (16)

where B.sub.xz, B.sub.xz, B.sub.xy are the in-plane magnetic field vector generated by each group of permanent magnets 1. As in FIG. 10b, the composed magnetic field B can be written in three components form:

B=[B.sub.x,B.sub.y,B.sub.z].sup.T=[B.sub.xy cos α.sub.xy+B.sub.xz cos α.sub.xz,B.sub.yz cos α.sub.yz+B.sub.xy sin α.sub.xy,B.sub.xz sin α.sub.xz+B.sub.yz sin α.sub.yz].sup.T  (17)

[0111] where B.sub.xy, B.sub.xz, B.sub.yz are the field strengths generated by only one group of magnets 1 in the xy-, xz- and yz-planes, respectively, and α . . . are the angles between the in-plane vector and the axes, as shown in FIG. 10b.

[0112] In some embodiments, magnets 1 with the same size, the same magnetic moment and the same distances from the hub of their group are used, then the field strength in each directions are equal and the equation (16) is simplified with B.sub.xy=B.sub.xz=B.sub.yz=B.sub.1. Equating equations (15) and (17) results in the following equation:

[00003]$\begin{array}{cc}{B}_1\left[\begin{array}{c}\cos {\alpha }_{xy}+\cos {\alpha }_{\mathrm{xz}}\\ \cos {\alpha }_{yz}+\sin {\alpha }_{xy}\\ \sin {\alpha }_{\mathrm{xz}}+\sin {\alpha }_{yz}\end{array}\right]=B_0\left[\begin{array}{c}\sin {\theta }_w\cos {\phi }_w\\ \sin {\theta }_w\sin {\phi }_w\\ \cos {\phi }_w\end{array}\right]& \left(18\right)\end{array}$

[0113] The right side of equation (17) defined the required composed magnetic field with three parameters B.sub.0, θ.sub.w, φ.sub.w, and solving equation (18) will lead to the three unknown parameters α.sub.xy, α.sub.xz, α.sub.yz on the left side of the equation. From the instrument controlling point of view, three input parameters of the angles in each direction α.sub.xy, α.sub.xz, α.sub.yz results in full control of three output parameters B.sub.0, θ.sub.w, φ.sub.w, which are the magnitude and the three-dimensional direction of the magnetic field vector. In some embodiments, the equation (18) is solved numerically in Matlab (R2017a, MathWorks).

[0114] In some embodiments, the groups of magnets are not orthogonal to each other, but the equation (16) is still valid. Decomposition of each magnetic field vector into the three axes will result in a new set of equations (17) and (18), but the general principle is the same as demonstrated herein, ie by controlling three input parameters of the angles α . . . in three different directions results in the full control of three output parameters B.sub.0, θ.sub.w, φ.sub.w, which are the magnitude and the 3D direction of the magnetic field vector.

[0115] With the solved angles in each direction α . . . , the angle of each magnet 1 in the group can be calculated using the following method. Considering the cross section of each group, eg with four permanent magnets 1 (n=4) in one group is illustrated in FIG. 11. In this embodiment, each magnet 1 rotates about an axis (the x axis in this case) that is orthogonal to its magnetic moment with the same angular velocity ω. The rotation angle of the ith magnet β.sub.i follows the following relationship:

β.sub.i. . . =2γ.sub.i−α . . . ,i==1,2,3,4  (19)

where . . . should be substitute with xy, xz, or yz that stands for the directions, γ.sub.i is the angle between the line of magnet centre to workspace 3 centre and one axis (the y axis in the current embodiment).

[0116] The equation (19) is always valid, if the number of magnets 1 in each group is larger than or equal to two (n≥2), regardless the number of magnets 1 is an odd or even number. One embodiment with five magnets, which are 30 mm in side lengths and whose centre points are arranged on a circle of diameter 70 mm, is also shown as an example in FIG. 12. Using equation (19), the angle of each magnet is calculated, and the design is verified by the finite element simulation of the magnetic field (Comsol multiphysics 5.2a, Comsol). In FIG. 12b, a sequence of images show the simulation results in a step of 90°, that the resulting magnetic field 2 is temporally and spatially homogeneous in the workspace 3, and the field direction rotates counter-clockwise as the five magnets 1 are positioned at the right angles according to equation (19) and rotate clockwise.

[0117] In another embodiment, it is required to generate a rotating resulting magnetic field 2 that is spatially and temporally homogeneous in the field strength, and the field direction rotates around a defined axis in 3D. An illustrated in FIG. 13, the rotational axis is defined by the unity vector û:

û=[u.sub.x,u.sub.y,u.sub.z].sup.T=[sin ϑ.sub.u cos φ.sub.u, sin ϑ.sub.u sin φ.sub.u, cos φ.sub.u].sup.T  (20)

The rotational magnetic field vector is a function of time:

B(t)=R(t)B.sub.0=B.sub.0R(t){circumflex over (ν)}  (21)

[0118] where {circumflex over (v)} is the unity vector in the direction of the magnetic field B(t), and with a given initial value, {circumflex over (v)} can be solved by the following equation:

û.Math.{circumflex over (ν)}=0  (22)

[0119] R(t) is the rotational matrix around the axis û by an angle δ:

[00004]$\begin{array}{cc}R\left(t\right)=\left[\begin{array}{ccc}\cos \delta +u_x^2\left(1-\cos \delta \right)& u_x{u}_y\left(1-\cos \delta \right)-u_z\sin \delta & u_x{u}_z\left(1-\cos \delta \right)+u_y\sin \delta \\ u_x{u}_y\left(1-\cos \delta \right)+u_z\sin \delta & \cos \delta +u_y^2\left(1-\cos \delta \right)& u_y{u}_z\left(1-\cos \delta \right)-u_z\sin \delta \\ u_z{u}_x\left(1-\cos \delta \right)+u_y\sin \delta & u_z{u}_y\left(1-\cos \delta \right)-u_x\sin \delta & \cos \delta +u_z^2\left(1-\cos \delta \right)\end{array}\right]& \left(23\right)\end{array}$

[0120] where δ=ω.sub.ut=2πft, in which ω.sub.u is the angular velocity in the unit of rad/s, f is the rotational frequency in the unit of Hz, and t is time in the unit of second.

[0121] Generating a Three-Dimensional Magnetic Field with One Group of Magnets on Rotational Stages

[0122] One group of four magnets 1 is able to achieve an in-plane rotational magnetic field (as shown above in FIG. 3). To realize the three-dimensional steering of the rotational axis of the field, the magnets are mounted to a 2 DoF rotational stage (shown as the rings in FIG. 14). The stage rotates the whole setup (relative to the patient) in two directions, β and γ. The disadvantages of the embodiment are: 1) The access to the workspace is only limited to one direction, ie along the γ axis is permanent; however, access from other directions, eg along the β axis is blocked due to the rotation of the whole device; 2) The connections to drive the magnets 1 are cumbersome and expensive due to the rotation of the whole device; 3) The rotation of the whole device requires much higher power and is more dangerous to the patient 11 or the operator.

Example: Generating a Three-Dimensional Magnetic Field with Six Magnets that Each can Rotate in Two Directions

[0123] As shown in FIG. 15, spherical permanent magnets 1 are arranged in three groups, and two magnets 1 in each group. The magnets 1 of each group simultaneously rotate with 2 DoF. It is also possible to achieve the full control of both the direction and the magnitude of the magnetic vector. Each magnet 1 (magnetic moment) can rotate around two orthogonal axes (two of the three axes, shown as α, β and γ).

Example: Experimental Methods of the Magnetic Generator

[0124] The magnetic set-up consists of four spherical magnets 1 with 30 mm diameter (K-30-C, neodymium N40, Supermagnete). They were held in spherical cavities in a custom-made coupler to connect to the motors. The orientation of the magnets 1 was maintained due to the large friction induced by the clamping force. Four stepper motors (1.8°/step, stall torque 0.15 N.Math.m, SH3537-12U40, Sanyo Denki, not shown) were used with two individual driver boards (US1D200P10, 2.0 A, 16-division, Sanyo Denki, not shown) to drive the rotations in two directions, respectively. The power was supplied by a DC power supply (HM7042-5, HAMEG). The initial orientations α.sub.0 of the four magnets 1 were adjusted manually, then they were rotated with the same absolute speed, controlled by a square wave signal generated from a function generator (33220A, Agilent, not shown). The motors were air cooled with four fans (not shown), as heat was generated, especially when the motors were held in a fixed static position against the magnetic torque.

[0125] The diagonal centre-to-centre distances of the magnets 1 were set at 120 mm. Changing the distance between the magnets 1 will change the maximal magnetic field strength. Decreasing the distance will result in a larger field, however, it also requires larger driving torque by the motor, which then exceeds the stall torque of this motor for particular orientations of the magnets 1.

[0126] A digital gaussmeter (HGM09s, MAGSYS) was used to measure the resulting magnetic field 2 at the centre of the magnetic field generator in both the x and z directions, respectively. The field 2 was changed in steps of 22.5° (200 pulses) and the results are plotted as markers in FIG. 7. The measurements were repeated for three times. At the same position, the magnitudes were reproducible within ±0.5 G, so the error bars are not plotted in the figure.

[0127] The magnetic field strength and direction were also simulated in Comsol 5.2a (Comsol Multiphysics). A three-dimensional simulation was carried out in a volume of 300 mm-side cube using a magnetic insulation boundary condition. Four spherical magnets 1 with 30 mm diameter were placed with a diagonal centra-centre distance of 120 mm, as shown in FIG. 3a. The relative permeability of air and the four magnets 1 are set as 1 and 4000, respectively. The magnetization strength of each magnet was set to be 955 kA/m, and each orientation was calculated according to Equations 6 to 9. A parametric sweep was carried out for α.sub.B=0°, 15°, 30°, 45°, 90°, and β=0°˜360° in 10° steps. The magnetic flux density is shown by the grayscale, and the direction of the field is shown as arrows in FIG. 6.

Example: Multiple Magnets in One Group

[0128] In each group, there are at least two magnets 1 (arranged on opposing sides of the workspace); and there can be more than four magnets 1, as more magnets result in a higher flux density over a larger workspace 3. The mechanical driving mechanism (not shown) of the magnets 1 does not require the direct connection to a particular magnet 1, and can include a belt drive, a gear drive or any other suitable means of actuation.

[0129] Each group of magnets 1 has plane and a hub and the magnets 1 are equidistantly in a circle. The hubs of the groups coincide with each other, and with the centre of the workspace 3. As shown in FIG. 16, the central symmetric axis of each group is perpendicular to that of another group, but it is not necessary to be perpendicular to the axis of the workspace 3 (the coordinate system of the patient in this case). Three groups the orientations of which are orthogonal to each other achieve full control of the direction and strength of the resulting magnetic field 2 in the workspace 3 by the disclosed method in the patent.

[0130] In one embodiment, the setup with multiple magnets 1 can be extended to human-scale, as shown in FIG. 16 and FIG. 17. In each group, there are 18 magnets 1 that are 100 mm in diameter and 200 mm in length. The inner diameter (gap) of each group is set to be 1000 mm, which fits a human through the opening space (access). The cuboid in FIGS. 16 and 17 represents the outer bounding box of a human, with a width of 500 mm, a thickness of 300 mm, and a length of 1700 mm. By finite element analysis of one group of 18 magnets with a coercive field strength of approximately 955 kA/m, the magnetic flux density is homogenous in the workspace and reaches approximately 448 Gauss.

Example: Powering a Linear Actuator with the Magnetic Field Generator

[0131] As one application of the oscillating magnetic field generated by the device, a linear actuator was powered wirelessly, as shown in FIG. 18a. When the external field equals to zero, the soft structure stays at rest in its original shape (FIG. 18b). When a magnetic field in the z direction is applied, magnetic torques are applied on the embedded small magnets, which result in the rotation of the soft linkages and compress the actuator (FIG. 18a). The actuator with an original length l.sub.0=8.8 mm decreases to a minimal length of l=3.7 mm. When a magnetic field is applied in the opposite direction, it extends to l=10.5 mm. Thus an overall linear displacement of approximately 6.8 mm is realized by the actuator without external load, which is more than 70% of its original length. The displacement at compression (5.1 mm) is much larger than at elongation (1.7 mm), as the magnetic torque changes non-linearly with the orientation of the magnets, and it is maximal when the angle is 90° (close to the situation shown in FIG. 19).

[0132] The load characteristics of the actuator was also tested. The maximal displacement is plotted as a function of the external load in FIG. 20b. As the load increases, the displacement decreases non-linearly due to the variance in the orientation of the magnets. The output work of the actuator also drops dramatically as the displacement gets smaller. Further optimization of the structure and matching the soft material's elastic modulus with the load will enhance the performance of the actuator. The current miniature actuator can provide a maximal force of approximately 84 mN. It lifts more than 40 times of its own weight, while still achieving 10% displacement. It is also worthwhile to point out, as the soft structure is planar, it is fully compatible with traditional soft photolithography process, and thus it can be scaled down to the micrometre scale.

[0133] The features as described in the above description, claims and figures can be relevant individually or in any combination to realise the various embodiments of the invention.