Experimentally Validated Modelling of Electromechanical Dynamics on LocalMagnetic Actuation System for Abdominal Surgery

Florence Leong1, Alireza Mohammadi1, Ying Tan1, Pietro Valdastri2, Denny Oetomo1

1 Dept of Mechanical Engineering, University of Melbourne, Australia2 School of Electronic and Electrical Engineering, University of Leeds, UK

fleong@student.unimelb.edu.au, doetomo@unimelb.edu.au

AbstractThis paper builds on the emerging idea of the Lo-cal Magnetic Actuation (LMA) system for roboticabdominal surgery, that allows the rigid linkagesfor the surgical manipulator in minimally invasivesurgery to be replaced by magnetic linkages acrossthe abdominal wall. In this paper, the equation ofmotion for the internal unit, inserted into the ab-dominal cavity, is derived in all 6 spatial degrees offreedom. Firstly, the resultant magnetic field at thelocation of the rotor, generated by a source at anarbitrary displacement from the rotor, is modelled.Secondly, the model of the wrench acting on theinternal rotor unit generated by the magnetic fluxlinkage between the above mentioned field and thatof the permanent magnet rotor is derived (by New-ton Euler approach). The contributions of multi-ple sources of magnetic field on the forces and mo-ments acting on the internal rotor unit are taken intoaccount by the principle of superposition. The pa-per then carries out system identification on an ex-perimental set up. Numerical computational andexperimental validations were carried out on themagnetic field model and magnetic-torque model,as well as confirming the validity of the principleof superposition for our problem.

Keywords:Local magnetic actuation (LMA), Electromagneticactuation, abdominal surgery,robot assisted surgery,minimally invasive surgery.

1 IntroductionLocal Magnetic Actuation [Di Natali et al., 2015] techniqueshave been investigated recently as a variant to the conven-tional minimally invasive surgical (MIS) [Richardson et al.,2000] approach to improve the dexterity and mobility of thesurgical robotic manipulators while maintaining the mini-mum level of surgical trauma. This improvement is done byremoving the need for rigid link transmission to the surgi-

cal manipulator inserted through the incision hole. Currentlytargeted at abdominal surgeries, the technique allows a sur-gical manipulator to be completely inserted into the insuf-flated abdominal cavity and its motion regulated through theuse of magnetic linkages between external stator units andthe internal rotors. The absence of a rigid link transmissionmeans that the manipulator is no longer constrained by the lo-cation of the incision point. The entire surgical manipulatoris therefore completely inserted into the abdominal cavity andis free to move to cover different quadrants of the abdomen.The incision hole therefore now serve only as the entranceand exit point for the internal units. As such, it is envisagedthat this approach will bring about significant improvementto the dexterity and mobility of a surgical robot, reaching dif-ferent quadrants of the abdominal cavity, while maintainingthe minimal level of surgical trauma achieved by the currentstate-of-the-art MIS systems. The summary of the techniqueis depicted in Figure 1.

Review of the magnetic-based surgical manipulators waspresented in [Leong et al., 2016]. The use of magnetic cou-pling to address the need to remove rigid mechanical link inlaparoscopic devices was experimented in the form of themagnetic anchoring and guidance (MAGS) surgical devices[Cadeddu et al., 2009], [Park et al., 2007] which can becompletely deployed intra-abdominally via a single incisionpoint. These internal devices statically held surgical instru-ments such as tissue retractor and camera onto the inside wallof the abdominal cavity with the help of permanent magnetanchors. These systems are generally not actuated. A surgicalmanipulator actuated by on board DC micromotors [Tortoraet al., 2013] was anchored with the MAGS and was demon-strated to provide a maximum pulling force of 1.53N witha resulting dimension that could be inserted through a 5mmincision. While improved dexterity was demonstrated, the re-sulting torque was insufficient for surgical procedures work-ing with high payload (e.g. a liver tissue retraction task istypically rated at 5N load) [Leong et al., 2016] and the spaceconstraint of the abdominal cavity means that there is littleroom for future improvements.

To allow a more powerful (thus larger) system, actuation

Figure 1: Schematic representation of the simplified LEMA system involving a single coil-single rotor model where torque atpermanent magnet rotor, i is transmitted to the robotic manipulator through an appropriately designed mechanism, e.g. cable.

external to the abdominal cavity was studied, thus alleviatingthe space constraint. This was attempted by externally gener-ating the actuation magnetic field using a magnetic resonanceimaging (MRI) machine [Vartholomeos et al., 2013] to driveneedle insertion for neurosurgery, using multiple electromag-netic coils to regulate for the pose of a micro robot for eyesurgery [Kummer et al., 2010], or by the use of a externalmagnet placed around the patient to navigate magnetically-driven internal surgical devices (e.g. wireless capsule endo-scopes) [Munoz et al., 2015], [Carpi et al., 2009]. Thesemethods however, are geared towards manipulating lowernumber of independent degrees-of-freedom (DOFs) in themechanisms, as it produces a uniform field across the entireworkspace.

Instead of a uniform field across the workspace, LocalMagnetic Actuation (LMA) [Di Natali et al., 2015] ap-proaches exploit localised magnetic coupling between anexternal source of actuation and an internal rotor across theabdominal wall. The localised nature allows for multipleof such stator-rotor pairs to be deployed, thus allowing(ideally) multiple independent degrees-of-freedom (DOFs)of actuation within the workspace, which is crucial in theapplication of robotic surgery. The multiple DOF LMAimplemented using permanent magnet stator and rotor wasshown to effectively actuate a 2DOF continuum arm roboticcamera system [Hang et al., 2015] and a 3DOF surgicalmanipulator [Mohammadi et al., 2015]. Electromagneticcoils were investigated for the LMA approach for a moredirect method of regulating the resulting magnetic field. Todifferentiate this approach from the permanent magnet basedLMA, the term localised electromagnetic system (LEMA) isused in this paper. A LEMA system with two stator coils waspresented in [Mohammadi et al., 2015][Mohammadi et al.,2015] which demonstrated empirically the robustness of thesystem with some uncertainties, e.g. coupling misalignmentof the internal unit deployment and the variation in abdom-inal wall thickness. The model presented only involvedthe dynamics of the internal rotor unit in the generalised

coordinate (in the axis of rotation of the rotor). Practicaluncertainties, resulting from simplifying assumptions such asone that assumes all other degrees of freedom are perfectlyrigid, or the disturbances caused by the magnetic fields fromthe neighbouring stator-rotor pairs, were not considered andhandled by feedback controller.

The LEMA system setup in the abdominal surgery envi-ronment is illustrated in Figure 1, where multiple stator - ro-tor units (electromagnetic stator coil and permanent magnetrotor) of LEMA configuration are utilised to drive a surgi-cal robotic manipulator with corresponding number of DOFs.A single incision is used as the entrance and exit point ofthe internal units to the abdominal cavity. Each DOF on therobotic manipulator is actuated by a LEMA rotor, throughsome transmission mechanism, e.g. cable. The external por-tion of the LEMA system, consisting of the electromagneticstator coils and the external permanent magnet anchor, can beattached rigidly to a platform, hence providing stable opera-tion.

In this paper, the model for the dynamics of the LEMA sys-tem is derived and presented. More specifically, the modelsfor (1) a magnetic field generated by an electromagnetic coilat an arbitrary location representing the centre of the internalrotor unit and (2) the 6 DOF force and moment (wrench) gen-erated by the magnetic flux linkage between the resultant fieldat the location of the rotor and that of the permanent magnetinternal rotor, as presented in Section 2. This provides a gen-eral case model that would account for any magnetic fieldacting on the rotor, generated by an external set of coil(s) forthe intended actuation, as well as any other fields generatedby other magnetic sources, such as the anchoring magnets,other rotors and stators. Note that the model takes into ac-count not only the generated rotor torque about its axis of ro-tation, but also the other 5 degrees of freedom of interactionwrench which were ideally assumed to be rigid. In practice,however, these components will comprise non-rigid systems,such as the viscoelastic nature of the abdominal wall that the

system is magnetically anchored onto. The model also allowsother non-systematic uncertainties, such as the error in the es-timation of abdominal wall thickness and the misalignment inthe placement of the rotor relative to the external stator unit,to be taken into account. Section 3 describes the experimen-tal set up while Section 4 describes the system identificationprocess. Section 5 presents the result of the numerical andexperimental validation exercise. T Additionally, the paperutilises Principle of Superposition to allow obtaining the re-sultant net magnetic field and torque acting on the internalrotor unit by multiple sources of magnetic field.

2 System ModellingIn this section, the model for a single coil-single rotor systemis defined. The relationship of the electromagnetic coil ac-tuation (input: current to the coil) to the generated magneticfield at an arbitrary location (representing the location of theinternal rotor unit) is derived in Section 2.2. The relationshipof the resultant magnetic field at the given location to the gen-erated wrench acting on the internal rotor unit (as the result ofthe magnetic flux linkage with the permanent magnet of therotor) is presented in Section 2.3. The case of having multi-ple sources of magnetic field on a single permanent magnetrotor is briefly summarised in this section using the Principleof Superposition.

2.1 Model DefinitionThe single coil-single rotor model in consideration for thisstudy is as illustrated in Figure 1. This represents the mostgeneral case model of the proposed LEMA concept, repre-senting a stator-rotor pair, where the stator is the externalelectomagnetic coil representing a source of magnetic fieldactuated by our system input while the rotor is a permanentmagnet internal rotor unit. The final system may be con-structed out of two electromagnetic coils as the stator, how-ever the principle of superposition could simply be applied, aswill be shown in this paper. The overall system will thereforehave n stator-rotor sets (i = 1,2,...,n). The internal device (de-ployed through the surgical port into the abdominal cavity) isanchored to the abdominal wall by the coupling of the inter-nal and external anchoring magnets, i.e. Aii and Aei, respec-tively. The stator coils, Si are actuated by the input current, Iiwhich produce magnetic field (Bi) across the abdominal wallwhich generate wrench acting on the corresponding perma-nent magnet internal rotor unit (rotor i). The stator coils, Siand the external anchoring magnets, Aei are assumed to berigidly fixed to an external platform such that its weight is notresting upon the abdominal wall. The model with the nota-tions are summarised in Figure 2.

2.2 Magnetic Field ModelThe magnetic field produced by an electromagnetic coil Simeasured an arbitrary point P(x,y,z) is modelled based on

Figure 2: ith coupling set of the simplified system where jcaters for multiple stator coils

the Biot-Savart Law [Furlani et al., 2001] (Figure 3) and ispresented as:

Bq =µ0µrINRc

4π

l/2∫z′=l/2

2π∫ϕ ′=0

Cq

Ddϕ′dz′ (1)

where q = x,y, and z, respectively, µ0 and µr are the perme-ability of free space (4π × 107H/m) and the relative perme-ability of the core material, respectively, Rc is the radius ofthe coil, N is the number of turns in the coil and

Cq =

(z-z′)cosϕ ′ i, q = x(z-z′)sinϕ ′ j, q = y(R− xcosϕ ′− ysinϕ ′)k, q = z

D = (x2 + y2 +(z-z′)2 +R2c−2Rc(xcosϕ ′+ ysinϕ ′))3/2 (2)

The resultant magnetic field, B ∈ ℜ3 on an arbitrary pointP is given by:

B = Bx i+By j+Bzk. (3)

This magnetic field model is applicable to the case of mul-tiple electromagnetically generated fields, e.g. the case ofhaving multiple stator coils for one rotor and the disturbanceproduced by the other stator/rotor sets in the vicinity, throughPrinciple of Superposition. The resultant magnetic field isobtained as the vector sum of the magnetic fields contributedby the multiple magnetic sources at point P [Furlani et al.,2001]. The resultant magnetic field, B is then obtained fromEquation 3 as discussed and will be utilized in the electrome-chanical model in the following subsection to determine thedynamics of the system.

2.3 Modelling of Flux Linkage Generated WrenchThe resultant magnetic field, B at Point P is essential forthe analysis of the system dynamics. Following the Newton-Euler approach, the free body diagram of the permanent mag-net internal rotor unit, given in Figure 4 shows the forces and

Figure 3: An arbitrary point, P(x,y,z) around an electromag-netic coil

Figure 4: Free body diagram of the ith rotor in consideration

moments acting on it in all directions in 3D space. Withoutthe loss of generality, the analysis is performed on rotor i, asdepicted in Figure 2.

The Case of Single Stator CoilNote that the intended motion in the system is the rotation ofthe permanent magnet rotor i.. The other 5 DOFs of the per-manent magnet rotor i are ideally rigidly constrained. How-ever, in practice, this may not be the case, and the modellingeffort in this paper takes into account the forces and mo-ments acting in these directions, through the Newton-Eulerapproach of rigid body modelling. Example of forces in thedirection of constraints are those exerted by the viscoelasticnature of the insufflated abdominal wall and by the anchoringmagnets. While these components are not explored in depthin this paper, the modelling effort allows them to be accom-modated in future studies.

As the stator coil and the external permanent magnet an-chor are attached to an external platform, the force of the an-choring magnet, Fanci is required to be sufficiently large toovercome the weight of the internal rotor unit which is hold-ing the internal permanent magnet anchor and rotor i at all

times. The lateral effect of the internal permanent magnet an-chor onto the rotor is assumed negligible with the presence ofthe shielding material in between the anchor and rotor withinthe internal device housing.

With the body attached coordinate frame as defined in Fig-ure 4, the forces acting on the rotor i can be summarised as:

∑F = FSi +Fanci +Fabd +FL−wig. (4)

where wi is the mass of the assembly of internal device, riis the radius of the corresponding rotor, Fanci ∈ ℜ3 is theforce exerted by the anchoring permanent magnets, whichis assumed to have only component in the zi direction, andFLi ∈ ℜ3 is the load. Fabd ∈ ℜ3 is the force acting on thepermanent magnet rotor i due to the abdominal wall, whichcould be modelled as a spring and damper system:

Fabd =

00

kabdz+babd z

(5)

and FSi ∈ ℜ3 is the force generated by the stator magneticfield and is given by:

FSi = (mi •∇)Bi (6)

where mi ∈ ℜ3 is the magnetic moment of the permanentmagnet rotor i, which is related to the magnetization Mi ∈ℜ3

and the length of the rotor, hi, given by:

mi = πr2i hiMi (7)

It should be noted that FSi is the attraction / repulsion forceson the rotor, in the direction of constraint, caused by the sta-tor. If the internal rotor unit is perfectly aligned to the centreof the magnetic field generated by the stator, then it wouldonly have non-zero components in the zi direction. It doesnot contribute to the desired actuation, which is the torqueabout the rotor axis.

Similarly, the torque on permanent magnet rotor i is givenas follows:

∑τi = Jiθi +biθi = τSi − τLi (8)

where Ji ∈ℜ3×3 and bi ∈ℜ3×3 are the total moment of inertiaand the viscous friction coefficient of the permanent magnetrotor respectively, and θi ∈ ℜ3 is the rotation position of therotor about each axis. The torque on the permanent magnetrotor by the electromagnet, τSi ∈ℜ3 and the load torque, τLi ∈ℜ3 are expressed as:

τSi = mi×Bi =

−Bymi cosθ

−Bzmi sinθ −Bxmi cosθ

−Bymi sinθ

τLi = ri×FLi

(9)

Figure 5: (a) Maximum τSi obtained at Mi at 90 degrees anglefrom the direction of Bi, and b) zero torque when Mi is alignedwith Bi

Figure 6: The net torque, τi resulted from the superpositionof the magnetic fields generated by stator coils, Si j ( j = 1,2)

When the angular displacements (misalignment) about x andz axes are zero (i.e. when the permanent magnet rotor is rigidand well aligned with the stator), Equations 8 and 9 simplifyto:

∑τi = Jiθi +biθi = τSi − riFLi

where τSi = mi×Bi = πr2i hiMiBi sin2(θi)

(10)

In order to analyse the maximum static torque produced bya coil Si on the generated torque on rotor i, the direction of themagnetization of the rotor, Mi has to be at 90 degrees to thedirection of the stator magnetic field at the point of evaluationBi (as illustrated in Figure 5). When the Mi is parallel to Bi,zero torque is produced on rotor i, the rotor will not rotate. Inthese scenarios, the generated force on the rotor will be purelyattractive or repulsive. This is an important consideration forthe design of the system, which is reflected in the simulationsand experiments discussed in the following sections.

The Case of Multiple Stator CoilsIn the presence of Ns (multiple) stator coils, the torque gen-erated on rotor i (τSi ) can be summed up by the Principle ofSuperposition as:

Figure 7: The Hall Effect sensor (circled in red) used to mea-sure the magnetic field contributed by the electromagneticcoil, at the rotor position

Figure 8: An additional coil is added to the setup to verify theassumption of the resultant magnetic fields at a given point inspace generated by multiple sources follow the principle ofsuperposition

∑τSi =Ns

∑j=1

(mi×Bij) (11)

where j = 1,2, ...,Ns is the number of magnetic sources con-tributing to the torque onto rotor i. The case of having twostator coils (ie. Ns = 2) is shown in Figure 6.

3 Experimental SetupTo validate the mathematical models described in Section 2,an experimental setup is constructed to facilitate two sets ofexperimental measurements, as described in the subsectionsbelow.

3.1 Setup for Magnetic Field Model ValidationThe first setup comprises an electromagnetic coil as the statorand a Hall effect sensor (UGN3503UA) as shown in Figure 7.In this setup, we are able to measure the resultant B in termsof Gauss, G (i.e. 1G= 1×10−4T) as contributed by the elec-tromagnet coil at the given rotor location. The magnetic field,B is measured at various inter-magnetic distances below thestator coil (i.e. 20mm, 30mm, 40mm and 50mm), generated

by input constant input current ranging from −5A to +5A,to validate that the mathematical model provides an accuratemagnetic field result with different current conditions. Thedifferent inter-magnetic distances simulates the variations inthe abdominal wall thickness separating the stator and the ro-tor, starting at 20mm away representing a slim patient, withaverage patient measuring 30-40mm in abdominal wall thick-ness. The magnetic field B at the rotor position in the hori-zontal, x-direction (i.e. from the centre of the coil, 0mm upto 80mm away from the coil) is also measured to observe theeffect of the magnetic field generated by the stator onto therotor at lateral offset positions.

Magnetic field superposition is tested by placing two statorcoils side by side and turning on one coil at a time (see Figure8) and both coils simultaneously. The x and z components(with zero lateral offset in y axis) of the magnetic field aremeasured using the Hall Effect sensor. These values obtainedwill be compared with the values simulated for validation inSection 5.

3.2 Setup for Magnetic flux Generated TorqueValidation

The second setup comprises the same electromagnetic statorand a permanent magnet rotor (in place of the Hall Effectsensor in the first setup). This setup is intended to validatethe relationship between the input current to the stator coil(s)and the output torque about the rotor. To measure the torquetransmitted by the electromagnetic coil onto the permanentmagnet rotor (τSi ), the rotor is attached to a torque sensor(ATI F/T Gamma), as shown in Figure 9. The rotor is fixed inits orientation with its magnetization (i.e. direction of southto north) at 90deg from the centre axis of the electromagnetto produce the maximum static torque, as illustrated in Fig-ure 5a. The electromagnet stator is supplied with a constantDC current ranging from −5A to +5A. The torque sensorthen measures the static torque acting on the rotor at differ-ent distance settings in the x and z directions, as explained inSection 3.1. The static torque measurements along the hor-izontal x direction allows the observation of the torque ontothe rotor at an offset position away from the centre of the sta-tor and the measurements along the z-axis simulate the statictorque experienced by the rotor at different abdominal wallthickness.

A two-stator coil scenario is also set up to validate the ac-curacy of the principle of superposition on the torque ontothe rotor. The coils are alternately turned on for individualτSi measurements and then both coils are turned on simulta-neously to obtain the resultant τSi value.

4 Parameter IdentificationSeveral parameters of the physical setup need to be identifiedfor the purpose of the numerical simulation and its compari-son to the experimental results. These parameters are the rel-ative permeability of the electromagnet core, µri in the mag-

Figure 9: A force-torque sensor is used to measure the torquegenerated by the coil onto the permanent magnet rotor

netic model (Equation 1) and the value of the magnetizationof the permanent magnet rotor, Mi, in the electromechanicalmodel (Equation 10).

To determine the relative permeability of the electromagnetcore µri , the magnetic field generated by the coil is measuredwith and without the iron core. The difference between thetwo readings is the compensated value for the particular µri .Even though the ferromagnetic core displays non-linear hys-teresis in the B-H curve, the system is assumed to operatewithin the linear operating region. Note that B and H referto the flux density and field strength, respectively. As thestator core is customized independently to fit into each coil,the permeability of each core is expected to be slightly differ-ent and this identification method can be repeated for otherelectromagnetic coils to obtain the specific µri . In this case,the relative permeability of the stator coil is identified to be,µri = 3.58.

Following the measurement of µri , the flux density Bi isobtained from Equation 3. The generated rotor torque τSi dueto Bi can be measured using a force torque sensor (elaboratedin Section 3) for a given rotor angular displacement θ fromEquations 10 and 11 (for the case with multiple stators). Themagnetization, Mi is dependent on factors such as the size andthe shape of the permanent magnet and this is usually simu-lated numerically using finite element methods. Nonetheless,for the purpose of the parameter identification, Mi can nowbe obtained from Equation 10, as all other variables are mea-sured or known. The static torque measurements obtained inSection 3 yielded an average value of Mi = 8.5×104 A/m inthis experiment setup.

5 Model ValidationsThe magnetic field model and the magnetic flux linkage gen-erated torque models discussed in Section 2 are implementedin numerical simulations, with the parameters identified froman experimental setup. The results are then validated againstan independent set of experimental measurements to evaluate

Figure 10: Comparison between simulated and experimentalresults of B from electromagnetic stator measured at 20mmto 50mm along z-axis simulating the varying abdominal wallthickness(separation distance between stator coil and rotor).The horizontal axis represents the input current to the statorcoil.

the accuracy of the model. The simulations and experimentsare carried out on a single (stator) coil and a single rotor con-figuration for the simplicity of the validation without loss ofgenerality.

The validation process involves simulations and experi-mental measurements of magnetic field, B with a variationalong the z-axis (simulating the different abdominal wallthicknesses that contribute to the inter-magnetic distance be-tween the stator and rotor) as well as the variations alongthe horizontal x-axis (simulating the lateral offset of the rotorfrom the centre of the coil upon intra-abdominal deployment)versus current.

The second part of the process utilises the B values ob-tained from the earlier magnetic model validation to numer-ically compute the static torque in the simulation for valida-tion against the static torque measured experimentally. Theexperiment was also performed with the rotor placed 20mmto 50mm below the stator in the z-axis to visualise the inter-magnetic distance due to the abdominal wall thickness versusthe variations along the x-axis to observe the stator torqueonto the rotor when it is misaligned from the centre of thestator coil.

5.1 SimulationsSimulations of the models described in Section 2 are per-formed for the case of single coil-single rotor system to ob-serve the computed numerical responses of the system inMatLab and its comparison to the experimentally measuredresponse described in Section 3. The parameters µr = 3.58and M = 8.5× 104 identified in Section 4 are employed intothe magnetic and electromechanical models to simulate themagnetic field, B as well as the torque, τ onto the rotor at any

Figure 11: Comparison between simulated and experimentalresults of B, measured at abdominal wall thicknes (distance inz axis between stator and rotor) of 20mm to 50mm. The hor-izontal axis represents the lateral misalignment of the rotorfrom the centre of the stator coil at 10mm intervals.

point in the workspace generated by a single coil.The results of the magnetic field with z-axis inter-magnetic

distance and x-offset variations are plotted along with the ex-periment data obtained from the experimental procedures (re-fer tp Section 3) in Figures 10 and 11, respectively.

5.2 Magnetic Field Model ValidationThe magnetic field readings B, measured using the HallEffect sensor as described in Section 3.1 are presented alongwith the Matlab simulated values in Figures 10 and 11with respect to current (A) to validate the accuracy of thenumerical model with respect to the actual measurements.The comparison shows a close fit between the theoreticalmodel and the actual experimental measurements, taken atdifferent locations of the rotor, simulating different inter-magnetic distances due to various abdominal wall thickness(Figure 10) and at different values of lateral offset (Figure11), simulating possible misalignment in the practical setup.Towards further x-offset (i.e. 60mm onwards away fromthe centre of the coil), the magnetic field is ideally zero insimulation. It is not ideal in the actual experiment as theHall Effect sensor is prone to measurement noises in theenvironment. Nonetheless, these measurement discrepanciesare considered negligible in term of its unit in Gauss. Themodel accuracy will greatly aid in the electromechanicalanalysis of the torque produced onto the rotor in Section 5.3.

5.3 Magnetic Flux Generated Torque modelValidation

The results obtained from the numerical computation of theresultant rotor torque, obtained from the magnetic flux gen-erated torque model in Section 2.3 are validated against the

torque values measured experimentally using the torque sen-sor. These simulation and experiment are also performedwith the variations in the z and x directions, simulating thestator-rotor inter-magnetic separation due to different abdom-inal wall thickness and stator-coil misalignment, respectively.This allows the observation of the rotor behaviour with thegiven torque at any possible intra-abdominal deployment po-sitions. Figure 12 shows the comparison between the simu-lated and measured torque. The results show good fit withsome noise observed. The torque onto the rotor decreases ex-ponentially along the x-direction. This information is impor-tant for the design specification so accurate intra-abdominalplacement of the rotor can be taken into consideration. Nev-ertheless, with position guidance and anchoring of the inter-nal device with permanent magnet anchors, the possibilityof the rotor being misaligned with the centre of the coil be-yond 20mm offset can be reduced, thus minimizing the lossof torque onto the rotor.

5.4 Magnetic Field and Torque SuperpositionFor the case of having two stator coils, the simulation and ex-perimental measurements are executed according to the pro-cedures described in Section 3. The magnetic field values arepresented and compared in Table 1. It is shown that the prin-ciple of superposition are accurate in accounting for the useof two stator coils in the resultant magnetic field.

Similarly, the principle of superposition of the generatedrotor torque by the two stator coils is tested. The superposi-tion B values obtained in the manner described above are alsoused to validate the computationally produced static superpo-sition torque, τSi onto the rotor with the values measured bythe ATI torque sensor. The plots for both the simulations andexperimental results are presented in Figure 13. The torquemeasured when only stator coil 1 is on is labelled as tau1, rep-

Figure 12: Comparison between simulated and experimentalresults of τ1 generated by the stator onto the rotor measured at20mm to 50mm vertical inter-magnetic distances and 0mm to80mm lateral distances from the centre of the coil (x-offset).

Table 1: Validation of magnetic field superposition

Stator, Si Bx component (G) Bz component (G)Status Exp Sim Exp Sim

S1 on, S2 off 78.95 77 -146.62 -148S1 off, S2 on 75.19 77 146.62 148S1 on, S2 on 154.14 153 -15.04 0

Figure 13: Comparison between simulated and experimentalresults of superpositioned τ2 from both stator 1 and stator 2

resented with the blue lines, while the torque measured whenonly coil 2 was turned on is labelled as tau2, represented withthe green lines. The resultant torque contributed by both thecoils, is represented by the red lines (Figure 13). The resultconforms to the summation of the torque from the individualcoils.

6 Conclusion and Future WorkThe model of system dynamics in the form of magnetic fieldmodel and and the model of the magnetic flux generatedwrench for the LEMA system is presented. This is a funda-mental and essential step to the design and performance anal-yses as well as the implementation of the system as it enablesthe contributions of various sources of magnetic fields as wellas the dynamics of the physical and environmental uncertain-ties in the vicinity of the rotor to be taken into consideration.The validation of the models provides a strong platform forfuture work which includes the establishment of the designspecifications for the LEMA system as well as the develop-ment of controllers to reject external disturbances onto thecorresponding rotor and to achieve desired speed or torqueaccurately for surgical manipulations.

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