9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
Haptic Sensing for MEMS with Application for
Cantilever and Casimir Effect
M. Calis
1,2
, M.P.Y Desmulliez
2
1
Corac Group plc
2
MIcroSystems Engineering Center (MISEC)
Brunel Science Park School of Engineering & Physical Sciences
Uxbridge, UB8 3PQ Heriot-Watt University, Edinburgh, EH14 4AS
This paper presents an implementation of the Cosserat
theory into haptic sensing technologies for real-time simulation
of microstructures. Cosserat theory is chosen instead of the
classical theory of elasticity for a better representation of stress,
especially in the nonlinear regime. The use of Cosserat theory
leads to a reduction of the complexity of the modelling and thus
increases its capability for real time simulation which is
indispensable for haptic technologies. The incorporation of
Cosserat theory into haptic sensing technology enables the
designer to simulate in real-time the components in a virtual
reality environment (VRE) which can enable virtual
manufacturing and prototyping. The software tool created as a
result of this methodology demonstrates the feasibility of the
proposed model. As test demonstrators, a cantilever microbeam
and microbridge undergoing bending in VRE are presented.
I. INTRODUCTION
Commercial MEMS are usually the result of many
manufacturing, characterisation, packaging and tests
iteration runs used to optimise their performance and
reliability. At the design and manufacturing phases,
engineers employ a variety of software tools that deal with
the analysis of complex geometrical structures and the
assessment of various component interactions that often
belong to different domains of energy. Software packages
such as CoventorWare [1], MEMSCAP [2] and ANSYS [3]
are based however on classical elasticity, which limits the
validity of stress results for large deflections of structures. In
addition, these software packages tend to be computationally
intensive when dealing with complex microsystems.
Commercial software packages such as CoventorWare [1],
MEMS Pro [4], SABER [5], IntelliSuite [6] do not allow
real-time simulation. An efficient and rapid modelling
approach that represents accurately the linear and nonlinear
dynamic behaviors of MEMS is therefore called for.
II. HAPTIC SENSING TECHNOLOGY
The term haptic originates from the Greek ?haptesthai?
and means the sense of touch with both tactile (cutaneous)
and kinesthetic (proprioception) feedback. The PHANTOM
Omni [7], an analogue interface, from the company
?SensAble Technologies? enables the interaction of the user
with virtual environments based on haptic rendering through
touch. This haptic device is a ?pen? (also called stylus, proxy
and haptic interface point) located at the end of an arm
controlled by electric motors. These new interfaces differ
from current computer systems and are changing the way by
which digital information is perceived and manipulated. One
of the most powerful ideas behind haptic technologies is to
design ideas creatively and not mathematically. A haptic
system consists of two loops, called haptic loop and display
loop that need to be maintained with an update rate of 1 KHz
and 30 Hz, respectively (Figure 1) [8]. The display loop
must be updated at 30 Hz since the Human Visual System
(HVS) has a flicker fusion frequency around 30-60 Hz. The
update rate of the haptic loop has been set at 1 KHz to avoid
force artefacts and due to the human being able to detect
discrete events at less than 1 KHz.
Fig. 1. Schematic of a haptic system
Haptic computers represent an important advantage in
simulated industrial product development, virtual
prototyping, in assembly/disassembly process, in final
design and finally for training. Haptic computers enable also
designers the possibility to scale-up to a human ergonomic
scale micro-assemblies (such as MEMS) which can consist
of millions of parts and then scale the product back to its
original size. These properties improve the manufacturing
lead times and the maintenance. In addition, in VREs,
scaling down MEMS allow designers to gain more
information and better understanding of their
devices/components since the designers will be immersed in
the VRE and any part of the system will be accessible. The
different needs of MEMS modelling and simulation
methodology for the precise performance verification of
9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
MEMS products are summarized as shown in table 1.
TABLE I
NEEDS OF HAPTIC TECHNOLOGIES FOR MEMS
Application Needs Benefits of haptic
technologies
CAD/CAM
design
? Guide designers during
assembly and
disassembly process
? Conception
? Tolerance
? Manufacturing of mould
at micro-scales for
LIGA processes
? Sense surface, shape of
components,
deformation
? Sense and effect of
forces at micro-, meso-
and nano-meters size
structures
Virtual
Prototyping
? Replace physical
prototype by virtual
model
? Enhance product
development
? For combining physical
and digital modeling
? Can guide designers
? Improve manufacturing
lead times
Visualization
? Analyses of any parts of
the system
? Ergonomic analysis
? Scale-up/down
? Increased information
flow between user and
the computer
? Better understanding
Maintenance
? Verification
? Diagnosis
? Quick analysis of any
default, the cause and
solution
? Security
Training ? Simulation
? A better understanding
? Useful for application
related to manipulation
? Force-feedback
? Sense gravity, inertia
? Motion of components
III. COSSERAT THEORY
Methods for modelling MEMS components can usually be
classified into two categories, as shown in Figure 2. The
exact methods include the Euler-Bernoulli [9] and the
Timoshenko techniques [10] which are solved using a power
series expansion. The FEA, BEM and lumped mass methods
are classified under the approximate methods and are solved
using superposition techniques. The FEM is also known as
the matrix displacement method. The word approximate is
used since it assumes that displacements can be represented
by simple polynomial expressions. Our approach uses a
semi-analytical method based on both power series
expansions and a multimodal approximate method [11].
Fig. 2. Taxonomy of MEMS modelling methods
One reason of using the Cosserat theory is its capability to
meet the update rate of both loops. To the best of the
authors? knowledge, we are the first to implement Cosserat
theory in haptic sensing technologies [8,12]. The motion in
space of a nonlinear Cosserat rod segment can be
represented as a vector (),rst , called a Cosserat curve, which
describes the position of the line of centroids of the cross-
sections (Figure 3, dotted line). Each (),s t is a right-handed
orthonormal basis where s denotes the length parameter of
the rod segment ()asb?? , t denotes the Newtonian time.
()
1
,dstand ()
2
,dst are a pair of orthogonal material lines
describing the principal orientations and giving information
about the location of the material cross section.
3
d is the
normal to the cross-section and defined by
312
() () ()ddds ss=? (1)
which provides an orthonormal frame (){ },
k
dDst=
with k
=1, 2, 3. ()
3
d s encodes the state of deflection of the beam at
each point along this line.
Fig. 3. A Cosserat rod: Deformed beam
The deformation of the slender MEMS structure represented by
the deformation of the centroid line depends upon three vectors
()r s , ()
1
d s and ()
2
d s . In the Cosserat theory, the accuracy will
depend on the method used to model the motion/deformation
of the centroid line. Unlike in [12] where the Newton?s
dynamical law and analytical solution are used, our approach is
based on a semi-analytical method and on the Euler-Bernoulli
equation of motion. In the solution process, the displacements
x
u and
y
u , in the transverse and axial directions, are
expanded in ascending powers of w [13].
01 2 3
23
01 2 3
....
aa a a
u
aa a a
xxx x x
yyy y y
u
ww w
u
???? ? ? ? ? ? ? ? ?
== + + + +??
?? ? ? ? ? ? ? ? ?
?? ? ? ? ? ? ? ? ???
(2)
By rewriting (2) as
42
00
0
riv iwt r iwt
ry ry
rr
cwaqewwaqe
??
==
?=
??
(3)
and using the shape function and the algebraic manipulation
presented in [14] , the equation of motion for a free end ? free
end horizontal nonlinear microbeam (Figure 3) can be rewritten
with the first order kinetic and strain terms
9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
()
111
222
T
22
TT
iNL L NL
22
dq dq
FMq K qqK q
dt dt
N
L
??
??
??
=++
??
??
??
(4)
where M and
L
K are the mass and the stiffness matrices,
respectively.
'
()EA L L
N
L
?
= is the axial force applied on the
microbeam and
NL
K is the nonlinear geometric stiffness
matrix. It is demonstrated in [14] that the proposed method
for modelling linear effects in MEMS valid and nonlinear
problems such as the buckling of beams have also been
tackled successfully.
IV. IMPLEMENTATION OF COSSERAT THEORY INTO HAPTIC
SENSING TECHNOLOGY
The algorithm structure to simulate a Cosserat microbeam
in real-time in a VRE using haptic sensing technologies can
be broken down into five stages. The first phase is to
convert/scale up the load generated with the PHANTOM
Omni to the appropriate MEMS micro-world. The second
step is to measure the displacement in the reference frame.
This displacement is then translated into the moving frame
where different forces are calculated and summed up to
obtain the total force. Afterwards, the total force is
transformed back to the system matrix.
Fig. 4. Haptic interface
A scale down/conversion is subsequently carried out; the
proper force feedback is then calculated and rendered. The
algorithm is implemented in Object Oriented language.
OpenHaptics is used to interact and to feel the MEMS
components, OpenGL for graphics and Microsoft visual
C++. A front end-user interface has been designed to readily
interact with selected MEMS components as shown in
Figure 5.
The model of a linear cantilever microbeam has then been
integrated into the haptic environment as shown in figure 5.
Deflection of the microbeam is occurring in real-time for a
load applied by the pen of the haptic device. Figure 6 shows
the deflection of another microstrcutre, a microbridge, when
a load is applied with the stylus in the y-direction.
Fig. 5. Linear cantilever microbeam in deflection for a vertical load
Fig. 6. Microbridge in deflection for a vertical load
Comparisons with the software packages ANSYS and
SABER were not possible as these packages are not suitable
for real-time simulation.
V. MODELLING SURFACES INTERACTION
The highly intensive market for faster computing power
for smaller electronic die sizes drives the development of
enhanced lithographic tools for greater miniaturization. This
capability is likely to be translated in the field of
MEMS/NEMS. Since these devices are generally movable
structures on a semiconductor and as the miniaturization is
increasing, the likelihood of the moveable elements to
collapse onto the substrate is augmenting concurrently
(Figure 7). Therefore, for efficient manufacturing process
and high performance of these devices, a thorough
understanding of these surfaces interactions during growth
and device operation are decisive for reliable performance. A
particular category of devices falling into this category is
RF-MEMS switches and relays. The effect in MEMS/NEMS
is known as stiction (static friction); the adhesion of
contacting surfaces which, in general results in permanent
stiction. Another example of phenomenon that can cause the
failure or reduce the performance of MEMS/NEMS is the
Casimir force, which is of quantum nature [15]. This consists
in the attraction between a pair of neutral, parallel,
conductive metal plates separated by a small gap causing
moveable parts to collapse into the substrate.
9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
Fig. 7. Stiction effect: a) Stuck finger on comb drive-Stiction. Courtesy
of Sandia National Labs, MEMS reliability departments b) Cantilever after
release etch adhering ti substrate. Stiction caused by capillary
forces/condensation [16].
This effect arises since the average of virtual particles is
greater surrounding the plates than between them since the
distance between the plates are so small that the range of
fluctuations is restricted causing the generation of an
attractive force (Figure 8). Casimir effect has been predicted
in 1948 by the Dutch physicist Hendrik Brught Gerhard
Casimir [15], but it has only been confirmed experimentally
in 1997, by Steven K. Lamoreaux using a torsion balance
[17].
Fig. 8. Schematic representation of fluctuating virtual particles
The Casimir effect is known to be a local version of the
van der Walls force between molecules and a proof for the
evidence of the quantum vacuum possessing infinite energy
density populated by virtual particles.
In this work, only the stiction effect which occurs when
component touch the substrate is considered. The modelling
of this surface interaction has been implemented in our
software to guide designers during the assembly process of
for training engineers quickly to operate in this field (Figure
9). With our user-end interface, the cantilever can be tested
for given parameters. Moreover, the range of load that can
be applied on the cantilever can be tested virtually and
corrected depending on the needs at the design stage. When
the cantilever is very close to the substrate, a warning
messages pops-up on the screen and once it touches the
substrate, the cantilever sticks to it. By pressing the ?Reset
Failure? on the left hand side of the window, the cantilever
will be placed back in its original position. The consideration
of such surfaces interaction in CAD/CAM tools can enable
to build physical prototypes late in the manufacturing cycle.
The advantages of using haptic sensing technologies allow
the designer to touch and feel the MEMS component and at
the same time to see the deflection in real-time. The
parameters of the beam, such as the Young modulus, the
density and number of elements composing the cantilever
can be changed readily using the left hand side menu.
VI. CONCLUSION
In this paper, it is demonstrated that Cosserat theory has
been successfully integrated into haptic sensing technologies
for modelling and testing simple structures such as a
cantilever and a microbridge. In addition, the modelling
surfaces interaction such as the stiction effect has also been
integrated successfully in the software.
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9-11 April 2008
?EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5
Fig. 9. Stiction effect caused by the cantilever surface touching the substrate