Actuation selection for multi-loop coupling mechanisms using geometric algebra

Multi-loop coupling mechanisms (MCMs) have been widely used in architectural design antennas and space-deployable. This paper proposes a general method for actuation selection of MCMs using geometric algebra. The constraint space is obtained by collineation and dual operators of twist space. This method determines additional constraints by analyzing the linear correlation between the constrained spaces of the two limbs within the closed-loop and making corrections to the constraint space of the basic limb. Through outer and dual operators, the input screw corresponding to the transmission wrench screw and output twist screw are obtained. The input transmission index (ITI) and output transmission index (OTI) corresponding to this input are calculated, which leads to generation of a local transmission index (LTI). The actuation selection with the best performance can be obtained by comparing and analyzing the motion/force transfer performance of all input combinations. The proposed method has the advantages of simple computation and clear physical significance, and three typical MCMs are applied to validate this method. Finally, an experimental analysis compared the power consumption of a test motor at different actuation positions, further proving the accuracy of the method.