Research on Displacement Mode and Path Tracking Method of Square Combined Deployable Mechanism

正方形组合可展机构的位移模态和路径跟踪研究

School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Received: 8 January 2019

Abstract

The motion path of the developable mechanism can not only grasp whether the mechanism can move according to the expected law, but also provide theoretical support for motion control. In order to accurately study the kinematics of the square combined mechanism, the mobility of the square combined expandable mechanism is analyzed based on the screw theory and the graph theory. Then, the balance matrix of the square combined expandable mechanism is derived, and the displacement mode of the square combined expandable mechanism is obtained through singular value decomposition. Secondly, the path tracking method of the square combined expandable mechanism is established by the iteration of the displacement mode. Finally, by means of the example analysis, the position of the bifurcation point of the square combined expandable mechanism is determined; the variation law of the bifurcation point and its positive correlation with the singular value of the balance matrix is analyzed. It is found that adding additional constraints and planning a reasonable path can avoid bifurcation phenomenon. This research provides necessary reference data for configuration design and parameter optimization of the square combined expandable mechanism.

摘要

可展机构的运动路径不仅可以掌握机构是否按预期规律运动，而且为其运动控制提供理论支撑。为了精确研究正方形组合机构的运动学特性，首先基于螺旋理论和图论分析了正方形组合可展机构的可动性，然后在此基础上，推导了正方形组合可展机构的平衡矩阵，将其进行奇异值分解，得到了正方形组合可展机构的位移模态。其次通过位移模态的迭代，建立了正方形组合可展机构的路径跟踪方法。最后借助算例分析，确定了正方形组合可展机构的分岔点位置，分析了分岔点位置的变化规律以及它和平衡矩阵奇异值的正相关性，发现增加额外约束和规划合理路径可以避免出现分岔现象，为正方形组合可展机构的构型设计和参数优化提供了必要的参考数据。