Bennett单元及Bricard单元等典型闭合环形机构具有可动自由度,可在无应变状态下产生连续、较为显著的几何构型变换,已广泛应用于可展结构工程中。基于此,建立了由闭合环形的刚性折杆组成,可进行旋转、镜像等对称操作,且在运动过程中始终保持一定对称性的过约束机构。任一折杆的两端通过扭转副单元分别连接至其它2根折杆,且扭转副单元的可转动方向与杆轴线重合。在刚性折杆单元平衡矩阵的基础上,建立结构的整体力平衡矩阵,从矩阵的左零空间、零空间分别求得结构的机构位移模态及自应力模态。引入群论方法预测机构位移模态的对称性,并对结构的可动性进行分析。为了验证该类对称体系的可动性,采用基于牛顿迭代技术的非线性预测-修正算法,对结构进行完整路径的运动模拟。针对2个不同对称性的六杆过约束机构算例进行对称分析及运动模拟,结果表明:算例所述的2个对称过约束体系均为单自由度可动结构,可作为可展结构推广应用。 Typical closed loop mechanisms, such as the Bennett unit and the Bricard unit, have the freedom to move and produce continuous and significant geometric transformations without strain, and are widely used in expandable structural engineering. Based on this, an over-constrained mechanism consisting of a closed ring-shaped rigid folding rod, which can be rotated, mirrored and other symmetrical operations, and always maintains a certain symmetry during the movement is established. The two ends of any one of the folding rods are respectively connected to the other two folding rods by the torsion subunit, and the rotatable sub-unit is rotatable in the direction of the rod axis. Based on the balance matrix of rigid element, the whole force balance matrix of the structure is established, and the mechanism displacement mode and self-stress mode of the structure are obtained respectively from the left zero space and zero space of the matrix. The method of group theory is introduced to predict the symmetry of mechanism displacement modalities, and the structure mobility is analyzed. In order to verify the movability of this kind of symmetry system, a nonlinear prediction-correction algorithm based on Newton’s iteration technique is used to simulate the structure of a complete path. The symmetric analysis and the motion simulation of two constrained six-bar over-constrained institutions are carried out. The results show that the two symmetrical restrained systems are both single-degree-of-freedom structures that can be used as expandable structures application.