两自由度机械手周期运动的倍周期分岔

Period-Doubling Bifurcations of Period Motion of Two-Degree-of-Freedom Manipulators

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F loquet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.

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.