导电聚合物驱动器悬臂梁模型建立及柔性抓取装置设计*

田素坤，王湘江

（南华大学机械工程学院，湖南衡阳421001）

导电聚合物驱动器悬臂梁模型建立及柔性抓取装置设计*

田素坤，王湘江*

（南华大学机械工程学院，湖南衡阳421001）

基于导电聚合物具有柔韧性好、驱动电压低、能耗小等特性，采用自制的多层弯曲型导电聚合物驱动器搭建实验系统，依据等效悬臂梁理论建立驱动器力学模型。通过测量驱动器的弯曲变形量建立偏转位移与电压、长度的函数关系式，并且计算出等效均布载荷值。实验结果表明，驱动器偏转位移与电压、长度成线性关系；当驱动电压达到1.0 V时，驱动器偏转速度趋于稳定，且偏转效果最佳。为改善普通微操作装置结构复杂、能耗大的缺点，采用导电聚合物智能材料设计并制作出微型手爪制动器，最后验证了手爪可稳定抓起0.011 1 g左右的重物。

导电聚合物；聚吡咯；柔性手爪；悬臂梁结构；等效模型；驱动器

EEACC:7230doi:10.3969/j.issn.1004-1699.2016.04.005

Electroactive polymers（EAPs）are one group of smart materials with unique electrical and mechanical properties［1］.Conducting polymers（CPs）have wide application prospect in biological robot and biomedical device because of its excellent properties of small energy consumption，light weight，biocompatibility，good flexibility，and ability to work in liquid and air environments，even are very similar with natural muscle in some performance，which are the best candidate as biomimetic muscles，and also quite general denominated as Artificial Muscles［2-5］.In 1984，Burgmayer and Murray［6］first reported the volume change of CPs under the electric field.The operation principle of polymer actuators is based on the volume expansion or contraction generated by the transfer of ions in and out of the active conducting polymer layers during an electro-chemical reaction.It follows that the electrochemical energy is converted into mechanical energy，to achieve the goal of actuation.This kind of material is widely used in bending actuators like a cantilever beam，its strain vary from 0.5%～10%and even reached at 39%［7］.Because of the limitation of diffusion speed and slow driving speed；while its stress varies from 1～35 Mpa［8］.Due to this feature，the actuators are suitable to activating micropumps，microswitches，microgrippers and microcantilevers that could be used for moving，positioning or holding micro objects，and manipulating biological samples［9-12］.Although such systems have already been demonstrated in the macroscopic scale，very little work has been published with regard to the miniaturization of the actuators［13-14］.In the earliest studies，Jager et al.［15］fabricated a serially connected micromanipulators，or microrobotic arm to pick up，lift and move micrometer-size objects within an area of about 250 μm by 100 μm，making the microrobot an excellent tool for single-cell manipulation. Han and Shi［5］synthesized tri-layer conducting polymer composite films of PPy/PTh/PPy，and it has been demonstrated that a 0.4 mg composite film can reversibly raise a 10 mg material（e.g.a copper wire）from the position of 0°to the position of～±90°at±1.0 V.However，these systems could only operate in specific aqueous media，as the media provided a source of ions（electrolyte）necessary to achieve actuation.

In this paper，with reference to the operation principle of the actuators，we present an equivalent mechanical model of the cantilever beam，and through experiment，we can determine the accuracy of the equivalent beam model for design purpose，and the model is also accurate enough to mimic the bending behavior of the polymer actuators.Furthermore，it was verified by the fact that this flexible gripper using a type of smart material called conducting polymer can grasp an object whose weight is about 0.011 1 g.

1　Actuator structure and operational principles

The structure of the polymer actuators in this study is depicted in Fig.1.The polymer actuator considered consists of five layers of three different materials. two outside PPy layers are the electroactive elements providing actuation（30 μm），which are clamped to two electrodes at one end of the polymer actuator.An inert andnonconductiveporouspolyvinylidinefluoride （PVDF）with thickness of 110 μm that serves as the electrochemical cell separator and as a reservoir for the electrolytic ions lithium triflouromethanesulfonimide（Li+TFSI-）in an organic solvent propylene carbonate（PC）at a concentration of 0.5 M，and two thin platinum layers（10 Å～100 Å）are sputter-coated on both sides of PVDF that served to increase the conductivity between the electrolyte and PPy layers，and can be negligible.This composite structure exhibits a simple bending motion like a bilayer cantilever［4］.

Fig.1　Schematic structure of the polymer actuator

There will be electric field inside the actuator when an electric potential is applied across the electrodes attached to the actuator.Under the action of electric field，the reduction/oxidation（redox）reaction will occur.The redox process can be described as:

The redox process occurs simultaneously on both PPy layers:the Ppy layer on the anode side is oxidized while is reduced on the cathode side.With reference to chemical reaction process and Fig.2.

Fig.2　Schematic representation of the bending principle

TFSI-serve as doped ions of PPy.In order to maintain the charge neutrality within the PPy layers，TFSI-anions will move from the electrolyte to the positively charged polymer（PPy）electrode and hence cause a volume expansion.While this is happening in the positive electrode，TFSI-anions will leave the negatively chargedelectrode as reduction of the PPy caused it to become uncharged and then a volume contraction occurs.The volume changed due to the movement of the charge balancinganionsinandoutofthepolymerlayers.Theotherfactor is because that some solvent molecules move inside the polymer layers which is caused by osmotic effects or the hydrophilous of the TFSI-anions.The overall result is that the cantilevered structure will bend towards the negativeelectrode，asdepictedinFig.2（b）.

2　Bending model and experimental verification

With reference to the operation principle of the actuators，and given its own characteristics and widespread application prospect，it will be equivalent to a cantilever beam structure starting from the practical application of the polymer actuators［13］.Bending deflection happens due to ionic migration，while equivalent model can not simulate the movement of the ions and molecules in and out of the polymer layers.So under a quasi-static condition，we think the internal stress field produced by the ion migration hypothesis as an uniformly distributed load applied on the beam.

2.1Bending model

Under the action of uniformly distributed load，a mechanics analysis model of constrained cantilever beam，there are two cases described in Fig.3.

（1）There is no blocking force on the tip of the bending-type polymer actuator（i.e.F=0）.

（2）The tip of the bending-type polymer actuator is blocked（i.e.F≠0）.

Fig.3　The equivalent cantilever beam model

Using the first case，list the flexural curve equation of beam at a distance x from the fixed:

whereEIis the flexural rigidity for the actuator.

When x=L，the maximum deflection length:

Equation（2）can be rewritten as:

According to compatibility condition，geometric equation can be obtained using a superposition method:

with reference to Fig.3（c），the blocking force（FB）can be obtained using a superposition method:

Substituting equation（2）and（5）into equation（4）:

Equation（6）can be rewritten as:

It is known［3］that the steady-state blocking force is proportional to the input voltage:

The proportionality constant a is identified experimentally from the relationship between the voltage and the blocking force.

2.2Eexperimental verification

All equipment used for experiment is shown in Fig.4，which was set up by multilayer bending PPy actuators to illustrate the relationship between bending displacement and output voltage.The input voltage signal was provided by an external digital function signal generator（F20A），electrode clamps was connected with cathode/anode of the generator by copper wire.A noncontact laser displacement sensor（FT50）was used to measure the tip displacement of the actuator，which has 0～10 V analog output voltage signal. The outputting proportional voltage measured by a DAQ Cord（PCI-1710U）interfacing with a personal computer.The image of the actuator strip was captured by a high-speed camera（Inline 1 000）.Wechoose the solution of which concentration ratio is 0.5 M as the final experimental electrolyte，and the polymer actuators must be soaked in this electrolyte for 30 min until use［4，13］.The actuator strips of different dimensions in experimentation are cut from the bulk sheet.

Fig.4　The experimental setup

The tip displacements of 2 mm wide actuators were measured，and are depicted in Fig.5.The results indicate that the actuators have shown the same trends at different lengths，i.e.the input voltage was higher，the tip displacement was larger.The steady-state gain of actuator has been calculated and is shown to increase proportionally to the length as presented in Fig.6.The curve fitted relationships（R2=0.989 65）are as follows:

Fig.5　The deflection displacement of 2 mm wide actuators

Fig.6　The deflection displacement of different lengths

With reference to equation（3）and bending rigidity value is EI=0.145 367 N·mm2.We can calculate the numerical values of uniformly distributed load，as shown in Table 1.When the actuator is longer，the load is smaller，and the blocking force is smaller（equation （7）），so we can measure the tip force of the actuators.

Table 1　The numerical values of uniformly distributed load

With reference the tip displacement of the actuators（Fig.5），the bending speed value of the different length of the three actuators were shown in Fig.7.It can be seen that the movement process slowed upward trend.These results also show that when the voltage reaches 1.0 V，the speed tended to be stable and bending effect can be considered optimal.So the gripper driving voltage were choosed 1.0 V.

Fig.7　Tip velocity response of different lengths

3　Gripper

The structure of the gripper is depicted in Fig.8. The main parts of the gripper are the two pieces of actu-ator strips that work as two micro fingers，other parts includes copper electrodes and holding device.The copper electrode is used for clamping the actuator strips （contact area is 1 mm2）and is connected with the cathode/anode of the electrical power supply.

Fig.8　Gripper structure

The parameters of the two actuator strips shown in Table 2，The weight of the whole gripper（including the wires）is 8.363 6 g and the object（foam）weight is 0.011 1 g，which measured by an electronic balance （FA1104N）.The working procedure can be simply explained and the movement process of the gripper under sinusoidal voltage is a opening-closing-opening process cycle.The gripper is arranged to operate in the vertical plane and grasp an object on a reference plane under a voltage of 1.0 V.When applying the sinusoidal voltage，the gripper bends towards the anode electrode，i.e.the gripper opened（Fig.9（a））.Changing the voltage direction of the copper electrodes，the actuators reverse bend and begin to grasp the object（Fig.9（b））. The gripper completes grasping the object and lifts up to a certain height（Fig.9（c））.Finally，the gripper opened and the object fall to the reference plane（Fig.9（d））.

Table 2　The parameters of the two actuator strips

Fig.9　Working process of gripper

With reference to Fig.3，the friction coefficient μ= 0.512 6 can be obtained in the literature［14］.On the premise of ignoring the weight of actuators，we can obtain every piece of actuators of grasping force:

The bending movement of actuator films were measured by experiment，as shown in Fig.10.The bending speed value of gripper actuators were shown in Fig.11.

Fig.10　The deflection displacement of actuators

Fig.11　Tip velocity response of different lengths

It could be seen that the properties of the first piece film was best and the negative maximum displacement is 5.11 mm，the positive maximum displacement is 4.2 mm，the maximum deformation speed was about 0.35 mm/s.Whatmore，the changes trend of the other piece film was similar to the first.From the above data，when the direction ofvoltagewaschanged，the maximum displacement change of the actuator was been found.In other words，when the deformation velocity was maximum and the film was closed to the maximal displacement.

4　Conclusions

This study is to build up an equivalent cantilever beam model to explain the tip deformation of PPy actuator strips based on the operation principle and the practical application of the polymer actuators.Through experimental verification that when applying the low voltage（0～1.0 V）to the actuators，with the increase of voltage，displacement increases，the relationship between displacement and voltage is approximate linear. A type of two fingers with 1.0 V voltages has been designed and developed for grasping small and precision object.Through these results，we can determine the model is also accurate enough to mimic the bending behavior of the actuator.Because of the instability performance of the actuator material and it is easily influenced by the external environment，the inaccuracy of measurement and model is still not sufficient enough. So it remains to be further researched.

［1］ Al-Jumaily A M，Jassim S.Prospective Optical Electroactive Polymers［J］.Smart Structures and Materials:Electroactive Polymer Actuators and Devices（EAPAD）.2003，5051:400-403.

［2］ Chiang C K，Fincher C B，Jr Park Y W，et al.Electrical Conductivity in Doped Polyacetylene［J］Physical Review Letters，1977，39 （17）:1098-1101.

［3］ Alici G，Huynh N N.Performance Quantification of Conducting Polymer Actuators for Real Applications:A Microgripping System ［J］.IEEE/ASME Transactions on Mechatronics，2007，12（1）: 73-84.

［4］ Wang X J，Alici G，Nguyen C H，et al.Adaptive Sliding Mode Control of Tri-Layer Conjugated Polymer Actuators［J］.Smart Materials and Structures，2013，22（2）:025004.

［5］ Han G Y，Shi G Q.Conducting Polymer Electrochemical Actuator Made of High-Strength Three-Layered Composite Films of Polythiophene and Polypyrrole［J］.Sensors and Actuators B:Chemical，2004，99:525-531.

［6］ Feldman B J，Burgmayer P，Murray R W.The Potential Dependence of Electrical Conductivity and Chemical Charge Storage of Poly（Pyrrole）Films on Electrodes［J］.Journal of the American Chemical Society，1985，107:872-878.

［7］ Hara S，Zama T，Takashima W，et al.Free-Standing Gel-Like Polypyrrole Actuators Doped with Bis（Perfluoroalkylsulfonyl）Imide Exhibiting Extremely Large Strain［J］.Smart Materials and Structures，2005，14:1501-1510.

［8］ Madden J D，Cush R A，Kanigan T S，et al.Hunter，Fast Contracting Polypyrrole Actuators［J］.Synthetic Metals，2000，113:185-192.

［9］ Fang Y，Tan X B.A Novel Diaphragm Micropump Actuated by Conjugated Polymer Petals:Fabrication，Modeling，and Experimental Results［J］.Sensors and Actuators A:Physical，2010，158: 121-131.

［10］余建平，李欣，张玉良，等.微型双模式耐蚀压力传感器设计及特性分析（英文）［J］.传感技术学报，2015，28（2）:193-197.

［11］Wallace G G，Spinks G M，Teasdale P R.Conductive Electroactive Polymers:Intelligent Materials Systems［M］.Lancaster:Technomic Publishing Co，1997.

［12］Gaihre B，Alici G，Spinks G M，et al.Pushing the Limits for Microactuators Based on Electroactive Polymers［J］.Journal of Microelectromechanical Systems，2012，21（3）:574-585.

［13］Gaihre B，Alici G，Spinks G M，et al.Cairney.Synthesis and Performance Evaluation of Thin Film PPy-PVDF Multilayer Electroactive Polymer Actuators［J］.Sensors and Actuators A:Physical，2011，165:321-328.

［14］徐运扬，徐康康，沈平.AFM压电陶瓷驱动器类Hammerstein建模与参数辨识［J］.传感技术学报，2015，28（1）:23-27.

［15］Jager E W H，Inganas O，Lunstrom I.Microrobots for Micrometersize Objects in Aqueous Media:Potential Tools for Single-Cell Manipulation［J］.Science，2000，288:2335-2338.

田素坤（1989-），男，山东滕州人，硕士研究生，研究方向为智能材料驱动控制和机电系统控制，tiansukun169@163.com；

王湘江（1972-），男，湖南邵阳人，教授，博士，硕士研究生导师，主要研究方向为机械设计理论和机电系统非线性控制，wangxiangjiang72@163.com。

Equivalent Beam Model Establishing and Design of Flexible Grippers for Conducting Polymer Actuators*

TIAN Sukun，WANG Xiangjiang*
（School of Mechanical Engineering，University of South China，Hengyang Hu'nan 421001，China）

Conducting polymers can be used to manufacture biomedical device due to their good flexibility，requiring low actuation voltages and small energy consumption.According to the equivalent cantilever beam theory，the mechanical model of conducting polymer actuators are given.The experimental system has been set up for the actuators which made by multilayer bending conducting polymer.Through researched the substrate bending deformation，we established the function relationship between the bending displacement and the voltage and the length，calculate the numerical values of uniformly distributed load.The experimental results indicate that the bending displacement of the actuators is linear related to its length and voltage，when the voltage reaches 1.0 V，the bending speed of actuators tended to be stable and bending effect can be considered optimal.To overcome disadvantages of high energy consumption and complex structures，a flexible gripper using a type of smart material called conducting polymer was designed and manufactured.It was verified by the fact that this gripper can grasp an object whose weight is about 0.011 1 g.

conducting polymer；polypyrrole；flexible gripper；cantilever beam structure；equivalent model；actuator

TH113

A

1004-1699（2016）04-0489-06

项目来源:湖南省教育厅重点项目（13A081）；湖南省研究生科研创新项目（2015SCX18）

2015-11-26修改日期:2015-12-27