3-RRRT并联机器人精度分析与综合
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摘要
本文对3-RRRT并联机器人精度分析与综合问题作了比较深入的研究。
通过对3-RRRT并联机器人的位置分析,建立了3-RRRT并联机器人输出位姿误差分析的数学模型。提出了3-RRRT并联机器人输出位姿误差的分析方法。该数学模型的建模方法亦适用于其他并联机器人及空间结构的精度分析;对于3-RRRT并联机器人的类似机构及其演化构型,给定各结构参数误差,应用此数学模型可直接得出并联机构输出位姿误差,从理论上为定量分析各结构参数误差对输出位姿误差的影响提供前提条件。
基于位置分析对3-RRRT并联机器人位置输入输出方程微分,获得机器人逆雅可比矩阵。当机器人处于非奇异位姿且结构误差与位姿误差为微小量时,分析并联机器人结构误差对机器人末端误差的影响,建立它们之间关系的数学模型,研究表明该模型为线性数学模型。当给定机器人微小的结构误差时,研究机器人位姿变化与结构尺寸变化对机器人精度的影响。
运用误差独立作用和等效作用的思想对3-RRRT并联机器人进行精度综合,将这一原本多目标多变量的非线性不确定最优化组合问题转化为线性问题,使并联机器人精度综合问题变得简单可行,具有一定的实用价值。
A deep theoretical study on the accuracy analysis and synthesis of 3-RRRT parallel manipulator has been carried out in this dissertation.
Based on the position analysis of the 3-RRRT parallel manipulator , the model for the pose error analysis method of the end executor of 3-RRRT parallel manipulator has been formulated and the analysis method of the pose error of the 3-RRRT parallel manipulator has been proposed .As for the 3-RRRT parallel manipulator and its relevant configuration ,the pose errors of the end executor can be directly obtained when the structural parameters are given. It provides the precondition of the quantitative analysis of the influence of errors of the structural parameters laid on the pose error of the end executor in the theory. This modeling method can also be used to the accuracy analysis of other parallel manipulators and spatial mechanisms.
The relationship between the structure error and the end executor error of the 3-RRRT parallel manipulator has been studied through differential equations, which are obtained from the position analysis .As long as the 3-RRRT parallel manipulator is not on the singular location ,the errors are contained in the linear mathematics model when they are minuteness. The inverse Jacobi matrix of the 3-RRRT parallel manipulator is obtained from differential equations. Effects of pose changes and the structure changes on the accuracy of the 3-RRRT parallel manipulator has also been studied in the paper .
The independent and equal effect principle of error is applied to the accuracy synthesis of the 3-RRRT parallel manipulator, which changed the multivariable , multi-object and non-linear problem into the simple linear problem. The algorithm studied in this paper has practical value.
通过对3-RRRT并联机器人的位置分析,建立了3-RRRT并联机器人输出位姿误差分析的数学模型。提出了3-RRRT并联机器人输出位姿误差的分析方法。该数学模型的建模方法亦适用于其他并联机器人及空间结构的精度分析;对于3-RRRT并联机器人的类似机构及其演化构型,给定各结构参数误差,应用此数学模型可直接得出并联机构输出位姿误差,从理论上为定量分析各结构参数误差对输出位姿误差的影响提供前提条件。
基于位置分析对3-RRRT并联机器人位置输入输出方程微分,获得机器人逆雅可比矩阵。当机器人处于非奇异位姿且结构误差与位姿误差为微小量时,分析并联机器人结构误差对机器人末端误差的影响,建立它们之间关系的数学模型,研究表明该模型为线性数学模型。当给定机器人微小的结构误差时,研究机器人位姿变化与结构尺寸变化对机器人精度的影响。
运用误差独立作用和等效作用的思想对3-RRRT并联机器人进行精度综合,将这一原本多目标多变量的非线性不确定最优化组合问题转化为线性问题,使并联机器人精度综合问题变得简单可行,具有一定的实用价值。
A deep theoretical study on the accuracy analysis and synthesis of 3-RRRT parallel manipulator has been carried out in this dissertation.
Based on the position analysis of the 3-RRRT parallel manipulator , the model for the pose error analysis method of the end executor of 3-RRRT parallel manipulator has been formulated and the analysis method of the pose error of the 3-RRRT parallel manipulator has been proposed .As for the 3-RRRT parallel manipulator and its relevant configuration ,the pose errors of the end executor can be directly obtained when the structural parameters are given. It provides the precondition of the quantitative analysis of the influence of errors of the structural parameters laid on the pose error of the end executor in the theory. This modeling method can also be used to the accuracy analysis of other parallel manipulators and spatial mechanisms.
The relationship between the structure error and the end executor error of the 3-RRRT parallel manipulator has been studied through differential equations, which are obtained from the position analysis .As long as the 3-RRRT parallel manipulator is not on the singular location ,the errors are contained in the linear mathematics model when they are minuteness. The inverse Jacobi matrix of the 3-RRRT parallel manipulator is obtained from differential equations. Effects of pose changes and the structure changes on the accuracy of the 3-RRRT parallel manipulator has also been studied in the paper .
The independent and equal effect principle of error is applied to the accuracy synthesis of the 3-RRRT parallel manipulator, which changed the multivariable , multi-object and non-linear problem into the simple linear problem. The algorithm studied in this paper has practical value.
引文
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[19]卢强,张友良. Stewart平台误差的蒙特卡洛模拟[J ] .机械科学技术,2001 ,4(7) :513～514.
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[22]张虎,周云飞.数控机床空间误差的无模测量与补偿.华中科技大学学报,2002 ,30(1) :74～77.
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[34]焦国太,冯永和.多因素影响下的机器人综合位姿误差分析方法[J].应用基础与工程科学学报,2004,12(4):435-442.
[35]焦国太,于越庆,梁浩.机器人位姿误差的结构矩阵分析方法[J].应用基础与工程科学学报,2001,9:259-265.
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[2]赵新华,赵连玉,温殿英等.并联机器人运动学传动性能研究.机械设计,2002,3:12-16.
[3]黄真.机器人学,北京:清华大学出版社,2000. [4 ]熊有伦,尹周平,熊蔡华等.机器人操作[M] .武汉:湖北科学技术出版社,2002. [5 ]张曙,U.Heisel.并联运动机床.北京:机械工业出版社,2003.
[6]赵永杰.6-SPS并联机器人精度分析与综合,硕士学位论文,天津理工学院,2003.
[7]苗志怀.基于3-RRRT并联机器人位置反解的精度分析,硕士学位论文,天津理工大学,2005.
[8]赵永杰.6-SPS并联机器人精度分析与综合,硕士学位论文,天津理工学院,2003.
[9]张森.MATLAB仿真技术与实例应用教程,北京:机械工业出版社,2004.
[10]余晓流,王洪光,赵明扬等.五轴并联铣床特征参数误差灵敏度分析.安徽工业大学学报,2001,18 (3):181-184.
[11]余晓流,王启义,赵明扬等.基于测量数据反演并联机床非线性位姿误差模型.东北大学学报,2001, 37(2):38-42.
[12]余晓流,王洪光,赵明扬等.并联机床平面约束机构误差分析与建模.东北大学学报,2001, 22(1):32-35.
[13]邹豪,王启义姿余哓流等.五轴并联铣床特征参数误差灵敏度分析.安徽工业大学学报,2001,21(3)301-304.
[14]于大勇,韩俊伟,李洪人.并联机器人位姿误差分析,哈尔滨商业大学学报,第20卷第三期,2004.6.
[15]阎华,刘桂雄,郑时雄.机器人位姿误差建模方法综述,机床与液压,2000,1:3-5.
[16]于大勇,韩俊伟,李洪人.并联机器人位姿误差分析,哈尔滨商业大学学报,第20卷第三期,2004.6.
[17]李嘉,王纪武.基于广义几何误差模型得微机器人精度分析[J ] .机械工程学报,2000 ,36(8) :20～24.
[18]乔俊伟,詹永麟,王旭永. 6-SPS并联机器人位置姿态误差分析[J ] .机械科学技术,2001 ,1(1) :58～59.
[19]卢强,张友良. Stewart平台误差的蒙特卡洛模拟[J ] .机械科学技术,2001 ,4(7) :513～514.
[20]王海军,王君英.关节间隙对并联机床精度的影响规律研究[J] .中国机械工程,2007 ,18(4) :471～474.
[21]刘得军,车仁生,叶东.三自由度并联机构坐标测量机误差建模与仿真[J ] .中国机械工程,2001 ,12(7) :752～756.
[22]张虎,周云飞.数控机床空间误差的无模测量与补偿.华中科技大学学报,2002 ,30(1) :74～77.
[23]赵俊伟,徐振高,范光照等.一种串并联型机床及其误差分析.中国机械工程,2001 ,12(8) :861～864.
[24]洪林.并联机器人精度分析与综合研究.博士学位论文,天津大学,2004.
[25]梁师望. MATLAB在并联机器人运动仿真中的应用.机电一体化,2000,6:56-57.
[26]翟瑞彩,谢伟松.数值分析.天津:天津大学出版社,2000.
[27]陈桂明.应用MATLAB建模与仿真.北京:科学出版社,2001.
[28]陆君安.偏微分方程的MATLAB解法.武汉:武汉大学出版社,2001.
[29]王沫然. MATLAB7.0与科学计算.北京:电子工业出版社,2006.
[30]苏晓生.掌握MATLAB6.0及其工程应用.北京:科学出版社,2002.
[31]汪汇.3-RRC并联机器人运动仿真的MATLAB实现.机械工程师,2008,1:127-129.
[32]罗继曼,于恒.3-TPS型并联机器人约束链的几何误差分析[J].机械工程师,2005,7:81-83.
[33]罗建国,陆震.冗余驱动直角坐标串并联机器人位姿误差分析.机械设计,2007,1:66-69.
[34]焦国太,冯永和.多因素影响下的机器人综合位姿误差分析方法[J].应用基础与工程科学学报,2004,12(4):435-442.
[35]焦国太,于越庆,梁浩.机器人位姿误差的结构矩阵分析方法[J].应用基础与工程科学学报,2001,9:259-265.
[36]汪劲松,白洁文.Stewart平台铰链间隙的精度分析[J].应用基础与工程科学学报,2001,9:259-265.
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