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

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.

Keywords

• square combined deployable mechanism
• screw theory
• mobility
• balance matrix
• displacement mode
• path tracking
• kinematics
• singular value decomposition
• bifurcation