A multi-axis MEMS force-torque sensor for measuring the load on a microrobot actuated by magnetic fields.
ABSTRACT This paper presents the design of a multi-axis micro force-torque sensor. The sensor is able to measure forces along two axes and a torque perpendicular to these forces. The load is measured by capacitive comb drives which provide a high sensitivity. The microfabrication process, the sensor readout electronics as well as the calibration procedure are presented. The sensor was used to measure the force and torque on a magnetically actuated microrobot. This microrobot is assembled from microfabricated nickel parts for directed drug delivery inside the human body. Precise knowledge load on the microrobot is required for accurate positioning and control of the robot. The three-axis micro sensor is used to simultaneously measure the forces and torques acting on the microrobot in a magnetic field and thus provides valuable data for magnetic control methods of microrobots.
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ABSTRACT: Motivated by the need for torque sensing in the Nm range for experiments with insect-sized flapping-wing robots, we present the design, fabrication and testing of a custom single-axis torque sensor. The micorobots in question are too large for MEMS force/torque sensors used for smaller live insects such as fruit flies, but too small to produce torques within the dynamic range of commercially available force/torque sensors. Our sensor consists of laser-machined In- var sheets that are assembled into a three dimensional beam. A capacitive displacement sensor is used to measure displacement of a target plate when the beam rotates, and the output voltage is correlated to applied torque. Sensor bandwidth, range, and resolution are designed to match the criteria of the robotic fly experiments while remaining insensitive to off-axis loads. We present a final sensor design with a range of 130 Nm, a resolution of 4.5nNm, and bandwidth of 1kHz.2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2011, San Francisco, CA, USA, September 25-30, 2011; 01/2011
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ABSTRACT: At the microscale, surface forces influence the behaviour of micro-objects more than volumic forces. During micro-assembly processes, contacts occur between a microgripper and a micro-object or between a substrate and a micro-object. The pull-off force, which represents the force required to break a contact, is one of the predominant problems in micro-assembly. Current force measurements are mostly focused on sphere-plane geometries, and models are based on nanoscale theories. The aim of this letter is to propose an evaluation of the pull-off force for a planar contact, which is the most frequent kind of contact in micro-assembly. Experimental force measurements based on a capacitive microforce sensor and micro/nano robotic systems are carried out. The proposed device enables the study of pull-off forces according to the preload force and the contact angle. Finally, experimental results are discussed and compared with a model.Micro & Nano Letters 10/2009; · 0.85 Impact Factor
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ABSTRACT: En microrobotique, la mesure de micro et nano force figure parmi les informations nécessaires pour caractériser les interactions mécaniques présentes à l'échelle micrométrique. Dans cette optique, nous avons développé un capteur de mesure micro et nano force reposant sur un principe de flottaison-magnétique. L'organe sensible du capteur est une plate-forme macroscopique rectangulaire sur laquelle s'appliquent les forces et couples à mesurer. La sustentation et le maintien de la plate-forme sont assurés par le biais de forces magnétiques et de la poussée d'Archimède appliquée à quatre flotteurs placés à ses coins. La plate-forme est conçue pour mesurer uniquement des forces dan le plan horizontal ainsi que le couple vertical associé. L'étendue de mesure des forces varie entre -100 et +100 micronN avec une résolution de l'ordre du nanoNewton. elle travaille en mode actif grâce à un asservissement autour de sa configuration d'équilibre (établie en absence d'efforts à mesurer). La nature des efforts de rappel utilisés pour la mise en oeuvre de l'asservissement est électromagnétique. Les modèles magnétique et électromagnétique développés permettent alors de déterminer les forces qui s'appliquent au centre de gravité de la plate-forme par le biais de la connaissance de la configuration spatiale de cette dernière et des courants dans les bobines de commande. En termes d'application, cette plate-forme peut être utilisée dans le cadre de la caractérisation des micro-objets déformables (micromécanismes, cellules, etc...) et des microsurfaces.01/2009;
A Multi-Axis MEMS Force-Torque Sensor for
Measuring the Load on a Microrobot Actuated by
F. Beyeler, S. Muntwyler, Z. Nagy, M. Moser, B. J. Nelson
Institute of Robotics and Intelligent Systems
ETH Zurich (Swiss Federal Institute of Technology Zurich)
CH-8092 Zurich, Switzerland
micro force-torque sensor. The sensor is able to measure forces
along two axes and a torque perpendicular to these forces. The
load is measured by capacitive comb drives which provide a
high sensitivity. The microfabrication process, the sensor
readout electronics as well as the calibration procedure are
presented. The sensor was used to measure the force and
torque on a magnetically actuated microrobot. This microrobot
is assembled from microfabricated nickel parts for directed
drug delivery inside the human body. Precise knowledge load
on the microrobot is required for accurate positioning and
control of the robot. The three-axis micro sensor is used to
simultaneously measure the forces and torques acting on the
microrobot in a magnetic field and thus provides valuable data
for magnetic control methods of microrobots.
Index Terms – MEMS, Capacitive Force-Torque Sensor,
Microrobot, Magnetic Actuation
Abstract - This paper presents the design of a multi-axis
(microelectromechanical system) devices incorporating
sensors, actuators and electronic circuits has rapidly
progressed. The popularity of minimally invasive medical
diagnosis and treatment has also risen remarkably.
Furthermore, there is increasing interest in untethered
microrobots that are capable of performing drug delivery to
parts of the human body that are difficult if not impossible to
access with other methods.
A key challenge with untethered microrobots is power.
A promising power option is the use of externally applied
magnetic fields to enable the wireless transfer energy to the
microrobot. By the use of ferromagnetic material as a
building block for the microrobot, forces and torques can be
applied to it and thus be used for propulsion inside the body.
Yesin et al  demonstrated that an assembled microrobot
can be wirelessly controlled in a liquid environment. A
magnetic model necessary for control of axially symmetrical
magnetic bodies has recently been developed . Precise
knowledge of the forces and torques acting on the
microrobot is required for accurate control. However, the
soft-magnetic properties of the microrobot are not precisely
known due to material and geometrical variations of the
microrobot in the fabrication process . Therefore,
experimental measurements of the forces and torques are
In recent years, the development of biomedical MEMS
required in order to design an efficient control system.
Preliminary experiments show that the forces acting on a
microrobot range from micronewton (10-6N) to millinewton
(10-3N) when the microrobot is a few centimeters from the
surface of a strong permanent magnet . No commercially
available sensors are able to measure both force and torque
simultaneously at these scales. In the literature, a small
number of multi-axis MEMS sensors have been reported. In
 a capacitive MEMS force sensor is presented which is
able to measure force along two axes. In  and  the
design of a piezoresistive three-axis force sensor is
described. A piezoresistive torque sensor has been presented
This paper presents the design of a three-axis capacitive
MEMS force-torque sensor. Forces can be sensed in a plane,
while a torque perpendicular to this plane can be measured.
The fabrication process as well as the characterization of the
device is presented. The design and fabrication of the
microrobot is briefly described. Finite element simulations
are used to estimate the magnetic field strength. The force
and torque on the fabricated microrobot are measured by
gluing it onto the 3-axis MEMS sensor and applying a
II. MULTI-AXIS SENSOR DESIGN
Figure 1 shows a photograph of the fabricated micro
force-torque sensor. It measures 5.4mm x 5.2mm x 0.45mm.
Fig. 1 Photograph of the multi-axis MEMS sensor
Proceedings of the 2007 IEEE/RSJ International
Conference on Intelligent Robots and Systems
San Diego, CA, USA, Oct 29 - Nov 2, 2007
1-4244-0912-8/07/$25.00 ©2007 IEEE.3803
The MEMS-based three-axis capacitive force sensor is
capable of resolving two orthogonal force components and
the torque orthogonal to the two forces. The sensor consists
of three main parts as shown in Figure 2:
the movable sensor body
four flexures which convert the load applied to the
movable body into a deflection
three pairs of capacitors which convert the
deflection into a change of capacitance
The four flexures are designed such that they allow the
movable body to translate in x- and y-direction and to rotate
around z-axis. The flexures are very stiff in z-direction, such
that force components in z-direction as well as torques in x-
and y-direction do not cause a measurable deflection of the
movable body. Linear elastic material properties can be
assumed. The deflections of the flexures are small compared
to the flexure length leading to a linear relationship between
the applied force and the deflection. The deflections in x-
direction dx and the deflection in y-direction dy are given by
where Fx and Fy are force components in x- and y-direction
and kx and ky the corresponding stiffnesses of the flexures.
Additionally, a torque around z-axis Mz causes a rotation of
the movable body. The rotation angle αz is given by
where kz is the rotational stiffness of the flexures.
The capacitance C of a parallel plate capacitor with the
plate area A and the gap d can be approximated by
The permittivity of air is ε = 8.85 x 10-12C2/(Nm2). In our
design transverse position sensing mode is used, which
means that the capacitance change ΔC is sensed by a change
of the gap width Δd.
Transverse position sensing allows high sensitivity
measurements, but the relationship between deflection and
capacitance is non-linear (and thus there is also a non-linear
relationship between deflection and applied load). Since
linearity is desired, a differential capacitor configuration 
has been chosen, consisting of a capacitor C1 and a capacitor
C2. C1 and C2 are given by
= ⋅⋅ ⋅+
where d1=5μm is the initial gap between the capacitor plates,
d2=20μm the distance between a capacitor pair and n the
= ⋅⋅ ⋅+
number of capacitors in the comb drive. The readout
electronics then generate and output signal S given by
which is proportional to the deflection for d2>>d1>> Δd.
The deflections of the movable body are sensed by three
pairs of differential capacitors. Ca (consisting of Ca1 and Ca2)
is used to sense displacements in x-direction, Cb (consisting
of Cb1 and Cb2) and Cc (consisting of Cc1 and Cc2) are used to
sense displacements in y-direction. Three readout signals Sa,
Sb and Sc are generated by the readout electronics as shown
in (6). By sensing the deflection of the movable body in y-
direction using two capacitor pairs instead of only one
capacitor pair, both forces in y-direction and torques in z-
direction can be distinguished (a rotation of the movable
body generates a deflection at the position of Cb and Cc with
an opposite sign).
In order to find the ideal configuration (body size,
position and size of flexures and capacitances), a finite
element (FE) based optimization was performed. An
optimization loop consisting of a structural and electrostatic
analysis was used to efficiently calculate the relationship
between load and change of capacitance for a large number
The sensor presented in this paper is designed to
measure forces up to 700μN and a torque up to 750 nNm.
The theoretical noise level (standard deviation) of the system
(sensor and readout electronics) is estimated to be 0.5μN for
the forces and 0.5nNm for the torque at a readout frequency
of 5000Hz. By using a moving average filter, the resolution
can be further increased.
Fig. 2 Three-Axis Force-Torque sensor schematic
Fig. 3 Sensor fabrication sequence
III. MICROFABRICATION PROCESS
The fabrication sequence is illustrated in Figure 3. The
minimum feature size of the structures on the device layer is
5μm, which corresponds to an aspect ratio of 1:10.
A. A silicon-on-insulator (SOI) wafer is used as a base
substrate. The 50μm thick device layer is highly
doped with boron to lower the resistivity to
B. The backside silicon is etched using deep reactive
ion etching (DRIE). The buried SiO2 acts as an etch
stop, which guarantees that the device layer
features the same thickness over the whole wafer.
Subsequently the SiO2 is removed by dry etching as
C. 150nm of Aluminum is evaporated and patterned to
form the electrical contacts for wire-bonding.
D. The SOI wafer is mounted on a support wafer. The
device layer including the flexures and the comb
drives are etched by DRIE. Etching a border around
the whole device will release it onto the support
IV. READOUT ELECTRONICS DESIGN
The most common readout method applied in today's
capacitive MEMS applications is based on an impedance
relation measurement, where two periodic, 180 degree phase
shifted excitation voltages are applied to a capacity pair. The
demodulated response of the common electrode is then
proportional to the ratio of the two capacities. This method
has produced good results in single degree force sensor
systems [8, 9]. However, it is not well suited for applications
where several capacity pairs have to be measured.
The capacity readout chosen in this work is based on a
capacitor discharge time measurement. Figure 4 shows a
measurement cycle. A change in capacitance ΔC induces a
time shift Δt in the discharge time (normally in the ns range)
which is measured by a time-to-digital converter. A resistor
is used to set the discharge time. The amount of time to
discharge a loaded capacitor is proportional to its electrical
capacity. Using this approach, three capacity pairs can be
joined with a common electrode therefore simplifying the
MEMS fabrication process and effectively reducing the
amount of connections (and wire-bonds) needed.
The readout system was implemented using a time to
digital conversion ASIC (ACCAM PS021). It has the
capacity to measure up to four capacitor pairs per device
with a minimal amount of wiring and additional circuitry.
The back-end features a Serial Peripheral Interface (SPI)
which allows direct digital accessibility to the measured
V. DESIGN AND FABRICATION OF THE BIO-MICROROBOT
structure built by microassembly of individual parts as
shown in Figure 5. The prototype robot reported in this
paper was fabricated entirely from electroplated nickel. The
length of the microrobot is 1mm, the width 0.4mm and the
thickness of the Nickel parts is 0.05mm.
An external magnetic field is used to align and pull the
robot along its long axis due to the shape anisotropy effect,
which aligns the robot to the field much like a needle always
becoming magnetized along its long axis.
The assembly process allows for the combination of
incompatible materials and processes for the integration of
MEMS based sensors and actuators. In this way, different
subsystems of the robot can be manufactured using the most
suitable process for the purpose.
The microrobot prototype is a three dimensional
Fig. 4 Change in capacitor discharge time
Fig. 5 Nickel parts (left), assembled microrobot (right)
VI. SENSOR CALIBRATION
torque sensor in order to measure the forces acting on it.
This assembly process is critical, since it has to be
accomplished without breaking the fragile springs of the
sensor. First, a small droplet of UV curable glue is pipetted
onto the sensor. Then, the microrobot is picked up by an
electrostatic microgripper (FemtoTools FTG-100) which is
mounted onto a 3-axis micromanipulator . The
microrobot is positioned in the cross-shaped cavity on the
device layer of the sensor and released. After that, the glue is
exposed to a UV light source to permanently fix the
microrobot on the sensor. The sensor is then glued to the
printed circuit board of the readout electronics and wire-
bonded to it. Figure 6 shows the assembly process using the
microgripper and Figure 7 the sensor glued to the printed
Precise calibration of multi-axis MEMS force sensors is
difficult for several reasons, including the need to apply
known force vectors at precise positions and orientations
and risk of damaging the small and fragile microdevices
. The goal of the calibration is to obtain the calibration
matrix A3x3, which characterizes the linear relationship
between the three sensor output signals Sa, Sb, Sc and the
loads Fx, Fy and Mz applied to the sensor.
For the calibration of the 3-axis force-torque sensors a
single-axis reference force sensor (Femtotools FT-S270)
was mounted on a 3-axis micromanipulator and pushed
against the sensor. Reference forces at different orientations
and positions have been chosen F1, F2 and F3 as shown in
Figure 8. No reference torques were applied to the sensor
since this is difficult to do in a controlled way at the
microscale. However, by applying the off-center force F3, a
superposition of both a force and a torque is acting on the
center of the sensor. The displacement for the reference load
vector F3 has been chosen l=550μm. The signal by all three
capacitor pairs has been monitored simultaneously while
applying the loads. The calibration matrix A is then
calculated by the known load vector [F1,F2,F3]T and the
measured data [Sa,Sb,Sc]T.
Figure 9 shows the signal output for F1, F2 and F3. In
theory, F1 induces a pure translation of the movable part of
the sensor in x-direction, F2 a pure translation in y-direction
and F3 a translation in y-direction as well as a rotation. It can
be seen that there is a significant crosstalk between the
capacitors measuring deflections in x-direction and the
capacitors measuring deflections in y-direction. However,
since all output signals show linear behavior this effect is
taken into account in the calibration matrix. For our design,
the calibration matrix A is given by
The microrobot has to be glued onto the MEMS force-
for Fx and Fy in μN and Mz in nNm. The calibration has been
performed multiple times for averaging.
Fig. 6 Assembly of the microrobot onto the force-torque sensor
Fig. 7. Force sensor glued and wire-bonded onto the PCB
Fig. 8 Reference load vectors applied to the microrobot
Fig. 9 Sensor output signals for reference force vector F1, F2 and F3
VII. EXPERIMENTAL RESULTS
A strong permanent magnet (Q-19-13-06-N from
Supermagnete.ch) (remanence BBr=1.1T) is used to generate
magnetic forces and torque on the microrobot. The
microrobot is glued to the force-torque sensor and placed a
few millimeters away from the magnet as shown in Figure
10. The load inside an area of 25mm times 10mm has been
evaluated, by moving the microrobot with a motorized stage
(Sutter MP-285). The forces and the torque acting on the
microrobot have been simultaneously measured with a
spatial resolution of 0.5mm. The analytical determination of
the magnetic forces and torques acting on the microrobot is
not trivial and the subject of ongoing research [2,3]. For a
qualitative understanding, we examine the force F and
torque M acting on a magnetic dipole Γ [Am ] in an external
H [A/m] is
where μ0=4π10-7Tm/A is the permeability of free space.
Equation (9) can be simplified since no electrical currents
are flowing (
=Γ⋅ Γ⋅ Γ⋅
We observe that the magnetic force on the dipole is
dependent on the gradient of the field, whereas the torque
depends on the field strength. The field of the magnet is
simulated using the commercial finite element (FE)
simulations MAXWELL and shown in Figure 10 together
with the orientation of the microrobot and the scanned area.
Examining (10) and (11) and the field vectors, we expect
that Fx has a symmetrical behaviour, and Fy as well as Mz are
expected to show the same magnitude but opposite
directions when moving the microrobot in the y-direction.
Fig. 10 Magnetic Field
Fig. 11 Force-Torque components measured by the multi-axis sensor
Figure 11 gives an overview of the distribution of the
three measured load components. A maximum force of
170μN in x-direction and a maximum force of 65μN in y-
direction have been measured. A very large torque of
335nNm has been evaluated. Both force and torque
components decrease by a large amount when moving the
microrobot farther away in x-direction. It can be seen that
the microrobot is pulled towards the magnet and the torque
tries to rotate the microrobot with the long axis pointing
towards the magnet. The plot shows that the force-torque
reading is not exactly symmetrical along the y-axis. It is
expected that this comes from the fact that there was a small
rotational misalignments between the magnet and the
microrobot when reading the output signal. Also, the torque
generates a large change of the output signal of the sensor
(compared to the forces). This causes numerical problems,
since small deviations in the calibration matrix A results in
large errors for the force components. In order to obtain
highly accurate data, the calibration process of the three-axis
sensor has to be improved.
A capacitive three-axis MEMS force-torque sensor has
been presented which is able to measure forces at sub-μN
resolution and torques at sub-nNm resolution. The design,
fabrication and the calibration is described. Additionally, a
microrobot prototype which may be used for drug delivery
inside the human body is presented. By mounting the
microrobot onto the sensor, the load acting on it has been
measured. The magnitude for the forces and torques range
up to 170uN and 335nNm respectively. The quantitative
data is valuable for designing magnetic position control
algorithms for untethered bio-microrobots.
 K. B. Yesin, K. Vollmers, B.J. Nelson, "Modeling and Control of
Unthedered Biomicrorobots in a Fluidic Environment Using
Electromagnetic Fields", International Journal of Robotics Reserach,
Vol. 25, 2006.
 J. J. Abbott, O. Ergeneman, M. Kummer, A. M. Hirt, B. J. Nelson, "A
Continuous Model for Magnetization Torque on Axially Symmetric
Bodies", Proc. Joint Magnetism
(MMM)/Intermag Conf., 2007.
 M. Kummer, J. J. Abbott, K. Vollmers, B. J. Nelson, "Measuring the
Magnetic and Hydrodynamic Properties of Assembled-MEMS
Microrobots", Proc. 2007 IEEE International Conference on Robtoics
and Automation (ICRA), April 2007.
 Sun, Y., Nelson B.J., Potasek D.P. and Enikov E., “A bulk
microfabricated multi-axis capacitive cellular force sensor using
transverse comb drives”. Journal
Microengineering, 12(6): pp. 832-840, 2002.
 J. Brugger, M. Despont, C. Rossel, H. Rothuizen, P. Vettinger, M.
Willemin, "Microfabricated ultrasensitive piezoresistive cantilevers for
torque magnetometry", Sensors and Actuators A, Vol. 73, pp. 235-242,
 W.L. Jin, C.D. Mote, "Development and fabrication of a sub-millimeter
three-component force sensor", Sensors and Actuators A, Vol. 65, pp.
 S. Butefisch, S. Buttgenbach, T. Kleine-Besten and U. Brand,
“Micromechanical three-axial tactile force sensor for micromechanical
characterization”, Microsystem Technologies, Vol 7, pp. 171-174,
 Y. Sun, S. N. Fry, D. P. Potasek, D. J. Bell and B. J. Nelson,
“Characterizing fruit fly flight behavior using a microforce sensor with
a new comb drive configuration”, J. Microelectromech. Syst., 14(1): pp.
 F. Beyeler, A. P. Neild, S. Oberti, D. J. Bell, Y. Sun, J. Dual, B. J.
Nelson, "Monolithically Fabricated Micro-Gripper with Integrated
Force Sensor for Manipulating Micro-Objects and Biological Cells
Aligned in an Ultrasonic Field", Journal of Microelectromechanical
Systems (JMEMS), Vol. 16, No. 1, pp. 7-15, 2007.
 K. Kim, Y. Sun, R.M. Voyles, B.J. Nelson, "Calibration of Multi-Axis
MEMS Force Sensors Using the Shape-From-Motion Method", IEEE
Sensors Journal, Vol 7, No. 3, March 2007.
and Magnetic Materials
of Micromechanics and