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10/7/2012




                       By
              Sakthivel.R (09MI08)
     PSG College of Technology Coimbatore.
                              ,

              Under the guidance of
     Dr. P. Radhakrishnan, Director, PSG IAS.

             And Co – Guided by
           Mrs. Bindu Salim, PSG IAS


                                                Courtesy: [1]




• Ability to attach or get clanged to inclined
  surfaces or elevated positions.


• To develop appropriate perching devices for
  Robots to perch on rough and glazed surfaces



• Small aircraft model robot can perch on vertical
  surfaces using simple mechanical and suction-
  based gripping systems.




                                                                       1
10/7/2012




•   Direct contact
•   Data on current condition
•   Bring samples
•   Accurate information
•   Automatic inspection and repair
•   Ride out bad weather
•   Preserve their energy
•   Interchangeability of technology
•   Watch out for the target




                 [3]




                [5]



                                       [4]




                                                    2
10/7/2012




The basic sequence of action through which the robot shall perch the vertical
surface shall be inspired from the perching action of birds.




 identifying      the slowing down itself striking the surface with Perching on the
 surface     in   the when on the path the help of spine            surface
 mode of flight       of perch


 (Courtesy : Lillian Stakes 2008; [2])




possible velocities and orientations

                             mecha nical properties of the s uspension

• action of impact over a sudden period of time
• for rough surfaces the mechanical strengths of
  the spine and asperity become the factors
• for smoother surfaces friction is more
  important and the ability to pull in toward the
  surface is much reduced




                                                                                             3
10/7/2012




• Arrays of small spines.
• Supported by a nonlinear suspension




• No power for clinging
• Relatively unaffected by films of dirt
  and moisture
• Support large loads
                                           [4]




                                                        4
10/7/2012




                   •   Spine tip radius
                   •   Distribution of asperities
                   •   Average asperity size
                   •   Surface roughness properties
                   •   Narrowness and slant of peaks and valleys
                   •   Number of spines per foot




              Normal Force
                                                                         SMD1
Tangential Force




                                         Spine



                                                                  SMD2


                   Spine Loading Cycle                     SMD3




                                                                                       5
10/7/2012




kinematic study.wmv




                             6
10/7/2012




       7
10/7/2012




• Spring Steel High Carbon
  of Indian Standard IS
  4454 Part I Grade 3
• Cutting a spring steel
  blank of 1mm diameter
• Grinding one edge
• Bent to the required
  radius at the top and tip
• Bent at the bottom




                         •Extruded acrylic sheet
                         •Laser cutting process
                         •5mm thick sheets
                         •Central sheet sawed
                          and cut for the invert
                          shape of the spine
                         •Holes using manual
                          drilling machine
                         •Load limiting pin was
                          glued.




                                                          8
10/7/2012




       9
10/7/2012




    Ty pe 1                    Ty pe 2                  Ty pe 3




•Type 1: the top was bent for 4 mm inclined to an angle of
45°and spine tip wasbent with a radiusof 1mm.
•Type 2: the top was bent for 4 mm inclined to an angle of
45°and spine tip wasnot bent.
•Type 3: the top was bent for 4 mm inclined to an angle of
50°and spine tip wasnot bent.

•Inference: Type 1 was more smooth due to the tip bent
and type 3 slipped off often due to steep top bent.




 Part                                                Amount (INR)

 Micro Spine                                                  10.00
 Spring Unit (one compression and
                                                              15.00
 two tensile springs)
 Fastening Rods and Load Limiting Pin                         10.00
 Spine holder, Side plates, Revolving
                                                             250.00
 joint and assembling
 Total                                                       285.00




                                                                            10
10/7/2012




• Shape change when stimulated by electric field
• When voltage applied, they contract in width
  due to electrostatic forces and become longer



• Perfluorinated ionic polymers sandwiched
between thin noble metal electrodes
• Selectively pass ions inside the polymer network
• Embedded distributed circulatory system




                                                           11
10/7/2012




BASE MATERIALS [6]




                           12
10/7/2012




•   Si l ver Oxi de Formation
•   Uni form Coat of Electrode
•   Surfa ce Roughening and Stretching
•   Annealing
•   Dehydration




               The chemical constituent solutions used in reference to the bottle numbers.
         II – Sodium Hydroxide, III – Millipore Water, IV – Chromic Acid, V – Ammonia Solution,
                     VI – Silv er Nitrate Solution, VII – Sodium Borohydrate Solution




                                                                                                        13
10/7/2012




• Pre-Treatment of Membrane
• Silver – Amine Complex Solution is prepared by using 30mg
  of silver nitrate in 10ml water and 1 ml of NH4 OH (1ml
  ammonia in 10ml of water).
• Rinsed Nafion® substrate was put into the prepared silver –
                  ®
  amine complex solution and kept immersed for 10 minutes.
  No colour change was observed in the membrane.
• The Strip is then rinsed, wiped and then immersed in
  Sodium Borohydrate solution (30mg of NaBH4 in 20ml of
  water) for 10 minutes.
• The silver deposition was identified from the appearance of
  bright silver colour on the substrate.




• Solution of Sodium Hydroxide (10 pellets of NaOH
  in 20ml of water) for 30 min and rinsed with water
• Dipped and taken at once in dilute chromic acid



• A substrate of Nafion® is dipped in a beaker
                       ®
  containing water and kept in ultrasonic cleaner
  for 10 minutes.




                                                                      14
10/7/2012




• The Membrane was dipped in Chromic Acid
  Solution for 20 minutes.
• The Membrane is then rinsed with water and
  wiped.


• A substrate of Nafion® was cleaned in a solution of
  water and wiped using tissue paper.
• The water used in the entire process of Silver
  coating over Nafion Membrane is de-ionized
  millipore water.




 Method 1


                                    Method 2




 Method 3




                                                              15
10/7/2012




Method 4




                 16
10/7/2012




• Contact wire soldered to
  nylon fixture.
• DC supply - 1 to 3 volts.
• AC supply - square wave
  of 1.5Vpp of 0.1Hz
  frequency.
• 5 mm of the 30mm length
  IPMC was kept inside the
  fixture.
• The IPMC was hydrated
  for 50 minutes.




                              • Responsive in the range
                                of 1 to 3 volts
                              • Response time - 2 to 3
                                seconds
                              • Step response
                              • Slow initial response due
                                to threshold limit of
   IPMC.DC.wmv                  energy




                                                                  17
10/7/2012




• Responsive in 2.5 to 3.5 volts
• Responded for 5 to 6 cycle times
• Degrading response for every
  cycle time
• No response change after
  3.5 volts.
• Back relaxation
• IPMC remained in its actuated position
                                           IPMC AC voltage.wmv




 • There was significant actuation response from
   the IPMC.
 • There was actuation response for both AC and
   DC voltages. Back relaxation was found clearly
   on application of AC voltage.
 • The IPMC was effectively responding only for
   the first actuation after every hydration.




                                                                       18
10/7/2012




                 Fig. 2. Bending Response of Venus Flytrap [12].


• The i ono-elastic tri gger hairs generates an action potential
• This move hydrogen ions into thei r cell walls, lowering the pH
a nd l oosening the extracellular components.
• Osmotic effect - K+ is released into the leaf tissues and makes
the cel ls on one surface of the leaves swell.




                                                                          19
10/7/2012




                       NEED FOR EFFICIENT ENERGY CONVERSION
DEMAND FOR ENERGY
                       DEVICE
                       USE OF DIRECT ENERGY CONVERSION
                       DEVICES

• Limitations of Vacuum Pump
   – Working area
   – Weight
   – Pressure drop
   – Usage of a pump




                                                                    20
10/7/2012




IPMC - proposed.avi




                            21
10/7/2012




     Development of IPMC model
• from membrane theory [9]
  The forces a cting on the displaced membrane, restoring
  forces and the dynamic equation governing the vi brating
  membrane a re given by
                                           F r is f orce in r-η plane
                                           F Ө is f orce in Ө-η plane
                                           P is the tension f orce
                                           σ is the mass per unit
                                           area of the membrane
                                           material




                                                                              22
10/7/2012




     Development of IPMC model
• from lipid bilayers [10]
  The converse flexoelectric effect describes the generation of
  curva tures induced by a pplied electric fields and the
  equilibrium radius of the tether as




   IPMC ANALYSIS CASE STUDY [11]




                                                                        23
10/7/2012




    Material Properties




                        orthotropic relativ e permittivity 0.031

density : 2975 kg/m 3




                                                           [12]




                                    dielectric constant of 0.00032 and
                                    corresponding ANEL Matrix




                                                                               24
10/7/2012




DEVELOPMENT OF IPMC MODEL FOR
    CIRCULAR CONFIGURATION

                                            Diameter = 40mm
                                            Thickness = 0.3mm




                    Results

                        Displacement = 14.436mm




• The maximal tip displacement can nearly reach radius
• create a cup shape.




                                                                      25
10/7/2012




 • No s i gnificant response.
 • Li ttl e a ctuation response - bending force created not enough
   to overcome the constrained provi ded by the hollow plate.




• Significant actuation
• Did not form cup shape
• Bend about an axis along the diameter determined by initial
  curvature of the membrane
• The IPMC was effectively responding for three actuations      MOV06819.AVI




                                                                                     26
10/7/2012




 • Cup shape by using two cantilever IPMC kept
   crossed to each other.
 • Suction creation using the setup.
 • Integration of micro spine and IPMC assembly
   to the robot
 • Gripping force to be generated to resist wind
 • Ways to detect failing of the grip is failing and
   recovery before the plane falls




1. Analysis And Development Of Technology For Perching Mechanism For Flying
   Robots for “National Seminar On Recent Adv ances In PIE And Remote
   Technologies For Nuclear Fuel Cycle (RAPT 2010)” on September 23-24, 2010
   at SRI Conv ention Centre, Anupuram, Kalpakkam.
2. Develop ment Of Technology For Perching Robots Using Ionic Polymer Metal
   Co mposite f or “The First National Conf erence On Energy Efficient Mechanical
   System Design And Manuf acturing” on 11th-12th March, 2011 at Department Of
   Mechanical Engineering, PSG College of Technology, Coimbatore
3. Develop ment Of Micro Spine Technology For Perching Robots, f or “The First
   National Conf erence on emerging Trends in CAD, Cam, CIM”, Department Of
   Mechanical Engineering” on 29th April 2011 at Department Of Mechanical
   Engineering, PSG College Of Technology, Coimbatore.
4. Develop ment And Performance Of Circular Shaped Ionic Polymer Metal
   Co mposite f or “National Conf erence on Design and Manuf acturing 2011” on
   27th – 28th May 2011 at IIT Madras Campus, Chennai. Also published in
   “International journal of Applied Engineering Research” Volume 6, No.5.




                                                                                          27
10/7/2012




[1] Mark R. Cutkosky and Alexis Lussier Desbiens: Bio-Inspired Perching and Crawling Air Vehicles: Biomimetics and
     Dextrous Manipulation Laboratory: October 2, 2008.
[2] Alexis Lussier Desbiens, Alan T Asbeck, and Mark R. Cutkosky: Scansorial Landing and Perching: Biomimetic and
                                   .
     Dextrous Manipulation Laboratory.
[3] Mirko Kovac, Jurg Germann, Christoph Hurzeler Roland Y Siegwart, Dario Floreano: A Perching Mechanism for
                                                       ,         .
     Micro Aerial Vehicles.
[4] M. J. Spenko et. al., : Biologically Inspired Climbing with a Hexapedal Robot : Journal of Field Robotics 25(4–5),
     223–242 (2008) C 2008 Wiley Periodicals, Inc.Published online in Wiley InterScience
     (www.interscience.wiley.com). DOI: 10.1002/rob.20238
[5] Robert T Pack, Joe L. Christopher Jr and Kazuhiko Kawamura: A Rubbertuator-Based Structure-Climbing Inspection
             .                             .
     Robot.
[6] Mohsen Shahinpoor et al.: Artificial Muscles – Applications of Advanced Polymeric Nanocomposites: T       aylor and
     Francis Group
[7] Keisuke Oguro: preparation procedure - ion-exchange polymer metal composites (IPMC) membranes.
     http://ndeaa.jpl.nasa.gov/nasa-nde/lommas/eap/IPMC_PrepProcedure.htm
[8]M. Shahinpoor et al.: Ionic Polymer-Metal Composites (IPMC) as Biomimetic Sensors and Actuators - Artificial
                   ,
     Muscles: Proceedings of SPIE's 5th Annual International Symposium on Smart Structures and Materials, 1-5
     March, 1998, San Diego, CA. Paper No. 3324-27.
[9] Eric J. Ruggiero: Modeling and Control of SPIDER Satellite Components: Virginia T   ech's ETD.
[10]Ben Harland: Voltage-induced bending and electromechanical coupling in lipid bilayers: The American Physical
     Society ©2010: 1539-3755/2010/81(3)/031907(9).
[11] Hanmin PENG, Yao HUI, Qingjun DING, Huafeng LI, Chunsheng ZHAO : IPMC gripper static analysis based on finite
     element analysis : Front. Mech. Eng. China 2010, 5(2): 204–211 - DOI 10.1007/s11465-010-0005-1.
[12] W.A.Lughmani: Modeling of bending behavior of IPMC beams using Concentrated Ion Boundary layer:
     International Journal of Precision Engineering & Manufacturing Vol.10, No. 5, pp. 131-139.




                                                                                                                                28

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Perching Robot

  • 1. 10/7/2012 By Sakthivel.R (09MI08) PSG College of Technology Coimbatore. , Under the guidance of Dr. P. Radhakrishnan, Director, PSG IAS. And Co – Guided by Mrs. Bindu Salim, PSG IAS Courtesy: [1] • Ability to attach or get clanged to inclined surfaces or elevated positions. • To develop appropriate perching devices for Robots to perch on rough and glazed surfaces • Small aircraft model robot can perch on vertical surfaces using simple mechanical and suction- based gripping systems. 1
  • 2. 10/7/2012 • Direct contact • Data on current condition • Bring samples • Accurate information • Automatic inspection and repair • Ride out bad weather • Preserve their energy • Interchangeability of technology • Watch out for the target [3] [5] [4] 2
  • 3. 10/7/2012 The basic sequence of action through which the robot shall perch the vertical surface shall be inspired from the perching action of birds. identifying the slowing down itself striking the surface with Perching on the surface in the when on the path the help of spine surface mode of flight of perch (Courtesy : Lillian Stakes 2008; [2]) possible velocities and orientations mecha nical properties of the s uspension • action of impact over a sudden period of time • for rough surfaces the mechanical strengths of the spine and asperity become the factors • for smoother surfaces friction is more important and the ability to pull in toward the surface is much reduced 3
  • 4. 10/7/2012 • Arrays of small spines. • Supported by a nonlinear suspension • No power for clinging • Relatively unaffected by films of dirt and moisture • Support large loads [4] 4
  • 5. 10/7/2012 • Spine tip radius • Distribution of asperities • Average asperity size • Surface roughness properties • Narrowness and slant of peaks and valleys • Number of spines per foot Normal Force SMD1 Tangential Force Spine SMD2 Spine Loading Cycle SMD3 5
  • 8. 10/7/2012 • Spring Steel High Carbon of Indian Standard IS 4454 Part I Grade 3 • Cutting a spring steel blank of 1mm diameter • Grinding one edge • Bent to the required radius at the top and tip • Bent at the bottom •Extruded acrylic sheet •Laser cutting process •5mm thick sheets •Central sheet sawed and cut for the invert shape of the spine •Holes using manual drilling machine •Load limiting pin was glued. 8
  • 10. 10/7/2012 Ty pe 1 Ty pe 2 Ty pe 3 •Type 1: the top was bent for 4 mm inclined to an angle of 45°and spine tip wasbent with a radiusof 1mm. •Type 2: the top was bent for 4 mm inclined to an angle of 45°and spine tip wasnot bent. •Type 3: the top was bent for 4 mm inclined to an angle of 50°and spine tip wasnot bent. •Inference: Type 1 was more smooth due to the tip bent and type 3 slipped off often due to steep top bent. Part Amount (INR) Micro Spine 10.00 Spring Unit (one compression and 15.00 two tensile springs) Fastening Rods and Load Limiting Pin 10.00 Spine holder, Side plates, Revolving 250.00 joint and assembling Total 285.00 10
  • 11. 10/7/2012 • Shape change when stimulated by electric field • When voltage applied, they contract in width due to electrostatic forces and become longer • Perfluorinated ionic polymers sandwiched between thin noble metal electrodes • Selectively pass ions inside the polymer network • Embedded distributed circulatory system 11
  • 13. 10/7/2012 • Si l ver Oxi de Formation • Uni form Coat of Electrode • Surfa ce Roughening and Stretching • Annealing • Dehydration The chemical constituent solutions used in reference to the bottle numbers. II – Sodium Hydroxide, III – Millipore Water, IV – Chromic Acid, V – Ammonia Solution, VI – Silv er Nitrate Solution, VII – Sodium Borohydrate Solution 13
  • 14. 10/7/2012 • Pre-Treatment of Membrane • Silver – Amine Complex Solution is prepared by using 30mg of silver nitrate in 10ml water and 1 ml of NH4 OH (1ml ammonia in 10ml of water). • Rinsed Nafion® substrate was put into the prepared silver – ® amine complex solution and kept immersed for 10 minutes. No colour change was observed in the membrane. • The Strip is then rinsed, wiped and then immersed in Sodium Borohydrate solution (30mg of NaBH4 in 20ml of water) for 10 minutes. • The silver deposition was identified from the appearance of bright silver colour on the substrate. • Solution of Sodium Hydroxide (10 pellets of NaOH in 20ml of water) for 30 min and rinsed with water • Dipped and taken at once in dilute chromic acid • A substrate of Nafion® is dipped in a beaker ® containing water and kept in ultrasonic cleaner for 10 minutes. 14
  • 15. 10/7/2012 • The Membrane was dipped in Chromic Acid Solution for 20 minutes. • The Membrane is then rinsed with water and wiped. • A substrate of Nafion® was cleaned in a solution of water and wiped using tissue paper. • The water used in the entire process of Silver coating over Nafion Membrane is de-ionized millipore water. Method 1 Method 2 Method 3 15
  • 17. 10/7/2012 • Contact wire soldered to nylon fixture. • DC supply - 1 to 3 volts. • AC supply - square wave of 1.5Vpp of 0.1Hz frequency. • 5 mm of the 30mm length IPMC was kept inside the fixture. • The IPMC was hydrated for 50 minutes. • Responsive in the range of 1 to 3 volts • Response time - 2 to 3 seconds • Step response • Slow initial response due to threshold limit of IPMC.DC.wmv energy 17
  • 18. 10/7/2012 • Responsive in 2.5 to 3.5 volts • Responded for 5 to 6 cycle times • Degrading response for every cycle time • No response change after 3.5 volts. • Back relaxation • IPMC remained in its actuated position IPMC AC voltage.wmv • There was significant actuation response from the IPMC. • There was actuation response for both AC and DC voltages. Back relaxation was found clearly on application of AC voltage. • The IPMC was effectively responding only for the first actuation after every hydration. 18
  • 19. 10/7/2012 Fig. 2. Bending Response of Venus Flytrap [12]. • The i ono-elastic tri gger hairs generates an action potential • This move hydrogen ions into thei r cell walls, lowering the pH a nd l oosening the extracellular components. • Osmotic effect - K+ is released into the leaf tissues and makes the cel ls on one surface of the leaves swell. 19
  • 20. 10/7/2012 NEED FOR EFFICIENT ENERGY CONVERSION DEMAND FOR ENERGY DEVICE USE OF DIRECT ENERGY CONVERSION DEVICES • Limitations of Vacuum Pump – Working area – Weight – Pressure drop – Usage of a pump 20
  • 22. 10/7/2012 Development of IPMC model • from membrane theory [9] The forces a cting on the displaced membrane, restoring forces and the dynamic equation governing the vi brating membrane a re given by F r is f orce in r-η plane F Ө is f orce in Ө-η plane P is the tension f orce σ is the mass per unit area of the membrane material 22
  • 23. 10/7/2012 Development of IPMC model • from lipid bilayers [10] The converse flexoelectric effect describes the generation of curva tures induced by a pplied electric fields and the equilibrium radius of the tether as IPMC ANALYSIS CASE STUDY [11] 23
  • 24. 10/7/2012 Material Properties orthotropic relativ e permittivity 0.031 density : 2975 kg/m 3 [12] dielectric constant of 0.00032 and corresponding ANEL Matrix 24
  • 25. 10/7/2012 DEVELOPMENT OF IPMC MODEL FOR CIRCULAR CONFIGURATION Diameter = 40mm Thickness = 0.3mm Results Displacement = 14.436mm • The maximal tip displacement can nearly reach radius • create a cup shape. 25
  • 26. 10/7/2012 • No s i gnificant response. • Li ttl e a ctuation response - bending force created not enough to overcome the constrained provi ded by the hollow plate. • Significant actuation • Did not form cup shape • Bend about an axis along the diameter determined by initial curvature of the membrane • The IPMC was effectively responding for three actuations MOV06819.AVI 26
  • 27. 10/7/2012 • Cup shape by using two cantilever IPMC kept crossed to each other. • Suction creation using the setup. • Integration of micro spine and IPMC assembly to the robot • Gripping force to be generated to resist wind • Ways to detect failing of the grip is failing and recovery before the plane falls 1. Analysis And Development Of Technology For Perching Mechanism For Flying Robots for “National Seminar On Recent Adv ances In PIE And Remote Technologies For Nuclear Fuel Cycle (RAPT 2010)” on September 23-24, 2010 at SRI Conv ention Centre, Anupuram, Kalpakkam. 2. Develop ment Of Technology For Perching Robots Using Ionic Polymer Metal Co mposite f or “The First National Conf erence On Energy Efficient Mechanical System Design And Manuf acturing” on 11th-12th March, 2011 at Department Of Mechanical Engineering, PSG College of Technology, Coimbatore 3. Develop ment Of Micro Spine Technology For Perching Robots, f or “The First National Conf erence on emerging Trends in CAD, Cam, CIM”, Department Of Mechanical Engineering” on 29th April 2011 at Department Of Mechanical Engineering, PSG College Of Technology, Coimbatore. 4. Develop ment And Performance Of Circular Shaped Ionic Polymer Metal Co mposite f or “National Conf erence on Design and Manuf acturing 2011” on 27th – 28th May 2011 at IIT Madras Campus, Chennai. Also published in “International journal of Applied Engineering Research” Volume 6, No.5. 27
  • 28. 10/7/2012 [1] Mark R. Cutkosky and Alexis Lussier Desbiens: Bio-Inspired Perching and Crawling Air Vehicles: Biomimetics and Dextrous Manipulation Laboratory: October 2, 2008. [2] Alexis Lussier Desbiens, Alan T Asbeck, and Mark R. Cutkosky: Scansorial Landing and Perching: Biomimetic and . Dextrous Manipulation Laboratory. [3] Mirko Kovac, Jurg Germann, Christoph Hurzeler Roland Y Siegwart, Dario Floreano: A Perching Mechanism for , . Micro Aerial Vehicles. [4] M. J. Spenko et. al., : Biologically Inspired Climbing with a Hexapedal Robot : Journal of Field Robotics 25(4–5), 223–242 (2008) C 2008 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/rob.20238 [5] Robert T Pack, Joe L. Christopher Jr and Kazuhiko Kawamura: A Rubbertuator-Based Structure-Climbing Inspection . . Robot. [6] Mohsen Shahinpoor et al.: Artificial Muscles – Applications of Advanced Polymeric Nanocomposites: T aylor and Francis Group [7] Keisuke Oguro: preparation procedure - ion-exchange polymer metal composites (IPMC) membranes. http://ndeaa.jpl.nasa.gov/nasa-nde/lommas/eap/IPMC_PrepProcedure.htm [8]M. Shahinpoor et al.: Ionic Polymer-Metal Composites (IPMC) as Biomimetic Sensors and Actuators - Artificial , Muscles: Proceedings of SPIE's 5th Annual International Symposium on Smart Structures and Materials, 1-5 March, 1998, San Diego, CA. Paper No. 3324-27. [9] Eric J. Ruggiero: Modeling and Control of SPIDER Satellite Components: Virginia T ech's ETD. [10]Ben Harland: Voltage-induced bending and electromechanical coupling in lipid bilayers: The American Physical Society ©2010: 1539-3755/2010/81(3)/031907(9). [11] Hanmin PENG, Yao HUI, Qingjun DING, Huafeng LI, Chunsheng ZHAO : IPMC gripper static analysis based on finite element analysis : Front. Mech. Eng. China 2010, 5(2): 204–211 - DOI 10.1007/s11465-010-0005-1. [12] W.A.Lughmani: Modeling of bending behavior of IPMC beams using Concentrated Ion Boundary layer: International Journal of Precision Engineering & Manufacturing Vol.10, No. 5, pp. 131-139. 28