A review on design and synthesis of compliant mechanism for micro
actuation
ARSHAD JAVED*
Graduate Student, Mechanical Engineering, Birla Institute of Technology and Science,
Pilani-333031,
arshadjaved@rediffmail.com
Dr. BIJAY KUMAR ROUT
Asst. Professor, Mechanical Engineering Group, Birla Institute of Technology and Science,
Pilani 333031
Prof. R. K. MITTAL
Dean, ARCD, BITS-Pilani, Birla Institute of Technology and Science, Pilani 333031
Abstract
At micro scale, joint frictions of mechanism become highly influencing parameter. Thus the mechanism at this
scale must avoid joints causing friction. A compliant mechanism is a mechanism that gets its mobility from the
flexibility of some or all of its members and eliminates the need of frictional joints. Though it exists at macro
level but it finds its larger application in MEMS. In this paper the study of compliant mechanism and its
applications in MEMS is carried out. Design and synthesis of compliant mechanisms is entirely different from
the conventional open or close loop mechanisms. Few approaches are developed by researchers and few other
methods are in development stage. In all these methodologies topology optimization is a major step as it decides
the final shape and structure of the mechanism. In the present work various topology optimization for compliant
mechanisms are reviewed, and study of its influence on the final design is been presented.
Keywords: Compliant mechanisms, Topology optimization, Micro-actuators
1. MICROACTUATORS
In recent years, enormous progress has been made in the design, fabrication, and commercialization of
Microsystems. Some of these microsystems require micro actuation to fulfill desired activity. An actuator is a
device that transforms a form of energy (mechanical, electrical or thermal energy) into controllable motion.
Similar to macro devices, MEMS also require micro actuation in terms of suspension, rotary, intermittent and
linear motion. At micro level the task become very challenging as the offered form of energy and the required
motion both are in terms of micron. Again, the requirement is to produce not just a motion but an “accurate
motion”. At this juncture the traditional actuator methodology/principals seem to be failing due to error and
difficulty in manufacturing.
1.1 TYPES OF MICROACTUATORS:
Various techniques are used to generate micro actuation in MEMS devices. The challenge is to find out an
efficient relationship between motion and energy input. Commonly theses are driven by electrostatic forces,
thermal phase change, shape-memory alloy, magnetic and piezoelectric forces. Each of these has its own
working methodology and their working principle is discussed briefly.
Electrostatic microactuators have been constructed of metal or doped semiconductors and designed with
flexures, rotary bearing surfaces and linear bearing surfaces. Typically tens to hundreds of volts are needed to
generate a few µN forces to achieve actuation on the order of a few micrometers. Range of motion is increased
in some improved designs [13]. The two well known designs are the lateral comb drive [14] and the rotary
micromotor [12]. The major difficulty is to provide comparatively large voltage. Again high voltages on small
scale create high electric field gradients that attract dust particles. Also, it will not function in conductive fluids.
Other electrostatic actuator is scratch drive stepper motor [15] which can work for few µN forces and can travel
distances in range of 6 mm. This is used to assemble complex hinged three-dimensional microstructures that are
used for optical applications [16].
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In thermal microactuators motion is amplified by thermal expansion of thin members. These members are
heated by passing a current through them. The thermal actuator design used in recent work is the thermo
mechanical in-plane microactuator (TIM). These actuators use bi-morph designs that take advantage of a
considerable difference in the thermal expansion coefficient of each material in the device [17]. Some other
methods of micro thermal actuation are nonsymmetrical heating of a single layer of patterned material [18];
force generated during the phase change from liquid to vapor [19]; shape-memory alloys; phase change from a
low-temperature and weak martensite crystal phase to a higher-temperature and very rigid austenite crystal phase
[20, 21].
In Magnetic microactuators straight macroscopic designs may be one of the solution of despite the
significant challenge involved in integrating ferromagnetic cores, rotors and copper coils around the cores [22,
23]. Magnetic actuation has an advantage over electrostatics actuation as it can achieve larger forces over larger
gaps than their electrostatic counterparts. Magnetic actuation can operate in conductive fluids and the lower
electric field gradients present in magnetic microactuators and it will not attract appreciable quantities of dust
particles. Magnetic microactuators can generate torque and large out-of-plane deflections (e.g., more than 90◦)
useful for microphotonic and millimeter wave applications [24, 25]. Magnetostrictive materials can also be used
for micro actuation, which experience a mechanical strain when magnetized.
Piezoelectric microactuators use piezoelectric materials that generate large forces over small displacement.
.MEMS devices for example accelerometer sensors and micro actuators are frequently use micro-fabricated
piezoelectric devices that convert a mechanical displacement to an electric signal.They also transform electric
signals to mechanical displacement with an inverse piezoelectric effect. Piezoelectric materials are used to
generate large forces over small displacements. Some piezoelectric materials like, ZnO and PZT are used for the
devices in surgical applications like a smart force-feedback knife [26], and an ultrasonic cutting tool [27].
2. MICRO-MECHANISM AND COMPLIANT MECHANISM
The function and requirement of a micro-actuator has been described earlier. Micro-mechanism is a part of micro
actuator. It basically modifies (amplify or reduce) or generates the desired motion in the system. There are few
basic elements in micro mechanism like Pits, grooves and channels, Microflexures and Microbearing surfaces.
Combination of these building blocks, bring new mechanisms at micro level. Pits, grooves and channels are
created by bulk micro machining. Microflexures are used to achieve simple kind of motion [28]. In many other
applications, combination of micro flexural elements is used. These basic elements are cantilever beams, bridges,
torsion bars, plates and membrane. A dry release etch (e.g., plasma etching, XeF2 etc) is used to fabricate these
since it does not have a fluid meniscus and will not generate surface tension forces [29].
Microbearing surfaces are nothing but the base surface for rotation and translation motion to enable fully
free structures capable of unlimited rotation. Major problem in these are wear and relatively small life [30]. New
methods are also developed to improve the bearing materials and they are partially successful [31] But in all the
cases requirement is to produce a specific motion with certain range and predefined behavior just like macro
mechanism. Also there is a requirement to reduce or amplify the motion in a desired manner. Due to limitations
in manufacturing, assembly methods, and friction it is difficult to fabricate mechanism at micro level [1]. In such
situation compliance mechanism is the effective solution. It is a single part mechanism providing a limited
deflection that is used as amplified or modified motion. The concept of compliant mechanisms is not new [4].
Basically it is a structure with zero degree of freedom. But the links are not rigid and shows small deflections
when force is applied. Combination of different deflection of each links creates a specific motion with respect to
an input force, and it works as macro mechanism. Thus, compliant mechanisms function as a synergistic
combination of a structure and a mechanism, or as a “structure with mobility” [5]. The links are having no
apparent joint as in the case of conventional macro mechanism. Compliant mechanisms are require fewer parts;
are easy to fabricate; have less wear, and backlash; have no need for lubrication; and have built-in restoring force
[2, 3]. Hence it reduces the major problem of friction, fabrication of micro joints, and reliability. A compliant
mechanism is a mechanism that gains its mobility from the flexibility of some or all of its members, as opposed
to its more conventional rigid body counterpart [6]
The application of compliant mechanism in MEMS device is shown in Fig. 1. It shows a compliant
suspension to guide the shuttle mass of a micro-linear electrostatic actuator (comb-drive actuator) [43]. This
suspension provides a very low stiffness (highly compliant) in the direction of motion and higher stiffness in the
direction perpendicular to the motion.
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Fig. 1 Compliant mechanism based motion amplifier [43]
2.1 DESIGN METHODOLOGY OF COMPLIANT MECHANISMS
A compliant mechanism has the characteristics of both structures and kinematic chain. Therefore, design method
can have two approaches: (i) taking it as a structure with some definite range of deflection, known as structure
optimization method [34-37] and (ii) taking it as a kinematic chain having flexible links and joints, known as
kinematic synthesis approach [32,33].
Analysis of compliant mechanism can be complex, often requiring nonlinear finite-element analysis, a
possible way is a pseudo-rigid-body model, which helps to simplify the analysis and improve understanding of
how compliant bi-stable mechanisms behave [44-63].
In other words design of compliant mechanisms can be classified into two types: lumped and distributed
compliant mechanisms. Lumped compliant mechanisms are based on rigid-body kinematic synthesis, and
distributed compliant mechanisms are based on of continuum topology optimization [6, 38]. Lumped compliant
mechanisms are typically analyzed by using the pseudo-rigid-body approaches [40]. In this approach some part
of the mechanism is considered as rigid while material near to the flexible joint is taken as flexible. But lumped
compliant mechanisms are not very suitable as it undergone unsymmetrical over strain around hinges [42]. Thus
distributed compliance is the remaining method in which compliance is distributed through structure. This
method was described through topology optimization by Ananthasuresh [41]. Distributed compliant mechanisms
are basically structure and obtaining their flexibility from topology and shape of the material continuum. They
are suitable for mechanisms at microscale with the characteristics of continuous and monolithic structures. To
adequately design a compliant mechanism, these criteria should be addressed [8, 11]. The criteria are, required
kinematic motion, desired mechanical or geometrical advantage, required stiffness to an external load, material
properties, stress limitations, weight limitations, buckling instabilities, dynamics and actuator characteristics.
Distributed compliant mechanisms synthesis eliminates the problems of load concentrations and poor
lifetimes by distributing the strain energy throughout the mechanism. Hence each member undergoes an elastic
deformation and transferring energy from the input to the output. This synthesis process is not exactly same as
the traditional kinetic synthesis process, as the links are not rigid. The synthesis process is typically completed in
two steps [9-11].
The first step is to construct a kinematic geometry that generates the desired displacement and force output
for a given input. This process is called topology synthesis which takes the form of a multi-criteria optimization
problem. The second step in the design of compliant mechanisms is size and shape optimization. In this step the
shape of the individual elements is optimized to ensure that the mechanism achieves prescribed performance
specifications such as maximum stress, motion amplification or force amplification etc [11].
In an additional step one can also enforce local constraints for the minimization of buckling instabilities,
enforcement of stress limitations to ensure the operation envelope of the device is within the elastic regime,
minimization of stress concentrations, as well as enforcement of fabrication and weight limitations[9-11].
3. TOPOLOGY SYNTHESIS AND OPTIMIZATION
Topology synthesis is the process in which a kinematic layout is created that is capable of giving the prescribed
output with respect to the input force and displacement. It also decides sufficient stiffness to with stand against
external loads. Topology optimization provides qualitative results, thus it provides a kinematically functional
mechanism.
3
In microstructures topology optimization has been applied in continuum structures [1] in recent years
particularly in compliant mechanism in micro structures [1-6]. Different approaches are chosen by different
researchers to find the optimum solution. Most of the effort has been spent in developing techniques for
optimization and associated difficulties. These techniques are summaries below:
3.1 DESIGN BASED ON DIFFERENT APPROACHES:
Few researchers tried to change the basic approach of designing. Initially researchers attempted to solve these
problems by taking lumped and distributed system as discussed in section 2.1, few others advancements in these
approaches are discussed below,
On of these approach is Energy based formulation [8]. In this approach objective function is selected to
maximize the energy throughput the structure to optimizing the performance [8, 11] (discussed in 2.1) of a
compliant mechanism. It is based on distributed compliance. These formulations can be implemented for
topology synthesis as well as size and shape refinement. This formulation can incorporate other energy domain
like electric, magnetic etc also. The next approach is Methodology based on flexible building blocks [72]. It
combines the kinematic and structural approach. A multi objective genetic algorithm is used for global
optimization of compliant building blocks assemblies. This algorithm allows discrete variables such as buildingblocks variables or boundary conditions variables in design problem. And different discrete possibilities can be
explored such as materials possibilities, fixed frames locations, actuators locations, and contacts locations.
3.2 DESIGN BASED ON DIFFERENT OPTIMIZATION TECHNIQUES:
By changing the mathematical techniques of optimization, various solutions are possible. Starting with Multi
physics Optimization Topology [65], It is a methodology to implement structural topology optimization via a
fully-coupled partial differential equation (PDE) expression. The multiphysical structural optimization capability
is integrated through specially derived Lagrange-Euler equations. Subsequently Wavelet-based interpolation
algorithm [66] was devised by Fu and Zhang. It is a methodology to implement structure topology optimization
via a fully-coupled partial differential equation (PDE) expression. The multiphysical structural optimization
capability is integrated through specially derived Lagrange-Euler equations. In most of the topology result
checkerboard pattern comes out. Checkerboard is a pattern, in which solid and void elements alternate in a
periodic fashion, are frequently encountered in the solutions to the topology optimization design. Such patterns
make topology extraction and subsequent fabrication very difficult. The methodology combining topology and
reliability based design optimization [67] for compliant design was proposed by Maute and Frangpol. This
method provides a stochastic method for compliant MEMS design. Topology optimization problem is also
solved by traditional optimization techniques [68]. The method of moving asymptotes is applied to solve the
optimization problem. It is classified to the sequential convex programming methods. To prevent numerical
singularities density filtering approach can also be applied. This method can handle problems such as
checkerboards, mesh-dependency and one-node connected hinges in resulting mechanisms. Another method is
Multi criterion Optimization technique. Initially optimization problems were solved utilizing the homogenization
approach, later, several objective functions were investigated, including a weighted-sum multicriteria approach
based on maximizing the flexibility of a mechanism while simultaneously maximizing the stiffness. Larsen et al.
[78] posed an objective based on maximizing the flexibility of a mechanism while obtaining a specific
mechanical advantage. Frecker et al. [77] reformulated the flexibility and stiffness criterion as a ratio while using
ground truss structure for topology synthesis. Nishiwaki et al. [79] also posed the two criteria as ratios, but
additionally used the homogenization approach and expanded the formulation for plural multi-flexibility cases.
This topology optimization is also solved using level set methods [76]. In this methodology a level-set method
for designing monolithic compliant mechanisms made of multiple materials as an optimization of continuum
heterogeneous structures was given. Also the formation of de facto hinges was dealt based on the shape gradient
information. Use of a random guided search method for multiobjective optimization of compliant mechanisms
through genetic programming techniques [73] is also attempted. Features that exploit the implementation of
genetic algorithms to compliant mechanism design, such as multiple criteria specification and multiple-design
parameter variation. The optimization of topology is attempted by suppressing intermediate density [74]. This
technique uses a constraint of explicit penalty with variable bound to suppress intermediate density in topology
optimization of compliant mechanisms, to ensure mesh independent and not to complicate the non convex
objective function in compliant design. The topology optimization using Sequential Convex Programming was
attempted by Ying and Luo [69]. To overcome the shortcomings of weighting methods, this method adopts the
compromise programming to convert the multi-criteria problem to one single problem. The fundamental idea of
the CP methods is to define the scalarized objective function to be minimized by metric form. In this method
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both the mechanical functionality and the structural stiffness are considered as optimization objective functions.
This topology optimization problem was dealt as a Multiobjective topology optimization problem [70] which is
based on minimal structural compliance and maximal structural output displacement of MEMS actuators.
Topological synthesis of compliant mechanisms was carried out using Linear Beam Elements concepts [71]. This
study employs a multi-criteria objective function comprised of mutual potential energy (MPE) and strain energy
(SE) to full ground truss structures.
3.3 DESIGN BASED ON DIFFERENT TYPE OF MATERIALS
Compliant mechanism should be designed for more realistic situations in which non linearity present in the
material and some special actuators. Topology optimization design of Flextensional Actuators (piezo-ceramic
attached to a fexible mechanical structure) [64] is based on the homogenization design method. The objective is
to determine the optimal material property (via material volume fraction) and structural topology to maximize
the performance of the structure in a given application. Essentially, the method consists of finding the optimal
material distribution in a perforated domain with infinite micro scale voids. This method can be applied to 3-D
model also. The design using general displacement functional with non-linear material model is used in the
topology optimization formulation [75]. Sensitivity analysis of this displacement functional is derived from the
adjoint method and the optimization problem is solved iteratively by the generalized convex approximation.
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Fig. 2 Year-wise publication in international journals
Fig.2 shows the number of research publication in the area of compliant mechanism particularly. The thrust of
research has started in the year 1994 and further exploration is continuing recently.
4. CONCLUSION AND FUTURE SCOPE
In this paper, the need of micro-actuator in MEMS is discussed. The compliant mechanism needed and issues
involved to fulfill this requirement are presented. Various topology optimization methods used in compliant
mechanism have been stated. The purpose of these methods is to tackle the real time difficulty in the design
process like de facto hinge, checker-board, non linear material problems etc. And thus provide an effective
methodology which can generate the optimum solution with respect to simplicity, computation time etc. Not
only MEMS, but most of the commonly used macro-mechanism are renovated using this concept. The design
based on energy formulation, incorporating thermal, magnetic, electrostatic and piezo-actuator with a compliant
micro-mechanism has been discussed. The future scope lies in considering non-linearities due to large
deformation, and dynamic aspects of micromechanical structures. The life and fatigue failure of these
mechanisms are not investigated so far. Though MEMS always deal with planner compliant mechanism but 3D
compliant micro mechanism may be an advancement which will open new frontier.
5
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