Dipole Field Controlled Micro- and Nanomanipulation

Maxime Latulippe, Student Member, IEEE, and Sylvain Martel, Fellow, IEEE

Abstract— A novel non-contact micro- and nanomanipulationmethod is proposed. This method, Dipole Field Manipulation(DFM), exploits the distortion of a uniform magnetic fieldinduced around ferromagnetic cores. While this distortion cangenerate strong magnetic gradients to induce pulling forces ona manipulated object, the direction of the field can be usedto induce magnetic torques. This paper presents a first insighton DFM capabilities and control possibilities. We show that byvarying the orientation and strength of the uniform field, DFMhas the potential to achieve effective manipulation in up to sixdegrees of freedom. Using conventional electromagnetic coilsas the uniform field source and a mobile core, gradients canreach 1-2 T/m or more in the whole manipulation workspace.Such coils provide fast directional force and torque variationcapabilities, and allow an easy access to the workspace forfeedback visualization and core positioning. A first concept fora 6-DOF DFM system is proposed. Results of a preliminaryexperiment where a particle was moved around a 0.5x1 mmrectangular path demonstrate the feasibility of the method toinduce sufficient forces in any direction.

I. INTRODUCTION

Non-contact micro- and nanomanipulation of particlesoffer a high potential for the development of future minia-turized technologies. Interesting applications include mi-croassembly of miniature devices, less invasive local mi-crosurgeries and studies of biological systems and chemicalreactions at the cellular or molecular level. In this latter areafor instance, the development of microfluidics and lab-on-a-chip technologies along with the ability to manipulate singlebioparticle allows to study fundamental biology such as cellor molecular interactions.

Various manipulation approaches have been investigatedfor bioparticle or micro-object handling. These include hy-drodynamic and acoustic cell or molecule trapping [1] aswell as haptic [2], optical [3] and dielectrophoretic [4]manipulation. For magnetic microdevices or particles suchas functionalized magnetic nanoparticles or bead-bound cells,magnetic manipulation is a non-invasive approach that canoffer high control capabilities [5], [6]. In the case of biopar-ticles, this approach also allows their manipulation withoutdamaging them.

Magnetic manipulation or actuation in general has beendemonstrated for various applications. Kummer et al. [7]

This work was funded by the Fonds Quebecois de la Recherche sur laNature et les Technologies (FQRNT) and by the Canada Research Chair inMedical Nanorobotics.

Maxime Latulippe is with the NanoRobotics Laboratory, Dept. of Comp.and Soft. Eng., Institute of Biomedical Eng., Polytechnique Montreal, QC,Canada, maxime.latulippe@polymtl.ca

Sylvain Martel (corresponding author) is the Director of theNanoRobotics Laboratory, Dept. of Comp. and Soft. Eng., In-stitute of Biomedical Eng., Polytechnique Montreal, QC, Canada,sylvain.martel@polymtl.ca

developed the OctoMag platform consisting of eight elec-tromagnetic coils used to navigate a millimeter-sized devicein 5 degrees of freedom (DOF) for intraocular microsurgery.The MiniMag [8] is the miniaturized version of this system,which has been presented recently for micromanipulation.Electromagnetic Actuation (EMA) systems [9] consist ofHelmholtz and Maxwell coil pairs typically capable ofmanipulation in 5 or 6 DOF. Martel et al. demonstratedthe 3-DOF navigation of particles in the vascular networkusing a magnetic resonance imaging (MRI) scanner [10]. TheStereotaxis platform [11] allows to orient the tip of a catheterby changing the orientation of a magnetic field, but does notprovide pulling forces. Other magnetic manipulation methodshave been proposed for microassembly, e.g. using a mobilepermanent magnet [12] or by pushing on micro-objects witha swarm of controlled magnetotactic bacteria [13]. In the areaof bioparticle manipulation, cell or molecule trapping andhandling were demonstrated using magnetic tweezers [14]and microcoil arrays [15].

Here, we propose a novel concept for magnetic micro- andnanomanipulation, inspired from Dipole Field Navigation(DFN) that we presented recently as a new navigation methodfor particles in the vascular network [16]. DFN consists inimmersing the patient in a strong and uniform magnetic field,which magnetizes the particles to be navigated. Magneticgradients, which induce directional forces on the particles,are generated from the distortion of the uniform field usingferromagnetic cores precisely positioned around the patient.Typically, to achieve the force strengths required to navigatemicroparticles in deep tissues, the patient is placed in thetunnel of an MRI scanner, where the high magnetic field(typically 1.5-3 T) allows to bring both cores and navigatedagents at full or close to saturation magnetization. Theapplication of DFN to micro- or nanomanipulation alleviatessome constraints. In particular, due to the smaller requiredsize of the workspace, a less cumbersome and expensiveuniform magnetic field source can be used. Since we assumethe working distances of the manipulated particles or micro-objects from the cores to be much smaller, the very highgradients generated near the cores can be exploited. There-fore, even using a much weaker magnetizing field comparedto DFN, very high gradients can be achieved. This allowsthe use of conventional electromagnetic coils as the magneticsource, for which currents can be controlled in order to varythe field, therefore offering more control possibilities.

This paper aims to provide a first insight on the manipu-lation capabilities of Dipole Field Manipulation (DFM) andits control possibilities. We propose a manipulation systemconcept, composed of three orthogonal Helmholtz coil pairs

for generating a uniform and real-time controlled magne-tizing field. A mobile core (potentially many) is insertedin the uniform field volume to generate high directionalgradients on the manipulated micro-objects or particles. Themagnetizing field and induced gradients can be controlled byvarying the currents in the coils and the core position. Weshow that this system could achieve 6-DOF manipulationwith fast directional force and torque variations. We thenpresent preliminary experimental results that demonstrate thefeasibility of the method. The main advantages of DFMcompared to existing magnetic manipulation methods arethe much higher gradients achievable in the whole andpotentially larger workspace, and the possibility to controltorques and forces at multiple locations at once when mul-tiple cores are used. Realization of DFM however raisessome challenges for the accurate prediction and control ofthe required core positions when multiple cores are used.

II. DIPOLE FIELD MANIPULATION

In magnetic actuation, the orientation of the magnetic fieldB allows to induce a torque on the manipulated object, whilethe magnetic field gradients induce a directional pullingforce. For a manipulated particle or micro-object of magneticmoment mp,

Fmag = ∇(mp ·B) (1)τmag = mp ×B (2)

wheremp = VmagM (3)

depends on the magnetic volume Vmag of the object andon the volume magnetization M of the magnetic material.To achieve good manipulation capabilities at the micro-and nanoscales, the very small magnetic volume of themanipulated objects must ideally be compensated by bothhigh magnetic field and gradient strengths. Using coils orpermanent magnets, such high values can be encountered inthe close proximity of these magnetic sources. For instance,MiniMag and EMA systems in general define a workspacevolume where the field and gradient strengths are sufficientfor the targeted application. For the design of such coil-basedsystem, there is generally a trade-off between the size ofthe workspace and achievable gradient strengths. In DFNor DFM, the gradient sources (cores) can be repositionedinside a uniform field volume. This suppresses the need tostay close to a fixed gradient source in order to reach highgradients. Thus, very high gradients can be achieved inde-pendently of the location inside the uniform field volume.Although being less desired while increasing the complexitylevel, a non-uniform field could also be considered.

A. Magnetized Cores as Gradient Sources

For simplicity, the following analysis is limited to spher-ical cores. For a single soft ferromagnetic sphere immersedin a uniform magnetic field B0, the induced magnetic fieldat any point r = (x, y, z) around the sphere is equivalent to

m

r

θ

B0

z

x

Fig. 1. Illustration of the core and convention used for analysis.

Fig. 2. Magnetic gradient field around a ferromagnetic core immersed ina uniform field.

that of a magnetic point dipole of moment m located at thecenter of the sphere (origin):

Bcore(r > R) =µ0

4π

[3(m · r)rr5

− m

r3

](4)

where µ0 = 4π × 10−7 H/m is the vacuum permeability, Ris the radius of the sphere and r = ‖r‖. Since the core ismagnetized by the external magnetic field B0, m is parallelto B0. As a convention, let B0 = B0z be in the z-axisdirection. Then, (4) simplifies to

Bcore =µ0m

4πr5[3xzx+ 3yzy + (3z2 − r2)z

](5)

The manipulated object is on the other hand magnetized bythe total field B = B0 +Bcore. Thus, its magnetic momentmp is parallel to B and (1) simplifies to

Fmag = mp∇B (6)

that is, the induced force is a function of the gradient of thetotal magnetic flux density. In the far field of the core, Bis approximately parallel to B0, therefore the force can beapproximated by

Fmag = mp∇Bz = mpG (7)

It can be shown that the magnetic gradient G is given by [16]

G =3µ0m

4πr4

sin θ cosφ(1− 5 cos2 θ

)sin θ sinφ

(1− 5 cos2 θ

)cos θ

(3− 5 cos2 θ

)T

(8)

where θ is the angle between m and r, as depicted in Fig. 1,and φ is the rotation angle around m. This gradient field isillustrated in 2D in Fig. 2. Note that such a magnetized corein a uniform field can generate gradients in any direction, asopposed to a permanent magnet alone. In fact, any gradientorientation is found at three angles θ around the core.

0

5

10

15

20

25

30+

(a) B0 = 50mT0

5

10

15

20

25

30+

(b) B0 = 1.5T

Fig. 3. Distortion of the magnetic field induced by a magnetized core in a uniform field of strength a) 50 mT and b) 1.5 T. Images on the right-hand sideof each subplot represent the angle of the distortion, in degrees. These results correspond to chrome steel beads from our lab.

−135

−90

−45

0

45

90

135

180

(a) Gradient angles obtained usingthe far field approximation.

−135

−90

−45

0

45

90

135

180

(b) Exact gradient angles calcu-lated from (9).

0

10

20

30

40

50

60+

(c) Error (absolute) on gradientorientation.

−0.5

0

0.5

1

1.5

2+

(d) Error on gradient magnitude(Gexact −Gapprox).

Fig. 4. Comparison of the gradients obtained using the far field approximation with the actual gradients for a chrome steel core immersed in a 50 mTfield. a) and b) compare the gradient orientations (in degrees). c) and d) show the error resulting from the far field approximation on the gradient orientation(degrees) and magnitude (T/m) respectively.

Because of the symmetry of the gradient field around m,any desired 3D gradient can be found at three differentpoints around the core. Equivalently, any 3D gradient at afixed point in space can be generated by changing only themagnetization (magnitude and orientation) of the core. Wepreviously reported a method for DFN [16] to position a coresuch that a desired gradient is generated on a particle at agiven point in space according to (8).

B. Gradients in the Near Field

The above approximation is typically acceptable in DFN,as the uniform magnetic field B0 of the MRI scanner isstrong and the working distances from the cores are larger(intervention in deep tissues). For DFM however, in order toexploit the higher gradients in the close proximity of the core,the more significant distortion in the near field of the coreshould be taken into account. Fig. 3 compares the resultingdistortion of the total field B and the absolute orientationangle of B relative to B0, for a spherical core immersed intwo different uniform field strengths B0 = 50mT and B0 =1.5T. These figures correspond to chrome steel beads fromour lab, for which M50mT = 123 000A/m and M1.5T =1.44× 106 A/m. At 50 mT, the core magnetization lies in thelinear region of the magnetization curve, whereas at 1.5 T itis at full saturation magnetization. When the core reaches itssaturation magnetization, the angular distortion of B reducesas B0 increases and thus the far field approximation (8)becomes acceptable from a closer distance to the core.

For a manipulated object in the near field of the core,(6) must be solved exactly in order to accurately predict theinduced magnetic forces. By symmetry of the field Bcore

around m, this can be analyzed in 2D in the xz-plane:

∇B = ∇(√

B2x +B2

z

)(9)

where

Bx =µ0m

4π

3xz

r5(10)

Bz =µ0m

4π

3z2 − r2

r5+B0 (11)

Although an analytical expression can be derived for theexact gradient ∇B, it is much more complex than (8) and isnot included here for reasons of simplicity. Fig. 4 comparesthe gradient field obtained using the far field approximationwith the actual gradient field calculated using (9), for thesame chrome steel core as above in B0 = 50mT. Usingthe far field approximation (Fig. 4a), the gradient orientationin the xz-plane is a function of θ only. Thus, given adesired gradient orientation, one can find the correspondingvalues for θ and φ and calculate the required distance r toobtain the desired gradient [16]. In the near field of the corehowever, there is a distortion of the gradient orientations(Fig. 4b), which become a function of both θ and r. Asolution for positioning the core could be to use precomputedgradient fields, similarly to [7]. Fig. 4c shows the error onthe calculated gradient orientation resulting from the far fieldapproximation, whereas Fig. 4d shows the error obtained

0 5 10 150

500

1000

1500

2000

h (mm)

G(m

T/m)

R = 0.5 mmR = 1 mmR = 2 mmR = 5 mm

Fig. 5. Gradient magnitudes achievable around chrome steel spherical coresof different radii (M = 123 kA/m, B0 = 50mT). Magnitudes vary with θ.

on the gradient magnitude. Note that the gradient strengthis mostly underestimated by the far field approximation inregions where orientation errors occur.

C. Gradient Strengths

As expressed by (8), the gradient magnitude is not constantas a function of θ for a fixed distance r. We define h = r −Rthe distance from the core surface. Fig. 5 depicts the gradientmagnitudes achievable in DFM as a function of h, for dif-ferent core radii (chrome steel). The values were calculatedusing the exact gradient expression (9). The areas plottedshow the range of gradient strengths achievable around thecore, which are maximized at θ = 0. Since we assume theworking distances to be relatively small, very high gradientsreaching 1-2 T/m or more can be achieved.

D. Inducing Torques

From (2), a micro-object or particle subject to an externalfield orients itself such that its magnetization is aligned withthe field. Since we assume the manipulated object to bemagnetized by the total field B, a magnetic torque in DFMcan be induced on anisotropic objects such as elongatedmicro-objects or particles, which are more easily magnetizedin a certain direction.

A straightforward method to induce torques in the far fieldof the core (or in the absence of the core) is to vary theorientation of B0. In the near field, although the variationsof the orientation of the total field B could be exploited, theseoccur very close to the core where the gradients are also veryhigh. Another strategy could be to exploit the dipole-dipoleinteractions between two cores positioned at angle in B0, anduse the small region between the cores where the orientationof B is changed and the gradients cancel. Fig. 6 illustrates anexample in 2D for two cores placed at 60◦ in a 50 mT field.The resulting magnetic field was obtained from numericalsimulations using COMSOL Multiphysics® in order to takethe magnetic interactions into account.

E. Controlled Manipulation

From the above sections, DFM has the potential to offerhigh control capabilities for the effective micro- or nanoma-nipulation of small objects. First, for any given direction of

Fig. 6. Distortion of the total field between two cores to induce torque.

the magnetizing field B0, magnetic forces can be generatedin any direction on a manipulated micro-object or particle.Using a non-magnetic robotic arm, a core could be positionedin real time in order to control the induced forces on themanipulated object. Such a mobile core would also allowto achieve very high gradients in the whole workspace. Ifthe strength and orientation of B0 can be varied, changesin the gradients around a statically positioned core can beinduced. Since soft ferromagnetic cores have a negligiblehysteresis and magnetic remanence, their magnetization canbe predicted accurately as a function of B0. Thus, controllingB0 using a static core would also allow to accurately manip-ulate an object in any direction. The combination of a mobilecore with a controllable field B0 would add flexibility andredundancy for controlled manipulation. In order to controlthe rotation of the object, one possibility would be to retractthe core from the workspace on a need basis to allow thegeneration of torques only by varying the orientation of B0.

Fig. 7 illustrates a 2D example of a control sequence(i.e. orientations and strengths of B0) allowing to movea particle along a rectangular trajectory using a staticallypositioned core in the workspace. In this example, a particle(red dot) is required to move from position 0 to positions1, 2, 3 and 4, and then back to 0 (Fig. 7a). Fig. 7bshows possible values of the orientations and strengths ofB0 in order to generate a constant gradient magnitude,arbitrarily set to G = 300mT/m, at the particle’s locationalong the path. These values were computed for a chromesteel core as above. For the purpose of this example, thefar field approximation (8) was used (the maximum erroron the actual orientation of B on this path is ~5◦). Thissimulation shows the nonlinearity of the gradient magnitudeas a function of theta and demonstrates the ability to generategradients in any direction using a static core.

More complex magnetic and gradient fields can be ob-tained using multiple cores in the workspace. As mentionedin Section II-D, this strategy could be used to distort the totalfield between two cores. By adequately positioning a set ofcores, it is also possible to control the magnetic forces andtorques at multiple locations in the workspace. Accuratelypredicting the resulting field however becomes a concernwhen magnetic interactions occur (cores located close toeach other). Indeed, significant magnetic interactions renderthe analytical models inaccurate. Another challenge lies in

0

1 2

34

m

θ

(a) Desired path goes through positions 0-1-2-3-4-0. Red dot andarrow depict the manipulated object and the required gradientorientation at this position. Schematic is to scale.

1 2 3 40

0.5

1

1.5

2

2.5

3

Position on path

B0orientation

θ(rad

)

0

20

40

60

80

100

120

B0strength

(mT)

(b) Sequence of the required B0 along the path.

Fig. 7. a) Simulation of a desired trajectory next to a statically positioned core and b) the corresponding control sequence of B0 (orientation θ andstrength B0) required to generate a constant gradient magnitude G = 300mT/m in the desired direction on a manipulated object along this path.

the solution to the magnetic inverse problem of positioningmultiple cores. Moreover, a control algorithm would have toavoid collisions between the moving cores or their support.

III. PROPOSED MANIPULATION SYSTEM

As a first dipole field manipulation system concept thatwould implement some of the aforementioned control ca-pabilities, we propose to generate the magnetizing fieldB0 using a three-axis Helmholtz coil configuration, and togenerate gradients using a ferromagnetic core attached to arobotic arm, as illustrated in Fig. 8.

While the three orthogonal Helmholtz coil pairs allow togenerate a uniform field in any direction within a workspacevolume in the center of the setup, the robotic arm allows tomove the core in and out of the workspace. This enables thegeneration of torques only when the core is retracted fromthe workspace, and high magnetic gradients when the core isinserted near the manipulated object. Since fast variations ofB0 can be achieved by controlling currents in the coils, fastchanges of the pulling forces (orientation and direction) andtorques can be achieved. Therefore, this system can in theoryperform 6-DOF manipulation. One limitation, however, is theinability to accurately and independently control rotationsand translations of the manipulated object simultaneously.A possible strategy could be to alternate between controlledtranslations and controlled rotations of the object. Since asmall core (mm-scale) can be used to generate high gradients,it could be moved back and forth relatively quickly using therobotic arm without generating high mechanical constraints.The field B0 could be turned off when moving the core toreduce the complexity of the controller. Furthermore, sincegradients can be generated in any direction at a given pointaround the core by varying the orientation of B0, the designof the robotic arm can be kept simple: a one-axis translationalrobotic arm going through the coil centers would satisfy theneed to bring closer or farther the core from the manipulatedobject.

It is noted that the controllability parameters of the system,such as time response, frequency response and accuracy ofthe position control, depend on the external setup (e.g., coils

coils

robotic armmanipulated object

Fig. 8. Illustration of the proposed 6-DOF manipulation system. Only twoHelmholtz coil pairs are shown for visualization simplicity.

specifications, amplifiers, etc.). Therefore, these specifica-tions should be chosen appropriately in order to achieve aneffective micro- or nanomanipulation.

Besides the real-time controllability of the magnetizingfield B0, another advantage of employing coils to generateB0 is the easy access to the workspace. This allows not onlyto insert the core in the workspace using a robotic arm, butalso the observation of the manipulated object (e.g., using amicroscope) for control feedback.

IV. EXPERIMENTS

A preliminary experiment was conducted in order todemonstrate the possibility of controlling a particle along atrajectory (i.e., induce translational forces in any direction),using a static core by varying the orientation and strengthof B0. The ability to rotate a magnetic object by varyingthe orientation of B0 is not demonstrated here since it is acommon feature of magnetic manipulation systems such asOctoMag [7], EMA systems [9] or Stereotaxis [11].

For the sake of these preliminary experiments, and to avoidthe complexity of a bulkier coil system, a single Helmholtzcoil pair was used (see Fig. 9a). The coils could be rotatedmanually about the vertical axis around the manipulationworkspace in order to orient the field in the 2D horizontalplane. This simple system could therefore achieve 3-DOFmanipulation. The coils had an inner diameter of 27 mmand were separated by a distance of 8 mm. The magnetic

(a) Top view of the Helmholtz coils used for the experiment. (b) Core and channel on the fixed plate. (c) Setup under the microscope.

Fig. 9. Setup used for the Dipole Field Manipulation experiment.

field strength produced in the workspace was measured tobe B0 = 52mT for a current of 4 A.

A carbon steel core of radius R = 3.18mm withmagnetization M52 mT ≈ 113 000A/m was glued onto afixed polymethylmethacrylate (PMMA) plate centered in themanipulation workspace. The coils could be rotated freelyaround this plate in order to orient the magnetic field B0.Note that, contrary to the system proposed above in Sec-tion III, no robotic arm was used in this experiment since thepurpose was to demonstrate the translational manipulationcapabilities of DFM using a static core. The micro-object tobe manipulated consisted in a 58 µm 440 stainless steel spher-ical particle, having a magnetization M52 mT ≈ 50 000A/m.This particle was confined in a rectangular shaped channel(width 200 µm) describing a 0.5×1 mm rectangular path,carved in a PMMA sheet using a micromilling machine(LPKF ProtoMat 95s/II). This microchannel allowed to fa-cilitate the manual manipulation of the particle in the absenceof a controller. The microparticle was put inside the channelmanually under a microscope. The channel was then placedon the fixed plate such that it was vertically aligned withthe center of the core. The configuration of the fixed plateis shown in Fig. 9b. In order to assess the manipulationsuccess, the whole setup was placed under a microscope(see Fig. 9c). Fig. 10a shows a close view of the fixedplate in the manipulation workspace, taken in between thecoils using the microscope. Note that both the core and thechannel lied inside the (approximately) homogeneous fieldvolume of the coils. The distance from the center of therectangular path to the surface of the core was 4.6 mm or1.45R. The theoretical gradient magnitudes at this distanceexceed 1.5 T/m. Although this setup is much simpler than thesystem proposed in Section III, it allows to demonstrate thefeasibility in DFM of inducing pulling forces in any directionaround a core by varying only the orientation of B0.

The experiment aimed at moving the particle aroundthe rectangular path in the clockwise direction. The coilswere turned on and off manually in short pulses during themanipulation, following the proper orientation of the coilsat each step. This orientation was set manually based onthe knowledge of the gradient field as depicted in Fig. 2

and using landmarks on the setup. Fig. 10 shows pictures ofthe particle inside the channel, taken using the microscopeafter each B0 pulse and showing the particle being movedaround the rectangular path. It is noted that for simplicity,during the experiment, the coils were turned on at full powerat each pulse (B0 = 52mT), which resulted in relativelylarge displacements of the particle. Using a controller withfeedback, finer displacements could be achieved by adjustingthe magnetic field strength. This simple experiment howeverdemonstrates the feasibility of inducing sufficient pullingforces in any direction with DFM using a statically posi-tioned core.

V. DISCUSSION AND CONCLUSION

We proposed a novel micro- or nanomanipulation tech-nique, dubbed Dipole Field Manipulation (DFM), that con-sists in distorting a uniform magnetic field B0 using fer-romagnetic cores in order to induce pulling forces on amanipulated object. While very strong magnetic gradientscan be obtained, the direction of the magnetizing field B0

can be used to induce torques. We have shown that evenusing small cores (mm-scale) in a much weaker magnetizingfield compared to DFN, gradients reaching 1-2 T/m and moreare achievable near the cores. Therefore, conventional coilscan be used to generate B0, which allows fast variations ofthe field and provide an easy access to the workspace. Usingthree-axis coils, DFM can achieve 6-DOF manipulation.

Control possibilities in DFM are manifold. First, a corecan be static or mobile. We have shown that even a staticcore can be used to induce pulling forces of variable strengthin any direction by controlling B0. Using a mobile coreincreases control flexibility and redundancy, and allows toachieve strong gradients anywhere in workspace. Second,multiple cores can be positioned in the workspace in order tocontrol the torques and forces induced on multiple objects atdifferent locations at once. In this case, however, predictingthe required positions of the cores becomes much morechallenging, especially due to magnetic interactions. A limi-tation of the method is the complexity to control translationsand rotations of the manipulated object simultaneously. Thismight be possible using multiple cores. Here, we proposed

(a) Top view of workspace. (b) Initial position of particle. (c) After 1st pulse. (d) After 2nd pulse. (e) After 3rd pulse.

Fig. 10. Results of the manipulation experiment conducted. a) Top view of the setup inside the uniform field volume of the coils. b) Initial position ofthe particle in the channel. c) to e) Pictures of the channel showing the particle being moved by subsequent magnetic field pulses.

to control translations and rotations in an alternated fashionby inserting and retracting the core from the workspace.

Examples of potential applications of DFM are micro-assembly, micro-surgery and bioparticle manipulation inmicrofluidics or labs-on-a-chip. A future step in this workwould be to implement the system proposed in Section IIIand integrate a controller for automated manipulation.

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