摘要
康复训练机器人作为新兴特种机器人近年来得到了快速发展,其能够帮助具有功能障碍的患者和老年人进行康复训练,使关节和肌肉功能得到更为有效的恢复,从而进一步提高他们的生活质量；其也作为国家中长期科学和技术发展规划纲要的主要发展内容。
本文以下肢康复训练机器人的骨盆运动控制为对象,研究绳索牵引骨盆运动控制机器人的关键技术。通过绳索牵引骨盆运动控制,用以满足躯干与下肢步态的协调运动,同时提供一定的辅助力,这样不但能对受训者进行减重训练,而且还能锻炼受训者的自身平衡能力,从而达到更好的训练效果。主要研究内容包括绳索牵引骨盆运动控制机器人的绳索布置方案、1R2T机器人运动学及欠约束控制特性分析、1R2T机器人动力学分析、机器人运动规划研究等,并研制了1R2T绳索牵引机器人实验样机,基于dSPACE半物理仿真系统对绳索牵引机器人的驱动控制特性和动力学性能进行了实验研究。
在总结国内外下肢康复机器人以及骨盆运动控制机构概况的基础上,提出了一种绳索牵引骨盆运动控制机器人,用以满足下肢步态康复训练需要；分析了绳索牵引并联机器人的特点,并探讨绳索牵引机器人的应用领域及发展趋势。
根据正常人步态中的下肢支撑状态,将下肢简化成等效的结构形式,分析了骨盆的自由度输出类型,确定步态康复过程中骨盆的运动空间。依据骨盆运动控制的需要,基于绳索牵引机器人的可控性,分析了存在能够满足该功能的绳索牵引机器人的结构形式,选取了一种欠约束绳索牵引机器人。对水平面内不同绳索牵引机器人布置形式的工作空间大小、质量进行了研究和仿真分析,最终确定了等效的机器人绳索布置方案。
针对水平面内所确定的机器人绳索布置方案,利用三角形方法对其的位置进行了正逆分析,通过影响系数法建立了机器人的运动学方程,得到绳索运行速度、加速度与骨盆运行速度、加速度之间的映射关系。建立了机器人静力学力螺旋平衡方程,通过广义逆求得绳索拉力解空间,包括最小范数解和零空间解。研究了欠约束绳索牵引机器人实际控制过程中对骨盆运动控制的影响情况,并进行了误差分析。
利用牛顿欧拉法建立了骨盆在水平面内的动力学方程,基于达朗伯原理,建立了骨盆运动与绳索拉力之间的力学方程；又分析了绳索本身弹性对机器人动力学特性的影响,建立了绳索驱动单元的平衡方程。由于绳索牵引系统与刚性系统不同的特点之一就是其刚度相对较小,在此研究了绳索刚度和绳索零空间拉力对骨盆静态刚度的影响以及在外力作用下绳索刚度所引起骨盆的振动情况,并进行了仿真分析。
根据骨盆在步态过程中的期望运动状态,利用MATLAB建立了机器人运动学模型,并利用ADAMS所建立的机构模型对数学模型进行了验证,同时完成了运动学运动规划分析；建立了未考虑绳索刚度时机器人的逆动力学模型,进行了逆动力学运动规划研究,判断绳索最小拉力阈值对绳索拉力大小影响的规律。建立了考虑绳索刚度的绳索牵引机器人机构模型,分析了绳索刚度、绳索拉力对动力学运动规划的影响。
依据水平面内骨盆运动控制需要,研制了绳索牵引机器人实验样机,介绍了实验系统的各部分构成及其功能。基于dSPACE半物理仿真系统对绳索牵引机器人进行了实验研究,主要包括机器人的驱动控制特性实验和轨迹跟踪实验等。通过对实验结果进行分析,表明机器人的控制性能和精度满足下肢步态康复训练时对骨盆运动控制的要求。
In recent years, rehabilitation robots as an emerging special robot are developed quickly. They could help the function-barrier patient and the elderly to carry on the recovery training in order to make the joint and muscle recovery effectively, which their quality of life are improved. It is also a main development content of the national guideline on medium and long term program for science and technology development.
In the paper, the pelvis motion control of the lower-limb rehabilitation robot was chosen, and the key technologies of wire-driven pelvis motion control robot were researched. Through the robot, the coordinated motion between the body trunk and the lower limbs was realized and simultaneously certain external force was got, which could make not only the trainer carry on the weight relief training but also exercise self-balance ability training, thus the better training effect could achieved. The research mainly included. the wire arrangement scheme of wire-driven pelvis motion control robot, the configuration analysis of 1R2T robot, the dynamics analysis of 1R2T robot, the motion planning and so on. An experimental prototype of the wire-driven 1R2T robot was developed. Based on the dSPACE system, the experimental study on robot's control characteristic and dynamics performance was carried.
On the basis of the researches results of the lower-limb rehabilitation robot as well as the pelvis motion control machine at home and abroad, a kind of wire-driven pelvis motion control robot was proposed to meet the requirement of the lower limb gait recovery training. The characteristics of wire-driven robot were analyzed and the trend of development was discussed.
According to the lower limb support condition of the normal human, the lower limbs were simplified as the equivalent structural style. Based on the equivalent model, the types of pelvis's degree of freedom were analyzed and the motion space of the pelvis was confirmed in the gait recovery process. Based on the requirement for the pelvis motion control and the controllability of wire-driven robots, the structural style of wire-driven robots which was able to satisfy this function was analyzed. A kind of incompletely restrained wire-driven robot was selected. In the horizontal plane, the size and quality of the working space on different arrangement form of the wire-driven robot was simulated. The wire arrangement scheme of the wire-driven pelvis motion control robot was determined finally.
Aiming at the arrangement scheme of wires in the horizontal plane, using the degenerated three-pyramid method, the direct and inverse position and pose were analyzed. The kinematics equations were established by the influence coefficients, so that the mapping relationship between wire's motion and pelvis's motion was obtained. The static wrench balance equations were founded. Through the generalized inverse method, the solution space of wire tension was got, which included smallest norm solution and null space solution. The influence of incompletely restrained robots on the pelvis motion control was studied, and the error analysis was carried on.
Using the Newton-Euler method, the dynamics equations were constituted. Based on the D'Alembert principle, the force equations between the pelvis movement and the wire tension were got. The influence of wire elasticity on the robot dynamics characteristics was analyzed. Because one of different properties between wire-driven system and rigid system was that the rigidity of wire-driven system was relatively small, the influence of wire rigidity and wire tension in null pace on the pelvis static rigidity was analyzed, and pelvis vibration situation was analyzed under the external force.
On the basis of the desired motion state of the pelvis in the course of gait training, the kinematics model was established using MATLAB, And is was confirmed by the machine model which was established using ADAMS. The inverse dynamics model was built, in which the wire rigidity was neglected. The motion planning was conducted, in which the influence of the wire smallest tension value on wire tension change was analyzed. The mathematical model of the wire-driven robot was founded in view of wire rigidity. The effects of wire rigidity and wire tension on dynamics motion planning were analyzed.
According to the requirement of the pelvis motion control in the horizontal plane, the experimental prototype of the wire-driven robot was developed. The components and function of the experimental system were described. Based on the dSPACE system, the experimental study was conducted, which mainly included. the actuation control characteristic experiment, the trajectory planning experiment and so on. Through the experimental analysis, the results showed that the control performance and precision of the wire-driven robot could meet the requirement of pelvis motion control in the process of the lower limb gait recovery training.
引文
[1]康复治疗专业技术人才准入标准.中国康复医学杂志.2004,19(6)：413-415页
[2]张文生.中医康复学比较研究.中国中医基础医学杂志.2000,6(10)：56-58页
[3]http://www.tsinghua-hb.com/news_View.asp?id=967
[4]H. I. Krebs, B. T. Volpe, M. L. Aisen, et al. Increasing productivity and quality of care:Robot-aided neuro rehabilitation. Journal of Rehabilitation Research and Development. Vol.37,May 2000
[5]David Jack, Rares Boian. Virtual reality-enhanced strocke rehabilitation. IEEE Transaction on neural systems and rehabilitation engineering. Vol.9 No.3 September 2001:308-318P
[6]http://www.most.gov.cn/tztg/t20061001_36446.htm
[7]http://www.carm.org.cn/index.do#
[8]燕铁斌,窦祖林.实用瘫痪康复.北京：人民卫生出版社,1999
[9]涂春兰,曾萍,徐海玲.下肢骨折患者早期康复依从性的评估及护理.现代护理.2006，12(16)：1525-1526页
[10]http://www.china.com.cn/chinese/2003/Oct/422325.htm
[11]C.G.Burgar, P.S.Lum, P.S.Shor,et al. Development of robots for rehabilitation therapy:the Palo Alto VA/Standford experience.Journal of Rehabilitation Research and Development.vol.37.n.6.2000:663-673P
[12]Ann M. Simon, R. Brent Gillespie, Daniel P. Ferris. Symmetry-based resistance as a novel means of lower limb rehabilitation. Journal of Biomechanics.2007,40(6):1286-1292P
[13]Peshkin.Michael, Brown.David A, Santos-Munne Julio J,et al. KineAssist:A robotic overground gait and balance training device.Source:Proceedings of the 2005 IEEE 9th International Conference on Rehabilitation Robotics, v 2005, Proceedings of the 2005 IEEE 9th International Conference on Rehabilitation Robotics, ICORR 2005,2005:241-246P
[14]G.Colombo, M.Joerg, R.Schreier,et al. Treadmill training of paraplegic patient using a robotic orthosis.Journal of Rehabilitation Research and Developnemt.vol.37.n.6.2000:693-700P
[15]张付祥,付宜利,王树国.康复机器人研究进展.河北工业科技.2005,22(2)：100-105页
[16]张立勋,颜庆,杨勇,等.下肢康复训练机器人AVR单片机控制系统.机械与电子.2004(10)：52-55页
[17]王婷.减重式步态康复训练机器人控制及实验研究.哈尔滨工程大学硕士论文.2008：14页
[18]黄真,孔令富,方跃法.并联机器人机构学理论及控制.北京：机械工业出版社,1997,12：4-5,22,100页
[19]冯志友,李永刚,张策,等.并联机器人机构运动与动力分析研究现状及展望.中国机械工程.2006,17(9)：979-984页
[20]Y.J.Ou, L.W.Tsai. Theory of isotropic transmission for tendon-driven manipulators. American Society of Mechanical Engineers, Design Engineering Division (Publication) DE, v 72, n 3,23rd Biennial Mechanisms Conference,1994:53-61P
[21]R.Ozawa, H.Kobayashi.Teaching. Programing for Robots. Control of Tendon-Driven Mechanical Systems with Nonlinear Elastic Tendons.Journal of the Robotics Society of Japan.1999,v.17,n.2: 275-281P
[22]J.Albus, R.Bostelman, N.Dagalakis. The NIST ROBOCRANE. Journal of robotic systems.1993,10(5):709-724P
[23]R.G.Roberts, T.Graham, T.Lippitt. On the inverse kinematics, statics, and fault tolerance of cable-suspended robots. Journal of Robotic Systems.199815(10),581-597P
[24]Motoji Yamamoto, Noritaka Yanai, Akira Mohri. Trajectory Control of Incompletely Restrained Parallel-Wire-Suspended Mechanism Based on Inverse Dynamics.IEEE Transactions on Robotics, v 20, n 5, October,2004:840-850P
[25]M Yamamoto, A Mohri. Inverse kinematics analysis for incompletely restrained parallel wire mechanisms.Proceedings of the IEEE International Conference on Intelligent Robots and Systems,2000,(1):504-509P
[26]Richard Verhoeven.Analysis of the Workspace of Tendon-based Stewart Platforms. Duisburg:Gerhard MercatorUniversity.2004:27-28P
[27]Jadran Lenarcic, Manfred L.Husty (Eds).Advances in Robot Kinematics:Analysis and Control.Kluwer Academic Publishere.1998:105-114,277-284P
[28]A.Ming, M.Kajitani, T.Higuchi. On the design of wire parallel mechanism. International Journal of the Japan Society for Precision Engineering,1995,29(4):337-342P
[29]隋春平.并联柔索驱动机器人建模与控制.中国科学院沈阳自动化研究所.2004
[30]Bosscher Paul, Riechel,Andrew T., Ebert-Uphoff Imme. Wrench-feasible workspace generation for cable-driven robots. IEEE Transactions on Robotics,2006,22(5):890-902P
[31]Bosscher Paul, Ebert-Uphoff Imme.Wrench-based analysis of cable-driven robots. Proceedings-IEEE International Conference on Robotics and Automation, v 2004, n 5, Proceedings-2004 IEEE International Conference on Robotics and Automation, 2004:4950-4955P
[32]Bostelman R., Albus J., Dagalakis N.,et al. RoboCrane project: an advanced concept for large scale manufacturing. AUVSI'96 Proceedings,1996:509-21P
[33]Bosscher Paul, Williams Ⅱ Robert L., Bryson L. Sebastian; et al. Cable-suspended robotic contour grafting system. Proceedings of the ASME Design Engineering Technical Conference, v 2006, Proceedings of 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006,2006:9P
[34]Bosscher Paul, Williams Ⅱ Robert L., Bryson L. Sebastian, et al. Cable-suspended robotic contour crafting system Automation in Construction, v 17, n 1, November,2007:45-55P
[35]Trevisani Alberto, Gallina Paolo, Williams Ⅱ Robert L. Cable-Direct-Driven Robot (CDDR) with passive SCARA support: Theory and simulation.Journal of Intelligent and Robotic Systems: Theory and Applications.2006,46(1):73-94P
[36]Robert L.Williams Ⅱ, Paolo Gallina. Planar Cable-Direct-Driven Robots,Part I:Kinematics and Statics.Proceedings of the ASME Design Engineering Technical Conference, v 2, Proceedings of the ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference. Volume 2:27th Design Automation Conference,2001:1233-1240P
[37]Williams Ⅱ Robert L.,Gallina Paolo Planar cable-direct-driven robots:Design for wrench exertion. Journal of Intelligent and Robotic Systems:Theory and Applications.2002,35(2):203-219P
[38]Williams Ⅱ Robert L.,Gallina Paolo. Translational planar cable-direct-driven robots. Journal of Intelligent and Robotic Systems:Theory and Applications.2003,37(1):69-96P
[39]Williams II Robert L.,Gallina Paolo,Vadia Jigar. Planar translational cable-direct-driven robots. Journal of Robotic Systems. 2003,20(3):107-120P
[40]Gallina Paolo, Rossi Aldo, Williams Ⅱ Robert L. Planar cable-direct-driven robots, part II:Dynamics and control. Proceedings of the ASME Design Engineering Technical Conference, v 2, Proceedings of the ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference. Volume 2:27th Design Automation Conference,2001:1241-1247P
[41]Williams Ⅱ, Robert L., Vadia Jigar. Planar translational cable-direct-driven robots:Hardware implementation. Proceedings of the ASME Design Engineering Technical Conference, v 2 B, Proceedings of the 2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2:29th Design Automation Conference, 2003:1135-1142P
[42]Kawamura, S.; Choe, W.; Tanaka, S.; et al. Development of an ultrahigh speed robot FALCON using wire drive system.Proceedings-IEEE International Conference on Robotics and Automation, v 1,1995:215-220P
[43]Kawamura Sadao, Kino Hitoshi, Won Choe. High-speed manipulation by using parallel wire-driven robots. Robotica, v18, n1, Jan,2000:13-21P
[44]Kino, Hitoshi; Kawamura, Sadao. Development of A serial link structure/parallel wire system for a force display. Proceedings IEEE International Conference on Robotics and Automation, v1, 2002:829-834P
[45]Homma, K.; Fukuda, O.; Nagata, Y.;et al. Study of a wire-driven leg rehabilitation system.2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), vol.2,2004:1668-73P
[46]http://www.onera.fr/images-science/souffleries/sacso-mirage-soufflerie.php
[47]Lafourcade P, Llibre M, Reboulet C. Design of a parallel wire-driven manipulator for wind tunnels. In:Proceedings of the Workshop on Fundamental Issues and Future Direction for Parallel Mechanisms and Manipulators. Quebec City, Quebec,2002
[48]Lafourcade, P.;Llibre, M.; First steps toward a sketch-based design methodology for wire-driven manipulators.Proceedings.2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics 2003 (AIM 2003).Volume 1,20-24 July 2003:143-148P
[49]Hiller M, Fang S Q, Mielczarek S, et al. Design, analysis and realization of tendon-based parallel manipulators. Mechanism and Machine Theory,2005,40(4):429-445P
[50]Huang J, Hiller M, Fang S Q. Simulation Modeling of the Motion Control of a Two Degree of Freedom, Tendon Based, Parallel Manipulator in Operational Space Using MATLAB.Journal of China University of Mining & Technology,2007,17(2):179-183P
[51]Varziri M S, Notash L.Kinematic calibration of a wire-actuated parallel robot.Mechanism and Machine Theory,2007,42(8): 960-976P
[52]郑亚青,刘雄伟.六自由度绳牵引并联机构的可达工作空间分析.华侨大学学报：自然科学版.2002,23(4)：393-398页
[53]郑亚青,刘雄伟.绳牵引并联机构的研究概况与发展趋势.中国机械工程.2003,14(9)：808-810页
[54]郑亚青,刘雄伟.六自由度绳牵引并联机构的轨迹规划.华侨大学学报：自然科学版.2003,24(4)：385-389页
[55]刘雄伟,郑亚青,林麒.应用于飞行器风洞试验的绳牵引并联机构技术综述.航空学报.2004,25(4)：393-400页
[56]郑亚青,刘雄伟.6自由度绳牵引并联机构的运动轨迹规划.机械工程学报.2005,41(2)：77-81页
[57]郑亚青,刘雄伟.4个1R2T绳牵引并联机构的工作空间质量之比较.中国机械工程.2005,16(5)：384-389页
[58]郑亚青,刘雄伟.绳牵引并联机构拉力分布优化.机械工程学报.2005,41(9)：140-145页
[59]郑亚青,刘雄伟.绳牵引并联机构的工作空间优化.机械科学与技术.2005,24(12)：1502-1506页
[60]郑亚青,林麒,刘雄伟.低速风洞绳牵引并联支撑系统的机构与模型姿态控制方案设计.航空学报.2005,26(6)：774-778页
[61]Zheng,Ya-Qing.Feedback Linearization Control of a Wire-Driven Parallel Support System in Wind Tunnels. Proceedings-ISDA 2006: Sixth International Conference on Intelligent Systems Design and Applications, v 3, Proceedings-ISDA 2006:Sixth International Conference on Intelligent Systems Design and Applications, 2006,9-13P
[62]郑亚青,刘雄伟,林麒.绳牵引并联机构奇异性分析及无奇异机构设计.机械工程学报.2006,42(4)：57-62页
[63]郑亚青,林麒,刘雄伟.低速风洞绳牵引并联支撑系统的运动学参数标定.中国机械工程.2006,17(6)：551-554,558页
[64]郑亚青.6自由度绳牵引并联机构的运动学参数标定.华侨大学学报：自然科学版.2006,27(2)：184-188页
[65]高峻岩,郑亚青,林麒,等.立面1R2T三自由度绳牵引并联机构的位姿运动学分析.厦门大学学报：自然科学版.2006,45(6)：771-774页
[66]高峻岩,林麒,郑亚青.立面1R2T三自由度绳牵引并联机构的速度、加速度运动学分析.暨南大学学报：自然科学与医学版.2007,28(5)：440-444页
[67]胡龙,郑亚青,林麒,等.低速风洞绳牵引并联机构的动力学分析.华侨大学学报：自然科学版.2008,29(2)：184-189页
[68]郑亚青.绳牵引并联机构若干关键理论问题及其在风洞支撑系统中的应用研究.华侨大学.2004：187-200,43,130-131页
[69]Zheng Y Q,Liu X W.Force Transmission Index Based Workspace Analysis of A Six DOF Wire-Driven Parallel Manipulator.CD Proceedings of the 2002 ASME Design Technical Conferences,27th Mechanism and Robotics Conference,DETC2002/MECH-34241, Montreal, Canada,29 September-2 October,2002P
[70]Lafourcade P, Zheng Y Q, Liu X W. Stiffness Analysis of Wire-Driven Parallel Kinematic Manipulators.In:Huang T ed. Proceedings of the 11th World Congress in Mechanism and Machine Science. Tianjin, China, Beijing:China Machine Press, 2004:1878-1882P
[71]汤奥斐,仇原鹰,赵泽.柔索驱动并联机器人定位误差的柔性补偿法.高技术通讯.2008,8(3)：277-281页
[72]汤奥斐,仇原鹰,赵泽,等.索原长求解算法在索驱动并联机构运动学研究中的应用.中国机械工程.2008,19(5)：505-509页
[73]魏强,仇原鹰,段宝岩,等.八根索系大型射电望远镜馈源舱运动轨迹规划.中国机械工程.2002,13(23)：2036-2039页
[74]保宏,段宝岩,陈光达.输入不确定的6自由度悬索并联机器人位置控制.机械工程学报.2007,43(7)：128-132页
[75]汤奥斐,仇原鹰,段宝岩,等.大射电望远镜新构型的结构优化设计、虚牵索的抑制分析及风致振动实验研究.机械科学与技术.2006,26(5)：610-614页
[76]黄进,董正良.一类柔性悬索结构的自适应滑模控制.西安电子科技大学学报.2007,34(1)：11-15,62页
[77]汤奥斐,仇原鹰,段宝岩.大柔性Stewart平台的刚度研究.应用力学学报.2006,23(4)：677-681页
[78]汤奥斐,仇原鹰,段宝岩.一种柔索并联机器人的可达工作空间分析与刚度评价.西安电子科技大学学报.2006,33(5)：730-734,791页
[79]訾斌,杜敬利,段宝岩,等.大射电望远镜柔性Stewart平台的动力学分析与控制.机械科学与技术.2006,25(7)：784-788页
[80]保宏,杜敬利,段宝岩.大型射电望远镜悬索馈源支撑系统静刚度分析.机械工程学报.2006,42(7)：119-125页
[81]保宏,段宝岩,陈光达.索系馈源支撑结构控制方法的研究.机械设计与研究.2005,21(2)：64-66页
[82]保宏,段宝岩,陈光达,等.大射电望远镜舱索系统的控制与实验.中国机械工程.2007,18(14)：1643-1647页
[83]Sui Chunping,Zhao Mingyang.Control of a 3-DOF parallel wire driven stiffness-Variable manipulator.Proceedings-2004IEEE International Conference on Robotics and Biomimetics, IEEE ROBIO 2004, Proceedings-2004 IEEE International Conference on Robotics and Biomimetics, IEEE ROBIO 2004,2004,204-209P
[84]张波,战红春,赵明扬,等.柔索驱动三自由度球面并联机构运动学
与静力学研究.机器人.2003,25(3)：198-200,204页
[85]张波,赵明扬,房立金.一种6自由度柔索并联机器人的动力学研究.机械科学与技术.2004,23(6)：735-738页
[86]张波,王洪光,赵明扬.约束机构在柔索并联机器人设计中的应用.机械科学与技术.2004,23(12)：1387-1389页
[87]隋春平,张波,赵明扬,等.一种3自由度并联柔索驱动柔性操作臂的建模与控制.机械工程学报.2005,41(6)：60-65页
[88]隋春平,赵明扬.3自由度并联柔索驱动变刚度操作臂的刚度控制.机械工程学报.2006,42(6)：205-210页
[89]藏红.人体运动学.人民卫生出版社,2008.3：1,20-26页
[90]李振波,李华.基于运动生物力学的三维人体运动模型.系统仿真学报.2006,10(10)：2992-2994页
[91]潘慧炬,马楚虹,沈水富.人体四肢各主要关节最大运动幅度的研究.浙江师范大学报.1995,18(3)：64-68页
[92]Darryl G. T, Frank C. A. Using computed muscle control to generate forward dynamic simulations of human walking from experimental data.Journal of Biomechanics.2006,39(6):1107-1115P
[93]胡雪艳,江晓峰.偏瘫步态的运动学评定.中国康复理论与实践.2005,11(5)：359-396页
[94]刘德俊,郦鸣阳,沈力行.正常青年人行走步态的实验研究.上海理工大学学报.2008,30(1)：67-70,74页
[95]杨廷力.机器人机构拓扑结构学.机械工业出版社,2004,3：10页
[96]杨东超,赵明国,陈恳,等.拟人机器人自由度的分析.中国机械工程.2003,14(3)：453-456页
[97]张立勋,赵凌燕,王岚,等.一种测量人行走时骨盆运动轨迹的新方法.哈尔滨工程大学学报.2006,27(1)：128-130,135页
[98]赵凌燕,张立勋,张今瑜,等.一种获取骨盆左右运动轨迹模型的方法.哈尔滨工程大学学报.2007,28(12)：1382-1386页
[99]熊有伦.机器人技术基础.武汉：华中理工大学出版社,1996.8：15-20页
[100]张志涌.精通MATLAB6.5版.北京：北京航空航天大学出版 社,2003.3：114页
[101]Paolo G, Giulio R. Manipulability of a planar wire driven haptic device. Mechanism and Machine Theory.2002,37 (2):215-228P
[102]隋春平,赵明扬.并联柔索驱动操作臂静刚度的理论分析.组合机床与自动化加工技术.2007(7)：27-30页
[103]J.H.金斯伯格著.白化同,李俊宝译.机械与结构振动——理论与应用.北京：中国宇航出版社,2005.1：16-19页
[104]中国标准研究中心.GB／T 17245-2004成年人人体惯性参数.北京：国家质检总局,2004
[105]郑凯,胡仁喜,陈鹿民,等.ADAMS2005机械设计高级应用实例.机械工业出版社,2006.1：203-205页
[106]杨涤,李立涛,杨旭,等.系统实时仿真开发环境与应用.北京：清华大学出版社,2002.10：339-347页
[107]马培蓓,吴进华,纪军,等.dSPACE实时仿真平台软件环境及应用.系统仿真学报.2004,16(4)：667-670页
[108]张立勋,董玉红.机电系统仿真与设计.哈尔滨：哈尔滨工程大学出版社,2006.9：232-246页
[109]卢子广,柴建云,王祥珩,等.电力驱动系统实时控制虚拟实验平台.中国电机工程学报.2003,23(4)：119-123页
[110]郑亚青,林麒,刘雄伟.低速风洞绳牵引并联支撑系统的运动学参数标定.中国机械工程.2006,17(6)：551-554,558页
