Period-Doubling Bifurcations of Period Motion of Two-Degree-of-Freedom Manipulators
-
摘要: 为了研究两自由度机械手系统的动力学稳定性,基于拉格朗日方程给出了它的运动微分方程,并用扰动理论确定系统周期运动具有周期系数的扰动微分方程;根据Floquet理论对该系统扰动微分方程的平衡点的稳定性进行了分析,并用数值方法研究了平衡点失稳后的倍周期分岔过程.研究表明,随系统参数的改变,当系统特征矩阵有特征值-1时,系统将发生倍周期分岔.Abstract: To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.Furthermore,the stability of the equilibrium point for the perturbed differential equations was analyzed by utilizing the Floquet theory,and the process of a period-doubling bifurcation after stability loss of the equilibrium point were investigated numerically.The research shows that a period-doubling bifurcation will occur if the eigen-matrix for the system has one eigenvalue-1 with the change of its parameters.
-
冯春,谢进,陈永.利用Lyapunov指数分析机械手反馈控制中的混沌运动[J]. 中国机械工程,2004,15(7):624-627.FENG Chun,XIE Jin,CHEN Yong.Analysis of chaotic motion for feedback-controlled robots with lyapunov exponent[J]. Chinese Journal of Mechanical Engineering,2004,15(7):624-627.[2] 魏金铎,王和祥,尹以灿.柔性变截面滑移式机器人手臂的动力学与控制[J]. 应用力学学报,1993,10(4):20-27.WEI Jinduo,WANG Hexiang,YIN Yican.Dynamics and control of a mobile flexible manipulator with variable sections[J]. Chinese Journal of Applied Mechanics,1993,10(4):20-27.[3] 刘新建,马宏绪,张彭.柔性机械手加速度反馈控制抑制振动的机理与稳定性分析[J]. 国防科技大学学报,1999,21(5):25-28.LIU Xinjian,MA Hongxu,ZHANG Peng.Mechanism and stability analysis of vibration suppression with acceleration feedback for flexible manipulator[J]. Journal of National University of Defense Technology,1999,21(5):25-28.[4] 丁旺才.调速器反馈控制系统的Hopf分岔[J]. 西南交通大学学报,2001,36 (6):624-628.DING Wangcai.Hopf bifurcation of flywheel governor with feedback control device[J]. Journal of Southwest Jiaotong University,2001,36 (6):624-628.[5] LINDTNER E,STEINDL A,TROGER H.Generic one-parameter bifurcations in the motion of a simple robot[J]. Journal of Computational and Applied Mathematics,1989,26:199-218.[6] 舒仲周.运动稳定性[M]. 成都:西南交通大学出版社,1989:238-256.
点击查看大图
计量
- 文章访问数: 1433
- HTML全文浏览量: 64
- PDF下载量: 322
- 被引次数: 0