A dynamic model of the flexible manipulator with variable crosssection 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 crosssections 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 crosssection shape without changing its mass.
ZHAO Jun1,YU Haidong2
. Dynamic Analysis of TwoLink Flexible Manipulators Based on
the Absolute Nodal Coordinate Formulation [J]. Journal of Shanghai Jiaotong University, 2017
, 51(10)
: 1160
-1165
.
DOI: 10.16183/j.cnki.jsjtu.2017.10.002
[1]SHAKER M C, GHOSAL A. Nonlinear modeling of flexible manipulators using nondimensional variables[J]. Journal of Computational and Nonlinear Dynamics, 2006, 1(2): 123134.
[2]DUBAY R, HASSAN M, LI C, et al. Finite element based model predictive control for active vibration suppression of a onelink flexible manipulator[J]. ISA Transactions, 2014, 53(5): 16091619.
[3]ZHANG X P, MILLS J K, CLEGHORN W L. Coupling characteristics of rigid body motion and elastic deformation of a 3PRR parallel manipulator with flexible links[J]. Multibody System Dynamics, 2009, 21(2): 167192.
[4]KHAIRUDIN M, MOHAMED Z, HUSAIN A R, et al. Dynamic characterisation of a twolink flexible manipulator: Theory and experiments[J]. Advances in Robotics Research, 2014, 1(1): 6179.
[5]YANG Z, ZHANG F B. Dynamics analysis of space robot manipulator with joint clearance[J]. Acta Astronautica, 2011, 68(7/8): 11471155.
[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): 1521.
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): 1521.
[7]NACHBAGAUER K, PECHSTEIN A S, IRSCHIK H, et al. A new lockingfree 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): 245263.
[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): 827831.
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): 827831.
[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): 3845.
ZHAO Chunzhang, YU Haidong, WANG Hao, et al. Dynamic modeling and kinematic behavior of variable crosssection beam based on the absolute nodal coordinate formulation[J]. Journal of Mechanical Engineering, 2014, 50(17): 3845.
[10]NACHBAGAUER K, GRUBER P, GERSTMAYR J. Structural and continuum mechanics approaches for a 3D shear deformable ANCF beam finite element: Application to static and linearized dynamic examples[J]. Journal of Computational and Nonlinear Dynamics, 2013, 8(2): 92110.
[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 Multibody Dynamics, 2014, 229(1): 8496.
[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): 11971205.