六自由度并联机床的运动学分析及控制系统设计
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摘要
并联机床又称并联结构机床、虚拟轴机床。并联机床是基于空间并联机构Stewart平台原理开发的,是并联机器人机构与机床结合的产物,是空间机构学、机械制造、控制技术、计算机软硬件技术和CAD/CAM技术高度结合的高科技产品。论文做的主要工作包括以下几个方面:
针对六自由度并联机床,首先在Matlab软件中建立其逆解数学模型,即定义其动坐标系和定坐标系,运动副的类型,动平台和和定平台等各个构件的空间位置。然后通过欧拉角坐标变换法求其数学模型,得到用于控制刀具运动轨迹的杆长变化函数。
在完成运动学逆解分析之后,在UG软件中建立其三维模型,并将模型导入ADAMS软件中对其进行运动学仿真,得到杆件的运动仿真曲线,通过与MATLAB求解获得的理论曲线相比较,结果是吻合的,从而验证了逆解模型的正确性,为进一步在开放式数控系统的运动模块中建立逆解模型奠定了基础。
为实现对六自由度并联机床的运动控制,本文提出以EMC2(Enhanced Machine Controller,增强的机器控制器)开放式数控系统为平台建立并联机床的控制系统。本文运用求得的逆解模型,在EMC2中重新建立其运动学逆解模块,并用数控加工实例加以仿真验证,得到了正确的结果,从而证明了所提方法的可行性,为本课题项目后续的样机制造及电机输出控制奠定了重要基础。
Parallel Machine Tools is also called Parallel Structured Machine Tools, Virtual Axis Machine Tools. Parallel machine tools is developed basing on principle of spatial parallel-mechanisms Stewart platform, which is the product of Parallel Robotic Mechanisms and machine tools. And parallel machine tools is high-tech products of powerful mixture of spatial machanisms, Mechanical Manufacturing, control technique, computer soft-hard wares technology and CAD/CAM technology. The paper is focused on the following pionts:
This paper analyzes 6-DOF parallel kinematic machine(PKM) kinematics character, solves its inverse model via MATLAB software. In this step, it needs to define the mobile and base coordinate system, the type of the movement and the LOCA of the base and mobile platform and all of the structual members. The mathematic model which used to control toolpath is completely ascertained with the method of Euler parameter transformation.
After the analysis of the kinematics inverse transformation, this paper constructs PKM model under UG environment. Kinematics simulation is performed through introducing the model into ADAMS, finally rod kinematic simualtion curve is obtained. By comparing simulation curve with the theoretical one obtained from MATLAB, the curves match each other well, which demonstrates the correctness of the inverse model. Therefore, the inverse mathematics model in Open Numerical Control System kinematics module is set up.
To realize motion control of 6-DOF PKM, this paper provides a way of applying EMC2(Enhanced Machine Controller) Open Numerical Control System as the platform to build PKM’s control system. In this paper, the obtained inverse model is used, and the kinematics inverse module is rebuilt in EMC2 and verified by simulation with CNC code, which lays an important foundation for later prototype construction and motor output control.
针对六自由度并联机床,首先在Matlab软件中建立其逆解数学模型,即定义其动坐标系和定坐标系,运动副的类型,动平台和和定平台等各个构件的空间位置。然后通过欧拉角坐标变换法求其数学模型,得到用于控制刀具运动轨迹的杆长变化函数。
在完成运动学逆解分析之后,在UG软件中建立其三维模型,并将模型导入ADAMS软件中对其进行运动学仿真,得到杆件的运动仿真曲线,通过与MATLAB求解获得的理论曲线相比较,结果是吻合的,从而验证了逆解模型的正确性,为进一步在开放式数控系统的运动模块中建立逆解模型奠定了基础。
为实现对六自由度并联机床的运动控制,本文提出以EMC2(Enhanced Machine Controller,增强的机器控制器)开放式数控系统为平台建立并联机床的控制系统。本文运用求得的逆解模型,在EMC2中重新建立其运动学逆解模块,并用数控加工实例加以仿真验证,得到了正确的结果,从而证明了所提方法的可行性,为本课题项目后续的样机制造及电机输出控制奠定了重要基础。
Parallel Machine Tools is also called Parallel Structured Machine Tools, Virtual Axis Machine Tools. Parallel machine tools is developed basing on principle of spatial parallel-mechanisms Stewart platform, which is the product of Parallel Robotic Mechanisms and machine tools. And parallel machine tools is high-tech products of powerful mixture of spatial machanisms, Mechanical Manufacturing, control technique, computer soft-hard wares technology and CAD/CAM technology. The paper is focused on the following pionts:
This paper analyzes 6-DOF parallel kinematic machine(PKM) kinematics character, solves its inverse model via MATLAB software. In this step, it needs to define the mobile and base coordinate system, the type of the movement and the LOCA of the base and mobile platform and all of the structual members. The mathematic model which used to control toolpath is completely ascertained with the method of Euler parameter transformation.
After the analysis of the kinematics inverse transformation, this paper constructs PKM model under UG environment. Kinematics simulation is performed through introducing the model into ADAMS, finally rod kinematic simualtion curve is obtained. By comparing simulation curve with the theoretical one obtained from MATLAB, the curves match each other well, which demonstrates the correctness of the inverse model. Therefore, the inverse mathematics model in Open Numerical Control System kinematics module is set up.
To realize motion control of 6-DOF PKM, this paper provides a way of applying EMC2(Enhanced Machine Controller) Open Numerical Control System as the platform to build PKM’s control system. In this paper, the obtained inverse model is used, and the kinematics inverse module is rebuilt in EMC2 and verified by simulation with CNC code, which lays an important foundation for later prototype construction and motor output control.
引文
[1]黄真,孔令富,方跃法.并联机器人机构学理论及控制[M].机械工业出版社,1997:3.
[2]张曙,U.Heisel.并联运动机床[M].机械工业出版社,2003:4.
[3] Hunt K.H. Structural kinematics of in parallel actuated robot arms[J]. J. of Mechanisms, Transmissions and Automation in Design, 105(4):705–712, March 1983.
[4] Herve J.M. Analyse structurelle des m′ecanismes par groupe de d′eplacements[J]. Mechanism and Machine Theory, 13(4):437–450, 1978.
[5] Herve J.M. Group mathematics and parallel link mechanisms[J]. In 9th World Congress on the Theory of Machines and Mechanisms, pages 2079–2082, Milan, August 30- September 2, 1995.
[6] McCarthy J.M. Mechanism synthesis theory and the design of robots[J]. In IEEE Int. Conf. on Robotics and Automation, pages 55–60, San Francisco, April, 24-28, 2000.
[7]刘辛军,汪劲松,高峰,等.并联机器人机构新构型设计的探讨[J].机械工程学报,2001,12 (12): 1339-1342.
[8]杨廷力.机器人机构拓扑结构学[M].北京:机械工业出版社,2004.
[9] Fichter E.F. A Stewart platform based manipulator: general theory and practical construction[J]. Int. J. of Robotics Research, 5(2):157–181, Summer 1986.
[10] Koliskor A. Sh. The l-coordinate approach to the industrial robot design[J]. In V IFAC/IFIP/IMACS/IFORS Symposium, pages 108–115, Suzdal, URSS, April, 22-25, 1986.
[11] Reboulet C. and Robert A. Hybrid control of a manipulator with an active compliant wrist[J]. In 3rd ISRR, pages 76–80, Gouvieux, France, October, 7-11, 1985.
[12] Hara A. and Sugimoto K. Synthesis of parallel micromanipulators[J]. J. of Mechanisms, Transmissions and Automation in Design, 111(1):34–39, March 1989.
[13]陈立平,张动清,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,2005.1.
[14]郭卫东.虚拟样机技术与ADAMS应用实例教程[M].北京:北京航空航天大学出版社,2008.6.
[15]郑建荣.ADAMS-虚拟样机技术入门与提高[M].北京:机械工业出版社,2001.11.
[16]王洋.并联机床开放式数控系统开发[J].天津:天津大学, 2002.
[17]魏永明.虚拟轴机床数控系统的建造[J].北京:清华大学, 1998.
[18]梅江平,倪雁冰,王辉,等.并联机床数控平台建造[J].组合机床与自动化加工技术,2002(1):9-11.
[19]谢红.五杆五环并联运动机床开发设计及关键技术研究[D].同济大学工学博士学位论文. 2007.
[20] K. Wohlhart: Mobile 6-SPS parallel manipulators, J. Robot. Syst. 20(8), 509–516 (2003)
[21]言川宣.机床结构的重大创新一VARIAX机床问世[J].世界制造技术与装备市场,1995,1:16一17.
[22]晓林“.六条腿”机床技术在英国机床公司的新进展[J].世界制造技术与装备市场,1997,2:87-88.
[23] J.-P. Merlet: Jacobian, manipulability,condition number, and accuracy of parallel robots. ASME J. Mech. Design 128(1), 199–206 (2006)
[24] Vrecher, C, Ostermnaa, T, Friderich, D.A. Control concept for PKM considering the mechanical coupling beteen actuators[J]. The 5th Cheemnitz Parallel Kinematics Seminar PKS 2006. April 25-26,2006:413-427.
[25] Prischow G, ET Al. Open controller architecture-past, present and future[J]. Annals of Cirp, 50(2):126-135, 2001.
[26]汪劲松等.VAMTIY虚拟轴机床[J].制造技术与机床,1998,2:42-43.
[27]蔡光起,胡明,郭成,等.机器人化三腿磨削机床的研制[J].制造技术与机床,1998,10:4-6.
[28]李兵,王知行,袁剑雄.新型并联机床的操作空间分析[J].机械设计与研究.1999,l:46-49.
[29]江崇民,王振宇,王哲元.XNZD2415型控制龙门并联机床简介[J].机械工程师,2003,2:53-54.
[30]黄玉美,史文浩,高峰,等.混联式六轴联动控制机床6PMZ的方案创新[J].制造技术与机床,2003,No.6:20-21.
[31] Kreidler V. Development and software methods for parallel kinematic machine accuracy[J]. In:Proccedings of 2nd parallel kinematic seminar, 241-256, Chemnitz,German:2000.
[32]吴振彪.工业机器人[M].华中科技大学出版社.1996:14-50.
[33]王启义.机械制造装备设计[M].北京:冶金工业出版社,2003:219-220.
[34]黄田,汪劲松,WHITEHOUSE D. GOUGH-STEWART平台运动学设计理论与方法[J].中国科学(E辑),1999,29(4):320-320.
[35]黄田,汪劲松等.STEWART并联机器人局部灵活度与各向同性条件解析[J].机械工程学报, 1999,35(5):41-46.
[36]姜兵,黄田等.6-PSS型并联机床姿态空间解析[J].机械设计与制造工程,1999,增刊:70-72.
[37]刘安心,杨廷力.空间并联机构位置分析的连续法[J].机械科学与技术.1994,(51):19-25.
[38]刘文涛,李建生,祁勇,王知行.并联杆系机床工作空间分析[J].机械设计.1998,11:24-27.
[39] Ku D M. Direct displacement analysis of a stewart platform mechanism[J]. Mechanism and Machine theory, 1999, 34(5):453-465.
[40] Ji Ping, Wu Hong Tao. A closed-form forward kinematics solution for the 6-6steward platform[J]. IEEE Transactions on robotics and automation. 2001,17(4):423-434.
[41] Bonev I A, Ryu J. Anew method for solving the direct kinematics of general 6-6stewart platforms using three linar extra sensors[J]. Mechanism and Machine theory, 2000,35(4):423:436.
[42] Pierre Renaud, Andres Vivas, Nixolas Andreff, Philippe Poignet, Philippe Martinet. Kinematic and dynamic idetification of parallel mechanisms[J]. Control Engineering Practice 14 (2006)1099-1109.
[43] G Pritschow, K.H.Wurst. Systematic design of hexapod sand other parallel link system[J]. Cirp Annals, 1997, 46(1):291-295.
[44] Merlet J-P. Parallel mechanisms and robots. Dordrecht: Kluwer Academic Publishers; 2000.
[45] Jinsong Wang, Jun Wu, Liping Wang, Tiemin Li. Simplified strategy of the dynamic model of a 6-UPS parallel kinematic machine for real-time control[J]. Mechanism and Machine theory 42(2007)1119-1140.
[46]金振林.新型六自由度正交并联机器人设计理论与应用技术研究[D].燕山大学工学博士论文,2001.
[47]李颖.五轴五去链并联机床控制系统的软硬件设计[D].河北工业大学硕士论文,2005.
[48] Lee K M, Park KW. Kinematic and dynamic models of hybrid robot manipulator for propeller grinding[J]. Journal of robotic systems. 1999,16:137-150.
[49]袁先垚,刘华,马明明,等.基于ADAAMS的并联机床运动学仿真[J].山东理工大学学报.2008,(6)11.
[50]陈宗雨,郭伟.基于WINDowsNT与实时扩展的开放式控制系统的研究[J].计算机集成制造系统,2006,4:90-94.
[51]王恒,陈恳,刘顺涛.基于软件模式的开放结构控制器平台的研究[J].计算机集成制造系统,2006,3:128-132.
[52] Protector F M. The enhanced machine controler. www.isd.mel.nist.gor/projects/emc/em.htm.
[53] www.isd.mel.nist.gov/projects/emcemcsoft.htm.
[54] The EMC team. The Enhanced Machine Contorl user handbook. Linuxcnc.org, 2008.
[55] The EMC team. The Enhanced Machine Control developer handbook. Linuxcnc.org, 2008.
[56] http://wiki.linuxcnc.org/cgi-bin/emcinfo.pl, 2008.
[2]张曙,U.Heisel.并联运动机床[M].机械工业出版社,2003:4.
[3] Hunt K.H. Structural kinematics of in parallel actuated robot arms[J]. J. of Mechanisms, Transmissions and Automation in Design, 105(4):705–712, March 1983.
[4] Herve J.M. Analyse structurelle des m′ecanismes par groupe de d′eplacements[J]. Mechanism and Machine Theory, 13(4):437–450, 1978.
[5] Herve J.M. Group mathematics and parallel link mechanisms[J]. In 9th World Congress on the Theory of Machines and Mechanisms, pages 2079–2082, Milan, August 30- September 2, 1995.
[6] McCarthy J.M. Mechanism synthesis theory and the design of robots[J]. In IEEE Int. Conf. on Robotics and Automation, pages 55–60, San Francisco, April, 24-28, 2000.
[7]刘辛军,汪劲松,高峰,等.并联机器人机构新构型设计的探讨[J].机械工程学报,2001,12 (12): 1339-1342.
[8]杨廷力.机器人机构拓扑结构学[M].北京:机械工业出版社,2004.
[9] Fichter E.F. A Stewart platform based manipulator: general theory and practical construction[J]. Int. J. of Robotics Research, 5(2):157–181, Summer 1986.
[10] Koliskor A. Sh. The l-coordinate approach to the industrial robot design[J]. In V IFAC/IFIP/IMACS/IFORS Symposium, pages 108–115, Suzdal, URSS, April, 22-25, 1986.
[11] Reboulet C. and Robert A. Hybrid control of a manipulator with an active compliant wrist[J]. In 3rd ISRR, pages 76–80, Gouvieux, France, October, 7-11, 1985.
[12] Hara A. and Sugimoto K. Synthesis of parallel micromanipulators[J]. J. of Mechanisms, Transmissions and Automation in Design, 111(1):34–39, March 1989.
[13]陈立平,张动清,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,2005.1.
[14]郭卫东.虚拟样机技术与ADAMS应用实例教程[M].北京:北京航空航天大学出版社,2008.6.
[15]郑建荣.ADAMS-虚拟样机技术入门与提高[M].北京:机械工业出版社,2001.11.
[16]王洋.并联机床开放式数控系统开发[J].天津:天津大学, 2002.
[17]魏永明.虚拟轴机床数控系统的建造[J].北京:清华大学, 1998.
[18]梅江平,倪雁冰,王辉,等.并联机床数控平台建造[J].组合机床与自动化加工技术,2002(1):9-11.
[19]谢红.五杆五环并联运动机床开发设计及关键技术研究[D].同济大学工学博士学位论文. 2007.
[20] K. Wohlhart: Mobile 6-SPS parallel manipulators, J. Robot. Syst. 20(8), 509–516 (2003)
[21]言川宣.机床结构的重大创新一VARIAX机床问世[J].世界制造技术与装备市场,1995,1:16一17.
[22]晓林“.六条腿”机床技术在英国机床公司的新进展[J].世界制造技术与装备市场,1997,2:87-88.
[23] J.-P. Merlet: Jacobian, manipulability,condition number, and accuracy of parallel robots. ASME J. Mech. Design 128(1), 199–206 (2006)
[24] Vrecher, C, Ostermnaa, T, Friderich, D.A. Control concept for PKM considering the mechanical coupling beteen actuators[J]. The 5th Cheemnitz Parallel Kinematics Seminar PKS 2006. April 25-26,2006:413-427.
[25] Prischow G, ET Al. Open controller architecture-past, present and future[J]. Annals of Cirp, 50(2):126-135, 2001.
[26]汪劲松等.VAMTIY虚拟轴机床[J].制造技术与机床,1998,2:42-43.
[27]蔡光起,胡明,郭成,等.机器人化三腿磨削机床的研制[J].制造技术与机床,1998,10:4-6.
[28]李兵,王知行,袁剑雄.新型并联机床的操作空间分析[J].机械设计与研究.1999,l:46-49.
[29]江崇民,王振宇,王哲元.XNZD2415型控制龙门并联机床简介[J].机械工程师,2003,2:53-54.
[30]黄玉美,史文浩,高峰,等.混联式六轴联动控制机床6PMZ的方案创新[J].制造技术与机床,2003,No.6:20-21.
[31] Kreidler V. Development and software methods for parallel kinematic machine accuracy[J]. In:Proccedings of 2nd parallel kinematic seminar, 241-256, Chemnitz,German:2000.
[32]吴振彪.工业机器人[M].华中科技大学出版社.1996:14-50.
[33]王启义.机械制造装备设计[M].北京:冶金工业出版社,2003:219-220.
[34]黄田,汪劲松,WHITEHOUSE D. GOUGH-STEWART平台运动学设计理论与方法[J].中国科学(E辑),1999,29(4):320-320.
[35]黄田,汪劲松等.STEWART并联机器人局部灵活度与各向同性条件解析[J].机械工程学报, 1999,35(5):41-46.
[36]姜兵,黄田等.6-PSS型并联机床姿态空间解析[J].机械设计与制造工程,1999,增刊:70-72.
[37]刘安心,杨廷力.空间并联机构位置分析的连续法[J].机械科学与技术.1994,(51):19-25.
[38]刘文涛,李建生,祁勇,王知行.并联杆系机床工作空间分析[J].机械设计.1998,11:24-27.
[39] Ku D M. Direct displacement analysis of a stewart platform mechanism[J]. Mechanism and Machine theory, 1999, 34(5):453-465.
[40] Ji Ping, Wu Hong Tao. A closed-form forward kinematics solution for the 6-6steward platform[J]. IEEE Transactions on robotics and automation. 2001,17(4):423-434.
[41] Bonev I A, Ryu J. Anew method for solving the direct kinematics of general 6-6stewart platforms using three linar extra sensors[J]. Mechanism and Machine theory, 2000,35(4):423:436.
[42] Pierre Renaud, Andres Vivas, Nixolas Andreff, Philippe Poignet, Philippe Martinet. Kinematic and dynamic idetification of parallel mechanisms[J]. Control Engineering Practice 14 (2006)1099-1109.
[43] G Pritschow, K.H.Wurst. Systematic design of hexapod sand other parallel link system[J]. Cirp Annals, 1997, 46(1):291-295.
[44] Merlet J-P. Parallel mechanisms and robots. Dordrecht: Kluwer Academic Publishers; 2000.
[45] Jinsong Wang, Jun Wu, Liping Wang, Tiemin Li. Simplified strategy of the dynamic model of a 6-UPS parallel kinematic machine for real-time control[J]. Mechanism and Machine theory 42(2007)1119-1140.
[46]金振林.新型六自由度正交并联机器人设计理论与应用技术研究[D].燕山大学工学博士论文,2001.
[47]李颖.五轴五去链并联机床控制系统的软硬件设计[D].河北工业大学硕士论文,2005.
[48] Lee K M, Park KW. Kinematic and dynamic models of hybrid robot manipulator for propeller grinding[J]. Journal of robotic systems. 1999,16:137-150.
[49]袁先垚,刘华,马明明,等.基于ADAAMS的并联机床运动学仿真[J].山东理工大学学报.2008,(6)11.
[50]陈宗雨,郭伟.基于WINDowsNT与实时扩展的开放式控制系统的研究[J].计算机集成制造系统,2006,4:90-94.
[51]王恒,陈恳,刘顺涛.基于软件模式的开放结构控制器平台的研究[J].计算机集成制造系统,2006,3:128-132.
[52] Protector F M. The enhanced machine controler. www.isd.mel.nist.gor/projects/emc/em.htm.
[53] www.isd.mel.nist.gov/projects/emcemcsoft.htm.
[54] The EMC team. The Enhanced Machine Contorl user handbook. Linuxcnc.org, 2008.
[55] The EMC team. The Enhanced Machine Control developer handbook. Linuxcnc.org, 2008.
[56] http://wiki.linuxcnc.org/cgi-bin/emcinfo.pl, 2008.