中文摘要：

针对四面体构架式可展天线机构的多环耦合特性,提出了一种空间多环耦合机构的自由度分析方法——拆杆等效法。首先拆除四面体基本可展单元机构的耦合约束链,将剩余部分视为一个并联机构,然后应用螺旋理论分析各输出节点的自由度数目及性质,进而构造各输出节点与定节点之间的等效串联运动链,最后复原拆除的耦合约束链得到四面体基本可展单元的等效机构,应用修正的G-K公式计算等效机构的自由度数目,并基于反螺旋理论分析等效机构的自由度性质,从而获得四面体基本可展单元的运动特性。根据四面体基本可展单元的等效机构及其组合方式对最小组合单元及大尺寸构架式可展天线机构的结构进行了化简,并根据其几何特征约束方程推导了最小组合单元及大尺寸构架式可展天线机构的自由度。建立了由27个四面体基本可展单元组成的构架式可展天线机构的仿真模型,对该机构的自由度进行了验证,结果表明提出的拆杆等效法求得的自由度正确,为进一步分析此类天线机构的运动学和动力学奠定了基础,同时为其他类型的空间多环耦合机构的自由度分析提供了一种新的思路。

英文摘要：

A method for Degree Of Freedom（DOF）analysis of spatial mechanisms with multiple coupled-loops is proposed based on the link-demolishing and equivalent idea,in view of the multi-loop coupling characteristic of a deployable truss antenna assembled by tetrahedral elements.The coupling constraint chain of the deployable tetrahedral element is removed,and the remainder is regarded as a parallel mechanism.The number and characteristic of the DOF of each output node are then analyzed using the screw theory,and the equivalent serial kinematic chain between the output nodes and the fixed node are then established.The equivalent mechanism of the deployable tetrahedral element is obtained by reconstructing the coupling constrained chain.The number and characteristic of the DOF of the equivalent mechanism are got using the modified G-K formula and the reciprocal screw theory,respectively.As a result,the kinematic characteristics of the tetrahedral element are known.The structure of the minimum composite unit and the large-scale truss deployable antenna are simplified,according to the equivalent mechanism and the combination of the tetrahedral elements.The numbers of the DOF of the minimum composite unit and the large-scale truss deployable antenna are derived on the basis of the geometric constraint equations.The simulation model for a deployable truss antenna assembled by 27 tetrahedral elements is built,and its DOF is verified.The result shows that the DOF of the antenna analyzed by the proposed method is correct.The method lays a foundation for further analysis of the kinematics and dynamics of similar type of antennas,providing a new idea for DOF analysis of other multi-loop coupling mechanisms.