基于绝对节点坐标法的柔性双臂机构动力学分析
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摘要
基于绝对节点坐标法对具有变截面特征的柔性双臂机构进行了动力学分析.通过将边界函数引入到质量矩阵和刚度矩阵的积分上下限,建立了新型变截面梁单元模型.基于牛顿方程建立了柔性双臂机构的动力学模型.通过数值仿真案例,分析了材料特性及几何参数对柔性双臂机构动力学性能的影响.结果表明:材料弹性模量的增长可提高结构刚度减少结构变形;保证机械臂质量不变可通过改变截面形状来减少结构变形,提高运动精度.
A dynamic model of the flexible manipulator with variable cross-section is established based on the absolute nodal coordinate formulation.Variable boundary conditions of the link are described with some functions which are used as the upper and lower limits in the integrations to calculate mass matrix and stiffness matrix of the element.With these matrices the dynamic model of the manipulator is proposed by using the Newton equations.Manipulators with different materials and variable cross-sections are employed in the numerical simulations.Results show that the increase of elastic modulus can improve the stiffness of structure and reduce its deformation.Kinematic accuracy of the structure can be improved by optimizing cross-section shape without changing its mass.
A dynamic model of the flexible manipulator with variable cross-section is established based on the absolute nodal coordinate formulation.Variable boundary conditions of the link are described with some functions which are used as the upper and lower limits in the integrations to calculate mass matrix and stiffness matrix of the element.With these matrices the dynamic model of the manipulator is proposed by using the Newton equations.Manipulators with different materials and variable cross-sections are employed in the numerical simulations.Results show that the increase of elastic modulus can improve the stiffness of structure and reduce its deformation.Kinematic accuracy of the structure can be improved by optimizing cross-section shape without changing its mass.
引文
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[10]NACHBAGAUER K,GRUBER P,GERSTMAYR J.Structural and continuum mechanics approaches for a 3Dshear deformable ANCF beam finite element:Application to static and linearized dynamic examples[J].Journal of Computational and Nonlinear Dynamics,2013,8(2):92-110.
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[12]刘铖,田强,胡海岩.基于绝对节点坐标的多柔体系统动力学高效计算方法[J].力学学报,2010,42(6):1197-1205.LIU Cheng,TIAN Qiang,HU Haiyan.Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1197-1205.
[2]DUBAY R,HASSAN M,LI C,et al.Finite element based model predictive control for active vibration suppression of a one-link flexible manipulator[J].ISA Transactions,2014,53(5):1609-1619.
[3]ZHANG X P,MILLS J K,CLEGHORN W L.Coupling characteristics of rigid body motion and elastic deformation of a 3-PRR parallel manipulator with flexible links[J].Multibody System Dynamics,2009,21(2):167-192.
[4]KHAIRUDIN M,MOHAMED Z,HUSAIN A R,et al.Dynamic characterisation of a two-link flexible manipulator:Theory and experiments[J].Advances in Robotics Research,2014,1(1):61-79.
[5]YANG Z,ZHANG F B.Dynamics analysis of space robot manipulator with joint clearance[J].Acta Astronautica,2011,68(7/8):1147-1155.
[6]卢剑伟,陈昊,孙晓明,等.考虑减速机构间隙的机械臂动力学建模分析[J].机械工程学报,2013,49(15):15-21.LU Jianwei,CHEN Hao,SUN Xiaoming,et al.Dynamic modeling and analysis of robot arm with consideration of clearance in gear reducer[J].Journal of Mechanical Engineering,2013,49(15):15-21.
[7]NACHBAGAUER K,PECHSTEIN A S,IRSCHIK H,et al.A new locking-free formulation for planar,shear deformable,linear and quadratic beam finite elements based on the absolute nodal coordinate formulation[J].Multibody System Dynamics,2011,26(3):245-263.
[8]李彬,刘锦阳.大变形柔性梁系统的绝对坐标方法型[J].上海交通大学学报,2005,39(5):827-831.LI Bin,LIU Jinyang.Application of absolute nodal coordination formulation in flexible beams with large deformation[J].Journal of Shanghai Jiao Tong University,2005,39(5):827-831.
[9]赵春璋,余海东,王皓,等.基于绝对节点坐标法的变截面梁动力学建模与运动变形分析[J].机械工程学报,2014,50(17):38-45.ZHAO Chunzhang,YU Haidong,WANG Hao,et al.Dynamic modeling and kinematic behavior of variable cross-section beam based on the absolute nodal coordinate formulation[J].Journal of Mechanical Engineering,2014,50(17):38-45.
[10]NACHBAGAUER K,GRUBER P,GERSTMAYR J.Structural and continuum mechanics approaches for a 3Dshear deformable ANCF beam finite element:Application to static and linearized dynamic examples[J].Journal of Computational and Nonlinear Dynamics,2013,8(2):92-110.
[11]ZHAO C,YU H,LIN Z,et al.Dynamic model and behavior of viscoelastic beam based on the absolute nodal coordinate formulation[J].Proceedings of the Institution of Mechanical Engineers.Part K:Journal of Multi-body Dynamics,2014,229(1):84-96.
[12]刘铖,田强,胡海岩.基于绝对节点坐标的多柔体系统动力学高效计算方法[J].力学学报,2010,42(6):1197-1205.LIU Cheng,TIAN Qiang,HU Haiyan.Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(6):1197-1205.