变拓扑机构的构型综合及运动特性分析
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摘要
为适应复杂、恶劣工作环境的变化或多功能要求的变化,现代机械系统要求现代机构向自重构性发展,即机构在运动过程中,可以改变其拓扑结构、运动学参数或动力学参数。变拓扑机构是在变胞机构的基础上提出的一类具有自重构性的新机构,变拓扑机构可以通过构件的缩并与裂变、邻接关系的变化和运动副类型的变化,以改变机构在运动过程中的构型,适应不同的工作环境,拓展了机构应用的范围。
目前,变拓扑机构在构型的综合与选择、构型间的关系、运动学和动力学分析等领域还有大量的问题没有解决。由于对变拓扑机构的分析涉及到多种构型分析,具有复杂性,因此寻找多种构型之间的拓扑结构变换关系就显得非常重要,同时变拓扑机构的变换点的选择以及对前后构型的影响也是机构分析的重点。
针对以上情况,本文进行了以下研究:
①提出了变拓扑机构构型综合的方法,对三种变拓扑方式下机构构型综合的规律进行了研究,得到了一种变拓朴机构构型综合的实用方法。
②通过对机构变换过程中前后构型之间关系的分析,建立了以瞬时功率差的平方最小为目标来选择机构变拓扑点的目标函数以及变换时的约束条件;通过分析机构两种构型间的关系,推导了机构速度矩阵在前后构型中的传递关系,为机构的奇异性分析提供了一种简便快捷的方法。
③利用MATLAB软件对5-4杆变拓扑机构进行了仿真分析,得到了5-4杆机构第一次出现奇异位形时的机构的最优变拓扑点,通过对变拓扑机构进行运动仿真,得到了其运动曲线,在此基础上提出了变拓扑区域选择的方法。
本文提出了的变拓扑机构的构型综合方法,分析了变拓扑点的选择和机构奇异位形计算中前后构型间的速度传递矩阵R;通过R阵的计算,简化了后一构型速度矩阵的计算步骤,充实了变拓扑机构的分析和设计方法。本文的研究工作对于变拓扑机构的设计及应用提供了比较重要的参考。
In order to adapt to the exploration and poor working environment or multi-functional requirements, the modern mechanical systems require the modern machine develops towards the reconstruction. That is to say, machine can change its topology configuration, kinematic parameters or dynamics parameters in the process of movement. Variable topology mechanism which is based on the metamorphic mechanism is a new type of machine of self-reconstruction. By the combination and split of the bar, the change of connecting relationship and changing the type of kinematic pair , variable topology mechanism can change the machine configuration in the process of the working motion to be adapted to different working environment and expand the scope of application of the mechiansms.
At present, variable topology mechanism hasn’t yet solved some problems such as the synthesis and the selection of the configuration, the relationship between the before and after configuration and the anslysis of kinematics and dynamics. It’s a very complex problem to analyse variable topology mechanism which involves in the variety of configurations. Therefore it is important to search the topology configurations transform relationships among the different configurations. And the selection of the topology transform point and the effect on the before and after configuration is the focus of the analysis of variable topology mechanism.
To the above situations, this paper has carried on the following research:
①The synthesis approach of variable topology mechanism configuration has been proposed.And the law of mechanism configuration synthesis under the three variable topology ways has been studied. Consequently, a method of the variable topology mechanism configuration synthesis has been obtained.
②By the analysis of the relationship between the before and after configuration in the process of mechanism transformation, objective function of the variable topology point of the mechanism chosen according to an objective whose square instantaneous power difference is minimum and constraint condition have been built. By analyzing the relationship between the two configuration, its transmission relationship of the machine speed matrix has been obtained, which provides a convenient method for the analysis of the singularity of mechanism.
③By using MATLAB software, the simulative analysis of five-four bar variable topology mechanism, has been carried on. Then the optimum variable topology point appears for the first time. Through the analysis of variable topology mechanisms, the mechanical motion curve has been obtained, Besides the method of selecting the variable topology region is proposed on the basis of the curve has been porposed.
This paper has proposed the metheods of configuration of variable topology mechanism, and analysed the choice of variable topology points and calculation of the mechanism singularity between the before and after configuration of the speed of the transfer matrix R . Through the matrix R, it has simplified the calculation speed matrix steps of the after configuration and enriched the variable topology mechanism analysis and design methods. The research has offered important reference for the design and applocation of variable topology mechanism.
目前,变拓扑机构在构型的综合与选择、构型间的关系、运动学和动力学分析等领域还有大量的问题没有解决。由于对变拓扑机构的分析涉及到多种构型分析,具有复杂性,因此寻找多种构型之间的拓扑结构变换关系就显得非常重要,同时变拓扑机构的变换点的选择以及对前后构型的影响也是机构分析的重点。
针对以上情况,本文进行了以下研究:
①提出了变拓扑机构构型综合的方法,对三种变拓扑方式下机构构型综合的规律进行了研究,得到了一种变拓朴机构构型综合的实用方法。
②通过对机构变换过程中前后构型之间关系的分析,建立了以瞬时功率差的平方最小为目标来选择机构变拓扑点的目标函数以及变换时的约束条件;通过分析机构两种构型间的关系,推导了机构速度矩阵在前后构型中的传递关系,为机构的奇异性分析提供了一种简便快捷的方法。
③利用MATLAB软件对5-4杆变拓扑机构进行了仿真分析,得到了5-4杆机构第一次出现奇异位形时的机构的最优变拓扑点,通过对变拓扑机构进行运动仿真,得到了其运动曲线,在此基础上提出了变拓扑区域选择的方法。
本文提出了的变拓扑机构的构型综合方法,分析了变拓扑点的选择和机构奇异位形计算中前后构型间的速度传递矩阵R;通过R阵的计算,简化了后一构型速度矩阵的计算步骤,充实了变拓扑机构的分析和设计方法。本文的研究工作对于变拓扑机构的设计及应用提供了比较重要的参考。
In order to adapt to the exploration and poor working environment or multi-functional requirements, the modern mechanical systems require the modern machine develops towards the reconstruction. That is to say, machine can change its topology configuration, kinematic parameters or dynamics parameters in the process of movement. Variable topology mechanism which is based on the metamorphic mechanism is a new type of machine of self-reconstruction. By the combination and split of the bar, the change of connecting relationship and changing the type of kinematic pair , variable topology mechanism can change the machine configuration in the process of the working motion to be adapted to different working environment and expand the scope of application of the mechiansms.
At present, variable topology mechanism hasn’t yet solved some problems such as the synthesis and the selection of the configuration, the relationship between the before and after configuration and the anslysis of kinematics and dynamics. It’s a very complex problem to analyse variable topology mechanism which involves in the variety of configurations. Therefore it is important to search the topology configurations transform relationships among the different configurations. And the selection of the topology transform point and the effect on the before and after configuration is the focus of the analysis of variable topology mechanism.
To the above situations, this paper has carried on the following research:
①The synthesis approach of variable topology mechanism configuration has been proposed.And the law of mechanism configuration synthesis under the three variable topology ways has been studied. Consequently, a method of the variable topology mechanism configuration synthesis has been obtained.
②By the analysis of the relationship between the before and after configuration in the process of mechanism transformation, objective function of the variable topology point of the mechanism chosen according to an objective whose square instantaneous power difference is minimum and constraint condition have been built. By analyzing the relationship between the two configuration, its transmission relationship of the machine speed matrix has been obtained, which provides a convenient method for the analysis of the singularity of mechanism.
③By using MATLAB software, the simulative analysis of five-four bar variable topology mechanism, has been carried on. Then the optimum variable topology point appears for the first time. Through the analysis of variable topology mechanisms, the mechanical motion curve has been obtained, Besides the method of selecting the variable topology region is proposed on the basis of the curve has been porposed.
This paper has proposed the metheods of configuration of variable topology mechanism, and analysed the choice of variable topology points and calculation of the mechanism singularity between the before and after configuration of the speed of the transfer matrix R . Through the matrix R, it has simplified the calculation speed matrix steps of the after configuration and enriched the variable topology mechanism analysis and design methods. The research has offered important reference for the design and applocation of variable topology mechanism.
引文
[1] Dai J. S, Jones J Rees.Mobility in metamorphic mechanisms of foldable/erectable kinds[J].Transaction of ASME.Journal of Mechanical Design,1999,12l(3):375～382.
[2] Dai J.S, Jones J Rees.Configuration transformations in metamorphic mechanisms of foldable erectable kinds[J].In:Proceedings of the Tenth World Congress on the Theory of Machines and Mechanisms ,Oulu,Finland,1999:542～547.
[3]杨廷力,刘安心,孙东锦.变拓扑机构组成原理及基本类型.北京:机械工业出版社.2003:262～264.
[4]刘川禾,杨廷力,刘毅.变拓扑机构的基本问题.机械工程学报,2005.8:56～62.
[5] Costabile V,Lumaca F.New antenna deployment,pointing and supporting mechanism.In: Proc. 30th AerospacemechanismsSymposium,California:NASA Conference1996: 65～76.
[6] Spence B R, Sword L F. Mars pathfinder rover egress deployable ramp assembly. In:30th Aerospace Mechanisms Symposium, NASA, 1996.
[7] Kuramasu R, Inoue K, Kanazawa I. Development of mechanism to extend the solar array paddle for advanced earth observing satellite (ADEOS).In:Proc. Of Sixth European Space Mechanisms and Tribology Symposium, Zurich,1995: 73～80.
[8] Takamatsu Kiyoshi, Onoda Junjiro, Higuchi Ken. New concepts of deployable truss units for large space structures.AIAA Paper 87-0868, 1987: 695～704.
[9] Takamatsu K A, Onoda J. New deployable truss concepts for large antenna structures orsolar concentrators. Journal of Spacecraft and Rockets, 1991, 1(3): 330～338.
[10] Shahnipoor M. An introduction to smart fiactal structures and mechanisms. In: ASME 14th Biennial Conf. on Mechanical Vibration and Noise, 1993: 67～74.
[11] You Z, Pellegrino S. Cable-stifened pantographic deployable structures part 1: triangular Mast. AIAA Journal, 1996, 34(4): 813～820.
[12] Gehling Russell N, Amstrong Joseph H, Misra Mohan S. High-performance, flexible, deployable array development for space application. NASA N95-20532, 1995: 287～297.
[13] Chirikjian G, Pamecha A, Ebert-Uphof I. Evaluating eficiency of self-reconfiguration in a class of modular robots. J. of Robotic Systems, 1996,13(5): 317～338.
[14] Cuddy H M, Rollett A P. Mathematical Models. London: Tarquin Publications, 1981.
[15] Dai J S,Zhang Q x.Metamorphic mechanisms and their configuration models.Chinese Journal of Mechanical Engineering,2000,l3(3):212～218.
[16] Parise J J.Howell L L.Magleby S P.Ortho-planar mechanisms.In:Proc.26th Biennial Mechanisms and Robotics Conference,Baltimore,2000,New York:ASME,2000.
[17] Lee C C.Herve J M .Discontinuous mobility of Four-linkmechanisms with revolute,prismatic and cylindrical pairsthrough the group algebraic structure of the displacementset.In:8th International Conference on the Theory ofMachines an d M echanisms,2001,Czech Republic:Liberec Elsemere,2001: 5～7.
[18]李端玲,戴建生,张启先等.基于构型变换的变胞机构综合.机械工程学报,2002,38(7):12～16.
[19] Carroll D W,Magleby S P,Howell L H.Simplifiedmanufacturing through a metamorhic process for compliant Orthoplanar mechanisms.In:2003 ASME Design Engineering Technical Conference,Chicago,2003,NewYork:ASME,2003.
[20] Liu C H,Yang T L.Essence and characteristics of metamorphic mechan isms and their metamorphic ways,In:Proc.1lth World Congress in Mechanism and MachineScience ,Tianjing,2004,China:Mechanical EngineeringPress,2004:1285～1288.
[21] Li D L,Dai J S,Sun H.Configur ation based synthesis of a Carton-like metamorphic mechanism of foldable and erectable.Journal of Engineering Design ,2005.16(4):375～386
[22]杨廷力.机器人机构拓仆结构学.北京:机械工业出版社.2003.
[23]金国光,丁希仑,张启先.变胞机构全构型动力学模型机器数值仿真研究.航天学报,2004,25(4),401～405.
[24]戴建生,丁希仑,邹慧君.变胞原理和变胞机构类型机械工程学报,2005.6:6～12
[25]丹宁,加拿大为国际空间站建造机械臂,中国航天,1998年,第4期,26～28.
[26] Murata, S.; Yoshida, E.; Kamimura, A.; Kurokawa, H.; Tomita, K.; Kokaji, S.; M-TRAN: Self-ReconfigurableModular Robotic System, Mechatronics, IEEE/ASME Transactions on ,Volume: 7 ,Issue: 4 ,Dec. 2002 ,Pages:431～441.
[27] I-Ming Chen, Hsi-Shang Li, and Arnaud Cathala, Mechatronic Design and Locomotion of Amoebot—A Metamorphic Underwater Vehicle, Journal of Robotic Systems, 20(6), 2003, Pages:307～314.
[28]李瑞玲.变胞机构的机构学分析及应用.北京航空航天大学,博士论文.
[29]刘勇,肖人彬.机构轨迹生成理论研究进展.计算机辅助设计与图形学学报.2005.4,17(4),627～636.
[30]王朝瑞.图论.第2版,北京:北京理工大学出版社,1997.
[31]刘溯,秦伟.1T3R并联机器人设计及其实验装置研制.重庆:重庆大学,硕士论文.
[32]张启先.空间机构的分析与综合.北京:机械工业出版社,1984.
[33]黄茂林,秦伟.机械原理.北京:机械工业出版社,2002.
[34]杨廷力.空间机构的结构分析与综合—I,空间单闭链的结构分析与综合.机械设计,1987 (2): 1～21.
[35] Liu Tyng, Yu Chung-Huang. Identification and classification of multi-degree-of-freedom and multi-loop mechanisms. J. of Mechanical Design, 1995, 117(3): 104～111.
[36]杨虎,刘琼荪,钟波.数理统计.北京:高等教育出版社,2004.10.
[37]郑建荣.ADAMS基础及应用.北京:机械工业出版社,2004.
[38]余载强,张艳冬.压力机双曲柄多杆机构运动分析和优化设计.锻压设备:1998(1) ,3～6.
[39]曹惟庆.连杆机构的分析与综合.北京:科学出版社.
[40]哈尔滨工业大学理论力学教研组.北京:高等教育出版社.1981.
[41]刘惟信.机械最优化设计.北京:清华大学出版社.1993.6.
[42]郝红伟编著.MATLAB 6实例教程.北京:中国电力出版社,2001 ,8-108.
[43] J.S. Dai, D. Li, Q. Zhang and G. Jin: Mobility Analysis of a Complex Structured Ball Based on MechanismDecomposition and Equivalent Screw System Analysis. Mechanism and Machine Theory, Vol. 39, 445-458, 2004.
[2] Dai J.S, Jones J Rees.Configuration transformations in metamorphic mechanisms of foldable erectable kinds[J].In:Proceedings of the Tenth World Congress on the Theory of Machines and Mechanisms ,Oulu,Finland,1999:542～547.
[3]杨廷力,刘安心,孙东锦.变拓扑机构组成原理及基本类型.北京:机械工业出版社.2003:262～264.
[4]刘川禾,杨廷力,刘毅.变拓扑机构的基本问题.机械工程学报,2005.8:56～62.
[5] Costabile V,Lumaca F.New antenna deployment,pointing and supporting mechanism.In: Proc. 30th AerospacemechanismsSymposium,California:NASA Conference1996: 65～76.
[6] Spence B R, Sword L F. Mars pathfinder rover egress deployable ramp assembly. In:30th Aerospace Mechanisms Symposium, NASA, 1996.
[7] Kuramasu R, Inoue K, Kanazawa I. Development of mechanism to extend the solar array paddle for advanced earth observing satellite (ADEOS).In:Proc. Of Sixth European Space Mechanisms and Tribology Symposium, Zurich,1995: 73～80.
[8] Takamatsu Kiyoshi, Onoda Junjiro, Higuchi Ken. New concepts of deployable truss units for large space structures.AIAA Paper 87-0868, 1987: 695～704.
[9] Takamatsu K A, Onoda J. New deployable truss concepts for large antenna structures orsolar concentrators. Journal of Spacecraft and Rockets, 1991, 1(3): 330～338.
[10] Shahnipoor M. An introduction to smart fiactal structures and mechanisms. In: ASME 14th Biennial Conf. on Mechanical Vibration and Noise, 1993: 67～74.
[11] You Z, Pellegrino S. Cable-stifened pantographic deployable structures part 1: triangular Mast. AIAA Journal, 1996, 34(4): 813～820.
[12] Gehling Russell N, Amstrong Joseph H, Misra Mohan S. High-performance, flexible, deployable array development for space application. NASA N95-20532, 1995: 287～297.
[13] Chirikjian G, Pamecha A, Ebert-Uphof I. Evaluating eficiency of self-reconfiguration in a class of modular robots. J. of Robotic Systems, 1996,13(5): 317～338.
[14] Cuddy H M, Rollett A P. Mathematical Models. London: Tarquin Publications, 1981.
[15] Dai J S,Zhang Q x.Metamorphic mechanisms and their configuration models.Chinese Journal of Mechanical Engineering,2000,l3(3):212～218.
[16] Parise J J.Howell L L.Magleby S P.Ortho-planar mechanisms.In:Proc.26th Biennial Mechanisms and Robotics Conference,Baltimore,2000,New York:ASME,2000.
[17] Lee C C.Herve J M .Discontinuous mobility of Four-linkmechanisms with revolute,prismatic and cylindrical pairsthrough the group algebraic structure of the displacementset.In:8th International Conference on the Theory ofMachines an d M echanisms,2001,Czech Republic:Liberec Elsemere,2001: 5～7.
[18]李端玲,戴建生,张启先等.基于构型变换的变胞机构综合.机械工程学报,2002,38(7):12～16.
[19] Carroll D W,Magleby S P,Howell L H.Simplifiedmanufacturing through a metamorhic process for compliant Orthoplanar mechanisms.In:2003 ASME Design Engineering Technical Conference,Chicago,2003,NewYork:ASME,2003.
[20] Liu C H,Yang T L.Essence and characteristics of metamorphic mechan isms and their metamorphic ways,In:Proc.1lth World Congress in Mechanism and MachineScience ,Tianjing,2004,China:Mechanical EngineeringPress,2004:1285～1288.
[21] Li D L,Dai J S,Sun H.Configur ation based synthesis of a Carton-like metamorphic mechanism of foldable and erectable.Journal of Engineering Design ,2005.16(4):375～386
[22]杨廷力.机器人机构拓仆结构学.北京:机械工业出版社.2003.
[23]金国光,丁希仑,张启先.变胞机构全构型动力学模型机器数值仿真研究.航天学报,2004,25(4),401～405.
[24]戴建生,丁希仑,邹慧君.变胞原理和变胞机构类型机械工程学报,2005.6:6～12
[25]丹宁,加拿大为国际空间站建造机械臂,中国航天,1998年,第4期,26～28.
[26] Murata, S.; Yoshida, E.; Kamimura, A.; Kurokawa, H.; Tomita, K.; Kokaji, S.; M-TRAN: Self-ReconfigurableModular Robotic System, Mechatronics, IEEE/ASME Transactions on ,Volume: 7 ,Issue: 4 ,Dec. 2002 ,Pages:431～441.
[27] I-Ming Chen, Hsi-Shang Li, and Arnaud Cathala, Mechatronic Design and Locomotion of Amoebot—A Metamorphic Underwater Vehicle, Journal of Robotic Systems, 20(6), 2003, Pages:307～314.
[28]李瑞玲.变胞机构的机构学分析及应用.北京航空航天大学,博士论文.
[29]刘勇,肖人彬.机构轨迹生成理论研究进展.计算机辅助设计与图形学学报.2005.4,17(4),627～636.
[30]王朝瑞.图论.第2版,北京:北京理工大学出版社,1997.
[31]刘溯,秦伟.1T3R并联机器人设计及其实验装置研制.重庆:重庆大学,硕士论文.
[32]张启先.空间机构的分析与综合.北京:机械工业出版社,1984.
[33]黄茂林,秦伟.机械原理.北京:机械工业出版社,2002.
[34]杨廷力.空间机构的结构分析与综合—I,空间单闭链的结构分析与综合.机械设计,1987 (2): 1～21.
[35] Liu Tyng, Yu Chung-Huang. Identification and classification of multi-degree-of-freedom and multi-loop mechanisms. J. of Mechanical Design, 1995, 117(3): 104～111.
[36]杨虎,刘琼荪,钟波.数理统计.北京:高等教育出版社,2004.10.
[37]郑建荣.ADAMS基础及应用.北京:机械工业出版社,2004.
[38]余载强,张艳冬.压力机双曲柄多杆机构运动分析和优化设计.锻压设备:1998(1) ,3～6.
[39]曹惟庆.连杆机构的分析与综合.北京:科学出版社.
[40]哈尔滨工业大学理论力学教研组.北京:高等教育出版社.1981.
[41]刘惟信.机械最优化设计.北京:清华大学出版社.1993.6.
[42]郝红伟编著.MATLAB 6实例教程.北京:中国电力出版社,2001 ,8-108.
[43] J.S. Dai, D. Li, Q. Zhang and G. Jin: Mobility Analysis of a Complex Structured Ball Based on MechanismDecomposition and Equivalent Screw System Analysis. Mechanism and Machine Theory, Vol. 39, 445-458, 2004.