构架式可展开天线自由度与奇异性分析

Degree of freedom and singularityanalysis of the deployable truss antenna reflector

针对以四面体为基本单元的构架式空间可展开天线,基于螺旋理论分析了多环耦合机构3RR-3RRR基本单元及多单元组网的自由度,降低分析此构架单元过约束与奇异性的复杂性。首先,根据螺旋理论能同时表示运动副轴线的位置和运动副类型的特点,建立了3RR-3RRR单元各铰链的运动螺旋并求解出单元过约束数;其次,运用修正的Kutzbach-Grübler公式求解出此单元的自由度,并分析出在特殊位形下的奇异性和瞬时性;最后,多单元组网成一个复杂耦合机构,采用等效构型的方法简化组网结构可得此天线反射器收展所需自由度,再通过计算各花盘的相对间距来验证构架可展开天线的收展协调性。研究表明构架式天线反射器3RR-3RRR四面体单元为单自由度机构且含有4个过约束,便于机构的展开控制,在同步杆铰链处于特殊位形下有约束奇异。组网后反射器桁架系统是单自由度机构,机构在单驱动运动过程中可展开完全,实现构架可展开天线各杆件在工作时运动协调,在空间机构领域具有良好的应用性。

For the deployable truss antenna composed of tetrahedral elements,the degree of freedom （DOF） of 3RR-3RRR element and multi-element was analyzed based on the screw theory,and the complexities of the over-constraint and the singularity analysis of the structural element were reduced. Firstly,the position and characteristics of the motion pair could be expressed simultaneously by the screw theory,so the motion spinors of hinges of the 3RR-3RRR element were established,and the number of the over-constraints was solved. Secondly,according to the modified Kutzbach-Grübler formula,the DOF of 3RR-3RRR element was solved,and the singularity and instantaneity of the special configuration were analyzed. Finally,the equivalent structure method was used to simplify the network′s structure and solve the DOF of the reflector. Then the relative distance between two disks was calculated to verify the deployable coordination of the antenna. The results show that the tetrahedral element has one degree of freedom and four over-constraints,and the constraint singularity is obtained under the special position of the hinge. After networking,the reflector is a single DOF mechanism,which can be fully deployed by the control of a single drive to realize the coordination of the deployable antenna at work,and has a good application in spatial mechanism field.