Magnetic link design for a robotic laparoscopic camera
Massimiliano Simi, Gastone Ciuti, Selene Tognarelli, Pietro Valdastri,a
 Arianna Menciassi,
and Paolo Dario
CRIM Lab, Scuola Superiore Sant’Anna, Pisa 56127, Italy

Presented 19 January 2010; received 31 October 2009; accepted 24 November 2009;
published online 19 April 2010
The use of magnetic fields to control and steer assistive and operative devices is increasing in
minimally invasive surgical applications. The design of the magnetic link between an external
permanent magnet, maneuvered by an industrial robot, and a robotic laparoscopic camera was
investigated in this paper, with the objective to obtain accurate positioning and steering in
visualization. © 2010 American Institute of Physics. doi:10.1063/1.3352581
I. INTRODUCTION
Laparoscopic surgery, also called minimally invasive
surgery, is a modern surgical technique in which operations
in the abdomen are performed through small incisions 
usu-
ally 0.5–1.5 cm as compared with larger incisions needed in
traditional surgical procedures. The widespread adoption of
such technique opened a new era in surgical treatments. Re-
cently, there has been an impetus to further reduce the inva-
siveness of laparoscopic surgery by introducing magnetically
guided devices that fit entirely inside the abdomen; thus pre-
venting the need of a dedicated access through the skin.
From the technical standpoint, the most advanced sys-
tems exploiting magnetic fixation and positioning for laparo-
scopic procedures are three imaging robots reported in Refs.
1–3. However, in these solutions the magnetic element on-
board the device is not intended to move during operation.
Therefore, device position and orientation are normally con-
trolled by manually maneuvering an external permanent
magnet 
EPM. This results in a poor accuracy and difficult
controllability of the internal device due to the exponential
variability of magnetic fields with distance. To overcome this
limit, the EPM can be fixed as the end effector of six degrees
of freedom industrial robot 
RV-3SB robot, Mitsubishi Elec-
tric, Japan and controlled by an intuitive user interface, as
proposed in Ref. 4. To further enhance precision in steering
and orientation of the surgical camera, a magnetic internal
mechanism 
MIM was introduced in Ref. 5.
An improved version of this device, presented in this
paper, consists of a cylinder 12.7 mm in diameter and 32 mm
in length. It incorporates one brushless motor, two internal
permanent magnets 
IPMs and a vision module with illumi-
nation. A wired connection to an external unit guarantees
signal transmission and powering, providing also an effective
retrieval from the abdomen especially in case of failure. The
internal mechanism consists of a motor connected to the IPM
by a set of gears. When the device is immersed in an external
magnetic field generated by the EPM, the IPM tends to main-
tain a precise alignment. Under a set of conditions, detailed
below, when the motor is activated, the entire capsule rotates
with it, while the IPM remains oriented according to the
external field. Thanks to this principle of operation, the MIM
enables a fine orientation of the device relatively to the sur-
rounding tissue, without moving the EPM. The complete
platform, including the robotic arm to support the EPM, is
represented in Fig. 1
a.
In the present work we model and design the EPM-IPM
magnetic link in order to achieve an effective magnetic in-
teraction between the robotic maneuvered EPM and the ac-
tive surgical camera. This may serve as methodological ex-
ample whenever a transabdominal magnetic link is required
in the design of novel surgical instrumentation.
II. MATERIALS AND METHODS
Based on the schematic representation reported in Fig.
1
b, the following relations must be satisfied for proper op-
eration:
Fm 
 Fw, 
1
Tm 
 
Tmim + Tfr , 
2
Tmot 
 
Tmim + Tfr , 
3
where Fm and Fw are the EPM-IPM magnetic attraction force
and the device weight force, respectively. Tm is the magnetic
torque exerted by the EPM on the IPM, Tmim is the maxi-
mum torque exerted by the weight of the device on the IPM
pivot, and T fr is the adverse torque between the device and
the tissue during the camera steering. Finally, Tmot is the total
aElectronic mail: pietro@sssup.it.
FIG. 1. 
Color online 
a The overall platform. 
b Schematic representa-
tion of the system.
JOURNAL OF APPLIED PHYSICS 107, 09B302 
2010
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torque that the brushless motor transmits to the IPM by
means of the internal mechanism.
Considering an abdominal wall thickness ranging from
19 to 47 mm 
Ref. 6 and a constant safety air gap of 5 mm
between the EPM and the patient skin, an IPM-EPM total
distance within 24 and 52 mm was considered. According to
the analytical background described in Refs. 7 and 8, IPM
and EPM must be selected in terms of size, shape, magnetic
remanence, and magnetization direction in order to fulfill the
above reported relations.
A. Magnetic and mechanical design of the robotic
device
As a first step, the IPM features were defined to maxi-
mize Fm and Tm, while minimizing the device diameter 
13
mm is the internal diameter of a typical trocar for laparos-
copy. Two diametrically magnetized commercially available
NdFeB N42 permanent magnets 
KJ Magnetics, Jamison,
U.S., having a disk shape 6.35 mm in diameter and 3.17 mm
in thickness, were selected. For a further maximization of the
interaction force with the EPM, two custom made magnets
with the same dimension, but higher remanence 
i.e., N52,
may be used.
In order to maximize the torque transmitted by the entire
mechanical system to the IPM 
Tmot, a brushless motor

SBL04-0829 Namiki precision Jewel Co. Ltd., Tokyo, Ja-
pan was selected as best tradeoff between high stall torque

Cmot 
5.7 mNm and small size 
4 mm in diameter and 17.5
mm in length. A mechanism with a low transmission ratio

 of 0.056 and composed by a helical gear and a worm gear
connects the IPM to the motor. Based on Ref. 9, the mecha-
nism efficiency 
mec due to internal friction was calculated
as 0.415. In order to introduce a safety margin for the mecha-
nism design, the half of the stall torque was adopted as the
operative value. Finally, considering the magnetic interfer-
ence with the electromagnetic actuator, motor efficiency

mot was defined to account for the performance reduction.
The total torque transmitted to the internal magnets by the
motor is described by the equation
Tmot =
0.5 · Cmot · mot · mec

. 
4
Once the internal magnets and all the other mechanical
parts of the camera device were selected and assembled, Fw
and Tmim were evaluated. The camera device is 7.7 g in
weight; therefore a minimal magnetic attraction force larger
than 75.5 mN 
Fw is required to lift the capsule. By knowing
mass and arrangement of all device components, its center of
mass 
8.5 mm from the IPM pivot was derived and Tmim
was analytically calculated as 0.64 mNm.
Finally, assuming a constant friction coefficient 
 be-
tween the tissue and the camera device equal to 0.1 
Ref. 10
and a distance 
b see Fig. 1
b between the rotation pivot
and the tissue equal to 6.35 mm, the friction torque for the
system is described by
Tfr = 
Fm − Fw ·  · b 
5
B. Magnetic and dimensional design of the EPM
Once the features of the modules on-board the device
were fixed, the magnetic and dimensional properties of the
EPM must be defined in order to address the requirements in
term of magnetic attraction force and torque. Axial magneti-
zation direction and cylindrical shape were purposely se-
lected to allow the required degrees of motion and to guar-
antee a symmetric field along the central axis of the EPM.
N52 magnetic remanence was chosen to maximize the EPM-
IPM attraction force and torque. The robotic arm payload

maximum weight of 3 Kg in our case and limitations of the
workspace must also be considered during selection of an
adequate EPM.
In order to refine our selection among commercially
available EPM candidates already fulfilling the above re-
quirements, finite elements method 
FEM analysis 
COMSOL
MULTIPHYSICS 3.4—COMSOL, Inc., Sweden was used.
Seven off-the-shelf permanent magnets having a volume
ranging from 6.44 to 51.5 cm3 were considered. Magnetic
attraction forces 
Fm and torques 
Tm were thus evaluated
by FEM analysis between the defined IPM and the different
external magnets. Magnetic flux density around the electro-
magnetic motor was also calculated in order to evaluate the
motor efficiency 
mot. All properties of the EPM, such as
magnetic permeability 
0=1.05 and different dimensions,
were set into the simulation. The selected mesh consisted of
about 500.000 elements with a maximum element size fixed
to 1/100 of the maximum geometric feature in the overall
scenario. The incremental ratio of the mesh elements was
fixed to 1.45, whereas the curvature factor and the mesh
curvature cut-off were chosen equal to 0.5 and 0.02, respec-
tively.
Based on simulation results, magnetic and physical re-
quirements, and off-the-shelf availability, an axially magne-
tized disk shaped NdFeB N52 permanent magnet 
KJ Mag-
netics, Jamison, U.S. 50.8 mm in diameter, 12.7 mm in
thickness, and 200 g in weight, was selected. Among the
magnets that satisfied the design relations 
1–
3, the se-
lected one represents the optimal solution in terms of mag-
netic force and torque.
C. Experimental validation
Once defined the EPM and IPM features, the simulation
results, in terms of magnetic attraction force and torque,
were assessed by several bench tests with a force/toque sen-
sor 
Nano17, ATI, U.S.. The IPM was fixed to the sensor
and the EPM was placed as the end-effector of the robotic
arm to achieve precise translational and rotational move-
ments. The experimental setup is represented in Fig. 2.
III. RESULTS AND DISCUSSION
The Fm values obtained by FEM simulations were 150
and 930 mN at EPM-IPM distances of 52 and 24 mm, re-
spectively. Tm, considering an IPM axial rotation of =2°

minimum step of the mechanism, ranges from 1.7 to 7.1
mNm. As required, the magnetic attraction force overcomes
the weight of the device 
75.5 mN. Once Fm was known, T fr
was analytically calculated as 0.05 and 0.54 mNm at EPM-
09B302-2 Simi et al. J. Appl. Phys. 107, 09B302 2010

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IPM distances of 52 and 24 mm, respectively. By consider-
ing mot equal to 0.9 at 5.2 mm and equal to 0.35 at 24 mm,
Tmot varies between 19 and 7.39 mNm. Fm, Tm, and all the
parameters described above confirmed Eqs. 
1–
3; thus al-
lowing a reliable and accurate dragging and steering of the
camera device. It is worth mentioning that the levels of force
obtained would not cause any injury to human tissues which
are in contact with the IPM 
Ref. 11.
By using the experimental setup described in Sec. II, the
results obtained by FEM analysis were confirmed in terms of
magnetic attraction force and torque at the EPM-IPM target
distances. In particular, a force of 883 and 143 mN and a
torque of 6.73 and 1.52 mNm were obtained at EPM-IPM
distances of 24 and 52 mm, respectively. The difference be-
tween FEM and experimental values 
maximum percentage
difference 12% was mainly derived from the interference of
the external magnetic field with the metal parts of the robotic
arm.
In conclusion, the present work outlined the required
steps to properly design a transabdominal EPM-IPM mag-
netic link for surgical robotic devices. This study may serve
as guideline for the development of novel intracavitary ro-
botic tools driven by magnetic fields, thus highlighting how
to apply basic theoretical models to surgical applications.
ACKNOWLEDGMENTS
This material is based in part upon work supported by
the European Commission in the framework of VECTOR

Contract No. EU/IST-2006-033970 and ARAKNES 
Con-
tract No. EU/IST-2008-224565 European Projects and in
part by the Intelligent Microsystem Center, Korean Institute
of Science and Technology 
KIST, Korea.
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FIG. 2. 
Color online Experimental test bench for measurement of mag-
netic force 
a and torque 
b. Inset: FEM simulation screenshot.
09B302-3 Simi et al. J. Appl. Phys. 107, 09B302 2010

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