Abstract

This article presents the dynamic modeling and nonlinear analysis of two-link flexible manipulator with generic payload whose center of gravity is different than the point of attachment with the link. The manipulator is driven by harmonic joint motions and subjected to a constraint force at the terminal end due to its interaction with working environment. Hamilton’s approach is adopted to dynamically model the multi-link manipulator for longitudinal and transverse vibrations incorporating the nonlinearities associated with axial stretching. The resulting set of eigenfrequency equations are solved numerically with subsequent generation of eigenspectrums. Further, this paper investigates the resonant behavior of manipulator links for the subharmonic and primary resonance conditions due to end follower force and revolute joint motions, respectively. The resonant responses show the jump phenomenon and existence of multi-valued solutions at pitchfork and saddle-node bifurcation points. The numerical and graphical results thus obtained, clearly indicate the significant influence of variation of system configurations and generic payload on eigencharacteristics and nonlinear responses, and hence must be given consideration during dynamic modeling of a manipulator in order to attenuate undesirable vibrations.

摘要

本文介绍了具有通用有效载荷的双连杆柔性机械手的动力学建模和非线性分析，其重心与连杆的连接点不同。机械手由谐波关节运动驱动，由于与工作环境的相互作用，在末端受到约束力。汉密尔顿的方法被用来动态模拟多连杆机械手的纵向和横向振动，并结合了与轴向拉伸相关的非线性。得到的一组特征频率方程通过随后生成的特征谱进行数值求解。此外，本文研究了机械臂连杆在次谐波和初级共振条件下的共振行为，这些条件分别是由于末端从动力和旋转关节运动引起的。共振响应表明在干草叉和鞍节点分岔点处存在跳跃现象和多值解的存在。由此获得的数值和图形结果清楚地表明系统配置和通用有效载荷的变化对特征特性和非线性响应的显着影响，因此在机械臂的动态建模期间必须考虑到以衰减不希望的振动。