空间杆系机构运动路径的多重分岔分析

运动分岔是杆系机构平衡路径分析的重要理论问题。基于按有限元法建立的杆系机构运动方程，对运动路径奇异点的多重分岔特征进行了讨论。对空间杆系机构的分岔条件进行了理论解释。面向多重分岔问题对常规的奇异点定位方法进行了改进。将与切线刚度矩阵特征向量相关的干扰力向量引入到弧长法中，以实现多重分岔路径的跟踪。以一个由Pantadome系统简化的空间杆系机构为例，对其顶升过程的运动路径进行了数值模拟，利用该文方法有效地实现了顶升过程的奇异点判别及多重分岔路径的跟踪。

ANALYSIS ON THE MULTIPLE BIFURCATION IN THE KINEMATIC PATH OF SPATIAL PIN-BAR MECHANISMS

Kinematic bifurcation is an important theoretical problem for the kinematic analysis of pin-bar mechanisms. Based on FEM, the basic kinematic equation of pin-bar linkages was established, and the multiple bifurcation characteristics of the kinematic path were discussed. The bifurcation condition of the kinematic path was explicated theoretically. The conventional method for pinpointing singular point was improved to adapt to the multiple bifurcation problem. A disturbing force vector, which depends on the eigenvectors of tangential stiffness matrix, was introduced into the arc-length method to trace the multiple bifurcation paths. A simplified spatial pin-bar Pantadome linkage was employed as an illustrative example. The lifting process of the linkage was numerically simulated. Using the proposed method, the singular points in the kinematic path are effectively identified, and multiple bifurcation paths are also traced.