matlab柔性杆仿真

武汉理工大学毕业设计（论文）目录摘要..................................................................................IAbstract.............................................................................II1绪论................................................................................11.1柔性机械臂的发展历史..........................................................11.2国内外研究现状...............................................................11.2.1建模...................................................................11.2.2数值仿真...............................................................21.2.3控制方法...............................................................21.3研究目的意义..................................................................22柔性臂动力学建模....................................................................42.1柔性臂的建模理论..............................................................42.2柔性体变形的描述.........................................................52.3建立动力学方程的方法..........................................................62.3.1Newton-Euler公式.......................................................62.3.2基于Lagrange方程的动力学建模..........................................62.3.3Kane方法和虚功原理：...................................................72.4模态分析......................................................................72.5近似分析......................................................................82.6逆运动学与逆动力学............................................................82.7刚-柔双连杆机械臂的动力学方程................................................102.7.1系统的能量............................................................102.7.2横向运动的模态分析....................................................122.7.3拉格朗日法求动力学方程................................................133动态仿真...........................................................................153.1.1给定运动轨迹..........................................................153.1.2运用龙格-库塔法解动力学方程...........................................163.1.3刚——柔双连杆的动态建模..............................................163.1.4给定另一运动轨迹......................................................173.1.5不同轨迹的振动.........................................................183.1.645°运动..............................................................193.1.7180°运动.............................................................21武汉理工大学毕业设计（论文）4振动抑制及其仿真...................................................................234.1抑制振动的基本方法...........................................................234.1.1主动控制..............................................................234.1.2被动控制..............................................................244.2采用N-M算法优化轨迹.........................................................244.2.1N-M优化算法...........................................................244.2.2N-M算法获得轨迹........................................................254.2.3优化轨迹的仿真.........................................................274.2.4振动分析...............................................................275总结与展望.........................................................................29参考文献.............................................................................30致谢.................................................................................31武汉理工大学毕业设计（论文）I摘要这篇论文的研究对象是刚——柔双连杆机械臂模型，研究希望通过优化运动轨迹的方法达到抑制振动的目的。首先，通过假设模态法和Lagrange原理建立刚——柔双连杆机械臂的动力学方程，然后运用四阶龙科库塔公式解出该动力学方程组，并且用matlab进行动态仿真。通过输入不同的运动轨迹，比较柔性机械臂末端的振动量，可以得出：在不同运动轨迹中，柔性机械臂的末端振动量是不同的。所以得出猜测：可以通过控制刚——柔双连杆机械臂的运动轨迹来抑制振动。最后运用N-M优化算法，使得运动结束后机械臂系统的能量达到最小值，计算出此时的运动轨迹，最后输入到刚——柔双连杆机械臂系统中，通过matlab验证了这种抑制振动的方法是有效果的。本文的特色在于：建立的刚柔双连杆机械臂模型既体现了刚性运动，又充分表现出了柔性连杆的运动特点。最后用一种优化算法成功抑制了柔性连杆末端振动，达到预期效果。关键字：柔性机械臂；动态仿真；振动抑制；轨迹设计；N-M算法武汉理工大学毕业设计（论文）IIAbstractInthispaper,atwo-linkrigid-flexiblemanipulatorismodeled,hopingthattrajectoryvibrationcanbesuppressedbyanoptimaltrajectoryplanningtechnique.Firstofall,thedynamicequationsofmotionofthemanipulatorarederivedbytheassumedmodalmethodandLagrangeapproach,andusingthefourthorderRunge-Kuttaformulaworkoutthedynamicsequations,thendynamicsimulationinmatlab.Byinputtingdifferenttrajectories,wecomparethevibrationoftheendsoftheflexiblemanipulator,knowingthat:Indifferenttrajectoriesthevibrationoftheendsoftheflexiblemanipulatorisdifferent.Soweguess:Bycontrollingtrajectoryofthetwo-linkrigid-flexiblemanipulatorcansuppressvibration.FinallyweusetheN-Moptimizationalgorithmtocalculatethereasonabletrajectory,andthencontrolthetrajectoryoftwo-linkrigid-flexiblemanipulator,successfullysuppressingthevibrationoftheflexiblemanipulator.Atlast,bymatlabtoverifythemethodiseffective.Features:thetwo-linkrigid-flexiblemanipulatormodeledreflectsnotonlytherigidmotion,butalsothemovementcharacteristicsoftheflexiblemanipulator.Finallyanoptimizationalgorithmisusedtosuppresstheflexiblevibrationsuccessfully,achievingthedesiredeffect.Keywords：Flexiblemanipulator；Dynamicsimulation；Vibrationsuppression；Trajectoryplan；N-Malgorithm武汉理工大学毕业设计（论文）11绪论1.1柔性机械臂的发展历史由于空间技术和机器人技术的发展，柔性多体系统的研究受到了很大的关注。柔性多体系统动力学相对来说是一门新兴的交叉学科，它是刚体力学、分析力学、弹性力学、矩阵理论、图论、计算数学和自动控制理论等多学科相结合的产物，