J Micro-Bio Robot (2013) 8:1–12DOI 10.1007/s12213-012-0053-1

RESEARCH PAPER

A novel micro-scale magnetic tumbling microrobot

Wuming Jing · Nicholas Pagano · David J. Cappelleri

Received: 29 February 2012 / Revised: 12 October 2012 / Accepted: 29 October 2012 / Published online: 30 January 2013© Springer-Verlag Berlin Heidelberg 2013

Abstract This paper presents a magnetic tumbling micro-robot design at the micro-scale. The microrobot has adumb-bell shape whose largest dimension is about 400 µm.When subjected to an exterior predefined magnetic field,the magnetic microagent performs a tumbling motion drivenby the interacting magnetic forces and momentums. Themagnetic field providing driven force is generated by a coilsystem consisting of five electromagnetic coils. Under theavailable driven field, we show that the prototype agent isable to tumble on various types of surfaces in both dry andfluid environments.

Keywords Tumbling motion · Magnetic microrobot

1 Introduction

Microrobotics in submillimeter scale has emerged withinthe last decade, especially with untethered microrobotswith the attractive features due to their small size andworking modes. As one of the next waves in intelligentsystems, microrobots have shown potential in advancedmanufacturing, the health care industry and in the contin-ued miniaturization of consumer products [1]. Especially in

W. Jing · N. Pagano · D. J. Cappelleri (�)Multi-Scale Robotics & Automation Lab, Department ofMechanical Engineering, Stevens Institute of Technology,Hoboken, NJ 07030, USAe-mail: David.Cappelleri@stevens.edu

W. Jinge-mail: wjing@stevens.edu

N. Paganoe-mail: npagano@stevens.edu

biotechnology and medical applications [2], such as min-imally invasive surgery and targeted drug delivery, vastpotential impacts exist. Features of untethered operation andsmall size are necessary for all these applications. Asidefrom the wireless operation, power delivery is still a majorchallenge for real applications and locomotion mechanismsstill need delicate designs in order to achieve controllablemotions. Thus, this paper explores a low-powered, dexter-ous microrobot design for practical real-world applications.

Tremendous efforts have been made in microrobotresearch with regards to real applications. Bistable mech-anism [3], optical controlled bubbles [4], and magneticlevitation [5] have been applied to develop the microrobotsfor MEMS assembly tasks. Ikeuchi et al. [6] used an opti-cally driven microrobot to derive realtime 3D images forbio-manipulation.

Various magnetic microrobotics designs [7–15] have alsobeen investigated for biological and medical industries.Swimming magnetic microrobots have been realized in aspiral structure [8] and flapping mechanisms [9]. Hagiwaraet al. took advantage of the permanent magnetic micro-robots to aid cell enucleation and manipulation in [10, 11].In [13] and [14], magnetic microrobots were tested in sim-ulated blood vessel environments. Martel et al. [15] haveconducted automatic navigation of au untethered magneticdevice in the artery of living animals. Additionally, anelectromagnetic system for 5-DOF wireless micromanipula-tion of intraocular magnetic microrobot has been developed[16].

To realize veritable untethered mobile microrobot insubmillimeter scale, a few agents with different workingprinciples have been designed and developed in the nearpast. The first representative work was done by Donaldet al. [17–19] applying electrostatic principles. The MEMSfabricated device consisted of a cantilevered steering arm

2 J Micro-Bio Robot (2013) 8:1–12

mounted on an scratch drive actuator (SDA), where bothwere made of conductive polysilicon. The microrobot wasdriven and steered by an engineered surface with buriedelectrical grids. Sul et al. [20] developed a thermally actu-ated locomotive device which consisted of three-legged,thin-metal-film bimorphs. The device was able to performstepwise translation on a low friction surface through curva-tures of legs induced by a focus laser. Different laser energyand parameters controlled the velocity and motion directionof the agent. Although these two types of microrobots haveshown fancy motion and control, their operating principleslimit their application potential especially in the bio andmedical fields. This is because it is difficult to incorporatean engineered surface into a living body for surgical applica-tion and also risky to apply the high voltage needed to powerthe device. The thermal actuation mechanism method facesa similar problem, which lies in the laser power delivery fora minimally invasive surgery site or in a cluttered biologicalenvironment.

Compared to the electrostatic and thermal principleddevices, magnetic fields can provide attractive features forpower and control. Nelson [21], Vollmers et al. [22] andFrutiger et al. [23] developed one delicate micro agentnamed the MagMite. The device is made of two nickel softmagnetic bodies connected by a gold nonmagnetic spring,so it can harvest energy for the external oscillating gradi-ent magnetic field and transform it into into inertia- andimpact-driven mechanical forces while being fully control-lable. This design shows fabulous mobility with low energylevel. However, it may be difficult to recognize the reso-nant frequency for stepping out due to the micro fabricationaccuracy. Another design applying magnetic energy wasdeveloped by Pawashe et al. [24, 25], Floyd et al. [26] andDiller et al. [27] using NdFeB permanent magnetic mate-rial. This microrobot made of a hard magnetic piece canperform stick-slip motion under alternating gradient mag-netic fields. This design also can perform omnidirectionaltranslation on surfaces in dry or fluidic environments. Onepossible limitation is that it needs relatively idealized envi-ronment, because it might be difficult to realize the slipphase in non-ideal environments.

Real bio-environments are usually not flat but complexsurfaces of flagella or tissue. Sliker et al. [28] and Terryet al. [29] investigated micropatterned treads with differentdesigns for in vivo robotic mobility and they also charac-terized the mechanical properties of the small bowel. Theresult showed the anisotropical behaviors of the tissue andthe mucoadhesion. So we need more adaptable mechanismsfor complex surface conditions in bio medical applications.Recently, Hou et al. [30] and Jiang et al. [31] designed arolling locomotion method for magnetic microrobots. Anexternal rotating magnetic field was generated by a rotatingpermanent magnetic block underneath the working surface.

(a) (b)

Fig. 1 The μT UM magnetic tumbling microrobot. a Schematic ofμT UM . b μT UM on a US dime

The magnetic force along with normal blocking and fric-tion force enables successive rotations. Besides translationon a plane, this microrobot can also climb slopes. One lim-itation of this design is that workspace is confined withinthe certain travel distance of the permanent magnetic bodyunderneath. If the robot rolls too far from the driven piece,it will be pulled back instead of rolling farther.

In this work we present a novel untethered tumblingmagnetic robot (μT UM) with a dumb-bell type struc-ture (Fig. 1) which can perform tumbling locomotion withpredefined magnetic field signals. First, we introduce thedesign of the micro agent and its working mechanism. Then,we introduce the coil drive system followed by validatingthe mechanism through magnetic field and force analysis.After the fabrication process for the μT UM agents is intro-duced, the experimental results are presented. Finally, weconclude with a discussion and suggestions on improvingwork performance.

2 Tumbling magnetic microrobotic design and motionmechanism

2.1 Microrobot design

A tumbling robot at the small scales can be more adapt-able for complex surface conditions, such as convex shapesand slopes, than traditional microrobot designs. Anotheradvantage of tumbling locomotion at the micro scale is thatit needs less driving force compared to the direct pullingmotion by gradient magnetic fields. This is key becausethe large driving forces required can be a big problem forthe magnetic locomotion principle at small scales. Bothdistance and agent volume scaling down will dramaticallydecrease the magnetic force required for actuation. How-ever, the surface forces (static friction) to induce locomotioncan be quite large and result in uncontrollable locomo-tion. As a relatively unexplored locomotion mechanism,tumbling shows potential to provide increased mobility onsmaller scales [32] with smaller actuation force. To realize

J Micro-Bio Robot (2013) 8:1–12 3

the tumbling motion in submillimeter dimensions, a com-posite magnetic structure of a dumb-bell shape has beendesigned (Fig. 1). The two bell parts of the dumb-bell struc-ture are permanent magnets with opposite polar directions.The bells are connected by a non magnetic bridge piece.

2.2 Motion mechanism

Suppose the agent lies on the working surface (Fig. 2a).When the magnetic field of upward direction (+z) turnson (Fig. 2b), bell A will be pulled down while bell B willbe repelled up. This pair of forces will generate a momen-tum. This momentum plus gravity, along with the resultantblocking force will cause the device to stand up in an equi-librium stance (transient state). If we turn off this verticalmagnetic field at the transient state, this device would fallback to surface to its original position. But if we turn onanother horizontal magnetic field pointing right (+x) at thesame time with turning off the vertical field (Fig. 2c), thedumb-bell device will experience a continuous momentummaking itself tumble forward. Thus, the device will fulfill atumbling cycle naturally with turning off the the horizontalmagnetic field (Fig. 2d). If the device needs to tumble to theleft, all we need to do is to turn on the magnetic field in theopposite direction. To easily adjust the device’s orientationin the horizontal plane, we can keep the device in the tran-sient state by holding the vertical magnetic field on and thensteer the agent’s heading by steering the horizontal mag-netic field direction. Only low field intensity is needed herebecause of the low friction due to the small contact area.The beauty of this tumbling mechanism is the adaptabilityto different non-idealized surfaces mentioned above. Dur-ing this locomotion process the surface does not need to beperfectly flat or horizontal as long as it has contact betweenthe microrobot and the surface.

(a) (b)

(c) (d)

Fig. 2 Motion mechanism of the magnetic tumbling microrobot. aInitial position; b Apply vertical magnetic field to erect the agent; cApply horizontal magnetic field to finish the tumbling; d Final positionafter one tumble action

3 Magnetic coil drive system

To fulfill the motion of tumbling mechanism with the sub-millimeter magnetic microrobot, a test bed consisting offive independently controlled coils has been constructedwith electromagnetic wire of the same gauge (Fig. 3). Onecoil is built with more turns than the others and mountedas the bottom coil to provide the vertical magnetic field.The other four coils are manufactured identically with thesame dimensions and number of turns to produce the hori-zontal magnetic fields. All five coils have cobalt-iron coreinserts with high magnetic permeability which dramaticallyincreases the field strength. The coil facts are summarizedin Table 1.

The work space area encompassed by the coil set isone square inch. The realtime imaging is accomplishedby an overhead CCD camera (Point Grey FL2-14S3C,ptgrey.com) along with a microscope lens (Edmund VZM300i, edmundoptics.com) of adjustable magnification. Thecombination is able to provide a 8.0 mm × 2.0 mm fieldof view. To observe the tumbling motion of the agentfrom the side, a side camera is also added to the systemwith an optical lens of larger magnification (Edmund VZM1000i, edmundoptics.com), the resultant field field of viewis 2.56 mm × 0.64 mm. The magnetic coils are controlledby individual series of solid state relays. Customized signalsare sent via computer control of a data acquisition board(LabJack U3-HV and CB15, labjack.com). The system canpulse signals with frequencies as high as 100 kHz.

Fig. 3 Photograph of the electromagnetic test bed. [A] CCD camera;[B] Microscope lens; [C] One of the four side coils set for the hori-zontal magnetic field; [D] Bottom coil for the vertical magnetic field;[E] X–Y stage; [F ] Chamber in workspace. Side camera and opticsare not pictured

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Table 1 Parameters of electromagnetic coils

Facts Vertical coil Horizontal coils

Number of turns 700 320

Inner diameter (mm) 17.3 17.3

Outer diameter (mm) 60 48

Length (mm) 110 90

Core material CoFe CoFe

Relative permeability 70 70

4 Theoretical analysis

The overall system design has to be calculated and ana-lyzed before the fabrication and testing of this novel μT UM

microrobot. Based on the intensity of the magnetic field andthe agent’s magnetization, we can know whether the agentwill stand up in transient state to fulfill the tumbling. Thefollowing force analysis is necessary to predict the motion.

4.1 Magnetic field

The magnetic field intensity is determined by the inputcurrent (I ) while the magnetic induction is due to thepermeability of the material. So we choose to have electro-magnetic coils wrapped on a core with a high permeabilityvalue to provide the magnetic field. The magnetic field dueto a current-carrying closed loop can be calculated based onthe Bio-Savart law [33]:

B = μ0

4π

∮C

Idl × rr2

(1)

where B is the magnetic field at the desired space point, μ0

is the permeability of air (4π×10−7H ·m−1), I is the currentflowing in the closed loop, dl is the differential element ofthe current-carrying wire, and r is the displacement vectorpointing from the wire element to space point computed,where r is the unit vector is this direction and r indicatesthe magnitude of this vector. Since the magnetic field at anarbitrary space point obeys the principle of superposition,the total magnetic field intensity generated by a solenoid canbe determined as:

B =∫ L2

L1

μ0

4π

∮C

Idl × r

r2(2)

where L1 indicates the loop on one end of the solenoid andL2 indicates the one on the other end, while the other sym-bols hold the same notions with Eq. 1. If a core of highpermeability μ is inserted inside the solenoid, the magneticfield B can be increased by μ times accordingly. Further,the magnetic field intensity caused by multiple solenoidscan be derived through the algebraic sum of each one’scontribution.

Assume the wire turns are distributed uniformly in space,theoretical calculations with Eq. 2 and Table 1 show thatboth the vertical and horizontal coils are able to providemagnetic fields of about 5 mT at a half inch distance (centerof the workspace) when 1A of current is flowing in the wireloop, with the gradient of the field around 500 mT·m−1.This theoretical estimation is corroborated by a DC Gauss-meter (AlphaLab Inc. www.trifield.com/) which works withthe Hall effect principle. The magnetic field generated bythe coil system has been modeled and simulated in a 1:1ratio using COMSOL software (www.comsol.com) (Fig.4). The results are consistent with the measurements andtheoretical calculations.

4.2 Force analysis

Any magnetized body within a magnetic field will experi-ence force and torque, which is the basic principle for thedesign of magnetic microrobotics [34–38]. The magnetizedbody always has the tendency to align its internal magne-tization into the alignment with the external field. In anycase, the acting force on the magnetic body is in the gradient

Fig. 4 Simulation of magnetic field generated by the electromagneticcoil system. Coils 4 and 5 are activated

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direction of the magnitude of the applied field. The generalcase of this acting force density is [39]:

Fmd = −μ0 �[∫ H

0

(∂Mv

∂v

)H,T

dH

]+ μ0(M · �)H (3)

where Fmd is the magnetic force density, H is the internalfield of the magnetized body (not the external field applied),T is the temperature, M is the magnetization, v is the vol-ume. Hence Mv = σ , which is the magnetic moment per kgof the magnet.

In this work, the neodymium magnet (NdFeB) is appliedin the magnetic part of the microrobot. The advantage ofthis permanent magnetic material is the high remanence andextremely high coercivity. Thus, to simplify the calcula-tions, we treat the magnitude of the inner field strength H

as constant value, which is 600 (kA·m−1). This is attractivewhen compared with soft magnetic materials whose largemagnetization depends on the high inputs for the externalmagnetic field. The acting force and torque can be derivedthrough:

Fm = Vm(M · �)B (4)

τm = VmM × B (5)

where Fm and τm are the acting force and torque on themagnetic body respectively, and Vm is the volume of mag-netic part. So with the facts of the μT UM microrobot(Table 2), we can determine that one bell part will get about30 nN acting force (This force is calculated in the exam-ple scenario referred in the above section), while the totalgravity force of the μT UM is around 0.06 nN.

After deriving the magnetic force, the general case offorce analysis for the tumbling robot is examined. As shownin Fig. 5, the arrows in orange color indicate the directions

Table 2 Parameters of μT UM microrobot

Facts Bell part Bridge part

Length (µm) 100 200

Width (µm) 300 100

Thickness (µm) 50 50

Material SU8, NdFeB SU8

Magnetic volume (µm3) 9.4 × 104 0

Density (kg·m−3) 1,600 1,200

Gravity (nN) 0.024 0.012

Note: The magnetic volume is derived by the mass/volume ratio usedto mix the NdFeB powder in SU8 photoresist

Fig. 5 Free body diagram of μT UM microrobot on a surface withapplied external forces and torques

of the magnetic field or the magnetization of the bell parts.The ones in black show the forces and torques that couldact on the agent. ϕA and ϕB are the angle contained by thevertical direction of the streamline of magnetic field at posi-tion A or B, respectively, whereas θ is the agent’s inclinedangle from the horizontal surface. Then general forces onthe microrobot in x–z plane can be expressed as:

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

mz = �Fz = FmBz − G − FmAz − Fa − Fdz + Nz,

mx = �Fx = FmBx + f − FmAx − Fdx − Nx,

Imθ = �τ

= τB − τA + (FmBz + FmAz − Nz + Fad)L

2cos θ

− (f − Nx + FmBx + FmAx)L

2sin θ

(6)

where m is the mass of the micro agent, Im is the momentof inertia about the center of mass, L is the length of theagent, Fm and τ are the magnetic force and torque actingon the bell parts respectively, G is the gravity force, Fa isthe surface adhesion, Fd is the damping force if the agentworks in fluid environment, N is the blocking force and f

is the resulting friction force where f = μNz, μ is theCoulomb friction coefficient. Subscript x and z show thedirection. Note that subscript A and B indicate the two bellparts, while normal B means the magnetic flux intensity

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elsewhere. Based on Eqs. 4 and 5, the magnitude of themagnetic force and torque can be calculated with:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

FmAx = VAMA � BA sin φA cos(π

2− θ

)

FmAz = VAMA � BA cos φA cos θ

FmBx = −VBMB � BB sin φB cos(π

2+ θ

)

FmBz = VBMB � BB cos φB cos (π − θ)

τA = VAMABA sin (θ − ϕA)

τB = VBMBBB sin (π − θ + ϕB)

(7)

where B is the magnetic flux intensity, �B is the gradientof the flux intensity, V and M are the volume and mag-netization of the bell parts. From Eqs. 6 and 7 we canrecognize the influence of surface and magnetic field on theagent’s behaviors, which is able to be summarized into thefollowing categories:

(1) Slipping case: �Fx = 0, �Fz ≤ 0, �τ > 0. Thesurface is at perfect horizontal plane (Nx = 0) with-out friction (f = 0), adhesion (Fa = 0), or damping(Fd = 0), and the magnetic field is in the perfect ver-tical direction (ϕ = 0). In this extreme ideal case,although the agent will rotate in the x − z plane, butwithout friction, only pure pure rotation is achievedwhich is not desired.

(2) Pulling up case: �Fz > 0. If the summed forces inz direction are positive , no matter the results of �Fx

and �τ , the agent will be pulled up and fly out of theworking plane. This is not an equilibrium state whichis also not desired.

(3) Sliding case: �Fx �= 0, �Fz ≤ 0. In this case, theagent will translate along the surface whereas the fric-tion force f will become sliding friction and turn tothe opposite way to the direction shown in Fig. 5. Thissliding behavior will cause adverse effects on the tum-bling motion which makes the motion control moredifficult.

(4) Tumbling case: �Fx = 0, �Fz ≤ 0, �τ > 0. Thedifference between this scenario and the sliding case isthat there is friction in the x direction. This case indi-cates there is no sliding or pulling up, which meansagent stays on the surface and the friction is static. TheμT UM will perform pure tumbling motion in this casewhich is the desired control state.

5 μTUM agent fabrication

This μT UM microrobot design has been fabricated througha custom surface micromachining process (Fig. 6). At first, a4′′ bare silicon wafer is prepared in step (1) and coated withOMNICOAT (MicroChem, www.microchem.com). This

Fig. 6 Schematic of fabrication process for the μT UM microrobotdesign

sacrificial layer assists the final release of the device. In fol-lowing step (2), a pure photoresist SU8-50 (MicroChem,www.microchem.com) is coated and baked. This layer ispatterned as the bridge part in step (3), which is used toconnect the two bell parts of agent. To manufacture the mag-netic bell part with specific polarization, magnetic particlesare mixed with controlled mass density in the SU8-50. Themagnetic particles are the grounded products of the NdFeBpermanent magnetic powder (MQP A, Neo Material Tech-nologies, www.mqitechnology.com), whose average size issmaller than the SU8-50 spinned thickness (about 50 µm).A customized mass/volume ratio is controlled during themixing to know the volume of magnetic particles in a cer-tain enclosed dimension. In order to configure the particles’polarization, we take advantage of the forming mechanismof SU8. In the soft bake process which evaporates the sol-vent in photoresist for solidification, a 4′′ diameter NdFeBdisk (K&J Magnetics, www.kjmagnetics.com) is set under-neath the silicon substrate while baking (step (4)). Thepolarization of the magnetic disk is along the thicknessdirection, so the bell part of the eventual micro agent willbe magnetized in the thickness direction. Because the bak-ing temperature of SU8-50 (95 ◦C) is much lower than theCurie temperature of NdFeB material (above 300 ◦C), theNdFeB disk will keep its magnetic property during the heat-ing process. Also because of the excellent heat conductivityof metal, the disk between the sample and hotplate does notimpact the baking result. After the soft bake, the magneticphotoresist layer is aligned and patterned as one bell partin step (5). Steps (6) and (7) are the repeat of steps (4) and(5) for the other magnetic bell part, whereas the polariza-tion process during soft bake is the opposite. Therefore, adumb-bell structure with two magnetic bell parts of oppo-site polarization is achieved after the final release by PGremover (step (8)).

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6 Experimental results

This proposed magnetic tumbling microrobot has beentested in the built electromagnetic coil system. Prelimi-nary manually controlled tests have verified the design andfabrication method of the agents and the tumbling motionmechanism at the submillimeter scale. The orientation of theagent in horizontal plane has also been successfully steered.

6.1 Polarization tests

The two opposite polarized magnetic bell structures arethe key to the tumbling motion mechanism. Therefore, thepolarization result of the agent is tested before perform-ing the motion tests. After releasing the agent, no featurecan be recognized as polarization direction on the two bellstructures. But we can tell the field direction of the electro-magnetic coil by the right-hand rule. As shown in Fig. 2b, ifthe field line points upward, the bell part with N-end facingdown will be lifted up. Therefore, with a known directionof magnetic field, the polarization of the bell part is able tobe detected. Furthermore, to verify whether the polarizationof the two bell parts are opposite, the current flowing in thebottom coil can be switched. Then, the direction of the ver-tical magnetic field will point downward, which means thebell part with S-end facing down will be repelled up. Resultsof such tests show that most of the μT UM are fabricated asdesired (Fig. 7). This proof of concept test also validates thefabrication method referred to previously for magnetic partsat the micro scale with desired polarization.

Fig. 7 Polarization test of a μT UM agent. a and b are the responseto the vertical field with opposite directions

Fig. 8 Steering tests after the μT UM agent reaches transient state

6.2 Steering tests

Steering tests have also been conducted along with the tum-bling motion tests. Without steering the orientation of theagent in horizontal plane, the tumbling motion can only berealized in the initial facing direction. So after achieving asteady transient state, horizontal magnetic fields from dif-ferent planar directions are applied separately. The agentturns to face along the field line accordingly, as shown inFig. 8.

The key of successful steering is observed to be the fluxintensity of the horizontal magnetic field. If the intensity ofthe horizontal field is comparable or even larger the the ver-tical one, the agent will be more likely to experience pullingthan steering. So the important tip for steering is to turnon the horizontal magnetic field in the magnitude a certainamount lower than the vertical field.

6.3 Tumbling motion tests

To test the feasibility of tumbling motion mechanism forthe submillimeter agent, a proof of concept experiment isconducted step-by-step according to the proposed activa-tion mechanism with manually controlled input signals tothe coil system. These manually controlled tests verify thatthe μT UM agent is able to perform the tumbling motion(Fig. 9) for locomotion.

According to the proposed tumbling motion mechanism(Fig. 2), after the agent is set on the surface in the workingspace (Fig. 9a),only the bottom coil is turned on. The direc-tion this vertical magnetic field line is customized upwardsby the current flow in the bottom coil, which corresponds to

Fig. 9 Steps in one cycle of a μT UM agent performing tumblingmotion

8 J Micro-Bio Robot (2013) 8:1–12

a magnet body with N-end on top. When the agent standsup in the transient state (Fig. 9b), the facing orientation isjudged by human observer, then the side coil located in thedesired tumbling direction is turned on. The direction of thishorizontal magnetic field line is customized to point awayfrom the agent to the coil, which equals to a magnet bodywith S-end facing to the agent. The key of this control is toturn off the vertical field at the same time as turning on thehorizontal field. Erratic response is observed in trial testswhen this fails. The function of the horizontal field is topull the agent past of upright position (Fig. 9c). Only a shortperiod of time is necessary for the corresponding side coil tobe on. Thus, unlike the input signal of bottom coil, a pulsesignal is used as an input for producing the fast horizontalfield signal. A successful case is observed if the agent passesby the upright position and then falls down forward fulfill-ing a wholesome tumbling cycle (Fig. 9d). Due to delays ofthe mechanical relay, this step can fail if the agent does notswing across the upright position. In this case the agent willfall back to its initial state.

It is recognized that the inclined angle θ (Fig. 5) is keyto fulfilling the tumbling motion cycle. Not enough inclina-tion leads to failure, including sliding and falling back to theoriginal horizontal position. This inclined angle θ has beeninvestigated in both theoretical and experimental methods.Assume the μT UM agent lays down at its original hori-zontal position (θ = 0) while the applied magnetic field isideally vertical. The acting magnetic force in the x directionis now zero. Analyzing the summed forces in the z directionand summing the torques based on Eqs. 6 and 7 we get:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

− VBMB � BB cos(π − θ) + VAMA � BA cos θ

+ Nz = 0

VBMBBB sin(π − θ) − VAMABA sin θ

+ (−VBMB �BB cos(π −θ)+VAMA �BA cos θ − Nz)

L

2cos θ = 0

(8)

Note that the gravity force G is neglected since it is verysmall when compared to the magnetic force. The adhesionFa and damping forces Fd are also neglected in the idealcase. We can solve this equation set and get the followingexpression for the inclined angle θ ∈ (0, π/2):

θ = arcsin

(BA − BB −√

(BA − BB)2 + 4(�BB)2L2

−2 � BBL

)

(9)

This indicates that the inclined angle θ depends on the mag-netic flux intensity B . Moreover, it is noted that all the itemsof B are in the first degree while B is proportional to the

current, I , in the wires, based on the Bio-Savart law (Eq.1). Because the value of θ is in fraction form with items ofB in both numerator and denominator, the resultant valuewill remain the same as the values of B change for the dif-ferent amounts of input current. This conclusion is verifiedby plugging the field intensity derived by the COMSOLsimulation into Eq. 9. For example, we simulate the verti-cal magnetic field with currents only flowing in the bottomcoil of our real system in COMSOL. Then the resultingfield intensity is plugged into Eq. 9 to derive the θ values.The simulation and calculation results are summarized inTable 3.

The theoretical reasoning indicates that the μT UM agentcan easily stand up as long as the magnetic force is domi-nating the gravity force, which is easy to achieve. However,this preliminary theoretical reasoning can not fully predictthe real performance of the agent due to two major fac-tors. The first is because the calculation is derived fromone specific stance at one specific time point. The mag-netic forces acting on the agent will change as the agentrotates up due to the different flux intensities at differentspots in the workspace. As the agent stands up, the mag-netic force in horizontal direction will increase from zero,which aids the tumbling motion if the robot doesn’t slideor slip. Another considerable factor impacting the inclina-tion are the adhesion, friction and damping forces, whichare currently not feasible to quantify in nano-Newton scale.But based on the tumbling motion mechanism, we can tellthat a certain amount of friction is beneficial for the motionwhile adhesion and damping are not helpful.

To further explore the critical inclined angle θ to accom-plish the tumbling motion, individual tests were conductedon different substrates with different current flows in thebottom coil (Fig. 10). The tracking accuracy is good to ±2◦.Compared to the theoretical calculation, the experimentalresults show consistency, which indicates the inclinationangle will be relatively constant as long as the agent canstand up, no matter how much the input current is. This fea-ture confirms the merit of the tumbling motion mechanism

Table 3 The inclined angle θ in the ideal case

I BA BB �BB θ

(A) (mT) (mT) (mT/m)

0.5 4.04 3.79 368.75 32.0◦

1.0 8.08 7.58 736.25 32.0◦

2.0 16.17 15.15 1,471.25 31.6◦

4.0 32.34 30.31 2,945 31.7◦

Note: I is the current flow simulated in our bottom coil. The magneticflux intensities are read assuming the agent is located at the center ofthe workspace

J Micro-Bio Robot (2013) 8:1–12 9

Fig. 10 Inclined angle θ on different substrates with different cur-rents inputs in the bottom coil. Each θ value is the average value of 3repeatable vertical standing up tests with the same current input

which does not need as much drive force as other loco-motion methods like sliding or stick-slip. The inclinationangles turn out to be slightly different on different sub-strates. This phenomenon can be explained by the fact thatthe friction does play critical role in the inclination angle ofthe microrobot.

6.4 Mobility tests

Tests in the above section have shown the mobility ofthis μT UM magnetic microrobot design. The translationvelocity v is able to be calculated out as:

v = L

T(10)

where L is the length of agent, T is the period time ofthe control signal to fulfill a tumbling cycle. For example,the L of the μT UM agent is 400 µm, the time of manu-ally controlled signal to fulfill a cycle T is 1.03 s accordingto the recorded video. Thus the translation speed of v =0.38 mm/s (≈ 1 body length/s) is expected when repeatingthe tumbling cycle. It is obvious that a faster control signalcycle will correspond to faster resulting speeds.

Most of the mobility tests were conducted on the backside of a silicon wafer, which is rough, but flat. Based onthe proposed tumbling motion mechanism, μT UM will beable to adapt to various types of surfaces and more com-plex environments. This feature is critical for future realbio-related applications. Therefore, mobility tests have alsobeen conducted on other types of surfaces in both dry andfluid environments: normal printing paper (Fig. 11a) whichis rough, a glass microscope slide (Fig. 11b), on the surfaceof one US penny in silicon oil (Fig. 11c), and on a biologicaltissue sample in normal saline (Fig. 11d).

(a) (b)

(c) (d)

Fig. 11 Tumbling motion test on various types of surfaces in dry andfluid environments. Traveling distance during the trial is noted in thebracket. a On normal printing paper (3.23 mm); b On a glass micro-scope slide (3.48 mm); c On one side of a US penny in silicon oil (3.36mm); d On piece of bio tissue in normal saline (4.81 mm)

On different types of substrates, the current inputs intothe bottom coil to stand up the agents are recorded (Table 4).These values are the lowest ones that tumbling locomo-tion has been observed repeatedly. The corresponding lowmagnetic field intensity in the workspace corroborates theproposed advantage of this tumbling magnetic microrobotdesign.

The paper and glass slide are meant to provide cross ref-erences for different surface frictions. The results in Table 4shows that the on paper it needs larger magnetic field tostand up the agent, probably due to the larger adhesion.However, it is noted that the more static friction the surfacehas, the less minimum inclined angle θ is needed to ful-fill the tumbling motion. It is also noted sometimes thereis a small initial inclined angle θ when the agent is set onthese non-conductive surfaces with no current input. This

Table 4 Magnetic fields for tumbling on different substrates

Substrate I (A) B (mT)

Unpolished Si 0.40 2.7

Paper 0.70 4.7

Glass 0.55 4.1

Penny 0.50 3.5

Tissue 0.50 3.5

Note: I is the current inputs into the bottom coil. B is the correspond-ing magnetic flux intensity in work area measured by Gauss meter. TheμT UM microrobot tested is approximately 400 µm × 300 µm in size

10 J Micro-Bio Robot (2013) 8:1–12

initial inclined angle can be explained by surface charge andelectrostatic forces. This phenomenon could also provide afeasible way to quantify the electrostatic force at the microscale (nN scale force).

The tests on biological tissue sample and US penny aredesigned to test the mobility of the μT UM agent on non-flat surfaces of 3D structures, which are more similar toreal bio-environments than flat surfaces. The trial tests showthat the agent is able to conquer the 3D features of thedimensions less than the size of microrobot body.

It should be noted that at least 3 trials on each substratewere performed for the mobility tests. Since these tests wereconducted with manual control of the drive signals, it is notpossible to compare repeatability performance of the robotson the different surfaces at this time. Instead, here we arejust concerned with the fact if the robot will be able tolocomote in the manner as designed and what the requiredcurrents/field strengths are to do so.

The low field intensity values shown in Table 4 demon-strates the advantage of the tumbling locomotion mobil-ity mode. It allows for limited magnetic volumes (9.4 ×104 µm3) with limited field flux intensities (several mT).This proves the μT UM’s adaptability for the complexenvironments found in biomedical applications.

7 Discussion

During the initial proof of concept tests, aspects open toimprovements have been identified. For the current elec-tromagnetic coil system, it is impossible for the μT UM

agent to tumble over the obstacle of the size comparable tothe robot body. However, the tumbling motion is adaptablefor the environment in all dimensions. In order to conquerthe large size that is comparable to the microrobot or evenlarger, a top coil can be incorporated into the coil sys-tem enclosing the workspace. When the agent encountersa “high wall”, the side coil can be on to set the agent totransient state and the top coil used to achieve the tumblingtask. A more adaptable μT UM system is expected with anupgraded coil system in our future work.

Further than adding a top coil to enhance the mobilityof μT UM , the form of the coil and system structure canalso be adjusted. Based on the tests, sliding phenomenon isobserved even on the surface with a high friction coefficient,which indicates that the agent experiences considerable lat-eral magnetic forces when only the bottom coil is turned on.This means the vertical field at the workspace in the cur-rent coil system is not perfectly upright. This judgement isalso corroborated by the simulation in COMSOL (Fig. 12a).In the future, Helmholtz coils will be adopted in this tum-bling system design. This type of coil system has beenapplied in some magnetic actuation work at small scales

(b)(a)

Fig. 12 Comparison of simulated vertical magnetic field produced bytwo different types of coil systems. The simulation is run by COM-SOL software. a The vertical magnetic field of the current coil systemdesign; b The vertical magnetic of a Helmholtz coil set-up

[40–42]. Although the Helmholtz set-up is not compact andthe magnetic field it generates is not as strong as the currentsystem for the same current input, the attractive advantageof Helmholtz coil is that it is able to provide magnetic fieldin a uniform direction in an enclosed workspace (Fig. 12b).The uniform upright field will be helpful to get the criticalinclination angle θ more predictable and reliable, which isideal for accomplishing the tumbling motion cycle.

Another aspect able to be improved lies in the fabri-cation process. During the polarization tests, not all therobots perform as desired, meaning that not all of the fab-ricated agents have the ideal desired magnetic properties.Because the NdFeB magnetic powder has uniform and reli-able magnetic properties, the problem happens during thepolarization step during the fabrication. In the polarizationstep, the permanent magnetic disk was set right underneaththe wafer substrate, thus the polarization field can be treatedas the field on the surface of magnetic disk. But the fieldmeasurement results of the disk show that the field inten-sity on the surface is not uniform along the radial direction,which means the NdFeB particles in SU8 would experiencesome lateral forces rather than just pure vertical force alongthe thickness direction of the sample and disk. Hence, theagents on the substrate position corresponding to large fieldgradient of the magnetic disk would fail to be polarized asin the proposed design. This drawback can be solved by animproved polarizing magnetic disk. The surface field gra-dient is dramatic at the fringe part of magnetic disk, so alarger disk will be able to provide more uniform fields in thecentral region of the wafer.

With the real biological and medical target applica-tions for the μT UM robot, the issue of force interactionsbetween the robot and blood vessel walls and other tis-sue is a concern. Preliminary testing of the manipulationforces that the μT UM robot is capable of have been con-ducted with microforce sensing probe from FemtoTools(www.femtotools.com). Results show forces are on the

J Micro-Bio Robot (2013) 8:1–12 11

order of 5 µN. Forces of this magnitude should allow forsafe operation within the targeted applications.

8 Conclusions

A novel magnetic microrobot system design applying a tum-bling mechanism is developed in this work. The μT UM

agent of 400 µm total length has a dumb-bell structurewith two opposite polarized magnetic bell parts. This micro-robot is able to perform the tumbling motion driven bya predefined sequence of external magnetic fields whichare produced by a coil set consisting of five electromag-netic coils. The key aspects of this mechanism is discussedthrough the manually controlled experimental results wherethe translation speed of 0.38 mm/s is achieved. Faster speedscan be expected based on an upgraded control system andsignal. The most appealing advantage of this μT UM sys-tem design is the adaptability to complex environments. Thefirst batch of fabricated prototype agents have shown mobil-ity on various types of surfaces, including 3D structuressuch as fibrous tissues. This tumbling design at the micro-scale has the potential to be effective tool in real biologicaland medical applications.

Acknowledgements Part of this work was supported by USNavy/Office of Naval Research Contract #N00014-11-M-0275. Theauthors would like to acknowledge Shi Bai and Sean Lyttle for theirhelp and discussions on the drive electronics and test bed develop-ment. We also acknowledge the Micro-Devices Laboratory at StevensInstitute of Technology, Prof. E.H. Yang and Dr. Seongjin Jang for pro-viding the fabrication facility and required equipment training neededfor this project.

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