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并联机构在奇异位置处的构型具有不确定性.如何控制机构按给定的构型通过奇异位置,是并联机器人机构控制的关键问题之一.采用奇异性理论对平面3DOF并联机构的分岔性态及其构型稳定性进行了研究.利用Liapunov-Schmidt(LS)约化,对构型约束方程进行了降维处理,得到一维分岔方程.分析了芽空间分岔点附近构型不确定的原因,根据强等价条件,得到了与原方程分岔性态一致的Golubitsky-Schaeffer正规形.通过对分岔方程普适开折,研究了输入构件长度误差等扰动因素对分岔点处构型保持性的影响,找到了具有构型保持性的构型分岔曲线.在该构型分岔曲线上,机构可以按保持的构型通过分岔点.
The configuration of the parallel mechanism at the singular position is uncertain.How to control the mechanism through a singular position in a given configuration is one of the key problems in the control of a parallel robot mechanism.By singularity theory, the bifurcation of the planar 3DOF parallel mechanism State and its configurational stability are studied.Using Liapunov-Schmidt (LS) reduction, the constrained equations are reduced to obtain the one-dimensional bifurcation equation.Finally, the configuration near the bifurcation point According to the strong equivalence condition, the Golubitsky-Schaeffer normal form is obtained which is consistent with the bifurcation behavior of the original equation.By the universal folding of the bifurcation equation, the effects of disturbance factors such as input component length error on bifurcation At the point of the configuration retention, we find the configuration bifurcation curve with configurational retentivity, on the bifurcation curve of the configuration, the mechanism can pass the bifurcation point in the retained configuration.