Mobility Analysis of Multi-loop Coupling Mechanisms Using Geometric Algebra

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).