摘要
编织型气动人工肌肉是气动人工肌肉的基本型和核心型,其基本特点是结构简单、功能特性优良。但是,编织型气动人工肌肉工作过程中受橡胶弹性变形、端盖的径向约束、橡胶与编织丝以及编织丝间摩擦等影响,导致精确建模十分困难,在此方面的理论研究还有待完善。编织型气动人工肌肉理论建模方法有两种：基于理想状态的能量守恒方法和基于理想状态的力平衡方法。这两种方法均假设编织型气动人工肌肉在工作过程中始终保持理想圆柱状态,而实际上,编织型气动人工肌肉两端受到端盖的径向约束作用,使其在工作过程中的几何形状为非理想圆柱,在两端部为回转曲面,因此,提高编织型气动人工肌肉几何形状的表达精度是建立其更加精确数学模型的关键。本文以编织型气动人工肌肉为对象进行了工作机理研究、理论建模研究以及设计研究。
从编织型气动人工肌肉的功能实现和构成其关键部件的材料特性两个方面对编织型气动人工肌肉的工作机理进行研究。一方面,编织型气动人工肌肉实现其功能的基本原理是具有可变形的封闭容腔,在压缩空气的作用下封闭容腔变化,从而产生位移效应；位移变化的范围受气动人工肌肉结构的限制,输出力的大小与压缩空气压力大小和气动人工肌肉结构有关。另一方面,以层合理论、复合材料理论及薄壳理论等为基础,分析了编织型气动人工肌肉的柔性材料的特性。编织网对柔性件的变形起着决定性的作用,柔性件的平面刚度为零,它在不均衡外力作用下会产生“机构式”的变形,同时,编织型气动人工肌肉的每个稳定状态下编织网应该处于力的均衡状态,从而编织型气动人工肌肉工作机理得到了理论上的表达。
利用缠绕理论、复合材料力学、薄壳理论以及微分几何等作为理论基础,对编织型气动人工肌肉端部进行了理论建模研究。编织纤维丝在编织型气动人工肌肉端部应为测地线缠绕。由于理论上端部曲线曲率发生了方向的变化,因此本论文建立的编织型气动人工肌肉端部数学模型由两部分构成：一部分是由最大直径到曲线曲率方向发生的变化点(拐点),此部分由理论分析得到；另一部分为拐点到端盖,这一部分用球面替代。尽管本文所建模型不是完全的理论解析,但在理论上使端部形状更接近精确解。同时,本文推导的编织角公式可以证明约束对编织型气动人工肌肉几何变形的影响作用。
从设计的角度给出了编织型气动人工肌肉的各结构参数的设计计算公式,以及各几何参数间的关系。着重研究了影响编织型气动人工肌肉工作范围的重要参数——编织角,建立其计算公式,确定了编织角极值。给出了橡胶弹性和厚度对编织型气动人工肌肉工作特性的影响公式,研究了纤维丝间的摩擦对编织型气动人工肌肉工作特性的影响,给出了摩擦力的计算公式。
利用ABAQUS软件从编织型气动人工肌肉结构出发对编织型气动人工肌肉进行了几何建模,通过分析计算得到了编织型气动人工肌肉的输出力、充气压力和长度之间的关系。同时,提取了编织型气动人工肌肉在工作状态下的外形尺寸、编织角、体积等几何参数。利用此模型模拟分析了约束对编织型气动人工肌肉工作特性的影响。
设计制造编织型气动人工肌肉实验台,并进行了实验研究。通过编织型气动人工肌肉的静态工作特性实验结果与圆柱理想模型及有限元分析的对比,有限元分析得到的结果与实验结果更接近,这是由于在有限元分析过程中考虑了橡胶特性和端部约束对编织型气动人工肌肉输出特性的影响。同时,开展了约束对编织型气动人工肌肉输出特性的影响的研究,从有限元仿真和实验两个方面证明了约束使编织型气动人工肌肉输出特性降低的结论。
Braided type pneumatic artificial muscle is the basic and core of pneumatic artificial muscle. The basic characteristic is simple structure and perfect performance. But the braided type pneumatic artificial muscle is under the influences of elastic deformation, friction and cover radial constraint in the work process of the pneumatic artificial muscle, the precise modeling is very difficult, the theory study remains to be perfect. There are two modeling methods for braided type pneumatic artificial muscle:the energy conservation law under ideal condition and the force balance law under ideal condition. The two laws are all assuming that braided type pneumatic artificial muscle always remaining in the ideal cylindrical state. In fact, there are constraints on both ends of pneumatic artificial muscle, the geometry in the process of the working is not the ideal column, the turning curved surfaces occur at the two ends. Therefore, the improvement of the geometry expression accuracy of braided type pneumatic artificial muscle is the key to establish the more precision mathematical model. This paper will study on the working mechanism, theory modeling and design research of braided pneumatic artificial muscle as the object.
The working mechanism research is from two aspects including the function realization and the material characteristics of the key components. On one hand, pneumatic artificial muscle can realize its functions, its basic principle is the deformable closed chamber, under the compressed function, the air closed chamber change, causing the displacement effect; the displacement change ranges are restricted by the pneumatic artificial muscle structure, the output force is related to the pressure of compressed air and the structure of pneumatic artificial muscle.
On the other hand, base on laminated theory, composite materials mechanics and thin shell theory, starting with the flexible characteristics mechanism of braided type pneumatic artificial muscle, the flexible material properties of braided type pneumatic artificial muscle has been analyzed. The weaving network has played a decisive role on the deformation of flexible pieces, the plane stiffness of flexible pieces is zero, it will produce "institution type" deformation in the balanced external force. At the same time, weaving network will be in the forces balance state under each stable state of braided type pneumatic artificial muscle. The theoretical expression of the mechanism of pneumatic artificial muscle has been got.
Based on the work principle of braided type pneumatic artificial muscle, using winding theory, composite material mechanics, thin shell theory and differential geometry as theoretical basis, the theoretical modeling of the ends of braided type pneumatic artificial muscle has been studied. Braided fibers at the end of braided type pneumatic artificial muscle should be geodesics winding, because of the directional changes of the curvature will happen in theory, so the established mathematical model at the end of braided type pneumatic artificial muscle consists of two parts:one part is from the biggest diameter to the change point of the curvature direction (inflection point), the model of this part can be got by the theoretical analysis; The other part is from the inflexion point to the end cover, this part can be substituted for the spherical surface. Although the built model is not the completely theory solution in this paper, but the end shape is more close to the exact solution, at the same time, the constraints effect on the geometry deformation of braided type pneumatic artificial muscle can be proved.
The design calculation formula of structural parameters of braided type pneumatic artificial muscle and the relationship between the various geometric parameters have been provided from the design view. The important parameter-the braiding angle which can influence the work scope of braided type pneumatic artificial muscle, has been focused on. The braiding angle calculation formula has been provided, the extreme value has been determined. The influence formula of rubber elasticity and thickness on the work characteristics of braided type pneumatic artificial muscle have been given; the friction influence between the fibers on the work characteristics of braided type pneumatic artificial muscle has been studied, and the calculation method of friction force has been provided.
The geometry modeling of braided type pneumatic artificial muscle has been made from the structure of braided type pneumatic artificial muscle with ABAQUS. By analyzing and calculating, the relationship of output force, inflation pressure and length of braided type pneumatic artificial muscle has been obtained. At the same time, the contour dimension, braided angles and volume of braided type pneumatic artificial muscle in the working state also have been drawn. By using this model, the work characteristics influence of constraints on braided type pneumatic artificial muscle can be simulated.
The test bench of braided type pneumatic artificial muscle has been designed and manufactured, and the experimental research has been done. Through the comparisons of the static working characteristics experimental results of braided style pneumatic artificial muscle, the ideal cylindrical model and the finite element analysis, the results of finite element analysis are more close to the experimental results, this is because rubber characteristics and end constraints have been considered in the process of finite element analysis of braided type pneumatic artificial muscle. At the same time, the constraint influence research of the output characteristic of braided style pneumatic artificial muscle has been developed. From two aspects of the finite element simulation and experiments, the conclusion that constraints can reduce the output characteristic of braided style pneumatic artificial muscle has been proved.
引文
[1]Caldwell D. G, N. Tsagarakis, D. Badihi. Pneumatic Muscle Actuator Technology a Light Weight Power System for a Humanoid Robot[C]. Proceedings of the 1998 IEEE International Conference on Robotics&Automation.Leuven, Belgium.1998,4:3053-3058
[2]王雄耀.介绍一种气动新产品—仿生气动肌肉腱[J].液压气动与密封,2002,(1)：31-35
[3]臧克江,顾立志,陶国良.气动人工肌肉研究与展望[J].机床与液压,2004,(4)：4-7
[4]陶国良,谢建蔚,周洪.气动人工肌肉的发展趋势与研究现状[J].机械工程学报,2009,45(10)：75-82
[5]张鹏翔,廖启征,魏世民等.液压驱动的四足机器人控制系统研究[J].液压与气动,2011,(1)：29-31
[6]沈婵,路波,惠伟安.气动技术的发展与创新[J].流体传动与控制,2011,(4)：7-10
[7]颜嘉男.伺服电机应用技术[M].北京：科学出版社,2010：161-180
[8]Klute G K, J.M Czerniecki, B.Hannaford. McKibben Artificial Muscles:Pneumatic Actuators with Biomechanical Intelligence[C]. Proceedings of IEEE/ASME 1999 International Conference on Advanced Intelligent Mechatronics. Atlanta,USA.1999:1-6
[9]苏生荣,应申舜.面向机器人驱动的人工肌肉技术研究进展[J].机械科学与技术,2009,28(6)：834-840
[10]张江涛,关胜晓,汪增福.一种新型人工肌肉驱动机理与仿真研究[J].系统仿真学报,2008,20(9)：2390-2394
[11]杨锋.妙不可言的人工肌肉[J].解放军健康,1999,(2)：34
[12]陈守良等.人类生物学[M].北京：北京大学出版社,2001,12：41-54
[13]工玢.人体及动物生理学[M].北京：高等教育出版社,1986,3：25-38
[14]Bar-Cohen, Y. S. Leary. Electroactive Polymers as Artificial Muscles Changing Robotics Paradigms[C]. National Space and Missile Materials Symposium,2000:1-8
[15]应申舜,秦现生,汪文旦.基于形状记忆合金弹簧阵列的人工肌肉设计与研究[J].中国机械工程,2008.19(15)：1782-1786
[16]Tondu B, P.Lopez. Modeling and Control of Mckibben Muscle Robot Actuator[C]. IEEE Control System. May,2000:15-38
[17]谭湘强,钟映春,杨宜民IPMC人工肌肉的特性及其应用[J].高技术通讯,2002,(1)：50-52
[18]林桂娟,宋德朝,陈明等.电活性聚合物的力学性能及发电应用[J].同济大学学报(自然科学版),2011,39(6)：908-913
[19]Shahinpoor.M. Conceptual Design, Kinematics and Dynamics of Swimming Robotic Structures Using Ionic Polymeric Gel Muscles[J]. Smart Materials and Structures Int J,1992, 1:91-94
[20]Shahinpoor M, Y. BarCohen, T. Xue. Some Experimental Results on Ionic exchange Polymer Metal Composites as Biominetic Sensors and Acutators[C]. In:Proc. SPIE Smart Materials and Structures Conference,1998:33-24
[21]李明东.形状记忆合金丝驱动的仿生驱动关节臂[J].上海交通大学学报,1999,33(10)：1284-1286
[22]Gilles Bourbon, Patrice Minotti, Philippe Langlet. Three Dimensional Active Microcatheter Combining Shape Memory Alloy Actuators and Direct-Drive Tubular Electrostatic Micromotors[C]. Proceedings of SPIE-The International Society for Optical Engineering,1998,35(14):147-158
[23]胡旭.基于形状记忆合金的四足步行机器人[J].机器人技术与应用,2002,(1)：29-31
[24]迟冬祥,颜国正.仿生机器人的研究状况及其未来发展[J].机器人,2001,23(5)：476-480
[25]Dominiek Reynaerts, Jan Peirs, Hendrik Brussel. Shape Memory Micro-actuation for a Gastro-intesitinal Intervention System[C]. Sensors and Actuators,1999,(77):157-166
[26]Ravi Vaidyanathan, Hillel J Chiel, Roger D Quinn. A Hydrostatic Robot for Marine Application[C]. Robotics and Autonomous Systems,2000, (30):103-113
[27]Toshio Fukuda, Hidemi Hosokai, Isamu Kikuchi. Distribute Type of Actuators of Shape Memory Alloy and Its Application to Underwater Mobile Robotic Mechanisms[C]. Proceeding of the 1990 IEEE International Conference on Robotic and Automation,1990:1326-1321
[28]Paynter H.M. High Pressure Fluid-driven Tension Actuators and Methods for Constructing them[P]. US Patent. No.4 751 869,1988
[29]Marcincin J, A. Palko. Negative Pessure Atificial Mscle-An Uconventional Dive of Rbotic and Hndling Sstems[C]. Transactions of the University of Kosice. Riecansky Science Publishing Co, Slovak Republic,1993:350-354
[30]C. P. Chou, B. Hannaford. Measurement and Modeling of McKibben Pneumatic Artificial Muscles[J]. Ransactions on Robotics and Automation,1996,12(1):90-102
[31]Tondu B, P Lopez. Modeling and Control of McKibben Artificial Muscle Robot Actuators[C]. IEEE Control Systems Magazine. April,2000:15-39
[32]Tsagarakis N, D. G.Caldwell. Improved Modelling and Assessment of Pneumatic Muscle Actuators[C]. Proceedings of the 2000 IEEE International Conference on Robotics and Automation, Apr.24-28,2000, San Francisco, CA, USA. New York:IEEE,2000:3641-3646
[33]Reynolds D.B, D.W Repperger, C.A Phillips, et al. Modeling the Dynamic Characteristics of Pneumatic Muscle[J]. BMES Annals of Biomedical Engineering,2003,31(3):310-317
[34]Bertetto M. A, M. Ruggiu. Characteristics and Modeling of Air Muscles[J]. Mechanics Research Communications,2004,31:185-194
[35]WALKER I D, DAWSON D M, FLASH T, et al. Continuum robot arms inspired by cephalopods[C]. Unmanned Ground Vehicle Technology Ⅶ, March 29,2005, Orlando, FL, USA. Bellingham, WA:SPIE,2005:303-314
[36]刘荣,宗光华.人工肌肉驱动特性研究[J].高技术通讯,1998,(6)：34-38
[37]杜经民,朱端阳,杨钢等.气动人工肌肉静态特性实验研究[J].液压与气动,2005,(5)：21-23
[38]隋立明,包钢,王祖温.气动人工肌肉改进模型研究[J].液压气动与密封,2002,4(2)：1-4
[39]杨钢,李宝仁.气动人工肌肉位置控制策略[J].华中科技大学学报(自然科学版).2006,38(6)：71-73
[40]Repperger D. W, K. R. Johnson, C. A. Phillips. Nonlinear Feedback Controller Design of A Pneumatic Muscle Actuator System[C]. Proceedings of the American Control Conference. San Diego, California,1999,(3):1525-1529
[41]王龙辉,金英子,朱红亮等.七自由度气动人工肌肉机械手臂的设计及研究[J].浙江理工大学学报,2012,29(1)：74-78
[42]Caldwell D. G, G. A. Medrano-Cerda, M. Goodwin. Control of Pneumatic Muscle Actuators[C]. IEEE Control Systems Magazine,1995 (2):40-48
[43]Hesselroth, K. Sarkar, P. Patrick. Neural Network Control of a Pneumatic Robot Arm[C]. IEEE Transact ion on Systems. MAN. and Cyber-netics,1994,24 (1):28-38
[44]Osuka K, T. Kimura, T. Ono. H∞ Control of a Certain Non-linear Actuator [C]. Proceedings of the 29th Conference on Decision and Control. Honolulu, Hawai,1990(1):370-371
[46]范伟,彭光正,黄雨.气动人工肌肉驱动器的研究现状及发展趋势[J].机床与液压,2003,(1)：32-36
[47]Cai D, Yamaura H. A robust controller for manipulator driven by artificial muscle actuator[C]. In:Proc. of the IEEE Conf. On Control Applications.1996,5:40-545
[48]宗光华.利用变结构理论实现人工肌肉夹持力控制[J].机器人,1990,12(4)：15-20
[49]田社平,林良明.人工肌肉静态特性及其测量[J].实用测试技术,1998,11(6)：12-14
[50]范伟,彭光正,李英.神经元自适应PSD控制在气动人工肌肉力控制中的应用[J].机床与液压,2004,(10)：53-54
[51]杨钢,李宝仁.气动人工肌肉位置控制策略[J].华中科技大学学报(自然科学版),2006,(8)：71-73
[52]董宗彬.气动人工肌肉伺服系统的位置控制研究[D].兰州理工大学硕士学位论文.2007：23-60
[53]沈伟,施光林.一种三自由度气动人工肌肉并联平台动态数学模型[J].上海交通大学学报,2011,45(2)：219-224
[54]施光林,沈伟.气动人工肌肉并联平台自适应模糊CMAC姿态跟踪控制[J].中国机械 工程,2012,23(2)：171-171
[55]王斌锐,周唯逸,许宏.智能气动肌肉的静态驱动特性研究[J].农业机械学报,2009,40(3)：208-212
[56]王斌锐,周唯逸,许宏.形状记忆合金编织网气动肌肉的驱动特性[J].中国机械工程.2009,20(4)：467-471
[57]鲍官军,高峰,荀一等.气动柔性末端执行器设计及其抓持模型研究[J].农业机械学报,2009,25(10)：121-126
[58]NORITSUGU T, TSUJI Y, ITO K. Improvement of control performance of pneumatic rubber artificial muscle manipulator by using electrorheological fluid damper[C]. IEEE Transaction on Systems, Man andCybernetics,1999(4):788-793
[59]GREENHILL R, ELIAS H, WALKER R, etal. Humanoid robotics[P]. United States, 10951332.2005-06-09.
[60]王龙辉,金英子,朱红亮.七自由度气动人工肌肉机械手臂的设计及研究[J].浙江理工大学学报,2012,29(1)：74-78
[61]CALDWELL D G, MEDRANO-CERDA G A, GOODWIN M. Control of pneumatic muscle actuators[C]. IEEE Control Systems Magazine,1995(2):40-48
[62]DAVIS S, CALDWELL D G Pneumatic muscle actuators for humanoid applications-sensor and valve integration[C]. Proceedings of the 6th IEEE/RAS International Conference on Humanoid Robots, Genova,2006:456-461.
[63]http://tech.xinmin.cn/2011/05/12/10685990.html
[64]Deutsch, J. J.Utonio, G Burdea, R.Boian. Post-stroke rehabilitation with the Rutgers Ankle system:a case study[J]. Presence,2001,10(4):225-227
[65]McMahon Th. A. Muscles, Rflexes, and Lcomotion[M]. Princeton University Press.1984,4:1-20
[66]Schulte H F. The Characteristics of the McKibben Artificial Muscle[C]. National Academy of Sciences-National Research Council, Publication 874, Lake. Arrowhead.1961:94-115
[67]Gavrilovic M M, Maric M R. Positional Servomechanism Activated by Artificial Muscles[J]. Medicaland.1969,(7):77-82
[68]Beullens Th. Hydraulic or Pneumatic Drive Device[P]. US. Patent No.4 841 845,1989
[69]Yarlott J M. Fluid Actuator[P]. US Patent No.3 645 173,1972
[70]Immega G, and Kukolj M. Axially contractible actuator[P]. Patent No.4939982,1990
[71]Kukolj M. Axially contractible actuator[P]. US Patent. N o.4 733 603,1988
[72]Morin H. Elastic Daphragm[P]. US Patent No.2 642 091,1953
[73]Baldwin H. A. Realizable Models of Muscle Fnction[C]. Proceedings of the First Rock Biomechanics Symposium. New York,1969:139-148
[74]Marcincin J, Palko A. Negative Pessure Atificial Mscle—An Uconventional Dive of Rbotic and Hndling Systems[C]. Transactions of the University of Kosice. Riecansky Science Publishing Co, Slovak Republic.1993:350-354
[75]Marcinc J, Smrc J. The Atypical Actuators for Advanced Robotic Devices[C].3rd International Workshop on Robotics in Alpe-Adra Region. Slovenia.1994:111-117
[76]Marcin J. N, Smrek J. The UPAM—New Actuator for Advanced Robotic Devices[C].25th International Symposium on Industrial Robots. Germany.1994:299-304
[77]Marcin J. N, Smrc J, Niznik J. Bioactuators—Most Efficient Actuators for Biomechanics[C]. 7th International IMEKO TC-13 Conference on Measurement in Clinical Medicine—Model Based Biomeasurements. Slovak Republic.1995:369-371
[78]Smrc J, Marcincin J. N, Niznik J. The Under Pressure Artificial Muscle UPAM—New Actuator in Biorobotics[C].5th International Symposium on Measurement and Control in Robotics. Slovak Republic.1995:199-203
[79]Paynter H. M. High pressure fluid-driven tension actuators and methods for constructing them[P]. US Patent. No.4 751 869,1988
[80]Paynter H. M. Hyperboloid of Rvolution Fuid-driven Tnsion Atuators and Mthods of Mking[C]. US Patent No.4 21 030,1988
[81]Daerden F. Conception and Realization of Pleated Pneumatic Artificial Muscles and their use as Compliant Actuation elements[D]. Vrije Universiteit Brussel.1999:1-20
[82]Daerden F, Lefeber D. The Concept and Design of Pleated Pneumatic Artificial Muscles[J]. nternational Journal of Fluid Power.2001,2(3):41-50
[83]Kleinwachter H, Geerk J. Device with a Pressurizable Variable Capacity Chamber for Transforming a Fluid Pressure into a Moment[P]. US Patent No.3 638 536,1972
[84]N.Yee, G Coghill. Modeling of a novel rotary pneumatic muscle[C].2002 Australiasian Congference on Robotics and Automation, Auckland,27-29 November 2002:186-189
[85]Mills J K. Hybrid Actuator For Robot Manipulators:Design, Control and Performance[J]. Mechatronics.1993(3):19-38
[86]K. Yamuna Rai, H. Unbehauen. Study of Predictive Controller Tuning Methods[J]. Automatica,1997,33(12):2243-2248
[87]刘锡礼,工粱权.复合材料力学基础[M].北京：中国建筑工业出版社,1984,2：4-6
[88]Kejiang Zang, Yan Ma, Ning Sun. Study on Finite Element Model of Pneumatic Artificial Muscle[J]. Advanced Materials Research Vols.430-432 (2012):383-386
[89]臧克江,郭艳玲,马岩.编织型气动人工肌肉几何特性研究[J].机床与液压,2010,38(1)：24-27
[90]冷兴武.纤维缠绕的基本理论[J].宇肮材料工艺,1986,(6)：13-17
[91]刘锡礼,肖军.纤维缠绕封头结构的一般性方程及其解[J].宇航学报,1987,(4)：90-97
[92]李国强.等张力封头曲线方程及其适用范围[J].纤维复合材料,1987,1(7)：53-61
[93]李国强.旋转壳封头缠绕中心角方程的解析解[J].复合材料学报,1985,2(1)：38-45
[94]谭宏伟.基于气动肌腱的拮抗式仿生关节研究[D].哈尔滨工业大学硕士学位论文,2011：9-22
[95]盖秉政.弹性力学[M].哈尔滨：哈尔滨工业大学出版社,2009：267-282
[96]李醒飞,郑奇,张国雄.类人气动肌肉模型与实验研究[J].天津大学学报,2005(3)：244-247
[97]刘增华.铁道车辆空气弹簧动力学特性及其主动控制研究[D].西南交通大学博士学位论文.2007：49-79
[98]张利国.串联双附加气室空气弹簧若干问题研究[D].哈尔滨工业大学博士学位论文.2009：10-50
[99]胡维,魏道高,李宏玲.带附加空气室空气弹簧垂向刚度有限元分析[J].汽车科技,2011,(3)：15-19
[100]郝玉密.低频高载荷空气弹簧研究[J].南京航空航天大学硕士学位论文.2007：20-51
[101]揭琳锋.基于复合材料理论的轮胎帘线受力模型及测试技术研究[D].江苏大学博士学位论文.2007：21-54
[102]刘新东,刘伟.复合材料力学基础[D].西安：西北工业大学出版社,2010,8：31-78
[103]顾太平,何琳,赵应龙.囊式空气弹簧平衡性分析[J].机械工程学报,2011,47(3)：69-72
[104]朱艳峰,刘锋,黄小清等.橡胶材料的本构模型[J].橡胶工业,2006,53(2)：119-125.
[105]HKS Co.Ltd, ABAQUS Analysis User's Manual 6.10
[106]HKS Co.Ltd, ABAQUS Theory Manual.3.7.3 Rebar modeling in shell, membrane, and surface elements
[107]HKS Co.Ltd, ABAQUS Keywords Manual 6.10
[108]HKS Co.Ltd, ABAQUS Theory Manual 3.8.1 Hydrostatic fluid elements
[109]HKS Co.Ltd, Getting Started with ABAQUS 6.10
[110]HKS Co.Ltd, ABAQUS Example Problems Manual 6.10
[111]HKS Co.Ltd, ABAQUS/CAE User's Manual 6.10
[112]刘昱,工涛,范伟.新型气动人工肌肉特性测试系统的研究[J].液压与气动,2011,(10)：63-66
[113]彭光正,沙俊伟,刘昊.新型气动人工肌肉特性测试系统的研究[J].液压与气动,2009,(11)：62-65