并联式燃气流冲击效应试验台运动模拟
|
摘要
本文以火箭燃气射流冲击效应实验研究需要为依据。构建了一种并联构型的可捷联各种被试模型的能模拟火箭弹与发射装置动态相对运动的通用实验平台。
首先分析了火箭燃气流研究任务的特点和以往试验平台的问题,提出非对称的3-(2SPS)三平动并联机构加回转工作台的混联构型方法,以满足被试模型与火箭发动机的多种相对位置关系需要。接着就并联机构进行尺度综合、位置解、工作空间以及运动学、动力学研究。
在位置解析与运动学方面,给出了机构的具体尺寸,建立机构的上下平台坐标系对机构进行位置正反解。建立机构的运动学模型,推导了机构的雅克比矩阵和海森矩阵,仿真分析了机构的运动学。
在工作空间方面,采用快速极坐标搜索法,给出机构的约束条件,搜索出工作空间轮廓。分别研究了机构的相关参数对工作空间的影响,以便对工作空间进行优化。研究了机构的奇异位置,得出机构的工作空间内无奇异位置。对机构的运动灵巧性进行评价,机构的灵巧度指标较低。
在动力学研究方面,先分析了机构的静力学特性,截取工作空间的2个截面,利用虚位移原理研究了支链在截面内的静力特性。接着研究机构单支链传动动力学,得到上平台等效到轴上的转动惯量,推导出电机输出量与支链输出量的传递函数框图。最后推导了机构的多体动力学拉格朗日方程。
文末利用多体动力学软件对系统进行了仿真,与之前的工作进行了对比,验证推导的正确性。
本文研究的燃气射流冲击效应测试平台对于火箭、导弹武器系统发射装置结构优化有巨大推动作用。
The purpose of this paper is to design a new kind of jet flow test system with parallel robotics which has high-precision, high stiffness. The paper studies the position, work- space, kinematic dynamic and so on of the system.
First, the article analyzes the structure of the system. The system is designed in the form of non-symmetrical parallel manipulator. It only has three translational degrees of freedom. According to the need of rocket jet flow test, define the specific size of every part. Establish coordinate system on both up and down platform. Analyze the inverse and forward position of the manipulator. Derive the Jacobian matrix and Hessian matrix of the system. At last we simulate the kinematics of the manipulator.
Followed by, we analyze the workspace of the manipulator. The boundary of the workspace is found using a fast search method. Giving the constraints of several limitations, we can scan the outline of the workspace. In order to optimize the workspace, several parameters which may affect the shape of the workspace are studied. Let the Jacobian matrix equals 0 find out the singular position in the workspace.
Then we analyzed the mechanical properties of the manipulator. At first, we analyze the static mechanical properties of the manipulator. We select two sections of the workspace, and use the virtual work method to calculate the static characteristics of the 6 screws. Then obtain the Lagrange equations of the manipulator.
At the end of this paper, we use the multi-body dynamics simulation software to simulate the system. Compared with the previous work we did, we can verify the correctness of the result.
The conclusions we get from the article are important to optimize the manipulator.
首先分析了火箭燃气流研究任务的特点和以往试验平台的问题,提出非对称的3-(2SPS)三平动并联机构加回转工作台的混联构型方法,以满足被试模型与火箭发动机的多种相对位置关系需要。接着就并联机构进行尺度综合、位置解、工作空间以及运动学、动力学研究。
在位置解析与运动学方面,给出了机构的具体尺寸,建立机构的上下平台坐标系对机构进行位置正反解。建立机构的运动学模型,推导了机构的雅克比矩阵和海森矩阵,仿真分析了机构的运动学。
在工作空间方面,采用快速极坐标搜索法,给出机构的约束条件,搜索出工作空间轮廓。分别研究了机构的相关参数对工作空间的影响,以便对工作空间进行优化。研究了机构的奇异位置,得出机构的工作空间内无奇异位置。对机构的运动灵巧性进行评价,机构的灵巧度指标较低。
在动力学研究方面,先分析了机构的静力学特性,截取工作空间的2个截面,利用虚位移原理研究了支链在截面内的静力特性。接着研究机构单支链传动动力学,得到上平台等效到轴上的转动惯量,推导出电机输出量与支链输出量的传递函数框图。最后推导了机构的多体动力学拉格朗日方程。
文末利用多体动力学软件对系统进行了仿真,与之前的工作进行了对比,验证推导的正确性。
本文研究的燃气射流冲击效应测试平台对于火箭、导弹武器系统发射装置结构优化有巨大推动作用。
The purpose of this paper is to design a new kind of jet flow test system with parallel robotics which has high-precision, high stiffness. The paper studies the position, work- space, kinematic dynamic and so on of the system.
First, the article analyzes the structure of the system. The system is designed in the form of non-symmetrical parallel manipulator. It only has three translational degrees of freedom. According to the need of rocket jet flow test, define the specific size of every part. Establish coordinate system on both up and down platform. Analyze the inverse and forward position of the manipulator. Derive the Jacobian matrix and Hessian matrix of the system. At last we simulate the kinematics of the manipulator.
Followed by, we analyze the workspace of the manipulator. The boundary of the workspace is found using a fast search method. Giving the constraints of several limitations, we can scan the outline of the workspace. In order to optimize the workspace, several parameters which may affect the shape of the workspace are studied. Let the Jacobian matrix equals 0 find out the singular position in the workspace.
Then we analyzed the mechanical properties of the manipulator. At first, we analyze the static mechanical properties of the manipulator. We select two sections of the workspace, and use the virtual work method to calculate the static characteristics of the 6 screws. Then obtain the Lagrange equations of the manipulator.
At the end of this paper, we use the multi-body dynamics simulation software to simulate the system. Compared with the previous work we did, we can verify the correctness of the result.
The conclusions we get from the article are important to optimize the manipulator.
引文
[1]张福祥.火箭燃气射流动力学[M].哈尔滨：哈尔滨工程大学出版社,2004.
[2]姜毅,张晓琳,刘琪.机载导弹发射时燃气流场的数值模拟[J].弹箭与制导学报.2002,22(3)：42-46
[3]王志军,姚建涛,工航等.并联预紧式六维力传感器动态力响应分析[J].机器人.2011,33(4)：455-460.
[4]贾振元,褚宏飞,刘巍等.基于Stewart结构六维大力传感器的性能分析及结构优化[J].仪器仪表学报.2010,31(2)：341-346.
[5]车林仙,何兵,易建等.对称结构Stewart机构位置正解的改进粒子群算法[J].农业机械学报.2008,39(10)：158-163.
[6]Tyapin Ilya,Hovland, Geir.The Gantry-Tau parallel kinematic machine-kinematic and elastodynamic design optimization[J]. Meccanica.2011,46(1):113-129.
[7]Zhen Huang.The Kinematics and Type Synthesis of Lower-Mobility Parallel Robot Manipulators[C]. World Congress in Mechanism and Machine Science v.1; 20040401-20040404; Tianjin; CN
[8]Syamsul Huda,YukioTakeda,Shuta Hanagasaki.Kinematic design of 3-URU pure rotational parallel mechanism to perform precise motion within a large workspace [J]. Meccanica.2011,46(1):89-100.
[9]车林仙.4-RUPaR并联机器人机构及其运动学分析[J].机械工程学报.2010,46(3)：35-45.
[10]李艳文,黄真,王鲁敏等.新型4自由度并联机器人运动学分析.机械工程学报[J].2008,44(10)：66-76.
[11]Jaime Gallardo, Rodriguez Ram6n,Caudillo Martin, Rico Jose M.A family of spherical parallel manipulators with two legs[J]. Mechanism and Machine Theory.2008,43 (2):201-216.
[12]J.K.Davidson,K.D.Chaney A design procedure for RPR planar robotic workcellsran algebraic approach[J]. Mechanism and Machine Theory.1999,34(2):193-203.
[13]Masory O.Wang J. On the accuracy of a Stewart platform. Ⅱ. Kinematic calibration and compensation[C]. Robotics and Automation.1993. Proceedings.,1993 IEEE International Conference on.
[14]Marco Ceccarelli.A Formulation For The Workspace Boundary of General N-Revolute Manipulators[J]. Mechanism and Machine Theory.1996,31(5):637-646.
[15]Yan Jin,I-Ming Chen,Guilin Yang.Workspace evaluation of manipulators through finite-partition of SE(3)[J]. Robotics and Computer-Integrated Manufacturing.211, 27(4):850-859.
[16]张彦斌,吴鑫,刘宏昭,张明洪.一种新型并联机器人机构的运动分析及完全各向同性设计[J].中国机械工程.2008,19(2)：213-216.
[17]覃艳明,郑魁敬,赵永生,张一同.5-UPS/PRPU五自由度并联机床的性能分析[J].机械科学与技术.2005,24(1)：100-103.
[18]刘永均,张静,李柏林.基于条件数的3-RRS并联机器人运动学性能优化[J].机械设计与研究.2008,24(6)：32-34.
[19]刘爽,郭希娟,刘彬.基于Hessian矩阵的3-RR(RR)R并联机构的性能分析[J].机械设计与研究.2006,22(5)：37-40.
[20]郭希娟,黄真.并联机器人机构加速度的性能指标分析[J].中国机械工程.2002,13(24)：2087-2090
[21]李永刚,宋轶民,冯志友,张策.基于牛顿欧拉法的3-RPS并联机构逆动力学分析.航空学报[J].2007,28(5)：1210-1215.
[22]冯志友,张燕,杨廷力,张策.基于牛顿欧拉法的2UPS-2RPS并联机构逆动力学分析[J].农业机械学报.2009,40(4)：193-197.
[23]郭祖华,陈五一,陈鼎昌.6-UPS型并联机构的刚体动力学模型[J].机械工程学报.2002,38(11)：53-57.
[24]Stefan Staicu.Dynamics of the 6-6 Stewart parallel manipulator[J]. Robotics and Computer-Integrated Manufacturing.2011,27(1):212-220.
[25]Stefan Staicu.Dynamics analysis of the Star parallel manipulator[J]. Robotics and Autonomous Systems.2009,57(11):1057-1064.
[26]Oscar Altuzarra.Asier Zubizarreta.Itziar Cabanes.Dynamics of a four degree of freedom parallel manipulator with parallelogram joints [J]. Mechatronics.2009,19(8): 1269-1279.
[27]Yingbo Wang,Shutao Zheng,Jun Jin.Dynamic Modeling of Spatial 6-Dof Parallel Manipulator using Kane Method[C]. E-Product E-Service and E-Entertainment (ICEEE),2010 International Conference on.
[28]赵剑波,高峰,岳义,刘伟6-PPPS型并联机器人的动力学建模[J].机械设计与研究.2007,23(6)：27-30.
[29]刘善增,余跃庆,刘庆波.3-RRC并联机器人动力学分析[J].机械工程学报.2009,45(5)：220-224.
[30]刘善增,余跃庆,刘庆波等.3-RRS并联机器人的动力学分析[J].中国机械工程.2008,19(15)：1778-1781.
[31]张典范,金振林,高峰.新型6-(P-2P-S)并联机器人逆动力学仿真分析[J].系统仿真学报.2009,21(23)：7640-7643.
[32]杨建新,汪劲松,郁鼎文.空间并联机构运动学与动力学逆解的模块化计算方法[J].机械工程学报.2005,41(5)：104-107.
[33]卿建喜,李剑锋,方斌.冗余驱动Tricept并联机构的驱动优化[J].机械工程学报.2010,46(5)：8-14.
[34]刘善增,余跃庆,侣国宁等.3自由度并联机器人的运动学与动力学分析[J].机械工程学报.2009,45(8)：11-17.
[35]赵晓东,丁文华,李仕华等.新型3-RPUR并联机构的逆动力学分析[J].机械设计与研究.2009,25(5)：17-19.
[36]杨永刚,刘玉斌,赵杰6-PRRS并联机器人的动力学建模研究[J].哈尔滨工业大学学报.2009,41(1)：53-57.
[37]Oren Masory,Jian Wang.Workspace evaluation of Stewart platforms[J]. Advanced Robotics.1995,9(4):443-461.
[38]Oscar Altuzarra,Jokin Aginaga,Alfonso Hernandez and Isidro Zabalza.Workspace analysis of positioning discontinuities due to clearances in parallel manipulators[J]. Mechanism and Machine Theory.2011,46(5):577-592.
[39]John S. Ketchel,Pierre M. Larochelle.Computer-aided manufacturing of spherical mechanisms [J]. Mechanism and Machine Theory.2007,42(2):131-146.
[40]Grigore Gogu.Full-Isotropic over-constrained parallel wrists[C]. International conference on robotics and automation, Barcelona, Spain, April 2005.
[41]Zeng Daxing,Hou Yulei,Huang Zhen,Lu Wenjuan.Type synthesis and characteristic analysis of a family [J].Chinese Journal of Mechanical Engineering.2009,22 (6) 833-840.
[42]Hexasphere-Redundantly Actuated Parallel Spherical Mechanism as a New Concept of Agile Telescope[J]. Advances in Astronomy.2010,2010(2010):1-6.
[43]G.R.Dunlop,T.P.Jones.Position analysis of a two DOF parallel mechanism-the Canterbury tracker[J]. Mechanism and Machine Theory.1999,34(4):599-614.
[44]张彦斌,吴鑫,刘宏昭,张明洪.一种新型并联机器人机构的运动分析及完全各向同性设计[J].中国机械工程.2008,19(2)：213-216.
[45]刘爽,郭希娟,刘彬.基于Hessian矩阵的3-RR(RR)R并联机构的性能分析[J].机械设计与研究.2006,22(5)：37-40.
[46]郭希娟,黄真.并联机器人机构加速度的性能指标分析[J].中国机械工程.2002,13(24)：2087-2090.
[47]覃艳明,郑魁敬,赵永生,张一同.5-UPS/PRPU五自由度并联机床的性能分析[J].机械科学与技术.2005,24(1)：100-103.
[48]刘永均,张静,李柏林.基于条件数的3-RRS并联机器人运动学性能优化[J].机械设计与研究.2008,24(6)：32-34.
[49]Ilian A. Bone,Jeha Ryu.A new approach to orientation workspace analysis of 6-DOF parallel manipulators[J]. Mechanism and Machine Theory.2001,36(1):15-28.
[50]高征,高峰.新型并联机器人的奇异位形分析[J].机械工程学报.2008,44(1)：133-138.
[51]Zhang Fan,Yang Jian-guo.A family of fully decoupled spherical parallel mechanisms[C]. Mechanic Automation and Control Engineering (MACE),2010 International Conference on.
[52]Chao Wu,Xin-Jun Liu,Jinsong Wang.Force transmission analysis of spherical 5R parallel manipulators[C]. Reconfigurable Mechanisms and Robots,2009. ReMAR 2009. ASME/IFToMM International Conference on.
[53]Seok-Hee Lee,Whee-Kuk Kim,Byung-Ju Yi,Il-Hong Suh.Analysis of two 3-DOF parallel mechanisms with constrained stewart platform structure[C].2006 IEEE International Conference on Robotics and Automation (ICRA), vol.10.
[54]Yunxia Qu.Anping Xu,Weimin Li,Shuncheng Fan.Velocity performance analysis of a novel 2-DOF fully-decoupled spherical parallel mechanism[C]. Intelligent Networks and Intelligent Systems,2009. ICINIS '09. Second International Conference on.
[55]Jianyong Zheng,Jinfei Shi.Zhisheng Zhang,Xiaoming Shi,Weimin Li.Workspace and kinematics analysis of a 2-DOF decoupled spherical parallel mechanism[C]. Mechatronics and Machine Vision in Practice,2008. M2VIP 2008.15th International Conference on
[56]黄真,孔令富,方跃法.并联机器人机构学理论及控制[M].北京：机械工业出版社.1997.
[57]黄真,赵永生,赵铁石.高等空间机构学[M].北京：高等教出版社,2006.
[58]赵景山,冯之敬,禇福磊.机器人机构自由度分析理论[M].北京：科学出版社,2009.
[59]周长省,鞠玉涛,朱福亚等.火箭弹设计理论[M].北京：北京理工大学出版社,2005.
[60]朱福亚.火箭弹构造与作用[M].北京：国防工业出版社,2005.
[61]刘正君.MATLAB科学计算与可视化仿真宝典[M].北京：电子工业出版社,2009.
[62]葛哲学.精通MATLAB[M]北京：电子工业出版社,2008.
[63]贾长治,殷军辉,薛文星MD ADAMS虚拟样机从入门到精通[M].北京：机械工业出版社,2010.
[64]陈立平,张云清等.机械系统动力学分析及ADAMS应用教程[M].北京：清华大学出版社,2005.
[65]郝永兴,田满香,罗小燕.机电传动控制[M].武汉：华中科技大学出版社,2010.
[2]姜毅,张晓琳,刘琪.机载导弹发射时燃气流场的数值模拟[J].弹箭与制导学报.2002,22(3)：42-46
[3]王志军,姚建涛,工航等.并联预紧式六维力传感器动态力响应分析[J].机器人.2011,33(4)：455-460.
[4]贾振元,褚宏飞,刘巍等.基于Stewart结构六维大力传感器的性能分析及结构优化[J].仪器仪表学报.2010,31(2)：341-346.
[5]车林仙,何兵,易建等.对称结构Stewart机构位置正解的改进粒子群算法[J].农业机械学报.2008,39(10)：158-163.
[6]Tyapin Ilya,Hovland, Geir.The Gantry-Tau parallel kinematic machine-kinematic and elastodynamic design optimization[J]. Meccanica.2011,46(1):113-129.
[7]Zhen Huang.The Kinematics and Type Synthesis of Lower-Mobility Parallel Robot Manipulators[C]. World Congress in Mechanism and Machine Science v.1; 20040401-20040404; Tianjin; CN
[8]Syamsul Huda,YukioTakeda,Shuta Hanagasaki.Kinematic design of 3-URU pure rotational parallel mechanism to perform precise motion within a large workspace [J]. Meccanica.2011,46(1):89-100.
[9]车林仙.4-RUPaR并联机器人机构及其运动学分析[J].机械工程学报.2010,46(3)：35-45.
[10]李艳文,黄真,王鲁敏等.新型4自由度并联机器人运动学分析.机械工程学报[J].2008,44(10)：66-76.
[11]Jaime Gallardo, Rodriguez Ram6n,Caudillo Martin, Rico Jose M.A family of spherical parallel manipulators with two legs[J]. Mechanism and Machine Theory.2008,43 (2):201-216.
[12]J.K.Davidson,K.D.Chaney A design procedure for RPR planar robotic workcellsran algebraic approach[J]. Mechanism and Machine Theory.1999,34(2):193-203.
[13]Masory O.Wang J. On the accuracy of a Stewart platform. Ⅱ. Kinematic calibration and compensation[C]. Robotics and Automation.1993. Proceedings.,1993 IEEE International Conference on.
[14]Marco Ceccarelli.A Formulation For The Workspace Boundary of General N-Revolute Manipulators[J]. Mechanism and Machine Theory.1996,31(5):637-646.
[15]Yan Jin,I-Ming Chen,Guilin Yang.Workspace evaluation of manipulators through finite-partition of SE(3)[J]. Robotics and Computer-Integrated Manufacturing.211, 27(4):850-859.
[16]张彦斌,吴鑫,刘宏昭,张明洪.一种新型并联机器人机构的运动分析及完全各向同性设计[J].中国机械工程.2008,19(2)：213-216.
[17]覃艳明,郑魁敬,赵永生,张一同.5-UPS/PRPU五自由度并联机床的性能分析[J].机械科学与技术.2005,24(1)：100-103.
[18]刘永均,张静,李柏林.基于条件数的3-RRS并联机器人运动学性能优化[J].机械设计与研究.2008,24(6)：32-34.
[19]刘爽,郭希娟,刘彬.基于Hessian矩阵的3-RR(RR)R并联机构的性能分析[J].机械设计与研究.2006,22(5)：37-40.
[20]郭希娟,黄真.并联机器人机构加速度的性能指标分析[J].中国机械工程.2002,13(24)：2087-2090
[21]李永刚,宋轶民,冯志友,张策.基于牛顿欧拉法的3-RPS并联机构逆动力学分析.航空学报[J].2007,28(5)：1210-1215.
[22]冯志友,张燕,杨廷力,张策.基于牛顿欧拉法的2UPS-2RPS并联机构逆动力学分析[J].农业机械学报.2009,40(4)：193-197.
[23]郭祖华,陈五一,陈鼎昌.6-UPS型并联机构的刚体动力学模型[J].机械工程学报.2002,38(11)：53-57.
[24]Stefan Staicu.Dynamics of the 6-6 Stewart parallel manipulator[J]. Robotics and Computer-Integrated Manufacturing.2011,27(1):212-220.
[25]Stefan Staicu.Dynamics analysis of the Star parallel manipulator[J]. Robotics and Autonomous Systems.2009,57(11):1057-1064.
[26]Oscar Altuzarra.Asier Zubizarreta.Itziar Cabanes.Dynamics of a four degree of freedom parallel manipulator with parallelogram joints [J]. Mechatronics.2009,19(8): 1269-1279.
[27]Yingbo Wang,Shutao Zheng,Jun Jin.Dynamic Modeling of Spatial 6-Dof Parallel Manipulator using Kane Method[C]. E-Product E-Service and E-Entertainment (ICEEE),2010 International Conference on.
[28]赵剑波,高峰,岳义,刘伟6-PPPS型并联机器人的动力学建模[J].机械设计与研究.2007,23(6)：27-30.
[29]刘善增,余跃庆,刘庆波.3-RRC并联机器人动力学分析[J].机械工程学报.2009,45(5)：220-224.
[30]刘善增,余跃庆,刘庆波等.3-RRS并联机器人的动力学分析[J].中国机械工程.2008,19(15)：1778-1781.
[31]张典范,金振林,高峰.新型6-(P-2P-S)并联机器人逆动力学仿真分析[J].系统仿真学报.2009,21(23)：7640-7643.
[32]杨建新,汪劲松,郁鼎文.空间并联机构运动学与动力学逆解的模块化计算方法[J].机械工程学报.2005,41(5)：104-107.
[33]卿建喜,李剑锋,方斌.冗余驱动Tricept并联机构的驱动优化[J].机械工程学报.2010,46(5)：8-14.
[34]刘善增,余跃庆,侣国宁等.3自由度并联机器人的运动学与动力学分析[J].机械工程学报.2009,45(8)：11-17.
[35]赵晓东,丁文华,李仕华等.新型3-RPUR并联机构的逆动力学分析[J].机械设计与研究.2009,25(5)：17-19.
[36]杨永刚,刘玉斌,赵杰6-PRRS并联机器人的动力学建模研究[J].哈尔滨工业大学学报.2009,41(1)：53-57.
[37]Oren Masory,Jian Wang.Workspace evaluation of Stewart platforms[J]. Advanced Robotics.1995,9(4):443-461.
[38]Oscar Altuzarra,Jokin Aginaga,Alfonso Hernandez and Isidro Zabalza.Workspace analysis of positioning discontinuities due to clearances in parallel manipulators[J]. Mechanism and Machine Theory.2011,46(5):577-592.
[39]John S. Ketchel,Pierre M. Larochelle.Computer-aided manufacturing of spherical mechanisms [J]. Mechanism and Machine Theory.2007,42(2):131-146.
[40]Grigore Gogu.Full-Isotropic over-constrained parallel wrists[C]. International conference on robotics and automation, Barcelona, Spain, April 2005.
[41]Zeng Daxing,Hou Yulei,Huang Zhen,Lu Wenjuan.Type synthesis and characteristic analysis of a family [J].Chinese Journal of Mechanical Engineering.2009,22 (6) 833-840.
[42]Hexasphere-Redundantly Actuated Parallel Spherical Mechanism as a New Concept of Agile Telescope[J]. Advances in Astronomy.2010,2010(2010):1-6.
[43]G.R.Dunlop,T.P.Jones.Position analysis of a two DOF parallel mechanism-the Canterbury tracker[J]. Mechanism and Machine Theory.1999,34(4):599-614.
[44]张彦斌,吴鑫,刘宏昭,张明洪.一种新型并联机器人机构的运动分析及完全各向同性设计[J].中国机械工程.2008,19(2)：213-216.
[45]刘爽,郭希娟,刘彬.基于Hessian矩阵的3-RR(RR)R并联机构的性能分析[J].机械设计与研究.2006,22(5)：37-40.
[46]郭希娟,黄真.并联机器人机构加速度的性能指标分析[J].中国机械工程.2002,13(24)：2087-2090.
[47]覃艳明,郑魁敬,赵永生,张一同.5-UPS/PRPU五自由度并联机床的性能分析[J].机械科学与技术.2005,24(1)：100-103.
[48]刘永均,张静,李柏林.基于条件数的3-RRS并联机器人运动学性能优化[J].机械设计与研究.2008,24(6)：32-34.
[49]Ilian A. Bone,Jeha Ryu.A new approach to orientation workspace analysis of 6-DOF parallel manipulators[J]. Mechanism and Machine Theory.2001,36(1):15-28.
[50]高征,高峰.新型并联机器人的奇异位形分析[J].机械工程学报.2008,44(1)：133-138.
[51]Zhang Fan,Yang Jian-guo.A family of fully decoupled spherical parallel mechanisms[C]. Mechanic Automation and Control Engineering (MACE),2010 International Conference on.
[52]Chao Wu,Xin-Jun Liu,Jinsong Wang.Force transmission analysis of spherical 5R parallel manipulators[C]. Reconfigurable Mechanisms and Robots,2009. ReMAR 2009. ASME/IFToMM International Conference on.
[53]Seok-Hee Lee,Whee-Kuk Kim,Byung-Ju Yi,Il-Hong Suh.Analysis of two 3-DOF parallel mechanisms with constrained stewart platform structure[C].2006 IEEE International Conference on Robotics and Automation (ICRA), vol.10.
[54]Yunxia Qu.Anping Xu,Weimin Li,Shuncheng Fan.Velocity performance analysis of a novel 2-DOF fully-decoupled spherical parallel mechanism[C]. Intelligent Networks and Intelligent Systems,2009. ICINIS '09. Second International Conference on.
[55]Jianyong Zheng,Jinfei Shi.Zhisheng Zhang,Xiaoming Shi,Weimin Li.Workspace and kinematics analysis of a 2-DOF decoupled spherical parallel mechanism[C]. Mechatronics and Machine Vision in Practice,2008. M2VIP 2008.15th International Conference on
[56]黄真,孔令富,方跃法.并联机器人机构学理论及控制[M].北京：机械工业出版社.1997.
[57]黄真,赵永生,赵铁石.高等空间机构学[M].北京：高等教出版社,2006.
[58]赵景山,冯之敬,禇福磊.机器人机构自由度分析理论[M].北京：科学出版社,2009.
[59]周长省,鞠玉涛,朱福亚等.火箭弹设计理论[M].北京：北京理工大学出版社,2005.
[60]朱福亚.火箭弹构造与作用[M].北京：国防工业出版社,2005.
[61]刘正君.MATLAB科学计算与可视化仿真宝典[M].北京：电子工业出版社,2009.
[62]葛哲学.精通MATLAB[M]北京：电子工业出版社,2008.
[63]贾长治,殷军辉,薛文星MD ADAMS虚拟样机从入门到精通[M].北京：机械工业出版社,2010.
[64]陈立平,张云清等.机械系统动力学分析及ADAMS应用教程[M].北京：清华大学出版社,2005.
[65]郝永兴,田满香,罗小燕.机电传动控制[M].武汉：华中科技大学出版社,2010.