空间柔性机械臂的动力学建模和分析

硕士学位论文空间柔性机械臂的动力学建模和分析DYNAMICMODELINGANDANALYSISOFSPACEFLEXIBLEMANIPULATOR魏进哈尔滨工业大学2013年7月国内图书分类号：O326，V11学校代码：10213国际图书分类号：531.3,534.1密级：公开工学硕士学位论文空间柔性机械臂的动力学建模和分析硕士研究生：魏进导师：梁廷伟高工申请学位：工学硕士学科：一般力学与力学基础所在单位：航天学院答辩日期：2013年7月授予学位单位：哈尔滨工业大学ClassifiedIndex:O326，V11U.D.C:531.3,534.1DissertationfortheMasterDegreeinEngineeringDYNAMICMODELINGANDANALYSISOFSPACEFLEXIBLEMANIPULATORCandidate：WeiJinSupervisor：SeniorEngineer.LiangTingweiAcademicDegreeAppliedfor：MasterofEngineeringSpeciality：GeneralandFundamentalMechanicsAffiliation：SchoolofAstronauticsDateofDefence：July,2013Degree-Conferring-Institution：HarbinInstituteofTechnology哈尔滨工业大学工学硕士学位论文-I-摘要随着航天技术和机器人技术的迅速发展，柔性机械臂由于其质量轻、速度快、耗能低等优点，在航空航天领域中获得了广泛的应用。但是机械臂在运行过程中，关节柔性和柔性臂杆弹性变形的耦合，给机器人柔性臂的振动控制带来了困难。建立准确、实用的动力学模型对于柔性机械臂的轨迹跟踪和主动振动控制的研究具有重要意义。为此，本文针对全柔性机器人的动力学问题展开了研究，主要内容如下：1、简要的介绍了多柔体系统的运动学和动力学模型的建模方法。分别以假设模态法与Lagrange方程相结合和全局模态法与Hamilton原理相结合建立柔性机械臂动力学方程。2、以典型柔性关节/柔性臂杆系统为研究对象，分析整个柔性机械单臂系统的复杂边界条件，建立柔性机械单臂系统的动力学模型，提出了柔性机械单臂全局模态的概念。首先，基于Hamilton原理导出单臂机器人的柔性臂杆和柔性关节的耦合运动微分方程。利用系统的边界条件和连接部件的匹配条件，导出了求解系统固有特性的特征方程，据此可以用数值方法求出系统的固有频率和全局模态。在求解全局模态的基础上，进一步证明了全局模态的正交性，采用Galerkin截断对系统进行离散，得到用常微分方程描述的柔性机械臂的动力学方程。将所得结果与采用假设模态法给出的频率和模态进行对比，据此说明这里提出的全局模态概念准确地反映了系统的固有特性，其求解方法借用了传统的模态求解方法的思路，但其适用范围更广。最后对所建立的柔性单臂模型进行了响应时程仿真，分析关节的变形和臂杆末端的弹性振动位移。3、采用全局模态法与Hamilton原理相结合的方法对具有柔性关节的双连杆柔性机械臂进行动力学建模。首先，分析整个柔性机械臂系统的复杂边界条件，基于Hamilton原理导出双臂机器人的柔性臂杆和柔性关节的耦合运动微分方程。利用系统的边界条件和连接部件的匹配条件，导出含有参数（肩部关节的角度变化）的系统特征方程，同时也可以容易地求出系统的固有频率和表征机械臂运动的刚体运动、柔性关节振动以及柔性臂杆弹性振动在内的全局模态。通过求解系统的特征方程，研究系统构型的变化对柔性机械臂系统的固有频率的影响，据此可以预测系统固有频率的变化趋势和变化范围。关键词：柔性机械臂；柔性关节；固有频率；全局模态；哈尔滨工业大学工学硕士学位论文-II-AbstractWiththerapiddevelopmentofspacetechnologyandrobottechnology,theflexiblemanipulatorarewidelyusedinthefieldofaerospace,duetoitslightquality,highspeed,andlowenergyconsumption.However,itisdifficultytocontrolthevibrationofflexiblemanipulatorowingtothejointflexiblityandflexible-linkelasticdeformationcoupling.Itisgreatsignificancethatestablishaccurateandpracticaldynamicmodelforthetrajectorytrackingandactivevibrationcontrolofflexiblemanipulator.Tosolvethisproblem,inthispaper,thedynamicproblemsofflexiblemanipulatorisatudied,themaincontentisasfollows:1、Thekinematicsanddynamicsmodelingofflexiblemultibodychainsystemisbrieflyintroduced.ByassumptionmodalmethodcombinedwiththoughLagrangeequationsandglobalmodalmethodcombinedwithHamiltonprinciple,dynamicsequationofflexiblemanipulatorareestablish.2、Basedontheanalysisoftheflexiblemanipulatorthatconsistsofflexible-linkandflexible-joint,theglobalmodeshapesoftheflexiblemanipulatorispresented.Thecouplingmovementdifferentialequationofflexible-linkandflexible-jointarederivedbyusingtheHamiltonprinciple.Throughtheirforceboundaryandmatchingconditions,theundampednaturalfrequenciesandmodeshapesofthelinearizedmodeloftheflexiblemanipulatoraredetermined,andorthogonalityrelationsofthemodeshapesareestablished.Theundampedglobalmodeshapesareusedtodiscretizethecouplingmovementdifferentialequationofflexible-linkandflexible-joint.Thesimulationresultsshowthatthejointflexibilityandtheelasticdeformationofflexible-linkcanhaveasignificanteffectonthesystemfrequencies.Acomparisonbetweentheresultsobtainedbytheproposedmethodandthosefromassumemodemethodisgiventoillustratethevalidityofourapproach.Accordingtotheglobalmodal,itcanreflecttheinherentcharacteristicsofthesystem.Anditssolvingmethodismoreused,whichborrowedfromthetraditionalmode.Finally,responsehistorysimulationistakentostudy,andthedeformationofjointsandtheendoflinkelasticvibrationdisplacementisanalyzed.3、Dynamicmodeloftwo-linkflexiblemanipulatorwithflexiblejointsisestablishedbyusingglobalmodalmethodcombinedwithHamiltonprinciple.Firstofall,thecomplexboundaryconditionsareanalyzed.Thepartialdifferentialequationsofmotionforatwo-linkflexiblemanipulatorarederived,alongwiththeirboundaryconditionsbyusingtheHamiltonprinciple.Combiningthegoverningequationsofflexiblelinkandflexiblejoint,theundampednaturalfrequenciesandmodeshapesofthelinearizedmodelofthetwo-linkflexiblemanipulatorare哈尔滨工业大学工学硕士学位论文-III-determined.Throughthefrequencyequationpresentedinthisarticle,astudyonthevariationofnaturalfrequencieswiththetime-varyingelbowanglesisperformedusingatwo-linkflexiblemanipulatorwithasetoftypicalgeometricalparametersandmaterialconstants.Thuswecanpredictthetendencyandrangeofthesystemnaturalfrequency.Keywords:flexiblemanipulator,flexible-joint,naturalfrequencies,globalmodeshapes哈尔滨工业大学工学硕士学位论文-IV-目录摘要..........................................................................................................................IABSTRACT................................................................................................................II第1章绪论...........................................................................................................11.1课题背景及研究目的和意义.....................................................................11.2国内外柔性机械臂的研究现状.................................................................21.2.1柔性机械臂的建模...................................................................