Multi-loop coupling mechanisms (MCMs) have been widely used in spacedeployable antennas. However, the mobility of MCMs is difficult to analyze due to their complicated structure and coupled limbs. This paper proposes a general method for calculating the mobility of MCMs using geometric algebra (GA). For the independent limbs in the MCM, the twist spaces are constructed by the join operator. For coupled limbs coupled with closed loops in the MCM, the equivalent limbs can be found by solving the analytical expressions of the twist space on each closed loop’s output link. Then, the twist spaces of the coupled limbs can be easily obtained. The twist space of the MCM’s output link is the intersection of all the limb twist spaces, which can be calculated by the meet operator. The proposed method provides a simplified way of analyzing the mobility of MCMs, and three typical MCMs are chosen to validate this method. The analytical mobility of the MCM’s output link can be obtained, and it naturally indicates both the number and the property of the degrees of freedom (DOFs).

多环耦合机制（MCM）已广泛应用于空间可部署天线。然而，由于其复杂的结构和耦合的肢体，MCM 的移动性很难分析。本文提出了一种使用几何代数 (GA) 计算 MCM 迁移率的通用方法。对于 MCM 中的独立肢体，扭曲空间由连接算子构造。对于MCM中与闭环耦合的耦合臂，可以通过求解每个闭环输出链路上的扭转空间的解析表达式来找到等效臂。然后，可以很容易地获得耦合肢体的扭转空间。 MCM输出链路的扭曲空间是所有肢体扭曲空间的交集，可以通过满足算子来计算。该方法提供了一种分析 MCM 迁移率的简化方法，并选择了三种典型的 MCM 来验证该方法。可以获得MCM输出链路的解析迁移率，它自然地表明了自由度（DOF）的数量和属性。