Magnetically Actuated and Guided Milli-Gripper for MedicalApplications

Franziska Ullrich1, Kanika S. Dheman1, Simone Schuerle2 and Bradley J. Nelson1

Abstract— This paper presents the design, kinematics, fab-rication, and magnetic manipulation of a milli-gripper formedical applications. The design employs a permanent magnetfor two purposes. It actuates the compliant gripper and allowsfor maneuverability of the milli-gripper in an externally appliedmagnetic field generated by an electromagnetic manipulationsystem. The modular milli-gripper can be manipulated directlyor attached to the distal tip of a magnetically steered catheter.Experiments show successful actuation of the gripper andguidance of the device with the integrated gripper in both thetethered and untethered configuration.

I. INTRODUCTION

Many advances in surgery have been directed towards min-imizing the invasiveness of surgical procedures. Minimallyinvasive surgery has become preferred to open surgery due toits manyfold advantages, including minimum tissue damage,less blood loss, decreased postoperative pain, reduction ofboth recovery time and infection risk [1]–[3]. Emphasis isplaced on reducing the size of surgical instruments givingrise to the field of micro-surgical instrumentation. How-ever, through small incisions, surgeons have minimal directaccess to the operative area. Thus, medical staff must behighly experienced and dexterous because their hand-eyecoordination is hindered. While smaller instruments facilitateearly detection of cancer or painless and swift removal offoreign objects, smaller instruments under manual control aredifficult to manipulate because of limits imposed by mini-mum force perception and hand tremor [4]. The challengeof manipulating small instruments precisely motivates thedevelopment of automated systems and robotic devices thatassist in minimally invasive surgery. Advances in endoscopetechnology, precise steering of catheters, and miniaturizationof flexible surgical tools promise to convert many proceduresinto minimally invasive endoscopic ones. The developmentof miniaturized and flexible tools and manipulators, such asmilli- and micro-grippers, is of great importance to performbiopsies and manipulation of tissue with minimum damageto tissue [5]. Several tethered milli- and micro-grippershave been developed utilizing different actuations systems,such as pneumatic [6], piezoelectric [7] and actuation basedon shape memory effects [8]–[10]. Microelectromechanicalsystem (MEMS) based micro grippers have been developedfor single-cell handling and manipulation of particles smallerthan 100 µm [11]–[13].

1Institute of Robotics and Intelligent Systems (IRIS), ETH Zurich,Tannenstrasse 3, 8092 Zurich, Switzerland, bnelson@ethz.ch

2Koch Institute of Integrative Cancer Research, MIT, 77 MassachusettsAve., Cambridge, MA, USA

Wireless capsule endoscopy was first clinically introducedin 2000 by Iddan et al. [14] and approved by the Food andDrug Administration (FDA) one year later. It describes aprocedure in which a capsule with an integrated camera ispassively moved through the gastrointestinal tract searchingfor obscure or occult bleeding. Currently, these capsulardevices do not offer therapeutic capabilities and discoveredlesions must be further investigated and intervened uponwith conventional surgical methods [15]. Navigation of thecapsules is passively controlled by peristalsis and gravity, andsurgeons are incapable of stopping the capsule or turning itaround. In order to eliminate these shortcomings, researchershave developed capsules with integrated biopsy devices[16]–[18]. Furthermore, magnetic steering with externallyproduced magnetic fields allows for control of capsulesinside the body. Carpi et al. [19] integrated a magnet into aconventional video capsule and moved it utilizing a magneticnavigation system. Yim et al. [20], [21] designed a softcapsule endoscope that can roll on the stomach surface andis steered by an external permanent magnet.

This paper proposes a modular milli-gripper for medicalapplications. The design employs a permanent magnet fortwo purposes. It enables the actuation of the gripper andis simultaneously used to steer the device in an externallyapplied magnetic field. The modular milli-gripper can bemoved without direct contact allowing for high mobility, or itcan be attached to the distal tip of a catheter, which can thenbe magnetically steered by an electromagnetic manipulationsystem.

II. GRIPPER DESIGNThe proposed system, illustrated in Fig. 1, consists of

a compliant gripper, an electromagnetic coil with a soft-magnetic cobalt iron (CoFe) core and a neodymium iron

Compliant gripper

Coil with CoFe core

NdFeB magnet

Polymer capsule

Fig. 1. The milli-gripper consists of a compliant gripper attached to a coilwith a CoFe core in close proximity to a NdFeB magnet, all integrated in apolymer capsule. By applying a current to the coil, the attractive magneticforce causes the gripper jaws to close.

2015 IEEE International Conference on Robotics and Automation (ICRA)Washington State Convention CenterSeattle, Washington, May 26-30, 2015

978-1-4799-6922-7/15/$31.00 ©2015 IEEE 1751

boron (NdFeB) magnet, which are all integrated into apolymer capsule. The gripper is fabricated from Nitinol, ametal alloy of nickel (Ni) and titanium (Ti) that exhibits largeelasticity, and is highly biocompatible. Thus, it is suitablefor medical applications. The coil is rigidly attached to thecompliant gripper and in close proximity to the permanentmagnet. When a current is passed through the coil, themagnetic interaction between the coil and the permanentmagnet produces an attractive force between the coil andmagnet, which actuates the gripper jaws. Additionally, thepermanent magnet allows for controlled motion of the entiredevice in an externally applied magnetic field in either acontactless or tethered configuration.

A. Kinematics Design

For modeling simplicity, the forward kinematics of thecompliant gripper are derived by applying a four bar linkagemodel [22] as illustrated in Fig. 2a. The objective is toestablish the cumulative effect of multiple hinges on theresulting motion of the gripper jaws. This analysis assumesperfect rigidity of each link and free rotation of every jointaround a single degree of freedom. The Denavit-Hartenbergconvention is applied for kinematics modeling and thehomogeneous transformation matrix for the effector bar is

c(α1) −s(α1) 0 l1c(θ1) + l2c(α2) + l3s(α1)s(α1) c(α1) 0 l1s(θ1) + l2s(α2) + l3c(α1)0 0 1 00 0 0 1

where α1 = θ1 − θ2 − θ3 and α2 = θ1 − θ2. Applying thegeometric simplification

θ3 =π

2+ θ1 − θ2, (1)

the vertical translation of the effector bar becomes

yeff = l1 sin(θ1) + l2 sin(θ1 − θ2)− l3. (2)

Figure 2b shows the vertical translation of the effector baryeff in relation to various magnitudes of angles θ1 and θ2for l1 =5 mm, l2 =2 mm and l3 =4 mm. It is observedthat, for all θ2, decreasing θ1 increases the vertical downwardmotion of the effector bar and, therefore, the gripping stroke.Analysis shows that for large θ1, i.e. a vertical link l1, thesystem becomes stiff and the displacement of the effector barbecomes small. Therefore, a small θ1 and large θ2 are desir-able to increase the motion range of the gripper. However, bydecreasing angle θ1, the width of the gripper increases. Thegraph helps to find the optimal value for parameters θ1 andθ2 to maximize the translational displacement of the effectorbar. These values are used as initial design parameters forfinite element modeling (FEM).

B. FEM Simulation

A model of the gripper was developed using computeraided design (CAD) software (NX 7.5, Siemens PLM) andparameters are tuned with FEM to derive the best grippingresponse utilizing the Nastran solver for simulation, which

Vertical translation

(xeff,yeff)

Closing stroke

l1

l3

l2

x1

y1

x2 y2

x3

y3 θ1

θ2

θ3

a) b)

20 30 40 50 60 70 80 90−5

−4

−3

−2

−1

0

1

2

3

e1 [°]

Tran

slat

ion

of y ef

f [mm

]

e2=20°

e2=40°

e2=45°

e2=60°

e2=80°

e2=90°

Fig. 2. a) Kinematics analysis of gripper model using Denavit-Hartenbergconvention. b) Relation between angles θ1, θ2 and the vertical displacementof the effector bar yeff .

predicts mechanical effects on a system in response tothe applied input force. The model is meshed with threedimensional tetrahedral meshing elements with element sizeof 0.1 mm. The material chosen for simulation is Nitinolwith mass density 6.54 g/mm3, elastic modulus 83 GPa andPoisson’s ratio 0.33. Although the elastic modulus of Nitinolchanges with stress, the highest value for the martensite formof the alloy was used for simulations to provide a worst-case scenario. Fixed constraints are introduced at the legsand a vertical force between 0 and 120 mN is applied to theeffector bar. Figure 3 shows the resulting jaw displacementsfor various input forces. FEM simulations suggest that thegripper closes, i.e. both jaws have undergone a horizontaldisplacement of 300 µm, with a vertically applied forceof 111 mN. Results for a vertical input force of 111 mNis illustrated in Fig. 4. The simulation results show thata displacement of 300 µm in x-direction is expected foreach jaw for the given input force, as illustrated in Fig.4a. The effector bar displacement (Fig. 4b) for the sameinput is 136 µm. Figure 4c illustrates the magnitude of totaldisplacement [mm ] of the gripper structure. The maximumVon Mises stress of 128.28 MPa is much smaller than theyield strength of Nitinol (>1100 MPa) and is found at theinner hinge of the gripper, shown in Fig. 4d.

0 20 40 60 80 100 1200

100

200

300

400

Vertical force (mN)

Jaw

dis

plac

emen

t in

x (u

m)

Fig. 3. FEM results for displacement of a single gripper jaw in relationto a vertically applied force. The gripper jaws fully close at 111 mN.

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0.324 0.297 0.270 0.243 0.216 0.189 0.162 0.135 0.108 0.081 0.054 0.027 0.00 Units = mm

128.28 117.59 106.90 96.21 85.52 74.83 64.14 53.45 42.76 32.07 21.38 10.69 0.00 Units = N/mm2 (Mpa)

0.300 0.250 0.200 0.150 0.100 0.050 0.000 -0.050 -0.100 -0.150 -0.200 -0.250 -0.300 Units = mm

0.001 -0.011 -0.022 -0.034 -0.045 -0.056 -0.068 -0.079 -0.091 -0.102 -0.113 -0.125 -0.136 Units = mm

a) b)

c) d) Units = mm Units = mm

Units = mm Units = N/mm2 (MPa)

Fig. 4. FEM simulation of Nitinol gripper with fixed constraints on legs andvertical force of 111 mN acting on effector bar. a) Displacement in x (max.value 300 µm), b) Displacement in y (max. value 136 µm), c) Magnitudeof displacement (max. value 324 µm), d) Von Mises stress (max. value128.28 MPa)

C. Gripper Fabrication

The two dimensional gripper structure is fabricated with amonolithic laser ablation process conducive to the choiceof material. A piezoelectric positioning stage (SmarAct,Germany) with three degrees of freedom supports and posi-tions a Nitinol sheet for micro-machining. The gripper wasmanufactured using a DUETTO picosecond micromachininggreen laser (Time-Bandwidth, Switzerland) with 532 nmwavelength and 100% power at a frequency of 300 kHz.Higher frequencies enable higher scan speed while loweringthe energy per pulse, hence, reducing heating effects. Thebeam width of the laser was measured as 33 µm, which issufficient to fabricate the gripper with minimum feature sizeof 100 µm. Figure 5a shows the fully fabricated gripper withthickness of 254 µm. The gripper jaws are 920 µm apart andare oriented at 6.92◦ in the open configuration so they alignwhen the gripper is closed. Figure 5b shows two differentgripper designs during the laser ablation process with thegreen laser.

D. System Assembly

A capsule with largest diameter 8.5 mm, smallest diameter5 mm, and length 18.5 mm is 3D printed (Objet500, Strata-sys, Eden Prairie, MN, USA). A permanent NdFeB magnetwith diameter 4 mm and length 8 mm is attached to one endof the capsule, and the gripper feet are attached to the otherend. A coil with diameter 4 mm and length 7 mm is wound

with copper wire with diameter 150 µm around a CoFe coreof dimensions 1.0 × 1.3 × 7.0 mm. The effector bar of theNitinol gripper is attached to the coil, such that the coil iswithout contact to the polymer capsule, as shown in Fig. 1.

III. EXPERIMENTAL VALIDATION

A. Methods

To characterize the gripper, the relationship between trans-lation of the effector bar and the gripping stroke is quantized.A thin needle is attached to a piezoelectric micropositioner(Smaract, Germany) that pulls on the effector bar. The needleis moved in steps of 50 µm and the tip closure is observedthrough a digital microscope (DNT, Germany) and post-processed in MATLAB. The gripping performance of themilli-gripper to manipulate biological tissue is analyzed. Asample of porcine liver tissue is prepared and moved towardsthe gripper jaws. When the gripper jaws touch the liversample, the gripper is actuated to grasp a small sampleof the tissue, as illustrated in Fig. 8. The liver sample isthen slowly moved away, while the gripper jaws remainclosed. To characterize the fully assembled gripping systemthe gripper is attached to the electromagnetic coil and placedin close proximity to the permanent magnet, all integratedin a polymer capsule. By applying current to the coil, themagnetic attractive force between coil and permanent magnetcauses the gripper to close. Currents between 0 and 90 mAare applied to the coil.

B. Results

Figure 6 illustrates the resulting tip closing behavior whenthe effector bar is displaced with 50 µm steps up to amaximum displacement of 300 µm. The graph shows a slighthysteresis for opening and closing of the tip. The averageamplification factor is 2.26, determined as the ratio betweenthe input displacement of the effector bar and the outputtip closure. Figure 8e shows a microscopic image of themilli-gripper after grasping the porcine liver. The imagedemonstrates that a small amount of tissue was grasped.Thus, the milli-gripper could potentially be used for biopsiesor harvesting of small samples of biological tissue. Figure

2 mm

•  Figure, chart, video…

•  Figure, chart, video…

1 mm

100 µm

100 µm

a) b)

Fig. 5. a) Fully fabricated Nitinol gripper with thickness 254 µm andsmallest feature size of 100 µm. b) Fabrication process of two differentgripper designs with a picosecond micro machining green laser.

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0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800

Displacement [um]

Tip

clos

ure

[um

]

Amplification factor: 2.2612

Displacement of effector bar

Tip closure

Fixed constraint

0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800

Displacement [um]

Tip

clos

ure

[um

]

Amplification factor: 2.2612

0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800

Displacement [um]

Tip

clos

ure

[um

]

Amplification factor: 2.2612

0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800

Displacement [um]

Tip

clos

ure

[um

]

Amplification factor: 2.2612

Fig. 6. Closing hysteresis of gripper jaws at 50 µm steps with averageamplification factor between effector bar displacement and tip closure of2.26.

7a shows the relationship between a current applied to thecoil and the gripper closing stroke with power of 550 mW.An average closing relation of 3.6 µm/mA is observed.The gripper jaws are fully closed when a current of 90 mAis passed through the electromagnet. Figure 7b shows thegripper jaws when currents of 0, 40 and 90 mA are appliedto the coil.

IV. MAGNETIC GUIDANCE OF GRIPPER

A. Governing Equations

The milli-gripper is equipped with a NdFeB magnet that issimultaneously used for actuation of the gripper and steeringof the device. The magnet has total magnetization M [A/m ]which is largest along its long axis while magnetization alongthe short axes can be neglected. When the device is exposedto an external magnetic field H [A/m ], generated by theelectromagnetic system, the magnetic flux density B [T ] isderived by B= µ0H, where µ0= 4π × 10−7 Tm/A is thepermeability of vacuum. When applying a magnetic field, amagnetic torque per volume

T = M×B (3)

in [ N/m2] acts on the milli-gripper and aligns it with thefield B. Assuming the gripper is not activated, the magnetic

I = 0 mA I = 40 mA I = 90 mA

0 10 20 30 40 50 60 70 80 900

100

200

300

400

500

Current [mA]

Tip

clos

ure

[um

]

I = 0 mA a)

b)

I = 40 mA

Fig. 7. a) Closing stroke of gripper jaws in [µm ] as a function ofcurrent [mA ] applied to the coil. The gripper closes at an average rate of3.6 µm/mA. b) Closing gripper jaws for changing current in the actuationcoil for currents of I = 0, 40 and 90 mA.

a) b) c) d)

e)

300 µm

Liver tissue

open closed closed open

Fig. 8. a-d) Actuation of gripper in porcine liver. e) Microscope image ofgripper after actuation with liver tissue visible.

force per volume [ N/m3] can be written as

F = (M · ∇)B. (4)

The device is steered with an electromagnetic manipulationsystem that consists of eight electromagnetic coils with softmagnetic core in a spherical arrangement. The magneticfields and gradients are precomputed and can be controlledby passing currents through the single coils. The magneticfield at a point P in the workspace due to a single coilis given by Be(P) = Be(P)ie, where Be is the unitcontribution and ie is the current in coil e, respectively.Superposing the fields generated by all coils at a point Pin the workspace, the field at this point is calculated as

B(P) =

8∑e=1

Be(P)ie = B(P)I (5)

where I is a vector that holds the current in each coiland B(P) is a 3 × 8 unit field contribution matrix thatcan be interpolated from precomputed or measured points.The magnetization vector M is normalized with respect tothe volume magnetization of the permanent magnet materialin [Am2 ] to remove any dependencies on the magneticproperties and is written as M. The currents in the eightcoils are mapped to magnetic force and torque acting on thecapsule through the 6×8 actuation matrix A(M,P). With adesired force and torque vector that are used to manipulatethe magnetic capsule and by applying the pseudoinverse ofmatrix A the required currents in the electromagnets can bederived as

I = A(M,P)†[

Tdes

Fdes

]. (6)

A more detailed mathematical model of the electromagneticsystem dynamics can be found in [23].

B. Magnetic Manipulation of the Milli-Gripper

Figure 9 shows the assembled device with integratedgripper and NdFeB magnet from the side (a) and the top

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10 mm

5 mm sideview topview

a) b)

c)

Fig. 9. The modular device with integrated gripper in a) sideview and b)topview. It is moved in an externally applied magnetic field. c) The devicecan be attached to the distal tip of a flexible catheter (diameter 5 mm) fortethered magnetic manipulation.

(b). The milli-gripper is moved in an external magneticfield. First, it is immersed in silicone oil with viscosityof 5000 mPa · s (Silitech AG, Gumligen, Switzerland) andplaced inside the workspace of an electromagnetic manip-ulation system. The workspace is observed with a CCDcamera (Point Grey, Richmond, Canada) with framerate15 Hz. A customized computer vision algorithm tracks thetwo dimensional position of the device utilizing a simple blobtracker. The visual information is used as sensor feedback bya proportional-derivative controller that controls the devicealong a predefined trajectory. Figure 10 shows the milli-gripper following a predefined square trajectory with sidelength of 25 mm. The applied field has a magnitude of15 mT and is oriented along the normal of the xy-planecausing the device to stand upright.

C. Manipulation of a Milli-Gripper tipped Catheter

The modular milli-gripper is connected to a flexiblesilicone catheter with inner and outer diameter of 4 and5 mm, respectively. The tethered device is shown in Fig.

10 mm

a) b) c) d)

e) f) g) h)

Fig. 10. The milli-gripper is steered magnetically along a predefined square(side length 25 mm) path with an externally applied magnetic field withmagnitude 15 mT.

9c. By applying external magnetic fields the device can bemanipulated magnetically. A two dimensional maze withseveral bifurcations was built from plexiglas and placed inthe workspace of the electromagnetic actuation system. Thelongitudinal motion of the catheter is governed manuallywhile the lateral motion of the catheter is controlled by theelectromagnetic manipulation system. The externally appliedfield, generated by the electromagnetic manipulation system,has a magnitude of 40 mT. When the magnetic field orien-tation is changed, the NdFeB magnet at the distal tip of thecatheter aligns with it, and, thus, the catheter tip orientationis controlled. The workspace is observed with a CCD camera(Basler AG, Ahrensburg, Germany) with framerate of 30 Hz.The images are transferred to the computer and allow theuser to steer the catheter open loop with a three dimensionaljoystick. Figure 11 shows magnetic catheter steering in theelectromagnetic manipulation system. The gripper capsule ona catheter is successfully steered through the two dimensionalmaze. Images a-d show motion into the left channel ofa bifurcation, followed by a retraction of the device andsubsequent motion along the right channel in images e-h.

V. DISCUSSION

The milli-gripper is designed to fit into a capsule withmaximum diameter of 8 mm while offering a stroke of600 µm. The gripper kinematics are tuned to allow for thelargest stroke while restricting the gripper width to the max-imum diameter of the capsule. The design of the compliantgripper makes full use of the elasticity of the material throughthe optimization of the flexure hinges where the entire struc-ture adds to the gripper’s compliance. The choice of material(Nitinol) is suitable for medical applications due to its highflexibility and biocompatibility. The gripper design does notexhibit sharp edges or corners that might injure tissue. Itcan be fabricated with a monolithic laser ablation process,a quick process allowing for high throughput. Experimentalvalidation shows a linear trend for closing the gripper jawswith displacement and current input. The standard devia-tion of measurements ranges between 3.5 µm and 46.6 µm.

b) c) d)

e) f) g) h)

a)

10 mm

Fig. 11. The tethered device with integrated gripper is successfully steeredthrough a maze by an externally applied magnetic field with magnitude40 mT.

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When actuating the gripper by displacing the effector bar,a slight motion hysteresis is observed which is presumablydue to relaxation of the material. The gripping stroke can bevaried with input current and exhibits a maximum of 300 µmfor each jaw.

An advantage of this milli-gripper design is the integrationof a permanent magnet that allows for steering the device inan externally applied magnetic field. The modularity of thesystem allows for both tethered and contactless manipulationof the gripper. The advantages of a minimally tethereddevice include the high agility of motion. Guided by externalmagnetic fields, the gripping device can be maneuveredinside narrow spaces and through bifurcations or aroundcorners. After attaching the milli-gripper to a flexible siliconecatheter, the gripper becomes a tethered device. Advantagesof a tethered system include the possible integration of moretools, such as irrigation or aspiration tubes, light and acamera. A tethered device can also exert higher forces ontissue in longitudinal direction of the catheter. The tetheredsystem is easily removable by pulling the catheter while ancontactless system has to be steered magnetically out ofan opening. The magnetization of the device is calculatedas 93.6 mNm/T and gives a measure for the torque perunit of the applied magnetic field and the force per unitof the field gradient. Therefore, the maximum torque andforce that can be applied to the milli-gripper in an externalmagnetic field with magnitude 100 mT and magnetic gradi-ent of 500 mT/m are derived as 9.36 mNm and 46.8 mN,respectively.

VI. CONCLUSIONS

This paper presented a magnetically actuated milli-gripperfor medical applications. The gripper is actuated by attrac-tive magnetic forces between an electromagnetic coil anda permanent magnet in close proximity to it. The systemcan be moved by itself or attached to the distal tip of amagnetically steered catheter. A kinematics model based ona four bar linkage model was developed to investigate thekinematic relation between a displacement of the effectorbar and the tip closure of the gripper jaws. The result of thekinematic analysis was used as a starting design to iterativelytune the design with FEM modeling. The resulting gripperdesign is fabricated from Nitinol, a super elastic and highlybiocompatible material, by a laser ablation process. Theassembled system is tested and steered in both a contactlessand in a tethered configuration through the workspace ofthe electromagnetic manipulation system. Experiments showsuccessful guidance of the milli-gripper in both configura-tions. As the gripping stroke is small with respect to thegripper size, future work includes optimization of the forcesbetween coil and magnet to increase jaw deflection andminiaturization of the device.

ACKNOWLEDGMENT

The authors would like to thank Maximilian Warhanek andthe Institute of Machine Tools and Manufacturing (IWF) atETH Zurich for support with fabrication of the gripper. We

acknowledge Prof. Robert J. Wood and Dr. Andrew Petruskafor fruitful discussions and suggestions. We also thank TaylorNewton for help with the catheter manipulation experiments.This work was supported by the European Research CouncilAdvanced Grant BOTMED.

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