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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 9, Issue 4, April 2018, pp. 312–327, Article ID: IJMET_09_04_036

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=4

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

FLEXURAL MECHANISMS FOR HIGH PRECISE

SCANNING APPLICATIONS: A REVIEW

Sharad Mulik

Research Scholar, Department of Mechanical Engineering,

Sathyabama Institute of Science & Technology, Chennai, Tamilnadu, India

A. Krishnamoorthy

Professor, Department of Mechanical Engineering,

Sathyabama Institute of Science & Technology, Chennai, Tamilnadu, India

Suhas Deshmukh

Associate Professor, Department of Mechanical Engineering,

Government College of Engineering, Karad, Maharashtra, India

ABSTRACT

In the era of high precision positioning, various mechanisms like piezo based

stages, spring loaded systems and ball screw mechanism have been developed till the

date to fulfil the need of precise scanning applications. Precision position is important

for achieving highly sophisticated manufacturing and measurements. Rigid body

mechanism (spring loaded and ball screw) have large range of motion but operating

at lower speed, positioning accuracy is also low and they suffer with friction and

backlash. Piezo based Nano positioning stages have high speed of operation and high

positioning accuracy but it has smaller scanning range. To overcome these issues,

researchers are favoring flexural mechanisms which exhibit high speed of operation,

large scanning range and a higher degree of positioning accuracy. Flexural

mechanisms offer frictionless, backlash free motion to achieve high degree of

repeatability and precise control. The current article reviews development of flexural

mechanism (both planar and hinge type) by various researchers across the globe. It

presents design aspects, structural aspects and application domains of precision

flexural mechanisms. The current status of the research in designing flexural

mechanisms for high precision applications is also presented. Scope of design and

development of flexural mechanisms for various applications are listed at the end of

the paper.

Keywords: High Precision Positioning, Precise Scanning, Flexural Mechanism,

Frictionless, backlash free motion.

Cite this Article: Sharad Mulik, A. Krishnamoorthy and Suhas Deshmukh, Flexural

Mechanisms for High Precise Scanning Applications: A Review, International Journal

of Mechanical Engineering and Technology, 9(4), 2018, pp. 312–327.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=4

Sharad Mulik, A. Krishnamoorthy and Suhas Deshmukh


1. INTRODUCTION

Precision scanning systems has numerous applications which demands high precision and

repeatability in order to achieve highly sophisticated manufacturing and measurements [1].

The necessity of precision scanning in commercial applications such as scanners used in

biomedical applications, stereo-lithography application for development of prototypes, laser

scanning, micromachining and scanning probe microscopy is gaining interest of researchers

[2]. In the recent years, technological advancements have witnessed fast progression of high

precision Micro-Electro-Mechanical-Systems with significant implications to several

traditional and developing industries like high resolution machining and micro systems

engineering. Hence to achieve precisely guided motion it motivates to model, design and

develop Micro/Nano stages which can be used in widespread applications, such as in various

consumer products [3], aerospace applications [4], precision alignment and actuation

instruments [5-7], scanning probe systems for precision metrology and Nano-manufacturing

[8-11] Nano-shaving and Nano-grafting [12-13], Micro-mirrors [14], Nano-steering systems

[15], multi-stable structures [15-18] and medical devices [18], as Micro/Nano manipulators,

Nanolithography [19], scanning probe systems [20-21], Micro-grippers [7-8], bistable

structures [22-23], energy harvesting devices [24], electrostatic comb drive actuators [25], and

so on.

Positioning accuracy depends on resolution of positioning sensor and precise actuator

which of high cost ultimately increase cost of scanning system. To achieve precision

positioning, various mechanisms are used. Piezo based Nano positioning stages have high

speed of operation and positioning accuracy but it has smaller scanning range. Rigid body

mechanism (spring loaded, ball screw, etc.) suffers with friction and backlash. The roller

bearing, air bearings and magnetic bearings may leads to nonlinear characteristics. Hence

these conventional mechanisms have several constrains such as limited range of scanning,

restricted performance in sense of accuracy, fixed degrees of freedom, reliance of motion on

one another etc. Moreover it is challenging to design a suitable control system and interface it

to endow precise control for desirable working.

To overcome these issues, researchers are favoring flexural mechanisms which offer

frictionless, backlash free motion and exhibit high speed of operation, large scanning range

and a higher degree of positioning accuracy [1,3]. Flexures are nothing but the bending

members which deforms in a particular direction on the application of load [26-27]. Flexures

are more suitable due their distributed flexibility in providing the desired motion in the

required direction along with the advantage of absence of development of assembly, no

wear/tear hence no need of greasing/oiling and exclusion of backlash [26-29]. These

mechanisms typically use high resolution non-contact type sensors such as optical encoders in

feedback loop to achieve high order of precision positioning. Next section provides rigorous

review of flexural mechanisms developed by researchers across the globe particularly for high

precision applications.

2. BASIC BUILDING BLOCKS

Flexures being monolithic structures produce precise guided motion by means of elastic

flexibility and deformation of their constitutive compliant elements which are commonly used

in compact precision positioning systems without nonlinear disturbances such as backlash and

friction present in bearings [30]. This leads to smooth and highly repeatable guided motion,

with zero maintenance and potentially infinite life, which are exclusive features of compliant

mechanisms [1]. Flexural mechanisms are commonly contrived by means of unconventional

machining such as wire Electro-Discharge-Machining (EDM) or water jet machining. For

Nano and Micro-scale applications monolithic construction is necessary but for large range

Flexural Mechanisms for High Precise Scanning Applications: A Review


mechanisms which are significantly big, it turns out to be a costlier process. They offer typical

benefits such as ease of fabrication, cost saving, optimized usage of materials etc. Only a

small number of investigators have recommended assembly of flexure links and apportioned

with the excess of constraining problems challenged for assembly beneficial in designing

more non-monolithic fashioned complex flexure mechanisms [26-28]. Several two axes

planar flexural mechanism exists which facilitates essential precise motion [29-32]. Any

flexure mechanism is composed of various basic building blocks such as cantilever,

parallelogram, double flexure etc. Arrangement of these basic building blocks plays important

role to achieve desired motion and transmission objectives.

2.1. Basic principle of planar flexural mechanism

Design of planar flexural mechanism emphasizes more on reducing some of its limitations

such as high stiffness along degrees of constrains, parasitic errors, vulnerability to

temperature effects and parasitic coupling-actuator cross sensitivity [7, 33-36].

Planar flexural mechanism consists of four rigid stages one is ground or fixed stage, two

are intermediate stages and one is motion stage as shown in figure 1.

Figure 1 Basic Principle of flexural mechanism [26-28]

Motion stage comprises mobility of two with translational motion with reference to fixed

stage. Intermediary stages are required to segregate the two axes motion and seclude the

actuators. Flexural units A, B, C, D have a different stiffness in different axes. Flexural units

A and C have high stiffness in Y-direction and B and D have high stiffness in X-direction.

Intermediate stage 1 befits ultimate position for application of the actuation force in X plane

and stage 2 for actuation force in Y plane. For any deformed configuration, intermediate stage

1 has a pure displacement in X plane whereas intermediate stage 2 has a pure displacement in

Y plane. This fundamental principle is used for designing two axis planar flexural

mechanisms. Further these basic building blocks of flexure mechanisms are discussed and

mechanisms developed using these building blocks are explained with their merits and

demerits as per present application concerned.

2.2. Single Cantilever Beam

When cantilever beam is loaded with end point load it will get deflected. Figure 2 illustrates

the bending of the cantilever beam under point load. Cantilever beam is important building

element in most of the flexural mechanisms. From beam bending analysis, beam tip translates

in Y-direction (δ) as well as rotates (θ) under the point load. A parasitic error exhibits due to

bending in the X plane (€) along with motion in Y plane (δ).



Figure 2 Cantilever beam with end point load [26-28]

Theoretically, deflection, parasitic motion and angular rotation are calculated by,

(2.1)

Where, L is length of the beam, E is Young’s modulus of the material, I is second moment

of the area of the beam cross-section.

The beam flexure is used for modeling of two axes mechanism with units A, B, C and D is

illustrated in Figure 3 (a). An actuation force in X plane yields very small displacement in Y

plane, and vice versa. The application of actuation force in X plane moved in the Y direction

on Intermediate Stage 1. Also, an application of force in Y plane moved the point of appliance

of the force in X plane. Hence, it was not possible to accomplish isolation of actuator. As a

result of the overhanging motion stage small amount of out of plane stiffness was observed.

Hence geometric symmetry was modeled using mirror design about a diagonal axis illustrated

in figure 3 (b).

(a) (b)

Figure 3 Planar flexural mechanism using simple cantilever beam as building block (a) Flexural

Mechanism using simple beam flexure (b) Flexural Mechanism using simple beam flexure [26-28]

As we apply actuation force in X plane, the both sides tend to yield the displacement in Y

direction which opposes each other, and therefore cancel out. Better plane stiffness was

acknowledged due to an upgraded structural loop, given that it was supported from two sides.

But it was observed that the design still underwent from absence of isolation of actuator.

Correspondingly, there were no major enhancements in the parasitic yaw of the motion stage.

Thus, it was concluded that symmetry may assist in relationship of some performance

parameters but does not fetch expansions in others. [26-28]



2.3. Parallelogram Flexure as a building block

Figure 4 shows parallelogram flexural unit. Analytically parallelogram flexure provides small

resistance to Y-direction relative motion however in X direction it offers very rigid motion

and rotation.

[

]

(2.2)

This unit undergoes adverse parasitic error in X-direction with respect to above stated

analytical expression. The two axis planer flexure mechanism with Flexure Units A, B, C and

D is shown in figure 5 (a).

Figure 4 Parallelogram Flexure [26-28]

Nevertheless undesired motions still occurs in spite of better accuracy. The actuation of

displacements with respect to actuation forces is same of earlier case. Hence complete

actuator isolation was not attained in this case also. Out of plane stiffness was also

comparatively low, as the motion stage was supported only from one side. Geometric

symmetry as shown in Figure 5 (b) shows some improvement in performance in terms of

parasitic error. To eliminate the additional rotational constraints arising from the

parallelogram flexures, the motion stage yaw should be more compact in size. On the

application of an X actuation force, the both sides of the mechanism incline to generates

displacements in Y direction that stand each other, and consequently reduce the cross-axis

coupling errors. Out of plane stiffness also progresses owing to better grip. Complete isolation

of actuator is still not attained in this design.

(a) Flexural Mechanism using parallelogram (b) Flexure parallelogram

Figure 5 Planar flexural mechanism using parallelogram flexure as building block [26-28]



2.4. Double Parallelogram Flexure as a building block:

Double parallelogram flexure is usually cited as a compound, folded beam or crab-leg flexure

as shown in figure 6. Analysis of the structure showed that displacement and rotation in X

direction is relatively stiff but it allows relative translational motion in Y direction between A

and B. Length contraction due to beam deformation is absorbed by a secondary motion stage

hence the parasitic error along X direction was observed to be considerably smaller. The

rotational parasitic motions may be eliminated by Y direction force in suitable location.

Hence, body A generates translation motion in Y direction with respect to body B on the

application of force in Y direction. This is true only in the absence of X direction forces. The

double parallelogram structure used to construct XY mechanisms as shown in figure 6. In

these cases, cross axis coupling and motion stage yaw is small and actuator isolation is also

being better than previous designs.

[

]

(2.3)

Double parallelogram flexure is more close to the ideal one as compared to other flexural

units. Analytical equation shows that it has zero parasitic error motion. Hence double

parallelogram flexural unit can be used for precise positioning for XY scanning system.

Figure 7 illustrates the planar flexural mechanism using double parallelogram flexural unit.

Hence it is the best suitable for opto-mechanical scanning system in micro-stereo-lithography.

Figure 6 Double parallelogram flexural unit [26-28]

(a) (b) (c)

Figure 7 Planar flexural mechanism using double flexure as building block [26-28]

Design of flexural mechanism is based on basic beam bending equations. Various flexural

elements are used for XY Mechanism and presented here. The review shows clearly that

double parallelogram flexure has zero parasitic error motion and small amount of rotation of

stage. Appropriate placement of actuator can eliminated rotation of stage. XY Flexural

mechanism is further designed using double parallelogram flexure and shown in figure 7.



Here two or four double parallelogram flexures are used for one direction and these flexures

work as spring in parallel.

3. OVERVIEW OF DESIGN AND STRUCTURAL ASPECTS

FLEXURAL MECHANISMS

Assumed the comprehensive benefits of flexural mechanisms, it persist a generous area of

design considerations. However flexural mechanism design has been commonly established

on artistic interpretation and technical insight; analytical software can support in design

development, assessment and optimization method. Flexure based mechanisms can be driven

by piezoelectric actuators which are used in ultra-precision positioning, e.g. atomic force

Microscopes (AFM), scanning probe Microscope (SPM), laser-based confocal Microscope,

by utilizing their inverse piezoelectric effect [37-39]. For a small output motion range, a

piezoelectric actuator can be directly used to achieve the output displacements. One such

study is carried out regarding flexure design using low stiffness actuators such as Lorentz

actuators [40]. Here, leaf spring flexures were selected to realize a low stiffness. The

advantage of this method is to maximize second resonance frequency with respect to first

resonance frequency which enables to a high control band width. A positioning system is

illustrated in figure 8. Lorentz actuators are used to generate the force Fz for the actuation in

Z plane. Due to utilization the Lorentz force, these actuators have no mechanical stiffness

between the moving mass and the fixed frame [43], which result into a low-stiffness actuator.

The positioning system was modeled with single leaf spring flexures as shown in figure 9 to

derive first resonance frequency and multiple leaf-spring flexures was modeled as shown in

figure 2.3 to derive the high resonant frequencies.

Figure 8 illustration of

positioning system [40]

Figure 9 Model of a single leaf-

spring flexure to derive first

resonant frequency of positioning

system. [40]

Figure 10 Model of multiple leaf-

spring flexures to derive the high

resonant frequencies [40]

The flexure-based mechanism can also be integrated with the voice coil motor (VCM) for

actuation purpose. A similar attempt is made for design of nanometer level resolution and

millimeter level operational ranged high accuracy XY-scanner [41-43]. The XY-scanner is

actuated with the integration of double compound linear spring flexure guide mechanism with

voice coil motor [44]. Leaf spring mechanisms having minor widths were used for escalation

of the working range of XY scanner to the millimeter level. It was designed to enhance the

first resonant frequency of the XY scanner to raise the response speed. The XY scanner has

position resolution of 10 nm and working range of 2 mm. The scanner comprises of a double

compound linear spring flexure guide mechanisms and a voice coil motor (VCM) to fulfill

travel range specifications & accuracy and to reduce parasitic motion during scanning. Due to

symmetric structure of double compound linear spring mechanism shown in figure 11 (a), it is

free from parasitic motions and free from effects of heat deformation. The conceptual design

of one axis scanning using the double compound linear spring mechanism integrated with a

voice coil motor is illustrated in figure 11 (b). [44]



Figure 11 Schematic of scanner: (a) leaf spring based double compound linear spring guide

mechanism; and (b) guide mechanism combined with VCM [44].

A modular mechanism design consists of monolithic 1 degree of freedom flexure

mechanism as shown in figure 12 (a). The separate modules can be integrated in sequence to

develop multiple degrees of freedom mechanism. Each of this module is driven by symmetric

kinematic arms and piezoelectric actuators. The input and output faces of each module

includes mounting holes in it which permits it to couple together in several configurations of

each arm consisting of two flexures. The experimental 2-DOF (XY) manipulator was

developed as shown in figure 12 (b). A webbed mounting bracket was designed and analyzed

to limit coupling between X and Y modules. Further the system is controlled through a tele-

operated haptic control scheme by coupling the master to the slave device. A scaled forced

pollution controller and a passivity controller were utilized to attain transparency and stability

of the controller. It provides significant design flexibility of flexure mechanism increasing

range of motion and allowing DOF. Haptic tele-operation control scheme enables in natural

performance of manipulation task [45]

(a) Planar view of 1-DOF module (b) Conceptual 2-DOF system design

Figure 12 Modular mechanism design features. [45]

A similar study on assembling of flexural mechanism is presented here [46]. The problem

is proposed to have mobility to be exactly zero while determining the number of dowel pins.

While defining a new concept called “half joint”, two additional rules are needed to be

introduced as proposed. This design of novel manipulator facilitates coupled mechanism to

meet task specific requirements. It provides significant design flexibility of flexure

mechanism increasing range of motion and allowing DOF. Haptic tele-operation control

scheme enables in natural performance of manipulation task. The system can be expanded

into DOFs through the coupling of additional stages and for this future work is intended to

investigate enhanced transparency and stability. According to Grubler’s criteria required

number of locating pins and their locations has been determined [46].



Researchers have also been concentrating on designing compact flexural mechanisms,

wherein monolithic and parallel manipulators are area of interest of many researches. Along

with the compacting of mechanism the errors encountered in flexural motion need also to be

reduced. One such research is carried out on a 2-legged XY parallel flexure motion stage with

minimised parasitic rotation shown in figure 13 (a) [47]. A XY compliant parallel manipulator

(CPM) has been proposed using the stiffness center based approach. This innovative design

approach makes all of the stiffness centers, associated with the passive prismatic (P) modules.

The proposed XY CPM has a millimeter-level motion range of 4 mm per direction and can

well deal with the issue of actuator isolation. In comparison with the emerging monolithic XY

CPMs obtained from the configuration of 4-PP kinematically decoupled translational parallel

manipulator (TPM) as shown in figure 13 (b), the present XY CPM mainly has a smaller size,

simpler modelling as well as smaller lost motion due to the use of only two legs. The study

takes into consideration 3-legged XY CPM (see figure 14) and two legged stacked CPM with

reduced size [47].

Figure 13 XY parallel manipulators: (a) 4-PP (Prismatic) kinematically decoupled TPM; (b) 2-PP

kinematically decoupled Translational parallel manipulator (TPM) [47]

Figure 14 A 3-legged XY CPM with minimised parasitic rotation [47]

Figure 15 Two-legged stacked XY CPM design I using basic parallelogram module as passive P joint [47].



Figure 16 Two-legged stacked XY CPM design II using double parallelogram module as passive P

joint [47].

Compared with the existing design of XY compliant parallel manipulators which are

obtained by using 4-legged mirror-symmetric constraint arrangement, the proposed design of

XY compliant parallel manipulators based on stiffness centre approach largely benefits from

fewer legs resulting in reduced size, simpler modeling as well as smaller lost motion.

Comparing with the existing 2-legged designs with the conventional arrangement, the

presented design has minor parasitic rotation is shown in figure 15 and 16, which has been

proved from the finite element analysis results [47].

One study is regarding a two-dimensional parallel Piezoelectric-actuator -driven Nano

positioner with a novel mechatronic structure of a large workspace and a high-natural

frequency. The parallel kinematic XY flexural mechanism provides good geometric

segregation. The proposed design has a large work space and high bandwidth which is

verified by FEA. The analysis shows that Nano positioner has a large workspace more than

200 μm and a high-natural frequency of 760 Hz. Furthermore, the dynamic model of the Nano

positioner, including the dynamics of the PZT actuators, is also generated from the

perspective of transfer functions and the parameters are identified by frequency-response

analysis, which can be used for Nano precision servo mechanism [48-49].

4. OVERVIEW OF CURRENT INVESTIGATIONS

A current requirement of precision scanning application is to design and develop a low cost

flexural mechanism and control system with high precision positioning accuracy. Researchers

across the world addressed the problem with monolithic design of flexural mechanisms and

used a high resolution position sensor such as optical encoders or piezo based position

sensors. These sensors are further used as feedback element for precision scanning. Flexural

mechanism has an advantage of zero backlashes, high order of repeatability and frictionless

operation is achieved by using a non-contact type actuator such as voice coil actuator. All

precision scanning mechanisms use high resolution sensor in feedback control system. Sensor

resolution plays a very important role to achieve high precision scanning. Optical sensors are

most commonly used in feedback loop and needs high degree of alignment and manufacturing

accuracy. Small misalignment leads to erratic variations in scanning system. Cost of the

sensor is also one of the important issues that need to be addressed carefully during mass

manufacturing. It is clear from the above discussion that accuracy of positioning needs a

feedback and following are the main disadvantages of feedback sensors in precision scanning

applications: 1. Mounting/alignment of the sensors into flexural mechanism is major problem.

2. Costly sensors are used in feedback and overall cost of the mechanism becomes high. XY

flexural mechanisms developed till date have following major limitations like:

Range of scanning is limited.

Positioning Resolution is limited due to type of sensor in feedback loop.



Mostly monolithic design and it complicate mounting of actuator and sensors for

scanning operations.

To achieve high resolution non-contact type optical encoders are to be used.

In case of flexural mechanism movement of the motion stage is mostly predictable and

predetermined. These mechanisms have linear characteristics within operational range and it

is very much possible to develop a model which predicts the behavior of such mechanisms.

Most of the flexural mechanisms use various actuators such as piezo, voice coil motors etc.

piezo type actuators offers high precision but has very low range of the motion and becomes

difficult to apply for large scanning applications. Whereas, Voice coil Actuator (VCM) can be

in the range of millimeters and also offers better precision and control of the position which

entirely depends on type of the driver used for control of the position. Till date VCM is used

for scanning purpose only, and none of the researchers have used VCM as sensor as well as

actuator simultaneously.

XY Flexural mechanisms developed by various researchers are based on flexibility of

structures to achieve the desired motion. Precision positioning is achieved in XY flexural

mechanism is possible using feedback control system which typically uses high resolution

position sensors (optical encoder, piezo sensors) and further needs contact-less actuation (e.g.

voice coil motor) to avoid friction during motion. Voice coil Actuator (VCA) generates a

force which can further be applied on to motion stage of the mechanism. It is further observed

that VCM has linear characteristics (force is directly proportional to current in the Voice Coil

Motor (VCM)) over the scanning range. This clearly shows that monitoring the current

supplied to VCM will help to exactly estimate the force generated by VCM. VCM is further

connected to Flexural stage which generates motion by application of the force. All flexural

mechanisms work in elastic range and have linear characteristics. Ultimately monitoring the

current drawn by VCM will estimate the position of the motion stage itself. This quality of

VCM (which work as actuator as well as sensor) provides us idea of position sensing by

monitoring a current and voltage drawn by VCM during motion. Here, VCM work as actuator

as well as sensor and in actual practice we need not to use a separate sensor for feedback in

precision positioning applications. Entire research work is planned to develop a position

estimator algorithm, validation of position estimator and real time implementation of position

estimator algorithm on flexural motion stage. Further, the demonstration of sensor-less

operation of flexural motion stage and its precision positioning at high speed of scanning is

presented [50]

Recently, a novel position estimator algorithm was designed by researchers for voice coil

motor actuators which will work as precision sensor instead of actual high cost, high

resolution non-contact type sensors. Further, it eliminates the use of actual sensor in feedback

loop and offers more flexibility and simplicity in design and development XY planar flexural

mechanism for precision scanning with low cost of complete system. The proposed position

estimator algorithm for VCM and XY scanning mechanism estimates position of motion stage

by measurement of current and voltage across actuator (voice coil motor) in position estimator

algorithm. Proposed work is to demonstrate high precision scanning of XY flexural

mechanism with and without position estimator (i.e stroke estimator) via due theoretical and

experimental investigations [51-54]

Another invention related to design and fabrication voice coil motor for high precision

applications is also proposed. It is integrated with dSPACE DS1104 R&D controller. PID

Control algorithm is developed in MATLAB Simulink and it is applied on the voice coil

motor. Static characteristic such as stiffness was found to be around 8.2 N/mm and dynamic

characteristics like damping factor and frequency response are found to be 0.06381 and

0.0102 respectively. PID parameters are tuned using Ziegler Nichols tuning method.



Accuracy of less than 5 μm is achieved at low speeds and amplitude of 500μm. Further as we

increase the amplitude and frequency of operation, error increases at it is a progressive error.

State space model was prepared for the VCM and its response was compared with

experimental results via implementation of LQR control. Voice coil motor involves smooth

and frictionless motion that can be further applied to laser scanner and precise positioning

stages for different applications like Atomic Force Microscopy, Stereo lithography and so on

[53-56]

The double flexural mechanism is developed by one of the researchers and it incorporated

to dSPACE DS11004 R&D controller. The characterization of DFM is carried out on the

basis of two distinct fields - (1) Static analysis is executed for finding out force deflection

attributes for the range of entire displacement and (2) Dynamic analysis is accomplished using

frequency response which gives characteristics of system with different frequency inputs.

This frequency response is further utilized to accomplish experimental modelling of DFM.

Empirical model of with the help of frequency response is found out using constrained

minimization approach. Evaluated empirical model is further used for PID control algorithm

implementation. PID control attributes (i.e. proportional gain, integral gain and derivative

gain) are adjusted using Ziegler Nichols approach. Empirical model at the outset was

examined and accuracy of lower than 1 micron was attained. PID algorithm was applied using

dSPACE DS1104 R and D controller and Control Desk GUI environment. Actual positioning

accuracy of lower than 2 microns is accomplished. PID control exhibited good disturbance

rejection and the least amount of error when being used for tracking at different frequencies.

LQR control could only be used for regulation purpose whereas LQI control attained good

disturbance rejection during regulation. To improve tracking, use of feed forward control with

LQI and with other control strategies and implement is suggested [52-60]

The XY mechanism that utilizes fundamental building elements such as beam of

cantilever structure, double parallelogram and parallelogram flexural structures with respect

to their execution aspects like parasitic error and stiffness was proposed. Distinguishing

amongst bi-flex mechanisms is done in view of various parameters like stiffness, parasitic

flaw and angular movement of deformation stage. Theoretical and finite element analysis is

done for this and it is noted that double parallelogram flexure gives great execution results

with respect to other flexural building structures. XY flexural system utilizing double flexural

mechanism (DFM) is further fabricated and test experiments are implemented. Experimental,

FEA and theoretical results show acceptable degree of accuracy. Load in weight pane

(maximum 35 N) is given such that maximum of 7.5 mm displacement is achieved. Maximum

displacement of 25 mm was observed and some variations were seen due to surface distortion

and flaws. Therefore, it is noted that there is no parasitic error takes place in Y-axis when

motion stage is moving in X-axis [53-56]

One research was carried on design, analysis and modeling of XY flexure mechanism

which is based on double parallelogram flexure (DFM). The XY flexural mechanism for

displacement developed using double parallelogram flexure module. The theoretical results

are verified using FEA results. The force-deflection curve found to be linear. The slope of this

curve shows stiffness which is constant. It is observed that error between FEA and theoretical

results is less than 3%. Mechanism has stiffness of 4.8986 N/mm. The mechanism has range

of ± 5 mm for a force of 25 N. The design parameters are optimized by using parametric

analysis. Mechanism presented in this paper can be used in various precision applications

such as atomic force microscope (AFM), laser cutting, laser surgery and scanning probe

microscope [55].

Six types of flexural joints in terms of stiffness, stress, deflection for the influence of

geometric parameters on the performance of hinges were evaluated in one of the



investigation. Further the operating range of each joint is stated within the considered

parametric range in hinge length and minimum hinge thickness. Guiding accuracies defining

the accuracy of motion are also derived. A catalog of design charts based on the parametric

modeling using FEA tool ANSYS® Workbench™ 14.5, characterizing the joints are

presented, allowing for rapid sizing of the joints for custom performance. XY planar scanning

mechanism employing elliptical flexure is designed to have a long travel range up to 5 mm in

both X- and Y-directions, while having a size of 300mm × 300mm × 3 mm. In the proposed

stage system, the stage would be driven by PZT (Piezo-Electric Amplifier) at amplifier legs

considering the driving force in the range of 20 to 35 N. The experimental measurements

validate the large travel range of the mechanism. Errors in motion direction displacement and

off axis displacement are near to 11 % and 15 % respectively. Analysis of flexural joints

providing actual numbers would require some normalization of parameters and is an interest

to be considered in future research. Ongoing work includes dynamic analysis to determine

natural frequency and mode shapes of the XY planar scanning mechanism was presented [61]

5. CONCLUSION

The current article reviews development of flexural mechanism (both planar and hinge type)

by various researchers across the globe. It presents design aspects, structural aspects and

application domains of precision flexural mechanisms. Precision position is important for

achieving highly sophisticated manufacturing and measurements. These precision positioning

systems generate precisely guided motion. To fulfil the need of precise scanning applications

various mechanisms like piezo based stages, spring loaded systems and ball screw mechanism

have been developed till the date. To overcome limitations of traditional mechanisms,

researchers are favoring flexural mechanisms which exhibit high speed of operation, large

scanning range and a higher degree of positioning accuracy. Flexural mechanisms offer

frictionless, backlash free motion to achieve high degree of repeatability and precise control.

The current status of the research in designing flexural mechanisms for high precision

applications is presented in the paper. From the rigorous literature review, authors have

proposed a novel position estimator algorithm for voice coil motor actuators which will work

as precision sensor instead of actual high cost, high resolution non-contact type sensors. This

eliminates the use of actual sensor in feedback loop and offers more flexibility and simplicity

in design and development XY planar flexural mechanism for precision scanning with low

cost of complete system. Scope of design and development of flexural mechanisms for

various applications are also conserved in the paper.

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